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Learning the language of math: supporting students who are learning English in acquiring math proficiency through language development

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Learning the language of math: supporting students who are learning English in acquiring math proficiency through language development

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Learning the Language of Math: Supporting Students who are Learning English in Acquiring
Math Proficiency through Language Development
by

Brittany Daley

A Dissertation Presented to the
FACULTY OF THE USC ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION

December 2020

Copyright 2020 Brittany Daley

ii

Dedication

I dedicate this work to my students, the Gaucho Family, who taught me that language is
power, teamwork makes anything possible and that love always wins. It was our conversations
about second grade Math and watching you speak about Math as you grew up that inspired this
work. I have endless memories of you all seeking to understand your peers through listening,
sharing your unique genius through speaking, practicing mathematical storytelling through
writing and joyfully acquiring new knowledge through reading. You are the best people I know
and my heart feels at peace knowing that the future belongs to you. You have done great things;
you will do great things and you inspire me to do great things.

iii

Acknowledgements

I first want to thank my dissertation chair, Dr. Emmy Min, for her relentless support and
her willingness to constantly meet me where I was at. You believed in my voice, vision and
potential. Ultimately, your confidence in me and your commitment to be in this process
alongside me through the finish line offered constant peace. I also want to thank Dr. Eric Canny
for consistently pushing me to be my very best self and for never wavering in his belief that I am
capable. You allowed me to be a student, researcher and human. Next, I’d like to thank my
committee members, Dr. Angela Hassan and Dr, Jennifer Park, for sharing new perspectives that
constantly pushed me to position my work within the context of education leadership at large.
Next I would like to thank my mom, Karen Daley for breaking generational cycles so that
I could have a life with fewer barriers. Thank you for believing in me always and working
alongside me to make my dreams a reality. Your hard work to get your GED, graduate college
and ultimately become a teacher paved the way for me. I am because you are. Thank you to my
dad, Thomas Daley. You have always seen the value in my education and you have made so
many sacrifices along the way to support me. To my very best friend and sister, Ariel Gory. Your
heart for equity, justice and radical love constantly encourage me to explore educational equity
and imagine what it would take to ensure all kids specifically brown kids have access to a joyful
and liberating education. You dream big and it encourages me to as well.
This work and my work would not be possible without the students and families that put
their trust in me as an educator. This work is for you. Thank you to the parents that taught me
about advocacy and culture. Thank you to the students who taught me that being seen, heard and
known in the classroom is the greatest predictor of achievement. Thank you to the students you
iv

taught me that joy is the biggest achievement accelerator. Thank you for teaching me how to be a
teacher and more importantly how to be a loving human.
As I reflect on this accomplishment, I thank God for having bigger plans for me than I
could ever imagine. I thank God for the opportunity to serve as an educator and the opportunities
He has brought me to and through.

v

TABLE OF CONTENTS

Dedication…………………………………………………………………………………………ii
Acknowledgements………………………………………………………………………………iii
List of Tables …………………………………………………………………………………..viii
List of Figures……………………………………………………………………………………. x
Abstract ………………………………………………………………………………………… xi
OVERVIEW OF THE STUDY………………………………………………………………… 1
Organizational Context and Mission ……………………………………………………………..2
Organizational Performance Status ……………………………………………………………….4
Organizational Performance Goal ………………………………………………………………5
Related Literature………………………………………………………………………………… 6
Importance of Addressing the Problem …………………………………………………………..9
Description of the Stakeholder Groups…………………………………………………………. 10
Stakeholder Group for the Study ………………………………………………………………..11
Purpose of the Project and Questions…………………………………………………………... 13
Methodological Framework ……………………………………………………………………..13
Definitions ……………………………………………………………………………………….14
Organization of the Project ……………………………………………………………………...15
REVIEW OF THE LITERATURE ……………………………………………………………16
Introduction…………………………………………………………………………………… 16
English Language Development ………………………………………………………………16
Evolving Models, Frameworks and Protocols of Language Development ……………………22
Language Support in the Math Classroom……………………………………………………… 25
vi

Challenges in Supporting ELL Students……………………………………………………… 32
Administrator Influence on ELL Achievement …………………………………………………35
Clark and Estes’s Knowledge, Motivation and Organizational (KMO) Influences Framework ..40
Stakeholder Knowledge, Motivation and Organizational Influences…………...……………… 41
Knowledge Influences …………………………………………………………………………..41
Motivation Influences …………………………………………………………………………50
Organizational Influences………………………………………………………………………..55
Conceptual Framework ………………………………………………………………………….60
Conclusion……………………………………………………………………………………… 65
METHODS ……………………………………………………………………………………66
Methodological Framework …………………………………………………………………….66
Participating Stakeholders ……………………………………………………………………..68
Survey Sampling Criteria and Rationale ………………………………………………………70
Survey Strategy and Rationale …………………………………………………………………71
Interview Sampling Criteria and Rationale ……………………………………………………72
Interview Strategy and Rationale ………………………………………………………………73
Data Collection and Implementation ……………………………………………………………74
Data Analysis ……………………………………………………………………………………78
Credibility and Trustworthiness …………………………………………………………………79
Validity and Reliability …………………………………………………………………………80
Ethics……………………………………………………………………………………………80
Limitations and Delimitations……………………………………………………………………82
RESULTS AND FINDINGS……………………………………………………………………84
vii

Knowledge Results and Findings………………………………………………………………89
Motivation Results and Findings ………………………………………………………………109
Organizational Results and Findings…………………………………………………………...119
Summary………………………………………………………………………………………136
RECOMMENDATIONS………………………………………………………………………140
Introductions and Overview……………………………………………………………………140
Recommendations for Practice to Address KMO Influences…………………………………142
Integrated Implementation and Evaluation Plan………………………………………………162
Evaluation Tools………………………………………………………………………………179
Data Analysis and Reporting…………………………………………………………………185
Summary………………………………………………………………………………………187
Conclusion……………………………………………………………………………………193
References………………………………………………………………………………………195
Appendix A: Survey Item………………………………………………………………………203
Appendix B: Interview Protocol………………………………………………………………..207
Appendix C: Evaluation Immediately Following Each Training Session……………………210
Appendix D: Pre-Training and Three Months Post Training…………………………………212
Appendix E: Sample Data Collection and Evaluation…………………………………………213
Appendix F: Sample Forms to Increase Key Stakeholder Participation ………………………214

viii

LIST OF TABLES

Table 1 Éxito Academy Total Student Enrollment by Language Acquisition Status…………..…4
Table 2 Language Data from Census Bureau American Community Survey……………………7
Table 3 Organizational Mission, Global Goal and Stakeholder Performance Goals……………12
Table 4 ELL Enrollment in California…………………………………………………………18
Table 5 Knowledge Influences, Types and Assessments for Analysis…………………………48
Table 6 Motivational Influences and Assessments for Analysis………………………………54
Table 7 Organizational Influences and Assessments for Analysis……………………………58
Table 8 Summary Table of Assumed Influences on Performance………………………………64
Table 9 Demographic Information of Teacher Participants……………………………………85
Table 10 Demographic Information of Administrator Participants……………………………86
Table 11 Survey Demographic Information of Teacher Participants……………………………87
Table 12 Survey Demographic Information of Administrator Participants……………………88
Table 13 Factual Knowledge Findings and Sub findings. ………………………………………90
Table 14 Procedural Knowledge Findings and Sub findings. …………………………………102
Table 15 Metacognitive Knowledge Findings and Sub findings. ……………………………106
Table 16 Self-Efficacy Findings and Sub findings. ……………………………………………110
Table 17 Attribute Theory Findings and Sub findings. ………………………………………113
Table 18 Value Theory Findings and Sub findings. …………………………………………117
Table 19 Cultural Models Findings and Sub findings. ………………………………………123
Table 20 Cultural Settings Finding and Sub findings. …………………………………………130
Table 21 Summary of Knowledge Influences and Recommendations…………………………144
Table 22 Summary of Motivation Influences and Recommendations…………………………151
ix

Table 23 Summary of Organization Influences and Recommendations………………………156
Table 24 Outcomes, Metrics, and Methods for External and Internal Outcomes………………165
Table 25 Critical Behaviors, Metrics, Methods, and Timing for Evaluation…………………169
Table 26 Required Drivers to Support Critical Behaviors……………………………………170
Table 27 Evaluation of the Components of Learning for the Program…………………………176
Table 28 Components to Measure Reactions to the Program…………………………………178

x

LIST OF FIGURES

Figure 1 Interaction of Knowledge, Motivation, Cultural Models and Settings……………….63

Figure 2 Evaluation Immediately Following Training or Professional Development (PD)…..179

Figure 3 Coaching Tool for Coaching Around ELD and Language Supports…………………182

Figure 4 Sample Rubric for Administrators and Teachers Following or Delayed after the PD..183

Figure 5 Data Dashboard to Measure Progress Towards Performance Goal…………………186
Figure 6 Sample Forms to Increase Key Stakeholder Participation……………………………189

xi

Abstract
This mixed methods study examined the language development support provided to English
Language Learners in the Math classroom. The research questions explored the knowledge and
motivation of Math teachers and the organizational influences at the school that impacted the
teachers’ ability to demonstrate competency in supporting language development appropriately
in the Math classroom given the unique language proficiency needs of students and the demands
of the mathematical content. The Clark and Estes Gap Analysis Framework (2008) was utilized
and the organization of the study related to the assumed knowledge, motivation and
organizational influences. As teachers described their instruction and support for students
learning English, gaps were revealed as related to their factual and metacognitive knowledge that
allowed them to specifically address language demands that aligned with the Math content as
well as the individual language development of students. While the teachers recognized the
benefit and importance of practices to support language development in the Math classroom,
there was a motivational gap pertaining to self- efficacy and attribute theory. A majority of
teachers did not express confidence in their ability to support students learning English nor did
they attribute student achievement or lack thereof to primarily instruction. Administrators were
also surveyed and interviewed as a means of strengthening the data gathered on the
organizational influences. Administrators expressed similar knowledge and motivation barriers.
The teachers perceived the organization as not explicitly addressing the needs of English
Language Learners especially considering the experience of ELLs in Math. This was evidenced
through a lack of training, best practices, feedback and organizational support for initiatives to
support teacher knowledge of developing language in all content areas (Math included). The
results and findings suggest that additional training is needed that includes modeling and
opportunity for reflection and feedback that increases teacher knowledge and motivation about
xii

supporting ELLs in Math. The training and opportunities for feedback should include
opportunities for explicit modeling of instruction that specifically targets the language
proficiency of students as well as addresses the rigor of grade level Math content in a way that is
developmentally appropriate. The results and findings from the research provided a framework
for developing a recommended training program based on the New World Kirkpatrick Model
(Kirkpatrick & Kirkpatrick, 2016). This training program addresses the knowledge and
motivation gaps aiding in the realization of the stakeholder and organizational performance
goals.

1

Chapter One: Overview of the Study
The organizational performance problem that serves as the focus for this research is the
achievement gap between English Fluent students and English Language Learners (ELLs) on the
state Math Assessments. For the use of this study, English Language Learners are defined as
students whose first language is not English (Echevarria, Vogt & Short, 2008). The 2019
California statewide results from the math portion of the Smarter Balance Assessment showed
that in Grades 3-11 English Only students were 28.98% in the category of standard not met while
students who are English Language Learners scored an overall 64.41% in the standard not met
category (CDE, 2019). The 35.43% difference demonstrates that this is a problem. In the year
2019, 2,714,375 ELLs took the state Math test and 1,492,906.25 were not proficient in grades
three through eleven (CDE, 2019). While this paper focuses on the achievement gap in Math,
similar gaps exist across all standardized assessments for students learning English (CDE, 2019).
The State level data mirrors a similar trend at the district and school level as well. At
“Éxito Academy '' the organization for this study, 52% of the students are classified as English
Language Learners, with a majority of students classified as Long-Term English Language
Learners (LTELS). On the Smarter Balance Math Assessment from 2018, 89% of EL students
did not meet the standard while only 11% of students who are ELLs performed at or above the
standard. The largest gap for grade level cohorts between English Fluent and ELLs in
performance was a 52% gap and the smallest gap was a 36% gap. In contrast, students who are
reclassified outperform both English Language Learners and English Only peers in each grade
level. 35% of the Ever-EL population at the school is reclassified while 65% are not reclassified
and are LTELs. Of the students who enter the school as English Language Learners, only 10-
15% graduate eighth grade being reclassified (based on the data from the past 4 years of
2

reclassification). Reclassification and language proficiency also impact a student’s ability to use
language in the Math classroom. Content specific language and academic language are
developed after students develop a use of formal and informal English. Development of
academic language often occurs years after initial language proficiency (Collier, 1987;
Cummins, 1981; Mitchell, Destino & Karam, 1997).
Organizational Context and Mission
The research for this study will take place in an urban downtown community called
“Coastal City” in California. 24% of all students in Coastal City are labeled as English
Language Learners. Coastal City is also a border town with Mexico which adds to the unique
culture as some students cross the border to attend school each day.
This research will focus on an organization made up of a group of schools called “Éxito
Academies”. The organization has a mission to provide an equitable education for underserved
communities that will dramatically change life outcomes (paraphrased from organizational
mission and vision statement). The organization values high expectations, academic
achievement, character development and a nurturing yet demanding environment. There are
more than 10 schools in the organization. Éxito Academy is part of a nationwide Charter
Management Organization (CMO) that has many schools across the nation. The school of focus
for the qualitative data is a secondary level charter school. A charter school is a publicly funded
school that is independently run. It is established by a “charter” which is a contract that describes
key elements of the school.
The school demographics show that the student body is 96% Latino and 97% students
from low income families. The schools are free schools that serve low-income students of color.
Of the 328 students there are 178 students who are still classified as ELLs. Of the 178 students
3

who are ELLs, 156 are LTELs. The school has an Instructional Leadership Team that is made up
of a Principal, Assistant Principal, two Deans and a Special Education Manager. The table in
Figure 1 shows the language acquisition status of the enrollment for Éxito Academy. This
number does not include the students who have been previously reclassified. This is important to
note because even after students have been reclassified, they are developing their academic
language. The vision of Éxito Academy is to be a community of schools that creates opportunity
for students so they can lead choice-filled lives and impact their community.
The Éxito Academy in Coastal City was founded in 2005 and is a Title 1 school serving a
large majority of students who receive free and reduced lunch due to income status. The school
serves four grade levels and there are twelve core content teachers, six special education
teachers, two art teachers, two physical education teachers and one interventionist. There is a
high turnover rate each year (near 50%) and each year the school receives novice teachers with
less than two years of experience. On the other hand, there is a group of teachers and staff
members who have been there for more than ten years. Both years of experience in education
and years of experience at Éxito Academy have created informal support systems based on years
of experience.
Despite a mission and vision that aims for high academic achievement, results at Éxito
Academy have consistently been below proficient. Between 2017-2019, the school saw minimal
increase. The minimal increase in results has caused frustration amongst staff members and led
staff to want an answer to why the results were slow. After looking at data and demographics
many staff members believe that language proficiency status is the root cause of performance.
Over 50% of the total enrollment at Éxito Academy identifies as an ELL and the staff lacks
resources and knowledge about how to serve ELL students in middle school. The school began a
4

designated English Language Development program in the 2018-2019 schools and saw that 78%
of the ELLs enrolled were making progress towards proficiency however ELL proficiency on the
State Math Exam remained under 36%.
Table 1
Éxito Academy Total Student Enrollment by Language Acquisition Status
Category Number of Students Percent
Total Enrollment 329 100%
ELL (LTEL, ELL,
Newcomer)
178 54%
LTEL only 156 47%
RFEP 100 30%
IFEP 38 11%
EO 13 4%

The above table shows that out of the 329 students 54% are not reclassified as English
proficient. 47% of all ELLs are LTELs. In addition to the ELL student numbers, 100 other
students were ELLs, but are now RFEP and may require extra support developing academic
language.
Organizational Performance Status
Currently English Language Learners are 64% of the total enrollment at the
organization’s dozen plus schools. The largest representation is 96% ELL at one school while the
lowest is 26% ELL. The organization had an overall score of 64% meeting or exceeding the
standard on the state Math assessments in 2019. 11 % of ELLs met or exceeded the standard
while 72 % of English proficient students met or exceeded the standards. This represents a gap of
61%.
5

In previous years a similar trend existed although there was growth for individual
schools. For example, in 2019, Éxito Academy in Coastal City increased ELL Math proficiency
from 13% to 32% as measured by the California Math assessment. In 2018, the largest grade
level gap was 56% while in 2019 the largest gap was 41% (in only one classroom). In 11
classrooms, the gap between ELLs and fluent English proficient students was cut in half and
overall proficiency increased by 10-13%.
The school also saw improvement in student performance on the English Language
Proficiency Assessment of California ( ELPAC) assessment with 38% of students growing one
proficiency level in a year and with 54% of students scoring the highest proficiency level. The
State of California determined that 78% of the students were progressing towards English
Proficiency. Reclassification rates also rose from >1% in 2018 to 19% in 2019.
The current performance impacts the organization’s ability to live out their mission. They
exist to prepare historically underserved communities for college and to ‘prove the possible’
through excellent student results. The Math data shows that students who are learning English
are not getting excellent results on the state Math assessment. The gap in proficiency shows a
lack of mastery of math content needed to be college ready.
Organizational Performance Goal
By 2023, 85% of English Language Learners will meet or exceed the standard as
measured by the California state math assessments. In order to increase student achievement on
the state math exam, the performance gap between ELL, EO and RFEP students will decrease
from the 56% gap that exists in the 2017-2018 school year to 15% gap. This goal was
established by the Instructional Leadership Team at Éxito Academy after reviewing the results
from the 2017-2018 state math exams. The Instructional Leadership Team also set benchmark
6

goals to support the overall organizational performance goal. Fifty three percent of the school
population identified as an English Language Learner (does not include the reclassified
students). The organizational performance goal is used for more than just the state math
assessments. As a form of progress monitoring towards the organizational goal, the daily exit
tickets, end of module assessments, interim assessments, class work and any other data are
measured against the goal of 85% proficient for English Language Learners and their English
Proficient peers. Realization of this organizational performance goal aligns with the mission
statement of the organization and a desire to provide excellent educational outcomes to
underserved communities that bring opportunities in the future.
Related Literature
The below literature relates to the educational context of ELL education, growing
demographics and potential barriers to quality education for ELL students. The literature review
in chapter 2 will provide a more in-depth presentation of related literature to the problem of
practice.
Legal History of ELL Education in the United States
Building on the research, there have been a variety of court cases and rulings that address
the educational needs of ELLs. In the 1974 Supreme Court case Lau v. Nichols, Chinese
American students sued San Francisco Unified School District for placing the students in
mainstream classrooms despite their lack of proficiency in English. The Supreme Court found in
Lau v. Nichols that placing Limited English Proficient (LEP) students in a mainstream classroom
was denying them a meaningful classroom experience and education (Douglas & Supreme Court
of The United States, 1973). Similar sentiments are expressed in the Equal Educational
Opportunities Act (EEOA) of 1974. In recent years, there have been numerous rulings on
7

bilingual education and funding for ESL programs such as (Equal Educational Opportunities
Act, Pub. L. 93–380, title II, § 202, Aug. 21, 1974, 88 Stat. 514.). In addition to the
representation in court cases, there is a growing representation in the population of people who
are learning English.
Growing Representation of ELLs in CA Schools
English Language Learners represent a growing population in the U.S. schools yet the
achievement gap between English Language Learners and their English only peers widens (CDE,
2019). The academic area where there is the largest performance gap is English Language
Learners and their English Only peers in state math assessments (CDE, 2019). According to the
Census Bureau’s American Community Survey (ACS) in 2014-2018 21.5 percent spoke a
language other than English at home. 13.3% of people at least five years old spoke Spanish.
When asked how well they spoke English, 8.5 percent reported that they did not speak English
"very well." That same survey showed that in California 16,181,010 people spoke a language
other than English at home and of that number 6,621,028 stated they spoke English less than
“very well”.
Table 2
Language Data from Census Bureau American Community Survey
Total Population over five years old 36,668,081
English Only 20,487,071
Language Other than English 16,181,010
Speak English less than “very well” 6,621,028
Spanish 10,529,621
Spanish: Speak English less than “very well” 4,253,679
Other Indo-European Language 1,641,520
8

Indo-European: Speak English less than “very
well”
498,572
Asian and Pacific Islander Language 3,636,258
Asian and Pacific Islander: Speak English less
than “very well”
1,743,664
Other Languages 373,611
Other Languages: Speak English less than
“very well”
125,113

Table 2 represents that the population of people who are learning English is a significant
portion of the population with nearly one sixth of the total population stating they speak English
less than “very well”. Meeting the needs of ELLs is not unique to California and is represented in
national census data.
Meeting the Instructional Needs of ELLs
Instructional Practices should be differentiated depending on the needs of the students
(Chang, 2008). This is true for the experience of English Language Learners in the classroom.
The evidence highlights that the needs of English Language Learners are diverse from their
English Only peers (Gersten & Russel, 1996; Menken, 2010; Chang, 2008). The diverse needs of
English Language Learners demand diverse practices in the classroom that are unique to English
Language Learners (Gersten & Russel, 1996). The challenge of meeting the diverse needs of
ELLs may influence a teacher’s tendency to see bilingualism as a deficit (Carley-Rizutto, 2017;
Menken & Kyel, 2010; Reeves, 2015).
Educator Mindset Towards Educating ELLs
Despite the research that lists bilingualism as an asset; educators tend to see bilingualism
and English Language Learners as a deficit (Carley-Rizutto, 2017; Menken & Kyel, 2010;
Reeves, 2015). A majority of English Language Learners are in monolingual settings where the
9

target language is English and their home language does not hold value in the school setting
(Menken & Kyel, 2010) Students who are in environments where their home language is not
valued, score lower than their peers in bilingual environments (Menken & Kyel, 2010). Failure
to address the diverse needs as well as the mindset about ELL students can adversely impact the
achievement of ELL students.
Importance of Addressing the Problem
Research about the achievement gap has existed for over 50 years, yet for ELLs that gap
continues growing and a solution has not been found. Not addressing the needs of English
Language Learners presents a variety of educational barriers. The performance and achievement
gaps are widening between English Fluent Proficient and ELL students as measured by the state
Math assessments (CDE, 2015-2019). Addressing the language needs of English Language
Learners as well as the support needed by students who are English Language Learners is
becoming increasingly important as state data shows that the percent of Long-Term English
Language Learners (LTELs) who are “at risk” is increasing (CDE, 2018). In the 2017-2018
school year in California there were 218,135 students who were LTELs and 144,146 students
who have five years of schooling and are at risk for becoming LTELs. LTEL is one of the ways
an ELL can be classified. Therefore, ELL Math performance is connected to LTELs as one
aspect of being labeled an LTEL is struggling academically. One risk of being an LTEL is an
increased chance for dropping out of high school and a higher likelihood to not be college ready
or enrolled in classes that prepare you for college such as Advanced Placement (AP) courses
(CDE, 2018). The priority of providing adequate services to students who are English Language
Learners is also reflected in current education laws and legislation (CDE 2017). Every Student
Succeeds Act (ESSA) was signed in 2015 and brought about legislative changes for the way U.S.
10

school serve English Language Learners including the classification and reclassification process,
standardized testing guidelines for ELLs, accountability reporting and structures to ensure
services are provided at each school site (CDE 2015).
In 2017 in California, approximately 25% of the student population identified as an
English Language Learner (CDE, 2017). This represents a steadily growing population of
students. Not only is the number of students who are considered English Language Learners
growing, but the achievement gap between English Language Learners and their English
proficient peers is widening in both Math and English Language Arts (CDE, 2017). The needs of
English Language Learners in the classroom are diverse and instruction needs to be
differentiated in order to close the academic gaps (Menken, 2010). Many states report a teacher
shortage for educators who are qualified to teach English Language Learners year after year
(CDE, 2018). The importance and impact of the problem of practice reach a variety of
stakeholder groups.
Description of Stakeholder Groups
Éxito Academy is a California charter school that is built by and for the community. At
Éxito Academy the stakeholders include teachers, operational staff members, school leadership,
families, students, board members and community members. The instructional leadership team
contributes to the achievement of the organizational performance goal as they are responsible for
setting the vision of what excellence looks like at the school as well as planning the support that
teachers receive to meet those goals. These supports include professional development, school
initiatives, resources, materials, vision, protocols and systems. Instructional leaders benefit from
the realization of the organizational performance goal due to market accountability as their
evaluation and reputation as successful school leaders is defined by student achievement results
11

(Firestone & Shipps, 2005). Teachers contribute to the success of the organizational performance
goal as they deliver lessons that directly align to the content measured in the CA state math
assessments and provide support to ELLs in the classroom. Teachers benefit from positive
contributions towards the organizational performance goal as it increases scores on performance
evaluations and supports the students in their classroom towards meaningful learning. Students
are the product and evidence of the progress the organization is or is not making towards the
organizational performance goal. Students contribute to the goal as they take the assessments that
measure the school’s effectiveness. Students benefit from the realization of the organizational
performance goal as they have the knowledge and skills to excel in college and beyond and live
choice filled lives.
Stakeholder Group for the Study
While a comprehensive analysis would involve all stakeholders that benefit and
contribute to the organizational performance goal at Éxito Academy, for the purpose of this
study, the focus is on Math teachers. The reason for the focus on teachers is because the
knowledge that Math teachers have about language directly contributes to the effectiveness of
the lesson which impacts student outcomes measured by the state assessments. Teachers also
interact with instructional leaders and students and can share perspectives and experiences on
interactions with other stakeholders as they interact with a wide range.
The stakeholder goal was developed by looking at the academic performance measures
where the organization needed to improve to realize their mission and vision. The Instructional
Leadership team analyzed the school wide data as well as student subgroup data and the area
where the largest discrepancy existed was in the Math data for ELLs as compared to their
English fluent counterparts. Achievement of the stakeholder goal directly drives the success of
12

the organizational performance goal as classroom instruction informs state assessment results.
Not meeting the goal risks the realization of the organization’s mission/vision to provide a high-
quality education that “dramatically changes life outcomes” for historically underserved
communities. Not meeting the goals also negatively impacts the reputation of the school and
could adversely impact the school’s oversight by the state and the charter renewal. Furthermore,
not meeting the goal denies students learning English a meaningful education that both supports
their identities and academics.
Table 3

Organizational Mission, Global Goal and Stakeholder Performance Goals

Organizational Mission
Éxito Academy’s mission is to teach the academic skills needed for our students to thrive in high
school, college, and beyond while also providing space to develop character and a sense of self.
Through the success of our students, the Éxito team and family will serve as a model of
excellence and collaborate with others to raise the quality of education in Coastal City.
Organizational Performance Goal
By 2023, 85% of English Language Learners will meet or exceed the standard as measured by the
standardized state math assessments. The gap between ELL and FEP students will be no more
than 15%.

Instructional Leader Goal Teacher Goal Student Goal
By 2021, 100% of
Instructional Leaders will
identify the English Language
Development (ELD)
proficiency levels of students
as determined by the state
ELD assessment and a
professional development plan
to meet the needs of the
proficiency levels.
By 2023, 100% of math
teachers will reach the
performance goal through the
use of differentiation and
engagement of ELL students.

By 2023, 85% of students who
are ELLs will meet or exceed
the standard on the CA state
math assessment.

13

Purpose of the Project and Questions
The purpose of this project is to conduct a gap analysis to examine the knowledge,
motivation and organizational influences of teachers in supporting students who are ELLs in the
Math classroom. The analysis will begin by generating a list of possible or assumed influences
that will be examined systematically to focus on actual or validated influences. While a complete
gap analysis would focus on all stakeholders, for practical purposes the stakeholder to be focused
on in this analysis is teachers. The gap analysis is guided by the following questions
1. What are teachers’ knowledge and motivation in relation to reaching the organizational
performance goal of 85% of ELL students meeting or exceeding the standard on the state
Math assessment through differentiated instruction?
2. How do teachers' knowledge and motivation interact with the organizational culture and
context in supporting students who are ELLs in meeting or exceeding the standard on
state Math assessments?
Methodological Framework
Maxwell (2013) stated that a conceptual framework is a visual that informs the rest of the
design of a study. Similarly, a conceptual framework is constructed by a researcher to fit the
study (Maxwell, 2013). Rocco and Plakhotnik (2009) built on the definition of a conceptual
framework when they stated it anchors a study in relevant knowledge and sets a foundation for
the research questions and methodology. The Knowledge Motivation and Organization (KMO)
gap analysis framework by Clark and Estes (2008) serves as a foundation for the study. An
organization’s performance goals are the central focus of the KMO framework (Clark & Estes,
2008). The KMO framework by Clark and Estes (2008) looks at the gap between the desired
14

goals and actual performance of an organization. The framework then analyzes if the gap can be
attributed to knowledge and skills (K), motivation (M) or organizational barriers (O).
Definitions
English Language Learners (ELLs): students whose first language is not English
(Echevarria, Vogt & Short, 2008)
Reclassified Fluent English Proficient (RFEP): Students who have met the 4 criteria set
by the California Department of Education and are now no longer considered ELLs, but rather
fluent English speakers
Initial Fluent English Proficient (IFEP): Students at this level have well developed oral
(listening and speaking) and written (reading and writing) skills. They are not considered ELLs
but may need language support (specifically with academic language).
English Only (EO): Fluent English Proficient Students that do not speak a language other
than English.
Fluent English Proficient (FEP): This category can include both IFEP and RFEP students.
In this dissertation this term included EO students as well as students who were English
Language Learners, but are now considered fluent by the CA State Guidelines
Long Term English Language Learner (LTEL): Long-term English learner (or LTEL) is a
formal educational classification given to students who have been enrolled in American schools
for more than six years, who are not progressing toward English proficiency, and who are
struggling academically due to their limited English skills (CDE, 2019).
Ever-EL: A group comprised of current and former ELLs
Charter School: A charter school is a public school that receives government funding but
operates independently of the established state school system in which it is located.
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Reclassification: Reclassification is the process whereby a student is reclassified from an
English learner to Fluent English Proficient (RFEP). Local districts determine when the student
has met the 4 criteria listed in Education Code (EC) Section 313(f), in accordance with the
California Department of Education (CDE).
Job Aid: A job aid is a resource that supports staff in following a procedure or
implementing a skill
Administrator: A leader in the school setting. In this study, the school administrators
include the Principal, Vice Principals, Instructional Coaches.
Instructional Coach: A school administrator responsible for observations, feedback and
supporting the professional growth of a teacher.
Organization of the Project
This dissertation consists of five chapters. This chapter provided details on key concepts
and terminology found in this study on teacher support for ELLs in the Math classroom. The
context, mission, organizational performance goal and stakeholder of the organization were also
introduced. Chapter 2 provides a review of current literature surrounding teacher support of
ELLs, strategies for supporting ELLs, theories of language development and other relevant
research. Chapter 3 details the purpose for this study as well as the methodology with a focus on
the choice of participants, sampling, data collection and analysis. Chapter 4 includes an analysis
of the data and results based on the qualitative and quantitative measures. Chapter 5 provides
recommendations, based on the findings and literature, for closing the achievement gaps as well
as recommendations for teacher support of ELLs in the Math classroom.

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Chapter Two: Literature Review
This literature review will examine the root causes in the achievement gaps between
English Language Learners (ELLs) and their English Fluent peers on the California standardized
math assessments. The literature review begins with general research on the importance of
language support for students who are ELLs as well as current research on ELL student
performance. This is followed by an overview of literature on English Language Development
(ELD) and support for ELLs in the K-8 classroom. This review will present an in-depth
discussion on research-based practices to support ELLs, ELL experience in the math classroom,
teacher perception and characteristics of excellent classrooms for supporting ELLs. This section
includes current research on teacher preparation and training, language support, math
interventions and the experience of ELLs in the math classroom. Following the general research
literature, the review turns to the Clark and Estes (2008) Gap Analysis Conceptual Framework
and, specifically, knowledge, motivation and organizational influences on teachers’ ability to
support students who are English Language Learners in the math classroom.
English Language Development
As evidenced by state standardized test results, the gap between ELLs and their FEP
peers is one of the largest gaps in the state of California and is growing at a national level (CDE,
2018). The achievement gap coupled with the growing enrollment of ELL students in California
schools puts a spotlight on ELD.
The Process of Being an ELL

Learning English is an arduous process that nearly 10% of the Nations students and
nearly 20% of the students enrolled in California public schools experience (CDE, 2018). The
process begins when students first enter a U.S. school and for some is a lifelong process.
Numerous research studies show the importance of language proficiency on student achievement
17

(Echevarria and Short, 2008). Students who are reclassified and considered fluent English
proficient have very little achievement gap if at all and at times outperform their English Only
(EO) counterparts (CDE, 2018). The State of California has launched initiatives like the CA
ELD standards, the ELD framework, CA reclassification process and the English Language
Proficiency Assessment (ELPAC) in an attempt to support the progress and achievement of
students who are ELLs. These initiatives combined with educational research on best practices,
instructional strategies, teacher preparation and teacher knowledge fail to close the gap between
students who are ELLs and their EO counterparts.
History and Growth of English Language Learners
The number of English Language Learners are rapidly growing in the state of California.
In addition to growing demographics, the achievement gap as measured by state standardized
assessments is also growing between ELLs and their FEP peers (CDE, 2019). With growing
numbers brings about changes in policies and protocols. In the 2018-2019 school year there were
approximately 1.2 million students who are English Language Learners (ELLs) in the state of
California (CDE, 2018). This does not include students who have an English Language
Acquisition status of Reclassified Fluent English Proficient (RFEP), Initial Fluent English
Proficient (IFEP) or To Be Determined (TBD). ELLs represent 19.3% of the total enrollment in
the state (CDE, 2018). In addition to the students classified as ELLs, there are 2,587,609 students
who speak a language other than English in their home which represents 41.8% of total public
school enrollment in California as reported by the state language census (CDE, 2018). Of the
total enrollment of ELLs, 70.2%of ELLs are enrolled in primary grades (K-6) while 29.8% are
enrolled in grades 7 through 12 (CDE, 2018). In the state of California, 81.56% of students who
18

are ELLs speak Spanish (CDE, 2018). The next largest represented language group was
Vietnamese with 2.21% of total ELLs (CDE, 2018).
Table 4
ELL Enrollment in California
Number of ELL Students in California 1,200,000
% of total state enrollment 19.3
% of Total ELL enrolled in primary grades
(K-6)
70.2
% of Total ELL enrolled in secondary grades
(7-12)
29.8
% of identified ELLs who speak Spanish 81.56
% of identified ELLs who speak Vietnamese 2.21
Students who speak a language other than
English in California
2,587,609
% of total enrollment 41.8

The latest National comprehensive statistics were from 2015. California has nearly 30%
of the Nation’s ELLs (NCES, 2017). While California has the largest number of students who
are ELLs nationwide statistics show a representation of students as ELLs (CDE, 2015). Between
the 2009-2010 and the 2014-2015 school years nearly all states experienced growth in ELLs with
the National total near 5 million students (NCES, 2015). This represented 10% of the total
national enrollment (NCES, 2015). This study found that nearly 80% of ELLs were Latino and
spoke Spanish.
ELL Performance at the State Level
According to current performance measures that show 12.57% of ELLs are proficient in
Math that means out of a kindergarten class of 30, only 4 students would be proficient (CDE,
2018). The state of California uses a standardized test called Smarter Balance (SBAC) to test
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students in grades 3 through 11 in Math and English Language Arts (ELA). While there are
achievement gaps in both Math and ELA, this literature review focuses on Math scores. In 2018,
44.03% of English Only (EO) students met or exceeded the standard while 12.57% of ELLs met
or exceeded that standard as measured by the California state standardized assessment (CDE,
2018). 41.51% of students who were reclassified (RFEP) met or exceeded the standard (CDE,
2018). When tracking progress over time we see that the amount of ELLs meeting or exceeding
the standard decreases over time. In 2018, 5.93% of ELLs in eighth grade met or exceeded the
standard while in 2016 this same cohort had 10% at meeting or exceeding the standard which is a
decline of 4.07% (CDE, 2018).
A second assessment English Language Proficiency Assessment of California (ELPAC)
captures how students who are ELLs are developing proficiency in the English language. The
scores on the ELPAC are used for reclassification, progress monitoring, goal setting and funding.
The first year of administration of the assessment (previously known as CELDT) was in the
2017-2018 academic year. The assessment is broken down into oral and written language with 4
subcategories: listening, speaking, reading and writing. The ELPAC assesses if a student is
developing language proficiency in English. The assessment is important because proficiency on
the ELPAC is one of the requirements to be reclassified from an ELL to RFEP. Only 30.56% of
students who are ELLs met the standard on the assessment (CDE, 2018) with grade levels
ranging from 10.88% to 46.60% proficiency. These numbers decreased on 2019, with 16% of
students being proficient on the ELPAC assessment (CDE, 2019) In 2018, 45.20% of ELLs met
the standard in oral language and 20.95% met the standard for written language with the lowest
subcategory, reading, only having 22.83% proficient (CDE, 2018). The results from the ELPAC
20

show that students need more language development so they can transfer these skills to content
areas like Math.
Current Frameworks to Support Students who are ELLs at a State Level
When we look at the goals set for ELLs by the state of California and the results on
assessments a gap is alarmingly clear. The state of California provides support for schools that
center around two goals set for students who are ELLs. The first is to support students who are
ELLs in acquiring full proficiency of the English language as rapidly and effectively as possible
(CDE, 2018). The second is to ensure that students who are ELLs achieve the same rigorous
standards as their English Only (EO) counterparts (CDE, 2018). The state of California has
developed English Language Development (ELD) academic standards, a framework for
instruction and a standardized assessment to progress monitor. The CA ELD framework sets a
vision for a comprehensive ELD framework that includes integrated and designated ELD and is
to be used in all CA schools where ELLs are enrolled. Integrated ELD refers to the content
classes where ELD strategies are used to support students in demonstrating content knowledge.
This occurs in the content classroom. Designated or dedicated ELD refers to instruction where
English language development standards are the focus of instruction. This occurs as a separate
class from the core content instruction. Outlined in the CA ELD framework are the CA ELD
standards which are K-12 standards that can be used during integrated ELD to support
demonstration of learning and access to content. The standards are broken down by grade level
as well as proficiency level and align with the state standards for ELA, Math and Science. The
ELPAC test measures proficiency on the ELD standards.

21

State Reclassification Policies and Procedures
English Language Proficiency and the reclassification process have many implications
for students identified as English Language Learners or Long-Term English Language Learners.
English Language Proficiency and reclassification have implications such as low high school
graduation rates, high incarceration, low math proficiency and the likelihood to repeat math
courses in high school (Henry, Nistor, Baltes, 2016). California’s reclassification process has
implications for the students who are identified as Long-Term English Language Learners,
meaning they have spent 6 or more years labeled as an English Language Learner (Henry,
Nistor, Baltes, 2016).
In a study, Fong (2008) found that Long Term English Language Learners had the
highest repetition rates for Algebra 1 than any other subgroup of students. Many studies prove a
correlation between English proficiency and Math performance on standardized state
assessments (Henry, Nistor, Baltes, 2016). The study by Henry, Nistor and Baltes suggested that
math proficiency drastically increased with English proficiency level and was more directly
related with proficiency than with any other change in subgroup. Given the implications that
language proficiency has on academic outcomes; the support given in order to allow students to
be reclassified is beneficial to students. In the state of California there are criteria for
reclassification that include an overall score of 4 (out of 4) on the ELPAC, score of 3 or 4 on the
state ELA test, grade of C or better in English Language Arts class, parent agreement and teacher
recommendation. The state reclassification criteria does not call out achievement in Math yet
ELLs, Ever-ELs and LTELS struggle in Math. as represented by the proficiency levels on the
state math assessments (CDE, 2017). Reclassification combined with test scores and state
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standards for learning create a model for English Language Development in California. While
these elements and instructional components are unique to California, they are part of larger
models, frameworks and protocols aimed at supporting students who are English Language
Learners.
Evolving Models, Frameworks and Protocols of Language Development
There are a variety of policies, frameworks and protocols that exist to support ELL
students. While research shows these frameworks and protocols can have positive results, it is a
relative impact (McIntyre, Ellen,Chen, Cheng-Ting, Muñoz, Marco, Beldon,2010). The growth
may not be enough to close the achievement gap, but rather shorten the gap slightly.
Models of English Language Development
There are many models of English Language Development and Education. Each model
differs in the target language, time spent in a language, target content and student groupings. The
California Education Codes (CDE, 2018) offers three models of language development. The
first being Dual-Language Immersion Program (DI)/ Two Way Immersion (TWI).This is defined
as a classroom setting that provides language learning and academic instruction for native
speakers of English and native speakers of another language, with the goals of high academic
achievement, first and second language proficiency, and cross-cultural understanding [Education
Code (EC) Section 306(c)(1)]. The second model is a Transitional or Developmental Program
which is defined as s classroom setting for English learners that provides instruction to pupils
that utilizes a pupil’s native language for literacy and academic instruction and enables an
English learner to achieve English proficiency and academic mastery of subject matter content
and higher order skills, including critical thinking, in order to meet the state-adopted academic
content standards [EC Section 306(c)(2)]. The third listed model is Structured English
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Immersion (SEI): SEI is a classroom setting for English learners in which nearly all classroom
instruction is provided in English but with a curriculum and presentation designed for pupils who
are learning English. At minimum, English learners will be provided a program of Structured
English Immersion. [EC sections 305(a)(2) and 306(c)(3)]. SEI is the most popular model in
California schools as well as schools across the nation.
While there are benefits of each model, there are some models that prove more effective
for students who are learning English as a second language. A large majority of English
Language Learners are in monolingual, English only schooling contexts (Menken and Kyel,
2010). In a study done by Menken and Kyel (2010) only .033% of participants were in a truly
bilingual educational environment. The .033% of participants were also the highest scoring
participants with a 90% grade point average after 6 years of schooling. One limitation of the
Menken and Kyel study is that the study does not show the impact on standardized testing and
achievement therefore statistically significant positive impact on achievement cannot be
measured. Carlos, et. al (2004) found that teaching comprehension strategies in students’ primary
language improved reading comprehension when students afterward read in English. The same
study found that home language is used to bridge concepts to English (Carlo et. al, 2004). In this
context, using the home language can be defined as using cognates, brief explanations not
complete translations in home language, background knowledge connections in home language,
preview and/or review in home language.
While research over time has proven achievement gains for students who are ELLs,
research also proves that a majority of the growth is not statistically significant and fails to cover
all content areas. Slavin (2011) studied the impact of English immersion on student
performance. In this study researchers randomly assigned ELLs to either Transitional bilingual
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or English Immersion. In the study they found in first grade, ELLs in English immersion did
significantly better on English achievement measures than did ELLs in bilingual education. By
fourth grade, English immersion students’ scores were somewhat higher than that of the bilingual
education students, but the differences were not significant. Another researcher, Green (1997),
draws the conclusion that a majority of research focuses on bilingual education results for
literacy and ELD, but there is little data on the impact on Math. Research over time has both
defined and evaluated the models of ELD. The research stated some positive outcomes for the
use of students’ native language in the classroom. However, there is a need for more research to
be done to address a wide array of content areas and show a statistically significant impact on
student achievement outcomes.
Evolving Frameworks and Protocols
In addition to models of ELD, there are also widely adopted protocols and frameworks
that offer strategies and systems to provide support to students who are ELLs in the classroom.
Two of the most widely adopted strategies are: Sheltered Instruction Observation Protocol
(SIOP) and Guided Language Acquisition Design (GLAD). While these tools are widely used by
educators, research does not prove there is a significant impact on student achievement
(McIntyre, Ellen,Chen, Cheng-Ting, Muñoz, Marco, Beldon,2010). The goal of sheltered
instruction is to support the learning of grade level content standards for students who may have
limited English proficiency (Echevarria and Short, 2008 ). While it does contribute to overall
English Language development, the primary purpose is content skills (Echevarria and Short,
2008). Some SIOP supports include: A) building on background knowledge, B) providing
background knowledge, C) frontloading, use of resources like graphic organizers, D) clear goals
and tasks, E) visual supports, F) additional practice, G) use of both content objectives and
25

language objectives, H) sentence frames and I) differentiation. One problem is that while there
are many studies describing the protocols there are not published data that shows the impact of
these measures on student understanding of the California Common Core Standards. One
researcher, McIntyre et. al (2010) asserts that while there are studies on SIOP’s impact on
student achievement, the results are modest and do not represent a statistically significant amount
that would lead to the closing of the achievement gap between ELLs and their English Fluent
counterparts.
Language Support in the Math Classroom

People often refer to Math as a “universal language”. However, there are distinct
language demands related to mathematical content knowledge. The Supreme Court’s decision in
Lau v. Nichols (1974) upheld the belief that classroom instruction must meet the needs of
students even if their English language proficiency is limited. As students develop language, they
develop both formal and informal language. As part of their formal language, they develop
academic language. Classrooms supporting ELL students have the demands of the content as
well as language demands. Research shows that while teachers acknowledge the need for
language support in the Math classroom, instruction rarely addresses both content and language
development (Turkan, de Jong; 2018). According to the National Council of Teachers of
Mathematics (NCTM) there are seven components of effective Math instructions (NCTM, 2014).
Those seven components include establishing Math goals to focus learning, implementing tasks
that promote reasoning and problem solving, using/connecting mathematical representations,
facilitating meaningful mathematical discourse, posing purposeful questions, building procedural
fluency from conceptual understanding, supporting productive struggles and eliciting student
evidence of thinking (NCTM, 2014).
26

Academic Language Development in Comparison with Oral Language Development
Students learning English must not only learn informal English, but they must also
acquire the formal academic language needed to navigate academia. While formal English is a
challenge, researchers have indicated that formal academic English may require more time and
support (Collier, 1987; Cummins, 1981; Mitchell, Destino & Karam, 1997). Collier (1987,
1995). Cummins (1981), and Mitchell, Destino and Karam (1997) estimated it may take up to ten
years before students learning English are fully competitive in the academic uses of English as
compared with their FEP counterparts. In a study by Hakuta (2000), the data from four different
school districts was compiled. The study found that it took students between two and five years
to develop oral English proficiency. The study then tracked academic English proficiency as
measured by a formal reading and writing assessment. The results showed that development of
academic language took between four to seven years (Hakuta, 2000). This means that it is not
enough to solely support the language development of students, but rather there is a need to
strategically support the development of academic language.
While the above-mentioned research shows that formal English requires more time and
support, there are diverse needs for ELL students in acquiring formal Math Language (Dale &
Cuevas, 1992; Jarret, 1999).
The ability to demonstrate mathematical problem solving and reasoning are closely tied
to language, specifically a firm understanding of mathematical vocabulary in context (Dale &
Cuevas, 1992; Jarret, 1999). According to Jarret (1999), a student needs to be able to make
meaning of the vocabulary in context in order to accurately apply problem solving and reasoning
strategies. This means teachers are not only teaching what the vocabulary words mean, but how
those words interact in Math (Jarret, 1999).Jarret (1999) asserts that students must begin to
27

equate mathematical vocabulary in context with symbols and functions. For ELL students the
context of a problem is crucial because one word in Math can equate with different procedures
based on the context. For example, if a word problem says ‘they ate some’ versus ‘they were
given some’ the mathematical procedure is entirely changed. Part of acquiring a firm
understanding means that vocabulary must be introduced, understood and used within the
context of the content (Moschkovich, 2008). Moschkovich (2008) presents the idea that
academic vocabulary is not enough in itself, but rather instruction on the extended discourse that
includes syntax, organization, the mathematics register, and discourse practices. According to
Moschkovich (2008), the academic vocabulary coupled with instruction of the extended
discourse allows students to make meaning of tasks and share their command of mathematical
practices.
Intersectionality of Math and Language
When considering the intersection of language and math proficiency, a student’s formal
education in their primary language is a factor (Bernardo, 2005). In a study of 111 fourth grade
(students attended 10 different private schools and also identified as middle/upper income), the
students whose first language was English exhibited higher mathematical proficiency despite the
fact that all students were described as being bilingual in English and Filipino (Bernardo,
2005).The students in the study did not have trouble with the mathematical concepts when they
had received a formal education in their primary language. Students were successful solving the
mathematical concepts when given the problem in their primary language (Bernardo, 2002).
However, when the students began to face word problems in a second language that they were
not yet proficient in they struggled (Bernardo, 2002). This shows that both mathematical
28

knowledge as well as specific formal language instruction is needed in the Math classroom in
order to demonstrate mastery on the tasks.
Language Support in Content Specific Instruction
Teachers struggle to create a rigorous Math curriculum and classroom environment that
both focuses on the language support needed by a student’s language proficiency while also
creating authentic learning that combines mathematical discourse and practice (Turkan & de
Jong, 2018). Teachers need knowledge, strategies and preparation for working with English
Language Learners in the field of Mathematics (Turkan & de Jong, 2018). In a qualitative study
by Turkan and de Jong (2018) that captured the instructional decision making of teachers about
supporting English Language Learners in math found that teachers often refer to language
proficiency when making instructional decisions but struggled in choosing an instructional
practice that appropriately addressed the language proficiency level. English Language Learners
are expected to master their conceptual understanding of math content, problem solving
competencies as well as their ability to have mathematical discussions which builds on the ability
to build on an answer, elaborate on responses and choose the language based on their purpose in
addition to learning English (Banse, Palacios, Merrit, Rimm, 2017). The study conducted found
that math instruction either focused on building conceptual understanding or developing the
ability to have a mathematical discussion, but failed to create authentic learning environments
that simultaneously build conceptual understanding and the math language needed to express it
for English Language Learners.
While students who are English Language Learners have distinct instructional needs;
they also have emotional needs in order to excel in the classroom (Lewis, Ream, Bocian,
Cardullo, Hammond, Fast, 2012). Many studies focus on the instructional needs of English
29

Language Learners in Math and the teacher’s instructional knowledge, but there is a correlation
between caring teacher-student relationships, student self-efficacy in math and math test scores
(Lewis, Ream, Bocian, Cardullo, Hammond, Fast, 2012). In a study of 1,456 students in grades
five through eight (799 students were English proficient and 657 were English Language
Learners), there was a consistent correlation between high math test scores, high math self-
efficacy and caring teacher relationships. The correlation was higher amongst the 657 English
Language Learners than English proficient students. For English Language Learners, math self-
efficacy was caused by caring teacher relationships while English Proficient students developed
math self-efficacy apart from caring teachers. Fostering learning environments that meet both the
instructional needs as well as the emotional needs of students who are English Language
Learners impacts the level of achievement for these students. Similar to the need for purposeful
differentiation of classroom instruction there is a need to examine the types of assessments and
the characteristics of the assessments that ELLs take in order to test content knowledge.
Language Supports and Typical Models of Assessment
While the student achievement statistics previously mentioned paint a broad picture of
student achievement in California, a closer examination of typical assessment models reveals
both challenges as well as opportunities in supporting students who are English Language
Learners. English Language Learners are scoring an average of 12.57% (CDE, 2018) proficient
on the state math assessments. The state math assessments are both mathematically rigorous and
also are linguistically demanding which may present a bigger barrier to English Language
Learners than the content itself (Schmitz, 2016; Choi, Milburn, Reynolds & Maroccia, 2013;
Newkirk-Turner, Brandi, Valerie, 2018; Martiniello; 2008).
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While many studies show that English Language Learners are not scoring proficient on
the state math exams, a study by Schmitz (2016) examines whether it is the math concepts or if it
is the ability to express them that is a barrier for English Language Learners. The qualitative
study found that the structure of peer dialogue coupled with rubrics resulted in higher test scores
for students (Schmitz, 2016). Clarity of target language and inclusion of the language demands
that are specific to math resulted in more mastery for students (Schmitz, 2016). A majority of the
research on mathematical support for English Language Learners is aimed at elementary
students, secondary students need support in vocabulary knowledge, negation, preposition use
and a typical sentence structure in the mathematical classroom as well. In the study by Choi,
Milburn, Reynolds and Maroccia (2013), two different versions of a mathematical test were
administered to nearly 100 secondary students who are English Language Learners. One version
included challenges in four categories: vocabulary knowledge, negation, preposition use and a
typical sentence structure; whereas the other mathematical task gave students the opportunity to
apply only procedural knowledge. Students did not struggle with the procedures, but were
negatively impacted by the language needs of the activities (Newkirk-Turner, Brandi,
Valerie,2018). State assessments have high lexile and linguistic demands and oftentimes
classroom instruction and curriculum assessments are written at a different level than the state
assessments. There is a larger number of word-based problems on the state math assessments. In
a study done by a Speech Pathologist they conducted a pre assessment to determine what English
Language needs would need to be instructed and assessed in order for students to show mastery
on the linguistically demanding state math assessment problems. In order to overcome the
culturally and linguistically biased questions on the state math assessments students needed
targeted math support. When students received these supports, proficiency increased.
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Achievement for English Language Learners in the state of California is measured by state
standardized tests.
The tasks students are asked to do are both mathematically demanding and also have high
lexile levels for the questions (Martiniello, 2009). Lexile level is a tool used to measure a
student’s reading ability as well as how difficult a text is. In a study of the fourth grade math
state standardized tests, the highest discrepancy in performance between English Language
Learners and their English Only peers occurred in the problems with the highest lexile
measurement (Martiniello, 2009). Linguistic complexity was a defining factor of proficiency.
The linguistically complex problems that included a visual representation as part of the problem
had a lower percent of discrepancy between English Language Learners and their English Only
peers.
Research shows that when ELLs received modifications such as scaffolded language
support and test administration in their native language, there was a positive impact on student
achievement outcomes (Zehr, 2010; Orosco, 2014). Given the linguistic demands of the test
material and instructions and therefore experience a barrier in demonstrating their knowledge of
mathematics on the assessments. Accommodations for English Language Learners may include
altering the linguistic difficulty while keeping the mathematical demands (Zehr, 2010). English
Language Learners and Reclassified English Proficient students performed higher when the
mathematical demands were not changed, but the lexile difficulty was lessened as part of the
modifications. There was little difference in performance for English Only students. In the
United States many English Language Learners are being referred to special education. The
students that are referred for special education as well as the students who are below grade level
experience specific challenges when it comes to word problems and math specific reading tasks
32

(Orosco, 2014). In a study by Orosco (2014), that designed a math language intervention
program in the native language, students experienced growth when they were instructed in their
native language then transferred to English therefore lessening the barrier. Research highlights
that the typical models of assessment fail to provide linguistic support for students who are ELL
students. In addition to a lack of support, English Language Learners often cannot show genuine
content knowledge due to the high linguistic demands of the assessments. While assessments are
one barrier to supporting ELL students, research highlights other challenges such as teacher
preparation programs and development, teacher perception, implementation of strategies and
identity.
Challenges in Supporting ELL Students
The gap between ELL students and their FEP peers is not new. An array of challenges
and barriers wedge themselves between educational equity and the inequity that currently exists
for ELL students based on state Math scores. Teacher preparation programs inadequately prepare
teachers to meet the needs of ELL students in the classroom (Kareva & Echevarria, 2013;
Harklau, 1994; Short, Fidelman, & Louguit, 2012). Educators tend to see bilingualism as a
deficit (Carley Rizutto, 2017; Menken & Kyel, 2010; Reeves, 2015). The development and
implementation of instructional best practices to support ELL students may not meet the needs
required to close the achievement gap (Menken, 2010; Chang, 2008). In addition to the
instructional needs, student identity, racial stereotypes, bias and privilege create distinct
challenges.
Teacher Preparation Programs and Professional Development
The evidence highlights that Teacher Preparation Programs as well as in service
professional development programs fail to prepare teachers for the diverse needs of English
33

Language Learners as well as the skills to create linguistically relevant classrooms (Kareva &
Echevarria, 2013; Harklau, 1994; Short, Fidelman, & Louguit, 2012). In a 2015 study of 3,289
novice teachers, only 17% of participants stated they received competency specific training
pertaining to effective instruction of English Language Learners (Goodsoon et. al, 2019). Less
than half of surveyed teachers reported some exposure to material about effectively serving ELL
students (Goodsoon et. al, 2019). Teacher preparation programs provide little guidance and
support on the complex needs of English Language Learners in Math which results in teachers
varying the instructional and socioemotional supports provided to ELLs or the absence of such
supports (Lewis, Ream, Bocian, Cardullo, Hammon & Fast, 2008; Turkan, 2018; Zhang, Jie &
Pelttari, 2013).
Although nearly every classroom in the nation has at least one student that is an English
Language Learner and nearly five million (CDE, 2018) English Language Learners nationwide,
many teachers lack the training to support students in second language acquisition (Ballantyne,
Sanderman, and Levy, 2008). In a 2008 study, Ballantyne, Sanderman and Levy found that less
than one third of teachers had received training focused on supporting English Language
Learners in the classroom. Even though California has requirements for teacher credential exams
that support Teacher knowledge of English Language Learners supports, not all teachers who
have ELL students in their classrooms possess the certifications (Gandara, Maxwell-Jolly &
Driscoll, 2005). In their 2005 study, Gandara, Maxwell-Jolly & Driscoll found that of the
teachers that had more than 3 ELL students in their classrooms only 29% had professional
certification in bilingual education or ESL (English as a second language) also referred to as
ELD (English Language Development).
34

The amount of LTEL (Long Term English Language Learners) which refers to students
who have been English Language Learners for over 6 years is steadily increasing (Ecchevarria
(2008). In a 2008 study Echevarria found that middle and secondary teachers were
underprepared to help English Language Learners make sense of content. During a three year
study that included 649 teachers using ELL supports coupled with receiving training and 372
Control classes, the seventh grade students who received ELL supports drastically outperformed
students in the control group (Echevarria, 2008).
In addition to the impact on the instructional needs of ELL students there is also an
impact on the emotional needs of ELL students (Zhang & Pelttari, 2013). Teachers who lack the
preservice training to support English Language Learners and have not experienced learning a
second language may not understand or address the complexity and emotional experience of
English Language Learners at school (Zhang & Pelttari, 2013). In a study with 155 graduate and
undergraduate preservice teachers where they experienced a lecture class delivered in Dutch,
65% of participants reported feeling confused while 71% felt frustration (Zhang & Pelttari,
2013). In the pre survey teacher notes supports for English Language learners like gestures,
visuals and repetition whereas after the experience they listed the need to feel comfortable, safe
and relatable to content. Various studies showed that teachers lack both the training as well as
the certifications that enable them to best serve English Language Learners. If teacher
preparation programs are not adequately preparing educators to meet the needs of ELLs, then the
validity of the certifications is also questionable. Due in part to the lack of support and
knowledge about the needs of English Language Learners, many educators have adopted a
deficit-based approach towards bilingualism and English Language Learners.
35

Research claims that teacher preparation programs do not adequately prepare teachers to
serve students who are ELLs (Gandara, Maxwell-Jolly & Driscoll, 2005). However, reference to
serving ELL students is not absent from California State credentialing programs. The California
Department of Education credential requirements mention that all preparation programs must
address content related to teaching and supporting ELL students in the classroom (CDE, 2019).
Furthermore, California requires that any teacher providing instructional services to a student
learning English must be authorized (CDE, 2019). As part of the authorization, teachers take an
exam called California Teacher of English Language Learners (CTEL) (CDE, 2019). In addition
to the assessments and program requirements, all teachers who receive a preliminary teaching
credential in California pass a Teacher Performance Assessment (edTPA). The TPA does ask
educators to write about how they will differentiate a lesson for students who are ELLs.
Teacher Perception
Despite research that indicates the need for differentiated instructional practices for
English Language Learners, there is little variance of instructional practices in the general
education classroom and educators tend to see bilingualism as a deficit (Rizutto ,2017; Menken
& Kyel, 2010; Reeves, 2015). Due to a lack of preservice training and in career training around
second language acquisition teachers don’t have the knowledge to best serve English Language
Learners and therefore a deficit mentality about students (Rizutto, 2017). The study by Rizutto
(2017) found that 70% of interviewed participants had negative perceptions of English Language
Learners specifically about the assets of their first language in the classroom and their ability to
participate. Teachers do not see English Language Learners as a part of the mainstream
classroom and their diverse needs are seen as something to be fixed (Reeves, 2015). In a study of
over 250 High School Teachers, nearly 70% of participants answered that they “did not have
36

enough time to deal with the needs of ELL” and 40% of interviewed participants held the belief
that all students don’t benefit from the inclusion of English Language Learners in the classroom
(Reeves, 2015). Due to the diverse needs of ELLs and lack of resources, many educators see
ELLs as a gap that needs to be filled. In contrast to deficit-based thinking, additive approaches
build on the strengths of English Language Learners both in their native language as well as their
second language (Reeves, 2015).
Implementation of Instructional Strategies
The evidence highlights that the instructional needs of English Language Learners are
diverse from their English Only peers (Krashen & Terrell 1983; Menken 2010, Gersten & Russel
1996, Chang (2008) ). The diverse needs of English Language Learners require diverse practices
in the classroom that are unique to English Language Learners (Gersten & Russel, 1996). In a
three year study that followed twenty six classrooms in two different regions, the classrooms that
showed the most growth for English Language Learners used distinct practices like transferring
the knowledge from their native tongue to the content and making academic language the focus
of a lesson (Gersten & Russel, 1996). In addition, Educators often overlook the diverse needs
and the variety of needs of English Language Learners (Menken, 2010). Among educators there
is a common misconception that the strategies that work for one English Language Learner will
work for all. In a study of 27 elementary classrooms, Menken (2010) found that the most
commonly identified teaching strategy for English Language Learners is a whole class lesson yet
when the impact was analyzed this strategy yielded the least amount of change on academic
outcomes for English Language Learners. Teacher instructional practices and groupings should
differ based on the student need, identity and ability. Bilingual students and Students who are
learning English benefited from different teaching practices in the math classroom than their
37

white and monolingual counterparts (Chang, 2008). While the above mentioned studies took
place in ELA lessons, the strategies mentioned are applicable to the Math classroom. In a study
that sampled 21,399 students in grades 3-5 over a period of 85,596 observations students
learning English were 2.86 years behind their English only counterparts. In addition, the students
learning English showed the least growth from Teacher lead whole class lessons while their
counterparts showed growth with this teaching strategy (Chang, 2008). The use of whole class
teaching or small group teaching is a decision that Math teachers make when planning their
lessons and differentiating for students who are ELLs. In order for English Language Learners to
both acquire language and master content, educators need to use a variety of research-based
practices to support growth and close the gap for English Language Learners. Teacher
preparation programs as well as in service professional development opportunities miss the
opportunity to equip educators with best practices to support ELLs. While there are many factors
in the classroom that impact ELL outcomes there are also external factors.
Student Identity and the Impact on Math
In addition to the previously mentioned influences, there are external influences that
impact student outcomes such as stereotypes, cultural identity and family dynamics (Matthews,
2018; Hernandez, Rana, Alemdar, Analia, 2016; Guttmannova, 2016). Young learners often
struggle to see the importance of math in their life as well as the real-world context of math. This
is especially true for Black and Latino communities as well as low income students
(Matthews,2018). In a quantitative study (Matthews,2018) of 419 urban Black and Latino
students, their ability to see math as useful increased when they were exposed to meaningful
real-world activities in the classroom. The qualitative study also revealed that Black and Latino
youth experienced pressures from collective identity, alternate messengers and stigma.
38

Stereotypes of Latino students and their families portray a lack of importance on education and a
lack of interest and emphasis on STEM and math careers (Hernandez, Rana, Alemdar, Analia;
2016). In a qualitative study, surveyed parents believed their children should attend college and
believed that STEM careers were admirable and important for their children. In addition to the
positive beliefs, the surveyed parents also listed numerous barriers for their children such as cost,
immigrations status, lack of information and language (Hernandez, Rana, Alemdar, Analia;
2016).There are also starkly different achievement outcomes depending on whether a student is
first, second or third generation (Guttmannova, 2016). In the quantitative study, first and second
generation Latino students demonstrated a significant advantage and increase in proficiency as
compared to third generation students (Guttmannova, 2016). A follow up study further proved
that more recent arrival to the United States predicted higher achievement. There was not a
similar advantage present in math (Guttmannova, 2016). In addition to the classroom barriers,
external barriers such as stereotypes and family dynamics also impact the achievement of
students who are English Language Learners.
Administrator Influence on ELL Achievement
Identifying the behaviors that make effective administrators is important as it impacts
student outcomes and ultimately the life outcome of students. While there have been many
studies on school leadership, Marzano (2005) conducted a meta-analysis consisting of 27 studies
representing 2,817 districts that serve over 3.4 million students. The study found that some
impactful behaviors of school and district leaders included collaborative goal setting, setting
non-negotiable goals for achievement and instruction, monitoring of goals and achievement and
providing resources that support the realization of those goals (Marzano,2005). Coupling the
39

above mentioned skills with instructional expertise and the ability to build relationships are seen
as necessary to be an effective administrator (Marzano,2005).
Behaviors of School Administrators Specifically for ELL Students
In addition to demonstrating highly effective leadership behaviors, there are specific
knowledge gaps as well as needs in order to support students who are ELLs (Brook et. al, 2010;
Zacarian, 2011). Before diving into the instructional needs to create school cultures that support
ELL students, studies show that an understanding of the student’s identity is the foundation for
support (Zacarian, 2011). Administrators need an understanding of the socio economic situation
of students, prior school experiences, disruptions in family life. School administrators need to
have knowledge of the types of programs to serve ELL students in order to create an effective
program at their school (Zacarian, 2011). The study by Zacarian (2011) found that
administrators were familiar with the different types of programs and some teaching strategy, but
had a difficult time naming them in classroom observations. School Administrators are often
found to focus on tertiary supports for ELL students like sign or document translations Brook et.
al (2010). According to their study, principals often placed isolated responsibility for ELL
students' success on the ESL or ELD teachers instead of a reflection of the school’s instructional
program as a whole (Brooks et. al, 2010). Similarly, ESL teachers end up not having professional
support networks due the specialty of their content and principals didn’t feel they shared that
expertise (Brooks et. al, 2010). The study by Brook et. al (2010) found that when Administrators
build up their own skills, they open up more support for teachers of ELL students.
Teacher Perception of School Administrators Support of ELL Students
A study by Gandara et. al (2005) shared teacher perception of what administrators need
to do to improve schools for ELL students .The mixed methods study consisted of a survey that
40

included 5300 teachers from 22 school districts and four focus groups in four different regions
represented by the survey participants. Teachers identified a need for administrators to put more
resources and training towards communicating with the families of ELL students. Teachers also
noted that administrators needed to give them time to teach all subjects to students learning
English and wanted administrators to teach them strategies to address different proficiency
levels. More than half of the surveyed stated they had one or less professional development
sessions on supporting ELL students. Teachers also noted the need for school and organization
administrators to gain more understanding about the challenges of, and solutions to, working
successfully with EL students (Gandara et. al, 2005).
Clark and Estes’ (2008) Knowledge, Motivation and Organizational (KMO) Influences
Framework
The gap analysis framework provided by Clark and Estes (2008) offers a structured,
systematic way to measure the organizational performance goals against the actual performance
outcomes in order to identify gaps. Once a gap has been identified the framework then analyzes
stakeholder knowledge, motivation and organizational influences as it pertains to the
performance gap and organizational goal (Clark and Estes, 2008). For the purpose of this study, a
modified version focusing on one stakeholder group will be conducted. Knowledge comprises
four types: factual, conceptual, procedural and metacognitive (Kratwhol, 2002). The knowledge
assessment and the four categories of knowledge help determine if a stakeholder group has the
knowledge necessary to reach a performance goal. Similarly, specific motivational influences
which can include self-efficacy, attributions, goal orientation, values and goals are foundational
when analyzing performance gaps (Rueda, 2011). Organizational influences such as work
culture, organizational culture, resources, processes and settings also influence a stakeholder’s
ability to perform (Clark & Estes, 2008).
41

The following section will address how a Math teacher’s knowledge, motivation and
organizational needs impact their ability to support students who are ELLs and meet the
performance goals of having 85% of ELLs meet or exceed the standard as measured by the CA
State Math assessments. The first section will discuss the knowledge and skill influences that
impact the stakeholder performance goal. In the following section, the motivational influences on
the stakeholder goal will be considered. Following the motivational influences, the literature
reviews shifts to discussion on the organizational influences that impact the stakeholder
performance goal. In Chapter 3, the knowledge, motivation and organizational influences will be
examined and tested through the methodology.
Stakeholder Knowledge, Motivation and Organizational Influences
This review of scholarly and education research focuses on the knowledge, motivation
and organizational influences required for teachers to achieve their performance goal. The
performance goal for this group of stakeholders is that 85% of students who are English
Language Learners (ELLs) will perform at “standard” or “exceeding standard” as measured by
the standardized state math assessments of California.
Knowledge and Skills
The review of literature focuses on the knowledge that teachers need in order to serve
students who are English Language Learners. The purpose of highlighting the knowledge
needed is to support the organization in reaching their performance goal as well as the
stakeholder goal.
Clark and Estes (2008) assert that it is necessary that change results from a systematic
analysis of performance gaps and is accompanied by a root cause analysis of the knowledge,
skills and motivation needed to succeed. In order for stakeholders to reach their performance
42

goal, it is necessary to examine the types of knowledge and potential methods of assessing and
identifying any existing gaps.
According to Krathwohl, there are four types of knowledge: factual, conceptual,
procedural and metacognitive (Kratwohl, 2002). Factual knowledge is basic to specific contexts
and includes details and terminology that one must understand in order to problem solve in a
certain context (Krathwohl, 2002). Conceptual knowledge focuses on the theories, categories and
concepts needed in a certain domain (Krathwohl, 2002). Procedural knowledge focuses on how
to do something which may include algorithms, techniques that are specific to a task (Kratwohl,
2002; Rueda, 2011). Metacognitive knowledge focuses on the cognitive processes in which one
examines internally to know when and why they do something, and what revisions to practice
may be needed to achieve their goals (Rueda, 2011). Further, for the purpose of this study,
knowledge broadly includes strategies, procedures, facts, concepts and schema (Mayer, 2011).
These are examples of the types of knowledge influences that the stakeholder group will be
asked about in the study.
Using research these sections will discuss three knowledge influences that could
influence a math teacher’s ability to facilitate the learning and achievement of students who are
ELLs. The following research discusses the factual, procedural and metacognitive knowledge
Math teachers need to support their students who are ELLs.
Variety of Instructional Strategies that Effectively Support ELLs
Teachers need to know a wide variety of strategies to assess, facilitate the acquisition of
and instruct math in the classroom. This factual knowledge is necessary so teachers can identify
and define a variety of strategies to support students. Instructional Practices should be
differentiated depending on the needs of the students (Chang, 2008). This is true for the
43

experience of English Language Learners in the classroom. The diverse needs of English
Language Learners demand diverse practices in the classroom that are unique to English
Language Learners (Gersten & Russel, 1996). Gersten and Russel conducted a three-year study
that followed 26 classrooms in 2 different regions and analyzed the impact of instructional
strategies on students who are ELLs. The classrooms that showed the most growth for English
Language Learners used distinct practices such as transferring knowledge from their native
tongue to the target content and making academic language the focus of a lesson (Gersten &
Russel, 1996). Educators often overlook the diverse needs and the variety of needs of English
Language Learners (Menken, 2010). In a study of 27 elementary classrooms, Menken (2010)
found that the most commonly identified teaching strategy for ELLs is a whole class lesson yet
when the impact was analyzed this strategy yielded the least amount of change on academic
outcomes for English Language Learners. The research shows that teacher instructional
practices and groupings should differ based on the student need, identity and ability (Chang,
2008). Based on the above research, a teacher’s ability to use a variety of research-based
practices to support growth for ELLs directly relates to their ability to lessen the gap for English
Language Learners.
Build Relationships and Create Partnerships that Support Students who are ELLs
Teachers need to know how to build relationships and create partnerships that support
students who are ELLs. This is a procedural knowledge as it involves educators knowing how to
complete a specific task which is building relationships and partnerships. Teachers who lack the
preservice training to support English Language Learners and have not experienced learning a
second language may not understand or address the complexity and emotional experience of
English Language Learners at school (Zhang & Pelttari, 2013). In a study done by Zhang and
44

Pelttari (2013) with 155 graduate and undergraduate preservice teachers where they experienced
a lecture class delivered in Dutch, 65% of participants reported feeling confused while 71% felt
frustrated. In the pre survey teacher notes supports for English Language learners like gestures,
visuals and repetition whereas after the experience they listed the need to feel comfortable, safe
and relatable to content. The implications of the above study are that teachers can support
students who are learning English by creating safe classrooms with relatable content (Zhang &
Pelttari, 2013).
Many studies focus on the instructional needs of English Language Learners in Math and
the teacher’s instructional knowledge, but there is a correlation between caring teacher-student
relationships, student self-efficacy in math and math test scores (Lewis, Ream, Bocian, Cardullo,
Hammond, Fast, 2008). Teacher’s knowledge in building relationships supports outcomes. In a
study by Lewis, Ream, Bocian, Cardullo, Hammond and Fast (2008) of 1,456 students in grades
five through eight (799 students were English proficient and 657 were English Language
Learners, there was a consistent correlation between high math test scores, high math self-
efficiency and caring teacher relationships. The correlation was higher amongst the 657 English
Language Learners than English proficient students. This highlights the importance of building
relationships for students who are ELLs. Given that caring relationships with teachers positively
impact self-efficacy and performance, teachers need to know how to build relationships with
students. Teachers need to know how to create classrooms that are safe spaces built on trust and
that value identity (Gonzalez & Ayala-Alcantar, 2008).
Stereotypes of Latino students and their families often portray a lack of importance on
education and a lack of interest and emphasis on STEM and math careers (Hernandez, Rana,
Alemdar, Analia, 2016). Teachers building partnerships with families provides powerful support
45

for students that create a counter narrative to those stereotypes. In a qualitative study, surveyed
parents believed their children should attend college and believed that STEM careers were
admirable and important for their children. In addition to the positive beliefs, the surveyed
parents also listed numerous barriers for their children such as cost, immigrations status, lack of
information and language. While these results are not driven by teachers, but rather focuses on
the viewpoints of families; the data illuminates what relationship building procedures could
focus on. Creating coalitions and partnerships can help demystify the barriers (Guttmannova,
2016). Teachers need to know how to build partnerships with families to provide support to
students (Guttmannova, 2016). After identifying the need to create these partnerships, a
procedural knowledge of steps or actions to build that partnership can create the structure for
these partnerships.
Metacognitive Knowledge to Support Language Acquisition at Varying Levels of Proficiency
Teachers need the metacognitive ability to know when a specific strategy is appropriate
for a student’s proficiency level as well as the Math content. Students at different proficiency
levels need different language supports. The CA ELD Continuum of proficiency gives an
example of this. A student with limited proficiency may need gestures and may reply with a one-
word answer. A student that is developing their language skills may give a complete sentence on
their own and receive a list of possible answers to choose from. A student at a higher level of
proficiency may modify their answer given their audience (formal vs. informal language). In
order to both challenge and support a student at their proficiency level a teacher may look at the
cognitive task and the language required to complete it then choose a strategy based on what the
teacher knows about their student’s language proficiency.
The ability to modify strategies based on a student’s proficiency level is reflected in
46

modifications of daily lessons, assessments, reteach strategies, curriculum modifications and
engagement strategies. A qualitative study by Turkan (2018) captured the instructional decision
making of teachers when making decisions about supporting English Language Learners in
math. The decisions included the different types of differentiation teachers implemented in a
lesson. This included decisions about grouping, scaffolds, visuals, language, assessment and
other supports. The study by Turkan (2008) found that teachers often referred to language
proficiency when making instructional decisions but struggled choosing an instructional practice
that appropriately addressed the language proficiency level of a student. This highlights that
teachers identified the need to provide support for students learning English but did not have the
metacognitive knowledge to choose a strategy that fit both the content as well as the student’s
language proficiency level. A study by Orosco (2014) found math language intervention
programs were most successful when they referenced specific proficiency levels as well as
distinguished between native and second language. Teachers in the study included some
modifications like using a student’s native language, making connections between English and a
student’s native language and modifying the type of language used in the lesson (Orosco, 2014).
Similarly, teachers in the study who saw the most success in the intervention programs made
more specific groupings based on proficiency levels rather than grouping all ELLs together
(Orosco, 2014). Overall, the study also found that teachers lacked the skills to modify based on
proficiency level and native language and that their groupings were both general and did not
build on a student’s native language (Orosco, 2014). The research by Turkan (2008) and Orosco
(2014) found that while teachers identified a need to support students who are learning English,
they lacked the metacognitive knowledge to match classroom supports with a student’s language
proficiency level. This resulted in general support rather than individualized support.
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Teachers need the ability to both teach mathematical content while also teaching the
language students need to demonstrate their learning. One study conducted in middle school
classrooms found that math instruction either focused on building conceptual understanding or
developing the ability to have a mathematical discussion but failed to create authentic learning
environments that simultaneously build conceptual understanding and the math language needed
to express it for English Language Learners (Choi, Milburn, Reynolds, Maroccia, 2013). The
study tested the idea that secondary students who are ELLs have diverse needs that include
support in vocabulary knowledge, negation, preposition use and a typical sentence structure in
the mathematical classroom (Choi, Milburn, Reynolds, Maroccia, 2013). In the study (2013), two
different versions of a mathematical test were administered to nearly 100 secondary students
who are English Language Learners. One version included challenges in four categories:
vocabulary knowledge, negation, preposition use and a typical sentence structure; whereas the
other mathematical task gave students the opportunity to apply only procedural knowledge.
Students did not struggle with the procedures but were negatively impacted by the language
needs of the activities. The study therefore highlighted the need for explicit language support
that is content specific so students can both express their procedural knowledge as well as their
ability to discuss math. Furthermore, the study results suggest that students need language
support in order for their mathematical proficiency to increase (Choi, Milburn, Reynolds,
Maroccia, 2013). In order to address the needs presented in the study by Choi, Milburn,
Reynolds and Maroccia (2013), teachers need to have metacognitive knowledge to know when
and why they need to differentiate instruction and what instructional modifications may be
needed to support student achievement in math. Teachers need to consider both the
mathematical task as well as the language demands presented by the task as they use their
48

metacognitive knowledge to differentiate for ELL students (Choi, Milburn, Reynolds, Maroccia,
2013).
Table 5 shows the organizational mission and performance goals as well as the
stakeholder goals. Furthermore, the table shows the knowledge influence as it pertains to the
stakeholder goals as well as the aligned knowledge type and influence assessment. The
information presented will assist in the exploration of any knowledge gaps as it relates to the
achievement of the stakeholder goal.
Table 5
Knowledge Influences, Types and Assessments for Analysis
Organizational Mission
Éxito Academy’s mission is to teach the academic skills needed for our students to thrive in high school, college,
and beyond while also providing space to develop character and a sense of self. Through the success of our
students, the Éxito team and family will serve as a model of excellence and collaborate with others to raise the
quality of education in Coastal City.
Organizational Performance Goal
By 2023, 85% of English Language Learners will meet or exceed the standard as measured by the standardized
state math assessments. The gap between ELL and FEP students will be no more than 15%.
Teacher Stakeholder Goal
By 2023, 100% of math teachers will reach the performance goal through the use of differentiation and
engagement of ELL students.
Knowledge Influence Knowledge Knowledge Influence Assessment
Teachers need to
know a variety of
strategies to teach
students who are
English Language
Learners in Math.
Factual

Survey
The strategies that I use in my classroom to differentiate for ELLs close
or significantly lessen the achievement gap.
I know a variety of different strategies to differentiate the math content
for students who are learning English.
I use a variety of different strategies to differentiate the math content
for students who are learning English.
I know a variety of different strategies to differentiate the math content
for students who are learning English based on their individual
proficiency level.
I know the specific proficiency levels and needs of the students who are
ELLs in my class.
(strongly agree, agree, disagree, strongly disagree)

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What resources do you use to support students who are ELLs?
Check all that apply with option to add some responses

Interview
Think about a time that represents how you differentiate for students
who are English Language Learners and describe that experience.
(both planning and how it went in the classroom). Describe the process
you go through in lesson planning to differentiate for students who are
ELLs.

Think about a time you used your knowledge of a student’s English
proficiency level to differentiate instruction. Describe the process you
went through and the choices you made.
Teachers need to
know how to build
relationships
resulting in
partnerships that
support students who
are ELLs.
Procedural
Survey
I know how to create strong relationships with students learning
English.
I have specific strategies to create inclusive and safe space for students
learning English
My relationships with students learning English are equally strong as
my relationships with students considered English fluent.
(strongly agree, agree, disagree, strongly disagree)

Interview
Describe a time when an ELL student was successful in your class.
What happened? What did you do to make it that way?
Describe a time an ELL student struggled. What happened? What did
you do or want to do to address it?
Describe your vision of excellent ELL instruction in your Math
classroom. What would we see? Hear? Feel? Do? What resources
would you need to make this a reality?
How would you describe yourself? Would you call yourself novice,
intermediate or proficient in teaching and supporting English Language
Learners? Tell me about that.
Teachers need self-
awareness about
using proficiency and
content knowledge to
appropriately
differentiate.
Metacognitive Survey
I can choose a specific strategy that best supports a student’s
proficiency level.
I modify my lessons daily to meet student proficiency levels.
I modify assessments to meet student proficiency levels.
I know what revision to make to my curriculum based on student
proficiency levels that support student achievement.
(strongly agree, agree, disagree, strongly disagree)

Interview
Think about a time you made an instructional choice either in planning
or execution that was based on language proficiency level? Describe
that.

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Motivation
Motivation is an internal process that initiates and maintains goal-oriented behaviors
(Mayer, 2011). Mayer (2011) indicates that motivation is personal as it is internal, activating
since it causes behavior, energizing in the way it impacts persistence and is directed or centered
around a goal. Motivation influences the way a person pursues a goal, perseveres and puts forth
the metal effort required by the goal (Clark and Estes, 2008). This review of motivational
literature focuses on the motivation influences as it pertains to math teachers serving students
who are ELLs.
Understanding the motivation influences needed to reach a performance goal is
important. A person’s knowledge does not mean they have the motivation, desire or drive to
accomplish the performance goal (Rueda, 2011). As organizations move forward towards a goal,
it is important to address any motivational gaps because a solution geared at knowledge will not
solve/resolve a motivation gap (Rueda, 2011).
Extrinsic and intrinsic motivation impact how a person orients themselves towards a goal
(Hulleman, Barron, Kosovich & Lazowski, 2016). Intrinsic motivation pertains to an individual’s
interest in a task while extrinsic motivation uses tangible benefits to add value (Hulleman,
Barron, Kosovich & Lazowski, 2016). There are six motivational theories that add specificity to
the motivational reality of an organization’s performance. The motivational theories are self-
efficacy, value, interest, attributions, goal orientation and emotions (Mayer, 2011; Rueda 2008).
By addressing the individual motivational theories differently, a root cause can be uncovered that
helps identify action needed to support the realization of the stakeholder performance goals. For
example, if an employee is self-efficacious and believes they can do something, but does not
believe it is valuable to their role, the organization can address the root cause of value theory
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instead of addressing motivation generally.
This section will focus on the motivational theories relevant to teachers supporting and
differentiating the math classroom for students who are ELLs as a means of reaching the
stakeholder performance goal. A focus will be on self-efficacy theory and attribution theory as
they influence teacher motivation towards the support of students who are ELLs. Understanding
how teachers perceive their ability or self-efficacy to differentiate for students who are ELLs as
well as to what they attribute ELL performance could reveal more about the impacts on
motivation. Coupling the research on motivation with the research on knowledge and skills will
allow for an organization to make changes necessary to reach the performance goal.
Self-Efficacy Theory
Self-efficacy is constructed from one’s beliefs and perceptions about their ability and
experiences (Pajares, 2006). A belief in one’s own self efficacy motivates a belief in one’s ability
to contribute to the achievement of a goal (Pajares, 2006). Beliefs about one’s self-efficacy come
from mastery experiences, vicarious experiences (observing others), social persuasions (reading
social cues) and physiological reactions (awareness of environment) (Pajares, 2006). A person’s
self-efficacy increases as they experience success and decreases with failures (Pajares, 2006).
Pajares (2006) adds that people build their self-efficacy by watching mastery experiences and
then applying what they see. Self-efficacy is context specific and can vary from context to
context (Pajares, 2006). Pajares (2006) asserts that higher self-efficacy results in motivation to
work hard, persist and engage in a task.
Teacher Self-Efficacy in Supporting ELLs. Teachers need to believe they are capable
of effectively differentiating instruction for students who are ELLs. One way to build this self-
efficacy is through mastery experiences (Pajares, 2006). In a 2016 study by Beecher, Knoll and
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Patti, school leaders identified that their self-efficacy could be improved in regard to observing
ELL instruction. The principals in the study rated their self-efficacy in strategies and instruction
benefitting ELLs as low. People build their self-efficacy by watching masters of the craft and
then applying what one sees (Pajares, 2006). Teacher self-efficacy and exposure to masters in the
field cannot occur if instructional leaders cannot provide both expertise in the area nor exposure
to masters in the field not to mention if the leaders lack self- efficacy themselves.
In a qualitative study, Ross (2014) found that teachers had a low self-efficacy when asked
about their impact on positively impacting the student achievement of ELLs. Teachers in the
study experienced reduced self-efficacy when working with students who are ELLs relative to
non-ELLs (Ross, 2014). All 181 teachers that were surveyed were K-12 Math Instructors.
Teachers identified high quality professional development targeted at supporting students who
are ELLs as a strategy for improving their self-efficacy (Ross, 2014). In a 2016 survey by Malo-
Juvera, Correll and Cantrell, teachers rated their self-efficacy lowest in regard to their work with
English Language Learners as compared to other subgroups. Closing the achievement gap in
Math for students who are ELLs may rely on a teacher’s belief in their ability to successfully
work with students who are ELLs.
Attribution Theory
According to Anderman and Anderman (2009), Attribution theory “examines individuals'
beliefs about why certain events occur and correlates those beliefs to subsequent motivation” or
to “specific things such as the lack of ability, lack of effort, and poor instruction”. Contributing
success or failures to effort rather than ability can create productive attribution (Anderman &
Anderman, 2009). Another way to build productive attribution is to provide feedback that
highlights the knowledge needed, communicate how that knowledge can be acquired and then
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provide the opportunity to learn the knowledge needed (Anderman & Anderman, 2009). Pintrich
(2003) adds that feedback should highlight the importance of effort and should give strategies.
Pintrich (2003) also adds that supportive and caring personal relationships are crucial to support
a community of learning.
Attributing ELL performance to Teacher Action. Teachers should feel that the
achievement of ELLs is due to their actions, rather than a deficit in the student themselves. If
teachers do not feel responsibility for the achievement of ELLs and therefore language
proficiency as a negative characteristic of their students; then a teacher may view classroom
support differently. In a 2015 study of teacher data analysis protocols, Bertrand and Marsh
found that teachers focused on stable student characteristics when analyzing root causes of
results. When analyzing low performance outcomes for ELLs teachers focused on the student’s
label as an ELL while for other student subgroups teachers attributed student performance to
their instruction (Bertrand & Marsh, 2015). Similarly, ELLs are portrayed as lacking language
and academically supportive home lives (Gutiérrez & Orellana, 2006). In a 2006 study by
Gutiérres and Orellana, teachers primarily attributed low ELL achievement to their native
language, lack of English acquisition and teacher perceptions of a student’s home life.
Supporting students who are ELLs in closing the Math achievement gap relies on teachers as
powerful agents of change. Teachers should attribute both the positive and negative outcomes to
their ability to meet the instructional needs of students who are ELLs rather than a deficit in the
student.
Table 6 illustrates the organizational performance goal and stakeholder performance goal
as well as the motivational influences that are assumed necessary to meet both goals as well as
realize the organizational mission. In addition, the table identifies the motivational theory and the
54

assessment that aligns with the theory. The assessment includes the potential questions and how
data would be gathered about the motivation theory.
Table 6

Motivational Influences and Assessments for Analysis
Organizational Mission
Éxito Academy’s mission is to teach the academic skills needed for our students to thrive in high school,
college, and beyond while also providing space to develop character and a sense of self. Through the
success of our students, the Éxito team and family will serve as a model of excellence and collaborate
with others to raise the quality of education in Coastal City.
Organizational Performance Goal
By 2023, 85% of English Language Learners will meet or exceed the standard as measured by the
standardized state math assessments. The gap between ELL and FEP students will be no more than 15%.
Teacher Stakeholder Goal
By 2023, 100% of math teachers will reach the performance goal through the use of differentiation and
engagement of ELL students.

Motivational Indicator(s)

Assumed Motivation
Influences

Motivational Influence Assessment

Self-Efficacy
Teachers need to believe they
are capable of effectively
differentiating instruction for
students who are ELL.
Survey:
I feel confident about my ability to build relationships with students
who are ELLs
I feel confident about my ability to modify and differentiate
instruction for students who are ELLs
I feel confident about my ability to adequately meet the needs of
students who are ELLs
I feel confident about the idea that your ELL students can outperform
or perform equally to your EO students
(strongly agree, agree, disagree, strongly disagree)

Interview:
What do you do well in supporting students who are ELLsl?
What is challenging about teaching students who are English
Language Learners?

What makes you feel confident or less confident about teaching
students who are ELLs?
55

Attributions
Teachers should feel the
achievement of ELLs is due to
their actions, rather than a
deficit in the student
themselves.
Survey:
When an ELL doesn’t understand a lesson or concept it is usually
because I didn’t adequately differentiate the lesson.
When my students who are ELLs achieve poorly, I believe it is due to
my instruction and knowledge.
The success of my students who are English language learners is most
impacted by factors inside the classroom.
The success of my students who are English language learners is most
impacted by factors outside the classroom.
(strongly agree, agree, disagree, strongly disagree)

Interview:
Describe what you see as having the biggest impact on ELL success
and achievement in your Math classroom. Describe the biggest barrier.

Organization
Culture is composed of both content and structure and has varying levels of
visibility/observability (Schein, 2017). An organization’s culture consists of both cultural models
and cultural settings (Gallimore & Goldenberg, 2001). Cultural settings are concrete and visible
(Gallimore & Goldenberg, 2001). Cultural models refer to cultural practices within an
organization like the values, beliefs and attitudes and are usually not visible (Gallimore &
Goldenberg, 2001).
Organizational Theory
Within one organization there are multiple levels of constantly changing culture that impact the
organization’s ability to perform ( Erez & Gati, 2004). Organizational culture is not exclusively
top down but can also be bottom up (Erez & Gati, 2004). This means that people with less
formal power mold the culture (Erez & Gati, 2004). While principals and other administrators set
the mission, vision and priorities of the school’s culture it is also molded by how teachers
embrace or reject the vision in their everyday actions. Analysis of the cultural model and settings
is necessary in reaching an organizational performance goal. Models and settings illuminate the
driving forces of change, the process of change and the specifics of what change will occur
(Kezar, 2001).
56

The cultural setting within many schools is dynamic and changes in response to shifts in
demographics (Erez & Gati, 2004). Students who are English language learners represent both
the largest and the most consistently growing subgroup in California (CDE, 2018). Given the
shifting demographics, there are both cultural models and settings that should be refined to
support students who are ELLs. Considering cultural settings, two specific needs may be at the
root of that gap of ELL achievement in Math. Teachers need strategic professional development
that targets supporting students who are ELLs in Math (Chang, 2008; Gersten & Russel, 1996;
Menken, 2010). A lack of competent role models and leaders leaves teachers without a model
and support in developing expertise to support students who are ELLs (Erez & Gati, 2004). In
addition to the visible settings the organization has a need to develop a cultural model that
creates a shared vision for excellent education for students who are ELLs and a shared belief that
students who are ELLs are capable of achieving.
Shared Vision for ELL Instruction. The connection between an organization’s vision
and a clear connection to a goal is known to improve outcomes (Clark & Estes, 2008; Dixon
1994; Carton, Murphy & Clark, 2014). In a 2014 study of 60 hospital employees, researchers
found that participants responded most strongly to visions that used imagery and painted a
picture of what successfully meeting the initiative would look like (Carton, Murphy & Clark;
2014). Alignment between a vision, goals, work procedures and progress monitoring are known
to be effective means of creating organizational change (Clark & Estes, 2008). School site
administrators hold the vision of the organization on a school based level.
Organizational Belief and Commitment to ELL Achievement. Seminal research on
the Pygmalion effect made the connection that positive expectations have a positive influence on
performance (Rosenthal & Jacobsen, 1933 ) In this study researchers falsely told teachers that
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some of their students had been identified as high performers. At the end of the research period,
students who teachers believed were gifted made more gains in academic performance due to the
higher expectations teachers set for them (Rosenthal & Jacobsen, 1933). The opposite was also
proved true. Having low expectations or limiting beliefs can result in lower performance for
students (Rosenthal & Jacobsen, 1933). The vision, mission, goals and behaviors of an
organization must reflect a commitment to high expectations for ELLs (Rosenthal & Jacobsen,
1933).
Instructional Leadership by Experts in ELL Instruction. Teaching is often
experienced as a solitary profession when collaboration with peers as well as skilled leaders in
the field is needed to create conditions for organizational improvement (Gallimore & Golden,
2001). By experiencing support from an expert in the field as well as receiving time practicing
the desired skills with said experts supports improvement (Gallimore & Golden, 2001). Modeled
behavior is more likely to be adopted if the model is credible, similar (e.g.,gender, culturally
appropriate), and the behavior has functional value (Denler et al.,2009). This highlights the needs
for organizations to have instructional leaders that can serve as competent role models in the
field. Similarly, a critical component to the success of organizational improvement is a leader’s
ability to connect back to the mission and vision and exhibit commitment to it in their everyday
actions (Clark & Estes, 2008).
Strategic and Quality Professional Development on ELL Instruction. The
knowledge and skills needed to provide quality Math instruction for ELLs is related to the
organizational setting created for professional development. By presenting tasks related to
organizational goals as well as demonstrating and modeling the new desired behaviors,
organizations can support stakeholders learning the behaviors needed to support organizational
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change (Denler et al, 2009). Research shows that teachers do not receive quality professional
development in how to best meet the needs of ELLs (Kareva & Echevarria, 2013; Harklau, 1994;
Short, Fidelman, & Louguit, 2012).
Table 7 illustrates the organizational performance goal and stakeholder performance goal
as well as the organizational influences that are assumed necessary to meet both goals as well as
realize the organizational mission. In addition, the table identifies the assessment that aligns with
the cultural setting or model. The assessment includes the potential questions and how data
would be gathered about the organizational theory. The columns labeled for research-based
recommendations and proposed solutions will remain empty until Chapter 5.
Table 7

Organizational Influences and Assessments for Analysis

Organizational Mission
Éxito Academy’s mission is to teach the academic skills needed for our students to thrive in high school, college,
and beyond while also providing space to develop character and a sense of self. Through the success of our
students, the Éxito team and family will serve as a model of excellence and collaborate with others to raise the
quality of education in Coastal City.
Organizational Performance Goal
By 2023, 85% of English Language Learners will meet or exceed the standard as measured by the standardized
state math assessments. The gap between ELL and FEP students will be no more than 15%.
Teacher Stakeholder Goal
By 2023, 100% of math teachers will reach the performance goal through the use of differentiation and
engagement of ELL students.
Assumed
Organizational
Influences

Organizational Influence Assessment Research-Based
Recommendatio
n or Solution
Principle

Proposed
Solution
(Cultural Models)
The organization
needs a vision of
what constitutes
excellent instruction
Survey: Teachers
My organization values equity for students learning
English
My organization sets achievement goals for students
learning English.

59

for students who are
ELLs.
My organization meets the goals set for students
learning English.
My organization has a vision of what excellent
instruction to students learning English looks like in
the classroom.
(strongly agree, agree, disagree, strongly disagree)

Interview: Teachers
Describe the vision/beliefs that your organization has
for supporting students learning English.
Describe the instructional best practices that your
organization has for supporting students learning
English.
(Cultural Models)
The organization
needs a culture of
belief and
commitment that
students who are
ELLs are capable of
achieving at high
levels.
Survey: Teachers
I believe my organization sets high expectations for
students who are ELLs.
My organization believes that ELLs are capable of
achieving at high levels.
ELLs in my organization achieve high levels.
(strongly agree, agree, disagree, strongly disagree)

Interview: Teachers
Describe the goals and performance measures that
your organization has for supporting students learning
English.

(Cultural Settings)
The organization
needs instructional
leaders with expertise
in supporting students
who are ELLs.
Survey: Teachers
My organization has experts in EL strategies and
education.
There is a teacher who is an expert in EL strategies
that I can learn from.
There is an admin who is an expert in EL strategies
that I can learn from.
(strongly agree, agree, disagree, strongly disagree)

Interview: Teachers
Describe what you would do if you needed help
supporting a student in your class who is an ELL. Who
would you go to? Why?

(Cultural Settings)
The organization
needs strategic and
quality professional
development for
teachers.
Survey: Teachers
My organization offers PD specifically focused on EL
support
The PD and support offered makes a positive impact
on the students learning English in my classroom
The PD provided allows me to lead positive change in
the classroom for students who are learning English.
(strongly agree, agree, disagree, strongly disagree)

Interview: Teachers
When a teacher needs help supporting an English
Language Learner how does your organization
respond?

60

Describe a time you received training or feedback on
supporting ELLs in your classroom. What happened?
What was it like? Describe the impact it had on your
classroom.
Think of the last time your organization
talked about ELLs. Describe it including
what the topic was, who was involved and
how you felt.

Conceptual Framework: The Interaction of Stakeholders’ Knowledge and Motivation and
the Organizational Context
A conceptual framework explains how various factors and elements interact in a study
(Maxwell, 2013). The conceptual framework allows for the literature to merge with personal
experience. Literature from both theoretical and empirical sources merges with a researcher's
personal experience and thought experiments to create a theory for the research. That theory
explains what is happening and why in the connections of the previously mentioned elements. As
presented by Merriam and Tisdell (2016) the constructed theory is used in conjunction with
previous research to make a case for the study can build and add to what has already been done.
In addition to justifying the research, the conceptual framework aids in choosing appropriate
methods and designs to explore the research questions (Maxwell, 2013).
The conceptual framework presented in this study uses previous research on the needs of
students who are ELLs, content specific research for the Math classroom as it pertains to ELLs
as well as the research on teacher motivation in instructing students who are ELLs. The
framework merges what is known and what is needed in order to make recommendations for
creating effective Math classrooms and prepared Math teachers. In creating the study, this
aforementioned conceptual framework will work in conjunction with the worldviews to inform
the study.
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Two worldviews are used in this study: constructivism and advocacy. The leading
worldview being constructivist while advocacy is at the core of the problem and purpose.
Constructivism is a worldview. Constructivists hold the assumption that people seek to make
meaning of the worlds in which they live and work (Creswell, 2014). Similarly, this worldview
uses the meaning to create an explanation about a phenomenon (Creswell, 2014). This study will
use the experiences and interactions of teachers in the instruction of students who are ELLs to
create an explanation about the organizational elements needed to support the knowledge and
motivation teachers need to support high math achievement for students who are ELLs. Given
that the study is centered on an educational equity problem, there is also a merge with advocacy/
participatory worldview. While the study itself does not include the voices of the students, the
study does focus on teachers advocating for what is needed to close the opportunity and
achievement gap for an underserved group of students. Creating equitable educational outcomes
is also a question of how power, oppression and empowerment work in the schooling of our
students who are ELLs. This world view is expressed in the literature as well as the personal
experiences of the researcher.
While the literature review presents the knowledge, motivation and organizational factors
separately the conceptual framework communicates the interaction between these factors and
teacher ability to create effective instructional opportunities for students who are ELLs. In order
to change to happen and progress towards organizational performance, these needs
simultaneously work together (Clark & Estes, 2008). The conceptual framework presents how
knowledge and motivation work in tandem with the organizational models and settings to
achieve the goal set by Éxito Academy that 85% of students who are ELLs will perform at or
above standard on the state Math assessments. Figure 1 illustrates this conceptual framework.
62

This figure illustrates the relationship between the factors influencing teacher
differentiation for students who are ELLs in the math classroom, both in isolation and also within
the larger organizational context. Ultimately the knowledge, motivation and organizational
contexts lead to the stakeholder goal. Below the stakeholder goal there is an arrow leading to the
long-term goal. Ultimately the differentiation that teachers give to students who are ELLs and
the achievement outcomes on the state math assessments both contribute to the long term social
and academic success of ELLs. The knowledge and motivation influences exist within the
organization because the resources and the culture created impacts a teacher’s knowledge and
motivation. There are arrows that align the organization, school, and teacher and flow both in
and out of the core. This represents the fact that teachers influence the organizational identity in
the same way that organizations impact teacher performance. Similarly, there is a rectangle at the
top of the visual that represents how an organization uses both demographics as well as language
theory to inform the decisions they make regarding instruction. More specifically the
organizational sphere includes models and settings that encourage a shared vision, belief in ELL
achievement, instructional expertise in leadership and strategic professional development. The
knowledge influences include the factual, procedural and metacognitive knowledge necessary to
effectively differentiate for students in the math classroom. In the same circle the motivational
constructs like self-efficacy and attribution impact teacher support and performance of students
who are ELLs.

63

Figure 1.
Interaction of Stakeholder Knowledge and Motivation within Organizational Culture Models and
Settings

64

This study seeks to understand the ways in which teacher knowledge, motivations and
organization influences interact with each other to support teacher differentiation for ELLs and
ultimately ELL achievement on the state math assessment. Therefore, Figure 1 situates Math
Instruction as the phenomenon resulting from the knowledge, motivation and organizational
factors. This phenomenon produces results and outcomes for students on state Math assessments.
When all these elements work together ELL student achievement is improved and ultimately the
long term academic and social success of ELLs as well.
Table 8.
Summary Table of Assumed Influences on Performance
Stakeholder Assumed Influences on Performance
Knowledge Motivation Organization
● Teachers need to know a
variety of strategies to
support students who are
English Language Learners
in Math.
● Teachers need to know how
to build relationships
resulting in partnerships
that support students who
are ELLs.
● Teachers need
metacognitive knowledge
about using proficiency and
content knowledge to
appropriately differentiate.

● Teachers need to believe
they are capable of
effectively differentiating
instruction for students who
are ELL
● Teachers should feel that the
achievement of ELLs is due
to their actions, rather than a
deficit in the student
themselves.

● The organization needs a
shared vision for what
constitutes excellent
instruction for students
who are ELLs.
● The organization needs a
culture of belief and
commitment that students
who are ELLs are capable
of achieving at high levels.
● The organization needs to
develop instructional
leaders with expertise in
supporting students who
are ELLs.
● The organization needs
strategic and quality
professional development
for teachers on ELL
Instruction

65

Conclusion

The purpose of this study is to research the knowledge, motivation and organizational
influences that impact teacher instruction of ELL students in the Math classroom. Chapter two
presented general literature on the problem of practice ranging from current models of language
development, teacher preparation programs, perception of teachers and instructional practices for
ELLs in Math classroom. The general literature was followed by the knowledge, motivation and
organizational influences on the key stakeholder group, teachers. The factual, procedural and
metacognitive knowledge research was presented as well as research on self- efficacy and
attribute theory. Then the study looked at the cultural models and settings of the organization that
impact teacher knowledge and motivation in supporting ELLs in Math. Chapter two concludes
with the conceptual framework for the study and an explanation of how it was designed for the
problem of practice. The general literature was moved into the theoretical framework of
knowledge, motivation and organizational influences on the key stakeholder group, teachers.
Chapter three will present the study’s methodological approach and rationale.

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CHAPTER THREE: METHODS
This chapter presents the research design, methods for data collection and analysis
protocols. The study centers on the research questions presented below.
1. What are teachers’ knowledge and motivation in relation to reaching the organizational
performance goal of 85% of ELL students meeting or exceeding the standard on the state
Math assessment through differentiated instruction?
2. How do teachers' knowledge and motivation interact with the organizational culture and
context in supporting students who are ELLs in meeting or exceeding the standard on
state Math assessments?
The chapter will begin with a description of the stakeholder groups participating in the
study. This section will include the sampling criteria and rationale as well as the strategy for both
the survey as well as the interviews. Following the first section, the methods chosen for use will
be presented as well as a rationale on why these methods will be used. Then the survey items and
interview protocol will be overviewed. A plan for data analysis will be shared. The chapter
closes with a plan to increase/maintain the credibility and trustworthiness, reliability and
credibility as well as the ethics of the study.
Methodological Framework and Rationale
Mixed Methods research is the blending of qualitative and quantitative data and often
provides a stronger understanding of the problem than any one method on their own due to the
depth of the data (Creswell,2018). Mixed method research employs the use of both open ended
(qualitative) and closed ended (quantitative) questions (Creswell, 2018). Mixed methods research
is both post positivist and constructivist as it combines reality with open ended questions that
67

allow for multiple realities to be expressed. Mixed methods research allows for comparison of
different perspectives, refining of measurement instruments as well as the development of a more
complex understanding of the problem (Creswell, 2018). Through the use of qualitative data, the
researcher becomes a key instrument in the research process (Creswell, 2018). The researcher
uses their experiences combined with thought experiments, pilot research and existing theories
and research to create the conceptual framework (Maxwell, 2018).
Within mixed methods research there are multiple ways to conduct it. This study will use
a concurrent triangulation design model that will first conduct qualitative and quantitative
research, evaluate the results from the mixed measures and then compare the results of the data
(Creswell, 2018). In addition to the separate analyses, the qualitative findings will help explain
the quantitative results.
Mixed Methods research and specifically concurrent triangulation was chosen for this
study due to the size of the group of teachers as well as the intended purpose and use of the
study. Quantitative methods allow the perspective of a larger group of educators to be
represented. Given the number of classrooms serving students who are ELLs and the fact that
over 20% of students in California are ELLs (CDE, 2018); quantitative measures like a survey
allows us to reach more teachers. The quantitative study will include Math teachers from more
than 10 schools within the organization and the qualitative study will include a purposeful
selection of teachers from Éxito Academy in Coastal City. The purpose of the study is to uncover
the trends that impact a large group of teachers and zoom in on the trends presented. The
research will gather data, analyze the data in order to synthesize trends and recommendations.
The combination of both quantitative and qualitative data and the ability to make meaning
68

through the qualitative data will allow for specificity that schools and organizations can use to
reach their organizational performance goals to serve students who are ELLs.
Participating Stakeholders
The stakeholder group of focus is math teachers who teach students who are ELLs in
upper elementary and middle school (grade 4-8). The reason for the range is to uncover the
knowledge and motivation necessary that can be used to create a set of best practices for
educators given that the language demands and developmental needs of students in grade 4-8
differs from students in K-3. All teachers selected work at Title I schools. Similarly, all
classrooms needed to have at least 25% of students identified as ELLs. All teachers chosen will
have California State credentials. Similarly, all teachers will have more than 1 year of
experience. It is important that the teachers share a similar experience working at Title 1 schools
as well as have a minimum percent of students who are ELLs in order to support the credibility
of the data gathered. For the qualitative portion, all classrooms represented are more than 50%
ELLs.
As a representation of the organizational cultures and models, Administrators will also be
represented in the survey. They will receive an almost identical version of the survey as teachers
however the wording is slightly changed to represent the administrator’s work with their school
versus a specific classroom of students. The survey will go to the administrators of the schools
where the teacher survey sample group comes from. The surveys are being added to compare
with the results of the teachers. This figure illustrates the relationship between the factors
influencing teacher differentiation for students who are ELLs in the math classroom, both in
isolation and also within the larger organizational context. Ultimately the knowledge, motivation
and organizational contexts lead to the stakeholder goal. Below the stakeholder goal there is an
69

arrow leading to the long-term goal. Ultimately the differentiation that teachers give to students
who are ELLs and the achievement outcomes on the state math assessments both contribute to
the long term social and academic success of ELLs. The knowledge and motivation influences
exist within the organization because the resources and the culture created impacts a teacher’s
knowledge and motivation. There are arrows that align the organization, school, and teacher and
flow both in and out of the core. This represents the fact that teachers influence the
organizational identity in the same way that organizations impact teacher performance.
Similarly, there is a rectangle at the top of the visual that represents how an organization uses
both demographics as well as language theory to inform the decisions they make regarding
instruction. More specifically the organizational sphere includes models and settings that
encourage a shared vision, belief in ELL achievement, instructional expertise in leadership and
strategic professional development. The knowledge influences include the factual, procedural
and metacognitive knowledge necessary to effectively differentiate for students in the math
classroom. In the same circle the motivational constructs like self-efficacy and attribution impact
teacher support and performance of students who are ELLs.

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Survey Sampling Criteria and Rationale
Math Teacher in Grades 4-8
The research questions specifically state the knowledge, motivation and organizational
structures needed to support students who are ELLs in Math. In both the 2016-2017 and 2017-
2018 state tests, students who were learning English had a larger performance gap in Math than
ELA. The purpose of the study is not to find general strategies to support ELLs, but rather
content specific supports for the Math classroom. Furthermore, given the language demands and
developmental needs, all teachers represented will represent grades 4-8.
Title 1 School
Attending a Title 1 school as well as the percent of students who receive free and reduced
lunch is an important criterion for this study because Title I schools share many resources in
common.
Minimum of 25% ELL Students
A teacher’s perception of how their instruction serves students who are ELLs may differ based
on the number of students they teach who are learning English. As a control, teachers surveyed
should have a similar percentage of students who are ELLs.
California State Credential
Teachers who complete credential programs go through a certain amount of professional
development. One assertion made by researchers (Goodsoon et. al, 2019) is that teacher
programs may not adequately prepare teachers to meet the needs of English Language Learners.
By controlling for this we can eliminate potential disparity due to participation or lack thereof in
teacher preparation programs.
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Years of Experience
All teachers surveyed and interviewed will have a minimum of one year of experience.
The rationale for this is so participants have experience to draw from as they are responding to
the survey items. When analyzing survey results trends dependent on years of experience will be
accounted for.
Survey Sampling Criteria and Rationale for Administrators
The survey sampling of administrators will align with the schools where the teachers are
selected using the above criteria. The teachers will be selected first and then the survey will be
sent to the administrators from the corresponding schools.
Survey Sampling (Recruitment) Strategy and Rationale
Probability
Teachers selected will be selected randomly and each participant that meets the above
criteria has an equal chance of participation. Participants will come from more than six schools
in the Éxito Academies Organization and there will be a minimum of 35 teachers and 15
administrators invited to participate in the survey. This will represent a large number of schools
and a large range of Math teachers. This is important because a lot of the research done on the
support of students who are ELLs has not been statistically significant either due to the number
of participants or due to the impact (Gersten & Russel, 1996). The survey will be administered
at the beginning of the data collection process.

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Interview Sampling Criteria and Rationale
The interview sampling will build on the above criterion in addition to what is below.

Math Teachers in Grades 4-8
Participants will be grouped by the grades they teach. The purpose for that grouping is
that the participants share a similar content knowledge and that may or may present differences
based on grade level. Furthermore, the academic language demands vary by grade level. A
student in kindergarten has different developmentally appropriate language demands than a
student in middle school.
Achievement or Performance Outcomes
This criterion will not be considered if all student achievement is within 15% or lower
than other teachers. This is because classrooms performing at or above the organizational
performance goal would offer perspective about promising practices and may not offer
perspective on the barriers as referred to in the research questions. If there are classrooms that
are achieving at or near the organizational performance goal their perspective may vary than the
teachers who are not performing at or near the performance goal.
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Interview Sampling Criteria and Rationale of Administrators
For the qualitative portion of the study, there is one school within the organization of
focus that is selected for interviews. The teachers will be selected using the above criteria
however the administrators of the school will be interviewed due to their leadership at the school
site. Three administrators will be interviewed. That represents the administrative team from the
school where the teachers interviewed reside.
Interview Sampling (Recruitment) Strategy and Rationale
The sampling strategy for the interviews is a purposeful sampling as it is based on the
purpose of the study as well as the shared criterion. The selection is a modified critical case
sampling as one organization is chosen as the focus based on a belief that studying it will reveal
insights that can be applied to other studies or cases. Participants will come from one school
within the larger organization.
Data Collection and Instrumentation
Survey and interviews will be used for the data collection method because the study is a
mixed methods study. The survey will provide quantitative data. The survey will be administered
to more than six schools in the larger organization. Then using the data gathered in the surveys,
comparisons will be made to the qualitative data. Interviews allow the researcher to dig into the
knowledge and motivation of the stakeholder group. The interviews also allow the researcher to
make meaning and understand the experience of Math teachers pertaining to the instruction of
students who are ELLs. This aligns with the two worldviews used in this study: constructivism
and advocacy. The leading worldview being constructivist while advocacy is at the core of the
problem and purpose. Constructivists hold the assumption that people seek to make meaning of
the worlds in which they live and work (Creswell, 2014). Similarly, this worldview uses the
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meaning to create an explanation about a phenomenon (Creswell, 2014). This study will use the
experiences and interactions of teachers in the instruction of students who are ELLs to create an
explanation about the organizational elements needed to support the knowledge and motivation
teachers need to support high math achievement for students who are ELLs.
Qualitative Data Collection and Instrumentation
In order to assess the knowledge, motivation and organizational influences, data will be
collected via qualitative interviews for the stakeholder of focus which is Math teachers. The
research questions specifically state the knowledge, motivation and organizational structures
needed to support students who are ELLs in Math. In both the 2016-2017 and 2017-2018 state
tests, students who were learning English had a larger performance gap in Math than ELA. The
purpose of the study is not to find general strategies to support ELLs, but rather content specific
supports for the Math classroom. Therefore, interviews will allow the specificity of the research
questions to be magnified. The qualitative interviews will allow the invisible to become visible
as it pertains to the KMO elements and ELL outcomes in Math (Patton, 2002 ). The perspective
of teachers is important as they facilitate the learning in the classroom. The perspective of
administrators is important because they create the organizational systems and culture that either
help or hinder the performance of both teachers and students learning English. The qualitative
interviews allow insight into the needs, but also the desired solutions to the organizational
performance goal.
Interviews
Interview Protocol
The interviews will be structured with options for structured follow up through the use of
probe questions. The reason they will be structured is to ensure alignment between the different
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teachers interviewed in order to pull out trends on the knowledge, motivation and organizational
influences related to the research questions (Patton, 2002 ). The standardized open-ended
interview structure will allow for all interviews to use the same stimuli and questions
(Patton,2002). Interviews will address all elements of the KMO model, but will emphasize the
knowledge and motivation influences. The reason that interviews will emphasize the knowledge
and motivation influences is because interviews highlight the experiences of stakeholders
(Cresswell & Cresswell, 2018). The inclusion of administrators into the data collection process
will allow for greater representation of the organization. The administrators will be asked nearly
identical questions as the teachers however instead of referencing a specific classroom,
administrators will reflect on the school as a whole. As stated by Creswell and Creswell (2018)
the interviews provide a window into the organization through the use of stakeholder’s
knowledge and experiences. The study includes 12 main questions with a variety of follow up
questions in order to get at the core of the research questions. The protocol includes 12 questions
divided into the categories: introductory questions, building background, knowledge, motivation
and organization questions.
Interview Procedures
Seven teachers and three school administrators will participate in the interviews. Since
the survey and the interviews are ultimately independent the time frame of the survey is longer in
order to provide ample time to increase the participant size. The rationale for this is the sampling
size. The survey will not be a method for selecting the interview participants. Each participant
will be interviewed once. Each interview will last between forty five minutes to one hour. This
means the total time spent conducting interviews will be between twelve and fifteen hours
amongst the 10 participants. The interviews will be formal interviews that take place in the
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teacher’s classroom or office. The choice in this location is to have them in their own personal
environment as well as have them immersed in the content. This will be beneficial because
teachers may reference learning materials around the classroom as they are answering the
interview questions. Some of the interviews took place during The Corona Virus quarantine of
2020 and therefore some data was gathered virtually with the consent of the participant. During
the interview, data will be captured via notes as well as two different methods of audio
recording. For any virtual interviews collected during quarantine, zoom was used.
Quantitative Data Collection and Instrumentation
Concerning research on the best practices to support students learning English, there is a
need to prove results that are statistically significant (Gersten & Russel, 1996). Gersten and
Russel conducted a three-year study that followed 26 classrooms in 2 different regions and
analyzed the impact of instructional strategies on students who are ELLs. The classrooms that
showed the most growth for English Language Learners used distinct practices such as
transferring knowledge from their native tongue to the target content and making academic
language the focus of a lesson (Gersten & Russel, 1996). While there was a positive impact, the
impact was not statistically significant enough to lead to a bridged gap. Another researcher
Green (1997) draws the conclusion that a majority of research focuses on bilingual education
results for literacy and ELD, but there is little data on the impact on Math.
While the qualitative methods of this study focus on a smaller quantity of people the
inclusion of a quantitative survey allows the study to reflect a larger participant size. This matters
to me personally because the idea of research on ELL education being statistically significant is a
social justice issue given that a statistically significant percent of the nation’s population
identifies as an ELL.
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Surveys
Survey Instrument
The designed survey includes items on the knowledge, motivation and organization as
aligned with the research questions. A portion of the survey will use a likert scale to address
motivation influences. An example of this is the statement: “The success of my students who are
English language learners is most impacted by factors inside the classroom.” Followed by the
statement: “The success of my students who are English language learners is most impacted by
factors outside the classroom.” Participants will answer and respond to the statement using a
likert scale of strongly agree, agree, disagree, strongly disagree. There will also be a list of EL
strategies for support as well as organizational constructs. Teachers will be asked to select the
strategies or constructs used to support students learning English.
The survey was designed in order to build on the interview protocol. The interview protocol
provides depth and the survey provides more breadth. Both the interview protocol and the survey
are designed to target the three research questions. There will be three questions on classroom
demographics, twelve likert scale questions KMO influences and three list questions.
Survey Procedures
The surveys build on the interview however the interviews are not dependent on the
results of the survey. The initial administration of the surveys will begin before the interviews
take place, but will continue after the interviews begin. The survey will be administered to all
Math teachers that have above 25% ELL in their classrooms and teach grades 4-8. The surveys
will be administered online using Qualtrics. This administration approach is appropriate because
of the size (50) as well as the fact that participants live in different counties.

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Survey Instrument and Procedures for Administrators
Administrators will take a nearly identical survey as teachers however the survey will
address the school as a whole as well as their work with teachers as opposed to a focus on an
individual classroom. The survey will be sent to the administrative team of any school where a
teacher has taken the survey.
Data Analysis
Frequencies will be calculated. For stakeholder groups of fewer than 20, the percentage
of stakeholders who strongly agreed or agreed will be presented in relation to those who strongly
disagreed or disagreed. For larger stakeholder groups, means and standard deviation will be
presented to identify average levels of responses.
Descriptive statistical analysis will be conducted once all survey results are submitted.
For interviews and observations, data analysis will begin during data collection. I will write
analytic memos after each interview and each observation. I will document my thoughts,
concerns, and initial conclusions about the data in relation to my conceptual framework and
research questions. Once I have left the field, interviews will be transcribed and coded. In the
first phase of analysis, I will use open coding, looking for empirical codes and applying a priori
codes from the conceptual framework. A second phase of analysis will be conducted where
empirical and a prior codes are aggregated into analytic/axial codes. In the third phase of data
analysis, I will identify pattern codes and themes that emerge in relation to the conceptual
framework and study questions. I will analyze documents and artifacts for evidence consistent
with the concepts in the conceptual framework.

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Credibility and Trustworthiness

Credibility and Trustworthiness are both necessary and challenging throughout the course
of a study. In order to enhance the trustworthiness of the study the data gathered will go through
the process of triangulation (Bowen, 2009). Similarly, the credibility and trustworthiness of the
study will be enhanced as my bias as a researcher is explicitly stated as well as planned for. A
third strategy to increase the credibility and trustworthiness is to ensure that rich data is collected
via verbatim field notes and re-coding the interviews (Merriam & Tisdell, 2016). Credibility will
also be enhanced through the use of a recording system (Evernote in addition to others) that will
aid in creating a transcript that can be reviewed by participants in order to lower the possibility
of human error. Another strategy I will use to increase credibility is to clearly state the purpose
of the study and also how both the organization and other people in the field will have access to
the findings in order to improve. Another way I will build credibility is to open the interview
with a preview of the questions that will be asked as well as close the time with an opportunity to
add or clarify any parts of the interview. This builds credibility as the participant can be
confident in what is being shared from their interview. Since credibility deals with people’s
perception of my trustworthiness, there will also be some interviews that I do not conduct myself
due to my title and the power dynamics at play. Concerning trustworthiness, another strategy to
increase trustworthiness between researcher and participant will be making the process of
crafting the interview questions transparent. In addition to how the questions were crafted, the
process for how data will be analyzed will be made available (Merriam & Tisdell, 2016).

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Validity and Reliability
Validity and reliability add meaning to the data gathered in the quantitative results
(Creswell, 2018). In order to ensure the study is valid and measuring what I want it to; each
question was mapped back to a KMO influence as well as a research question (Salkind, 2017).
Considering reliability and the survey’s ability to measure consistently, a pilot of the survey has
been administered and received feedback from other doctoral students studying quantitative
measures. Similarly, the survey was administered in various stages to teachers outside of the
participants for the study to tweak the wording and questions. Four teachers took the survey and
I was able to see how the responses aligned to the KMO influences and the research questions. I
was also able to measure if the four participant responses were measuring similar outcomes. To
further increase the validity and reliability I will have the survey edited by both my Chair and the
Capstone assistant. In order to get a sufficient response rate, I will send reminders. I will also
use the relationships I have with school principals to have them build in time in the grade level
meetings or staff development times for members to complete the survey.
Ethics
As Patton (2002) wrote, the trustworthiness and validity of research and data ultimately
depends on the trustworthiness of the researcher themselves. Working with the organization to
determine how the study will be used within the organization to support the mission, vision and
performance goals is a crucial first step so that the outcome can be shared with participants.
After having information on how the study will be used, the potential participants will hear the
purpose of the study and the process of how data will be collected. At that point they will give
informed consent if they are willing to participate in the research. As part of Informed Consent,
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participants are made aware that participation is voluntary, anonymity of data and that they may
cease participation at any point (Glesne, 2011). As part of the informed consent process, the
method for recording and storing data will be shared. Data will be kept on a password protected
laptop and any printed materials will be kept in a secure file cabinet in a locked office.
The organization of focus of the study is made up of more than fifteen schools in more
than three different districts. A majority of the schools are in one district while the other districts
host a single site. All schools share a common mission and vision. I hold a leadership position at
one of the single site schools in a district. I do not evaluate any of the Math teachers who will be
interviewed and hold no power or influence over their roles. For the other schools, I do not have
power nor title at their schools. Employees may feel their decision might affect performance
evaluations or job advancement; however, through sharing my role as researcher as well as the
process and purpose of the study to employees; the worry can be clarified. Furthermore, the
participants will be protected through anonymity and a right to privacy throughout the process
(Glesne, 2015). In addition to sharing how the research will be used to benefit teachers and
students. reciprocity will be considered to reward the research participants for their time (Glesne,
2015). On the day of interviews, research participants will read the agenda and question
summary before beginning in order to provide informed participation (Krueger, 2009)
Who I am as a personal and professional is central to my research yet is planned for so
biases do not invalidate the research. As a person, I am bilingual and was a language learner
myself. I see language learning as an asset which creates a positive bias in me towards language
learning. Professionally a majority of my experience in education has been in a dual immersion
school recognized across the state for high achievement outcomes for historically
underperforming communities. Our school focused on support for language learners and there
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were minimum expectations for all staff. As I interview participants that may potentially see
language learning as a barrier to success, this will present a viewpoint opposite to my own.
Similarly, as I analyze data, I will need to pick up on the enabling systems that support excellent
math instruction for students learning English. Coming from an organization that had an
extensive program, I cannot overlook the details in the data I collect no matter how elementary
they seem. Similarly, the study is researching an at risk population, therefore measures are taken
to protect the students who are learning English (Rubin and Rubin, 2015). My role as a
researcher is one of advocacy for excellent math instruction for ELLs (Glesne, 2011). Being
aware of my commitment to advocacy is a bias I will examine in all stages of the research
process.
Limitations and Delimitations
The study does present anticipated limitations. Respondents may exhibit varying levels of
truthfulness when answering questions. Similarly, respondents may use the same criteria to
judge their level of expertise in supporting students who are ELLs which may present
discrepancies. Limitations may also be present due to diversity of background knowledge and
prior experience with ELL instruction. Another limitation is that the study relies on respondent
description of implementation rather than gathering data through observations. What a
respondent says is done and what is actually executed in the classroom may be different. There
are delimitations considered in the design of the study. As the opening of the paper says, the
achievement gap for ELLs permeates across subject areas. An intentional choice was made to
narrow the study to focus on the gap in Math specifically. Other subjects are excluded from that
study even though an equitable education for ELLs would focus on all subjects. Similarly, the
study is limited to students in fourth through eighth grade. While there are performance gaps in
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all grades K-8. The gap widens in grades four through eight and students in these grades are
LTELS which present unique needs. While there are large gaps in high school ELL performance
the study intentionally focuses on secondary grades because the interventions needed in
secondary grades may lessen the gaps present in high school. The study focuses on a charter
school which may exhibit some circumstances, policies or practices that are not possible across
all types of schools.

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Chapter Four
Focus of The Study
This chapter includes the results and findings focused on the KMO influences and is based on the
following research questions that guided this study:
1. What are teachers’ knowledge and motivation in relation to reaching the
organizational performance goal of 85% of ELL students meeting or exceeding
the standard on the state Math assessment through differentiated instruction?
2. How do teachers' knowledge and motivation interact with the organizational
culture and context in supporting students who are ELLs in meeting or exceeding
the standard on state Math assessments?
Qualitative data was collected using individual interviews. The interview protocols
included questions designed to examine Math teachers’ knowledge and motivation in relation to
meeting the performance goal. In addition to the qualitative data, descriptive quantitative data
was collected via a survey. The survey protocol aligned to the knowledge, motivation and
organizational influences of the study as well as the interview protocol. The survey sampled a
larger population from multiple schools in the target organization (Éxito Academies) while the
interview focused on one school within the organization. In order to gather insight on the
organizational settings and models, administrators were both interviewed and surveyed. The
interview and survey protocol for administrators aligned with the protocols used with the teacher
stakeholder group.
Qualitative Data Participants
The participating stakeholders for the qualitative portion of the study were Math teachers
from one school within the organization. For the purpose of the study, fifth through eighth grade
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Math teachers, who hold valid CA credentials, were asked to voluntarily be a part of a face-to-
face interview. This included five Math teachers and two special education Math teachers. Seven
out of seven teachers responded to the interview invitation sent via email along with a digital
copy of the interview protocols and participant information sheet. Participants had varied years
of teaching experience ranging from two years to over ten years. One teacher interviewed was
brand new to the school site (Éxito Academy) but had worked at a different school site in the
organization (Éxito Academies) for five years. Table 9 shows the years of experience of the
teacher participants. The grade level is not included in order to protect anonymity of the
participant as there is only one Math teacher per grade level. All teachers represented in the
interviews had a class makeup that was more than 50% ELL.
Table 9
Demographic Information of Teacher Participants
ID Years of Teaching
Experience
Year at the Site Year Teaching Math
T1 8 years 3 years 8 years
T2 11 years 5 years 11 years
T3 10 years 1 year 10 years
T4 3 years 3 years 1 year
T5 2 years 2 years 1 year
T6 6 years 2 years 6 years
T7 13 years 13

years 11 years
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In order to gather insight into the organizational context of the organization, interviews
were also done with the administrative team at the school of focus. Three out of three
Administrators responded to the invitation sent via email along with a digital copy of the
interview protocols and participant information sheet. The years with the organization ranged
from seven to thirteen. The years as an administrator ranged from two to nine. Table 10 shows
the demographic data for the administrator participants. All administrators taught Math at one
point in their teaching career. Due to COVID-19 and the safety precaution needed, interviews
were conducted via zoom platform to which all participants consented both before scheduling the
interview as well as the day of the interview.
Table 10
Demographic Information of Administrator Participants
ID Years as an
Administrator
Years in the
Organization
Years at the Site
A1 5 years 6 years 1 year
A2 9 years 13 years 11 years
A3 2 years 9 years 7 year
Quantitative Data Participants
Due to COVID-19 and the change in the way the organization operated the survey did not
get distributed as widely as originally planned. Participants were invited based on criteria,
accessibility and availability during the pandemic. 12 out of 15 administrators invited to
participate completed the survey. 38 out of 44 teachers invited to participate in the survey
completed it. Teacher and Administrator Participants had varied years of teaching experience
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ranging from 1 years to over ten years. Table 11 shows the years of experience of the teacher
participants. Included in the Table is the years of experience as well as the grade levels taught.
Table 11 also includes the number of participants who identified as fluent in a language other
than English.
Table 11
Survey Demographic Information of Teacher Participants
Years of Teaching Experience
Years Number of Participants Percent of Participants
0-1 year 21 55.26%
2-5 years 3 7.89%
6-9 years 4 10.5%
10+ years 10 26.31%
Identify as being fluent in a language other than English
Language Status Number of Participants Percent of Participants
Yes 21 55.26%
No 17 44.73%

Table 12 shows the demographic data of the administrators who participated in the survey. The
table includes the years of teaching experience, years of experience as an administrator, percent
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of total student population identified as ELL as well as the number of administrators fluent in a
language other than English.
Table 12
Survey Demographic Information of Administrator Participants
Years of Experience as an Administrator
Years Number of Participants Percent of Participants
0-1 3 25%
2-5 8 66.67%
6-9 1 8.33%
10+ 0 0%
Identify as being fluent in a language other than English
Language Status Number of Participants Percent of Participants
Yes 4 33.33%
No 8 66.66%

CHAPTER FOUR: FINDINGS
The findings and sub findings of the study as presented in this chapter show the
relationship between the conceptual factors as well the relationship between the KMO elements
of the conceptual framework (Creswell & Creswell 2018). The sub findings and findings align
with the assumed influences of the study which included factual, procedural and metacognitive
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knowledge, self-efficacy, attribute theory, cultural settings and models. The expectancy value
theory is also referenced as an emerging influence based on the qualitative data (Pintrich, 2003).
Rooted in the responses from both the interviews and the surveys, sub findings emerged in
alignment with the KMO influences of the study. The sub findings based on the qualitative and
quantitative data are presented in this chapter and are organized first by the research question
then by KMO influence. This chapter includes the results and findings focused on the KMO
influences and is based on the following research questions that guided this study:
1. What are teachers’ knowledge and motivation in relation to reaching the organizational
performance goal of 85% of ELL students meeting or exceeding the standard on the state
Math assessment through differentiated instruction?
2. How do teachers' knowledge and motivation interact with the organizational culture and
context in supporting students who are ELLs in meeting or exceeding the standard on
state Math assessments?
Knowledge Findings
Factual Knowledge
Table 13 shows the sub findings and findings in relation to factual knowledge in response to
research question one. These sub findings and findings in Table 13 will be referenced in relation
to the data from the study throughout Chapter 4 and 5.

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Table 13

Factual Knowledge Findings and Sub Findings

Research
Question
KMO Type Finding Sub Finding
What are
teachers’
knowledge
and
motivation in
relation to
reaching the
organizational
performance
goal of 85%
of ELL
students
meeting or
exceeding the
standard on
the state Math
assessment
through
differentiated
instruction?
Factual
Knowledge
Strategies chosen do
not Match the language
demands and skills nor
the rigor of the skill or
concept.
Strategies for Language Learning
not just Learning
The strategies chosen correlated
to the teacher’s identity as
multilingual
The strategies chosen altered the
curriculum as opposed to
scaffolded it

Developmentally Appropriate
Strategies that align to the Math
content and Language demands
Teachers have transferable skills,
but need explicit knowledge to
make the connection to Language
supports
Teachers advocated for quality
not quantity of strategies to
support ELLS
A lack of factual
knowledge about
language development
leads to questions
around the needs and
abilities of students
who are ELLs.
Learning a language is more than
speaking a language
Recognizing the language
development phase of the
students in class allowed to
teachers to more strategically
differentiate
Teachers need knowledge to
distinguish between language
needs and the needs stated in a
student’s IEP
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Strategies Chosen Do Not Match the Language Demands Nor Math Concepts
Six out of seven teachers interviewed mentioned strategies not related to language while
seven teachers mentioned strategies that lowered the rigor of the curriculum as opposed to
scaffolding. In addition to a gap in rigor, 100% of teachers identified a gap in explicitly
connecting the strategies used to support ELL students with the Math content in a
developmentally appropriate way. All teachers interviewed listed strategies that have the
potential to support ELL students and given an explicit connection to language development,
could be transferable strategies to support the realization of the performance goal. Five teachers
noted strategies that rely on their ability to speak the first language of the students as a strategy.
In addition to strategies for lesson execution and engagement, a gap around strategies for
planning with ELLs in mind emerged. Two teachers interviewed exhibited a developing
knowledge of strategies to explicitly support ELL students in Math. The sub findings below
support the finding that Math teachers need explicit factual knowledge about developmentally
appropriate strategies to support ELLs that explicitly address both the Math skills as well as the
language demands.
Strategies for Language Learning not Just Learning. When teachers were asked to
identify what strategies they use to differentiate for student learning English, 100% of teachers
listed at least one strategy that did not uniquely address the language needs of ELLs. Five
teachers mentioned small groups as a strategy they use to support ELLs, but when asked what
the small group consisted of T3 stated:
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ELL students tend to always be in my small group follow up after exit tickets because
they struggle to follow along at the same pace of the lesson. So during small groups they
repeat problems until they can independently solve a similar problem.
While a small group could be an effective strategy for supporting ELL students, T3 did not
describe any component of the small group that was uniquely situated to address the needs of
ELLs, but rather focused solely on the computation. Three other teacher participants described
using small groups to support ELLs and said they “rely on multi-sensory learning,” “multiple
checks for understanding,” or by coaching students to ask for an explanation in a different way.
While those strategies (checks for understanding and advocating for help) are not harmful to
students, they do not specifically address the needs on ELLs. There is no explicit teaching of the
reading, writing, listening or speaking skills that allow ELL students to both acquire Math
knowledge nor demonstrate their acquisition.
Similar gaps in strategies for explicit language support were evident as teachers described
other strategies they use in addition to small groups. T4 described her use of visuals as a strategy
to support students learning English in a recent lesson on the Pythagorean Theorem and said:
“for ELL students I gave them the problem on an actual piece of paper as opposed to the
computer screen.” This strategy does not explicitly scaffold or modify for the language needs
pertaining to the four domains of language (speaking, reading, writing, listening).
When teachers did select a strategy that related to either speaking, reading, writing or
listening they tended to name a strategy that did not use English, but rather allowed students to
solely rely on the use of their primary language. Six out of eight teachers mentioned examples of
this. Teachers said, “sometimes my strategy may just be a translation of the problem”, “my
strategy is to let them bring in their language and then voice it out in their language or they will
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translate it” and “, “ [Student] was my helper last year and would translate the work for certain
students”. While these strategies do mention the domains of language, they do not support
students in explicitly developing English, but rather allow students to rely on their primary
language.
While this sub finding focuses on teachers, the three administrators interviewed also
listed strategies that did not explicitly address language learning therefore, a similar gap
emerged. When asked to describe a time she observed a lesson being differentiated for ELLs an
administrator said, “I want to say that the differentiation was not necessarily tailored to just
English Language Learners, but to different learners in general” and then listed the introduction
of new vocabulary words and reading the definition as the strategy observed.
Based on the data found in the qualitative interviews, the 89% response to the following
question does not align with what the interviews revealed whereas 89% of teachers selected
strongly agree or somewhat agree when asked to evaluate the statement “I know a variety of
different strategies to differentiate the math content for students who are learning English.”
When asked to evaluate the statement “The strategies I know to differentiate for English
Language Learners are specific to Math,” only 44.7% of participants selected strongly agree or
somewhat agree. This highlights that while teachers identify they know strategies there is a gap
in their knowledge of Math specific strategies. Additionally, teachers mentioned strategies that
were solely focused on increasing participation as opposed to increasing participation in
language development. One teacher said:
Something the students and I like is playing games and I know something that’s huge for
me is Simon Says especially for Geometry because there’s so much vocabulary so I will
put a motion with vocabulary words and it's just like an engagement strategy.
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The strategy is not specifically nor explicitly addressing the language students need to
access the content, but rather attempts to increase participation. When teachers were asked how
they knew their differentiation strategies were addressing student language needs teachers
answered with “the students raise their hand more” and they “don’t have blank papers.” This
shows that the strategies identified actually increase participation which is not directly related to
participation in language development nor participation that results in the student’s acquisition of
new Math knowledge. A gap in teacher knowledge and use of strategies that explicitly teach
language and link language to the Math content emerged in the responses from both teacher and
administrator interviews. In addition to knowing a variety of strategies, teachers need to know
how to select strategies that explicitly support language development.
Teachers Relied on Their Language Proficiency as Strategy. Four teachers identified
as multilingual and all four of these teachers reflected that they rely on their ability to connect
with students using the primary language. Solely using the primary language does not support a
student’s development of English. When describing the choices she makes to differentiate for
ELLs T3 said, “I’m fluent in Spanish so honestly I mostly rely on that. [Student Name] only
speaks Spanish and I find myself just speaking to her in Spanish.” T3 added:
I’m not sure I specifically call that a teaching support. I often see that with me, relying on
my ability to speak Spanish and then to teach in Spanish, rather than like providing tools
for them to be able to be successful in English.
Teachers supported their use of Spanish by saying “it lets [the student] feel comfortable and let’s
[students] get their point across” while all other teachers mentioned the primary language as a
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strategy where the purpose is to make students “feel comfortable”. T5 stated there was a shift in
her reliance on Spanish translation.
My differentiation was like what I thought would be helpful for them and what I was
able to do...so basically, I did a lot of translation and vocabulary instruction by translating
vocabulary instruction but now I know how to specifically model nuances of English that
students need. Then I ask them to try and I check for their understanding [of] the
language specifically.
T5 shows a shift from her reliance on Spanish to her ability to model the language in a way that
allows students who are ELLs to both practice the Math content while practicing specific aspects
of English language development. T5 attributes her growth to acquisition of knowledge about
language strategies and also receiving support from an EL specialist. T2 also received coaching
from the EL specialist and also shared a specific example of when she used the student's primary
language but explicitly linked it to English. T2 explained:
Something that’s on my mind right now since we are doing Units of Measurement is the
student’s need to understand how prepositions work in English or how root words work
to add manning. I will say something like 12 inches go into 1 foot and I realize students
don’t get ‘into’. I’ll look for patterns in the grammatical form [in Spanish] and make
connections [to English]. Like milli in millimeter and mil means thousand in Spanish and
millimeter is 1/1000 in our conversions.
T2’s example of differentiation highlights that Spanish or a student’s primary language
can be used to explicitly link and support the development of English. T2’s ability to use
strategies that do not rely on translation are due to her increased knowledge of how to teach
language as well as knowledge of strategies. Similar trends emerged in administrator interviews.
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Strategies Chosen Altered the Curriculum as Opposed to Scaffolded it. 100% of
teachers interviewed mentioned at least one example of modifying the curriculum as opposed to
scaffolding the learning. This shows a contrast between scaffolds which allow a student to
concentrate on the difficult skill they are acquiring (Bruner, 1978) and modifications which
change, lower or reduce the learning expectation (Nolet & McLaughlin, 2000). At Éxito
Academies, there is an average performance gap between ELLs and EO students with the least
gap being around 20% and the largest nearly 65%. Teachers mentioned that, “[ELLs] struggle to
follow along at the same pace of the lesson.” In response teachers mentioned they teach at a
“slower pace and give them less examples.” T4 stated:
When my ELLs weren’t doing too well I started changing the way I did my assignments.
I made sure the first two problems were very simple and straightforward like as long as
you’re paying attention to the lesson you would get them.
T4 describes lowering, reducing and changing the rigor of instruction as opposed to providing
scaffolds that support the student in acquiring the skill. Other teachers identified shortened
assessments, translated assessments or giving them work that was not grade level work where
“sometimes students do second grade Math instead of sixth grade.” Both of these examples from
the interview data support the idea that teachers are selecting differentiation strategies for ELLs
that lower the rigor of instruction and are reduce the learning as opposed to providing strategic
support that help students acquire the difficult skills. One administrator discussed their
observations of seeing modifications that lowered the rigor of instruction. A1 shared:
I feel like we don’t give kids enough of a chance to fail with language like we want to
always be the safety net. It’s okay to give them a hard task and if they do it wrong they
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can try again. I think that’s because the adult mindset is like don’t let them fail is it might
reflect back on teachers
This shows that in an attempt to make students feel comfortable, teachers choose strategies that
make the learning tasks less difficult for students.
Teachers Advocated for Quality not Quantity of Strategies to Support ELLS. Five of
the seven teachers expressed a desire for quality of knowledge as opposed to a larger quantity of
strategies. As teachers acquire the factual knowledge of strategies to support ELLs the
presentation of information in manageable parts as well as the exclusion of extraneous material
supports the teacher's cognitive load (Mayer, 2011). T1 stated: “Last year we did Professional
Development (PD) on sentence frames so regularly. Like we really focused on it in small chunks
so I really felt like oh yeah this is something that I can incorporate.” The focus on one strategy as
opposed to a superficial understanding of a variety of strategies allowed T1 to focus on sentence
frames and continue to apply the factual knowledge. Teachers said they want to know “what is
that one thing that I’m going to do well and I’m going to do a little bit of it each day and each
week” and mentioned that each year there are multiple priorities for teachers, teachers feel like
nothing ends up being done well (quality) due to the amount of demands. While building mastery
and expertise for Math teachers in supporting ELLs would involve knowledge of a variety of
strategies, the interview data advocates for an initial focus on the quality not quantity of the
strategies. This knowledge connects to organizational influences of planning professional
development to support Math teachers.
Lack of Knowledge About Language Development Lead to Questions Around Student Ability
The sub findings below support the finding that teachers need explicit factual knowledge
of language development. Explicit knowledge and understanding of language development will
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support teachers in identifying the diverse language needs of their students who are ELLs as well
as strengthening their ability to select instructional strategies to explicitly support the language
needs. Following the presentation of the data for each of the sub findings the finding will be
discussed in relation to all three sub findings.
Learning a Language is More than Speaking a Language. 71% of teachers
interviewed and 100% of administrators identified a knowledge gap in their ability to select
strategies to support ELLs that addressed the Math concepts in alignment with explicit language
development. Teachers were also able to mention strategies that could support ELLs but failed
to transfer the strategies to language learning. A piece of factual knowledge that emerged as a
gap in the interviews is an understanding of the nuances of what it means to be an ELL and then
the components of language development. Three teachers talked about a tendency to overlook
the needs of certain ELLs because those students speak English, but may need support with
reading, writing and listening. In turn there is a sort of invisibility attached with ELLs who speak
English. Each teacher interviewed was asked to identify a student who was an ELL that was
successful and then also asked to identify an ELL who struggled. Out of the 14 names given by
teachers and the 6 names given by administrators, 100% of teachers mentioned students' ability
to speak English with no account for other elements of language. This shows that teachers mostly
identified students for being an ELL based on their proficiency with speaking English, but failed
to identify ELLs who were developing their writing, reading or listening. Teachers' incomplete
knowledge of the four domains of English caused teachers to focus most on students speaking
language ability when answering interview questions.

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Teachers failed to identify how students develop spoken language at more advanced
levels and said, “it’s hard for [them] to pinpoint [student] needs, because [their] mind goes to
how they speak English.” Knowledge of the components of language could help teachers have a
more in depth understanding. Factual knowledge that there are simple, compound and complex
sentences could create a sort of criteria through which teachers analyze the speaking abilities of
students. Second, knowledge of what the development of reading, writing and listening looks
like would better help teachers have a comprehensive understanding of students who are ELLs.
A teacher added “they’re not beginners, but I think they’re still developing especially
with writing. So, I think their writing would fall somewhere on the lower end.” which shows an
inability to recognize language proficiency. Students who need development in their ability to
speak English tend to be most visible to teachers while students who appear to fluently speak
English almost appear invisible when it comes to language development. The label of ELL
becomes one of neither empowerment nor visibility, but rather invisibility as one teacher stated.
Because they’re (students) able to carry on a conversation, I don’t always see that they
need language support. Because they’re able to carry out a conversation in English, they
don’t think they need English Language Development (ELD).
Six of the teachers interviewed referenced a training that was held by the EL Specialist
in the year prior where they learned the levels associated with being an LL in California
(emerging, expanding, bridging). Prior to the training one teacher said they “weren't very aware
of who their ELLS were and what they could be doing to support them.” Teachers who attended
the training noted an increased knowledge about the levels of students in their classrooms. The
two teachers who were coached by the EL Specialist showed a heightened knowledge and ability
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to identify factual knowledge about language learning. Teachers said they “organize their lessons
around the four domains (speaking, reading, writing and listening)”, “look at the type of
language and language functions” and then “look at student proficiency levels to see what
students can do and where they may need help”. This highlights that knowledge of specific
components of language and language development that allow teachers to strategically and
thoughtfully plan for ELL students.
In the interview data a majority of teachers acknowledged a gap in identifying the
specific language needs of students apart from their ability to speak English. Five out of seven
teachers showed the foundations of foundational knowledge specifically about the definitions
and descriptions of language proficiency while still not having enough to accurately understand
the language development of their students nor select instructional strategies. Therefore 71% of
teachers interviewed have some level of identification of language needs. In the survey data,
63.16% of teachers somewhat or strongly agreed with the statement “I know the specific
proficiency levels and needs of the students who are ELLs in my class.” While this aligns with
the interview data, the data may change if teachers were given certain criteria to measure
themselves against. This will be discussed in the motivation section as it pertains to self-efficacy
and reflection.
Recognition of Language Proficiency Allowed for Strategic Support. Five teachers
mentioned that an increased factual knowledge about language development allowed them to
analyze the different parts of ELL supports and how they operate together in the Math classroom
(Anderson & Krathwohl, 2001). Eventually this knowledge leads to the ability to make
judgements based on criteria and apply strategies to new situations (Anderson & Krathwohl,
2001). Building on the knowledge gap in a teacher’s ability to identify ELLs and levels of
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language development, teachers often cannot address a language need when they cannot
recognize language. On the reverse end, when teachers can recognize a language need, they can
more strategically differentiate based on language. When describing how she supported and ELL
who was struggling in her class T2 said:
There’s just certain things he would ask me that showed me he didn’t understand the
question. Like it would take us a couple of times for me to even understand what his
misconceptions were. And most of the time it wasn’t with the Math. It was with the
wording or the format of the sentences. So then I was able to model and chunk the
language for him as opposed to the calculations.
Teachers also explained how their knowledge of the details of language allowed them to
better support ELLs while others said they wouldn’t recognize the language needs and “would
just keep giving sample problems because [they] didn’t know how to pinpoint what about
language caused the student to struggle.” T1 gave an example from her unit on division:
“students didn’t know how to talk about it or understand it as it was not totally literal so instead
of modeling or drawing the calculation I was able to use those strategies about the language.” T1
showed how her response to student misconceptions changed due to her newly acquired
knowledge about language development.

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Procedural Knowledge
Table 14 shows the sub findings and findings in relation to procedural knowledge in
response to research question one. These sub findings and findings in Table __ will be referenced
in relation to the data from the study throughout Chapter 4 and 5.
Table 14

Procedural Knowledge Findings and Sub Findings

Research Question KMO Type Finding Sub Finding
What are teachers’
knowledge and
motivation in
relation to
reaching the
organizational
performance goal
of 85% of ELL
students meeting
or exceeding the
standard on the
state Math
assessment
through
differentiated
instruction?
Procedural
Knowledge
Teachers identify a
positive classroom and
school climate as
foundation to success
for ELLs.
Elements of School and
Classroom Culture that Support
Relationship Building with
Students who are ELLs
An Informed and Empowered
Culture for Family Involvement

Relationship building
and collaboration
amongst staff supports
both teacher and
student achievement.
The procedures of collaboration
supports teacher knowledge.

Teachers Identify a Positive Classroom and School Climate as Foundation to Success for
ELLs
The sub findings below support the finding that teachers need procedural knowledge
about building a classroom and school culture that support ELLs. Explicit knowledge and
understanding of components of building an inclusive school and community culture included
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both formal and informal relationships as well as relationships with all stakeholders including
staff, students, families and the community at large.
Elements of Supportive School Culture for ELLs. When teachers were asked to
describe both the barriers to ELL success as well as the structures that supported ELL success in
the Math classroom; 100% of teachers mentioned a set of values present in the classroom culture.
All teachers mentioned the importance of taking risks, making mistakes, helping others and
advocacy. At least half of the interview participants also noted the need for an understanding and
pride in one’s identity, multiculturalism, dedication and an awareness of the political context
associated with being an English Language Learner. These values represent procedural
knowledge as they are specific skills required to accomplish a specific skill (Krathwohl, 2001).
When describing advocacy T3 stated: “In my classroom, building advocacy is important.
[Student Name] is an ELL and she will always ask when she doesn't understand something.”
Advocacy in the form of asking for help is a skill all interview participants mentioned. Teachers
describe how they build a positive culture. Teachers said “at the beginning of the year, I shared
my story of self with students. When they hear that my story is similar to theirs… that I didn’t
learn English until I was forced to in third grade.” T3 highlights that there are specific moves
such as sharing her story of self that helps students understand the role that identity plays in
education. Other teachers mentioned a “love of learning” as a foundation for classroom culture
for ELLs when they said “[Student Name] curious to read books and will read all levels and
kinds of books and is constantly developing herself through reading and so are her classmates
which makes me know they will get to their goals.” Teachers mentioned they “see ELLs being
successful when they advocate, participate and show zest”. T3 and T1 both mention specific
behaviors like participation, advocacy, zest and structure as systems that support ELLs. Teachers
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identified the process of teaching those values by saying, “I teach them. I make them equally as
important as Math. We practice them. We praise them” while another teacher said, “of course it
has a lot to do with their natural ‘ganas’, but honestly it does have a lot to do with building
classroom culture because if they aren’t willing to try or if they are too nervous and don’t feel
safe then they won’t try.
Administrators said, “it’s important that classrooms have opportunities for questions
where students can say and advocate like I don’t get this or say this is confusing me” and “there
should be a continued reference to the fact that learning and that knowing another language is a
huge asset”. Administrators considered the inclusion a wide variety of languages as a way to
demonstrate the value of language in the school community because “students who are ELLs are
receiving many mixed messages about their identities and many of them are deficit based.”
Four teachers explicitly referenced the need to build up skills and processes that address
the intersectionality between students who may be learning English and students who also
experience immigration challenges or racism. Teachers said they “saw a lot of English Language
Learners feel more insecure about their language identity over the past few years”, “there were
so many jokes going around about ICE and immigration”, and that there is a “need to know how
to build a classroom culture that confronts what's out there, but honors who students are”.
81% of participants interviewed mentioned some of the factors outside of school that may
uniquely impact students who were English Language Learners and the need for the culture at
the school to address and empower students. Teachers also named that building community is
dependent on the individual teachers. Teachers and administrators also highlighted the need for
procedures to build formal and informal relationships. Teachers noted “Kids who have been most
successful have also been socially successful”. This shows another procedural need for building
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a supportive culture for ELLs that addresses formal and informal relationships. Teachers noted
there could be “more specific instructions on how to do that”.
An Informed and Empowered Culture for Family Involvement. All administrators
and five teachers interviewed talked about the importance of involving parents in the school and
classroom culture; highlighting that here are a variety of key stakeholders who support an
organization’s realization of their performance goal (Clark & Estes, 2008). While parent
involvement is not a novel finding, the way the teachers and administrators described
relationship building with the parents of ELLs presents a novel focus on data, empowerment and
advocacy. Teachers also noted examples where parents ask about Reclassification, ELD or
request staff call in the Designated ELD teacher to give an update on student progress. Teachers
noted this as a shift in culture. The administrator interviews were able to add some insight into
how the shift in these parent relationships started. They named the EL specialist as the person
who started the process. The EL Specialist had data meetings with each student and parent and
A2 added that she believes the meetings included “an explanation of what it means to be an ELL,
data about where students were at in relation to their goals and just celebrating language.” T3
said:
This school seems to have parents more involved in the experience of being an ELL.
During virtual learning and COVID I’ve had parents ask about how reclassification will
be impacted and ask for more resources to practice for the ELPAC during school closure.
When the school was open parents would message me, even though I’m not an ELA
teacher, to ask how students could raise their grade because they knew that they needed a
C to be reclassified.
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This highlights the specific skills and procedure to building relationships that specifically
empower families through knowledge and advocacy. Teachers are learning how to build
empowering relationships and instructional practices that support ELLs, but knowing when to
use the knowledge and an awareness of those choices (metacognitive awareness) is necessary.
Metacognitive Knowledge
Metacognitive knowledge refers to one's awareness of their own cognition and cognitive
processes that allows them to know when and how to solve problems (Rueda, 2008).
Specifically, metalinguistic awareness refers to one’s awareness of language and to reflect on
how language is used. Table 15 shows the sub findings and findings in relation to metacognitive
knowledge in response to research question one. These sub findings and findings in Table 15 will
be referenced in relation to the data from the study throughout Chapter 4 and 5.
Table 15

Metacognitive Knowledge Findings and Sub Findings

Research Question KMO Type Finding Sub Finding
What are teachers’
knowledge and
motivation in relation
to reaching the
organizational
performance goal of
85% of ELL students
meeting or exceeding
the standard on the
state Math
assessment through
differentiated
instruction?
Metacognitive
Knowledge
There is a gap in
metacognitive and
metalinguistic awareness
amongst teachers that
impedes them from knowing
how and when to
differentiate effectively for
ELLs, but metacognitive
awareness is developed in
reflection with a competent
role model.
Teacher Awareness
and Understanding of
language in their
instruction.

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A Gap in Metacognitive Awareness, Reflection and Feedback
The sub findings as presented in Table 15 support the finding that teachers need
metacognitive knowledge as well as metalinguistic awareness. While teachers can list aspects of
a classroom that supports language development, they are not using the strategies in their
instruction. Therefore, there is a metacognitive gap in the Math teacher’s ability to know when
and how to use the strategies to support ELLs. Teachers also had an overall low awareness of
how, when and why students needed access to language in order to demonstrate their knowledge
of Math. Building an awareness of language, how and when to use strategies to support ELLs
requires a level of self-reflection and awareness.
Teacher Awareness and Understanding of language in Their Instruction. Five out of
seven teachers did not show an awareness of the student’s language needs when asked to identify
a time that they used their knowledge of a student’s language proficiency to modify or scaffold a
Math lesson. Two teachers who were coached by the EL specialist did identify nuances of an
awareness of a student’s language needs. Furthermore, four out of the five teachers who did not
show an awareness of using a student’s language proficiency also gave examples of how they
modified for the whole class as opposed to one student. A gap in teacher awareness and
understanding of supporting language instruction shows the need for metacognitive knowledge
about how and when to use strategies (Baker, 2006). When T4 was asked to talk about a time she
used her knowledge of a specific student’s language needs to differentiate instruction, they
shared an example of when she gave students printed instructions as opposed to having them
read the instructions on the computer which neither includes knowledge of language
development nor knowledge of an individual student’s need. Another teacher responded to the
same question with “well I’m fluent in Spanish so I really just rely on that and I’ll use that for
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just a few students or a lot of students.” This shows a lack of awareness about why or how they
chose this strategy to support ELLs as they are not using specific knowledge about a student’s
language to make instructional choices. Two other teachers said they “let the students just do the
work in Spanish because then at least they are doing the Math” and “students share however they
feel comfortable so they can use any language or way”. Both mentioned things they do for the
whole group as opposed to one student which showed a lack of awareness about individual
student needs as well as a gap in their ability to determine how and when to differentiate for
ELLs.
However, it is important to note that two teachers did demonstrate an ability to determine
how and when to apply strategies to support ELLs. Both T2 and T5 mentioned examples that
showed a foundational understanding of how and when to differentiate for ELLs. T5 specifically
talked about metalinguistic awareness as crucial to her own process of supporting students who
are learning English. Metalinguistic awareness refers to a teacher's awareness of language and
their ability to consciously reflect on language. T5 has taught both Math and Designated ELD
and stated:
So I had one student who is in my group and he has lower English proficiency. I realized
that he struggled with actually saying the sentences and therefore was struggling to write
accurately. So I decided to pull him one on one. We practiced making choices about
language. And my modeling was specific to metalinguistic awareness like why is this
certain word choice more fitting. Then after we both talked and practiced he tried writing
it.
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This shows T5’s ability to use her knowledge of language, content and the student to then
think through how she will apply that knowledge to support the student. T2 also shared an
example:
I had a student who moved to the U.S. for the first time and only knew a few words in
English. I knew her first step was to understand patterns or connections between words in
Spanish. So we were doing a lesson on decimals and converting cents into dollars. So I
thought of the phrase 70 cents. Cents and in Spanish centavos. Centavos….cien which is
100 in Spanish. Cents are 1/100 or there are 100 cents in a dollar. So I just like explicitly
made those connections.
T2’s awareness of language development helped her make instructional choices based on
language proficiency and T2’s awareness that patterns and connections to home language is an
early language skill allowed her to effectively differentiate. Her knowledge of language and the
student’s language development allowed T2 to know that cents and centavo were an appropriate
language scaffold. Both teachers received 1-2 years of coaching from the EL Specialist and had
opportunities to reflect on their own knowledge of language, how and when to differentiate for
students specifically ELLs at times. This shows the role metacognitive knowledge plays in
teacher knowledge and implementation of strategies to support ELLs.
Motivation Findings
Self-Efficacy Theory
Bandura (2008) describes self-efficacy as the judgements people make about their ability
to organize and execute and ultimately attain a certain level of performance. Self-efficacy
consists of personal choice, persistence, and mental effort and is influenced by many factors like
prior knowledge, the amount and quality of feedback received as well as experiences with related
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successes or failures. Table 16 shows the sub finding and finding in relation to self-efficacy in
response to research question one. The sub finding and finding in Table 16 will be referenced in
relation to the data from the study throughout Chapter 4 and 5.
Table 16

Self-Efficacy Findings and Sub findings.

Research
Question
KMO
Type
Finding Sub Finding
What are
teachers’
knowledge and
motivation in
relation to
reaching the
organizational
performance
goal of 85% of
ELL students
meeting or
exceeding the
standard on the
state Math
assessment
through
differentiated
instruction?
Self-
Efficacy
Teacher self-efficacy is both
strengthened in the presence
of feedback, reflection and
coaching and hindered in
the absence
Teachers expressed low self-
efficacy as they rated
themselves in their ability to
differentiate for ELLs.

Teacher Self-Efficacy is Both Strengthened by Feedback, Reflection and Coaching
The sub findings below support the finding that teachers express low self- efficacy in
supporting ELL students in Math. Explicit knowledge of how to support ELLs coupled with
opportunities for feedback and reflection support teachers as they close the self-efficacy gap.
Teachers Expressed Low Self- Efficacy in Their Ability to Support ELLs. In the
survey data, 35 teachers were surveyed and 50% expressed that they feel confident in their
ability to adequately meet the needs of their students who are ELLs. 51% felt confident in their
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ability to modify or differentiate the curriculum to meet the needs of ELLs. While the survey
results are higher than the interview results, a self-efficacy gap is concerned as half of survey
participants do not feel confident in their ability to support ELLs.
All Administrator and Teacher participants were asked to rate their perceived ability to support
ELLs. Five teachers chose novice, two teachers chose intermediate and no teachers chose
proficient. Similarly, each administrator identified that they were between novice and
intermediate. This is important because high self-efficacy can positively impact motivation
(Pajares, 2006). T1 described herself as novice and added:
I get a lot of feedback and input on how I’m teaching Math, but I don’t get feedback on
how to support language development so it’s not at the front of my mind. I know there
are practices that I can do to support ELLs, but I don’t think I do them well enough or
consistently enough to say yeah my students are learning Math, but they are also learning
English.
This shows a lack of feedback as a barrier to improving her self-efficacy in supporting ELLs.
Other teachers who described themselves as novice or maybe intermediate mentioned having “a
lot of room to grow” and that their “skills to specifically target EL needs are not as strong as they
need to be”. Five teachers mentioned they never get feedback on supporting ELLs. T3 described
herself as intermediate because “[she herself] was an English Language Learner”. Other teachers
mentioned they “rely on things like understanding their experience”, “knowing that when they
struggle to understand something they can use Spanish to help them”, but said they are “lacking
in skills to help them use English more or to implement English language learning in the math
classroom”. However, a different trend emerged when teachers had access to an expert in the
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field and opportunities to reflect on their practice supporting ELLs. T5 and T2 both identified an
increase in self- efficacy.
I used to always think like oh I wish I could speak Spanish. I wish I could translate. I
don’t really have those feelings anymore which I think is good. In the past I had a
teaching partner who was Spanish speaking and I relied a lot on her and so as I’ve gotten
more confident with some strategies I’ve moved away from that.
Furthermore, four teachers interviewed related learning to support ELLs with years of
experience implying that they needed more experience before they could focus on supporting
ELLs thus signifying lower self- efficacy. Teachers said, “next year will be my fifth year
teaching so I’m hoping that maybe then I can focus on that”, “I should be good at basic
instruction so I can focus on ELL supports” and “maybe that’s something that like next year I
can convince my coach since it will be my fifth year.” This shows that teachers saw years of
experience as a barrier to building self -efficacy. Similar gaps emerged from the data from
administrator surveys. 33% of administrators expressed confidence in their ability to coach Math
teachers in modification and differentiation specifically for students who are ELLs. Only 25% of
administrators agreed with the statement, “I feel confident about my school’s ability to
adequately meet the needs of students who are ELLs in Math.” There is a clear self- efficacy gap
in both the surveys and interviews for teachers and administrators. Administrators are
responsible for giving feedback to teachers and Administrators also reported low self- efficacy in
supporting ELLs which indicates a lack of instructional support for teachers in relation to serving
ELLs. This will be discussed in the findings for research question two.

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Motivation Attribute Theory
Learning and motivation are enhanced when individuals attribute success or failures to
their own effort rather than ability (Anderman & Anderman, 2009) and ultimately shows the
degree of control they believe they have in affecting outcomes (Rueda, 2011). Table 17 shows
the finding in relation to Attribute Theory in response to research question one. The finding in
Table 17 will be referenced in relation to the data from the study throughout Chapter 4 and 5.
Table 17

Attribute Theory Findings and Sub Findings

Research Question KMO Type Finding Sub Finding
What are teachers’ knowledge and
motivation in relation to reaching the
organizational performance goal of
85% of ELL students meeting or
exceeding the standard on the state
Math assessment through
differentiated instruction?
Motivation
Attribute
Theory
Teacher found
external influences
as the primary
contributor to ELL
student success

Student Success is
often attributed to
Character Traits or
behaviors of
Students.

Teacher Found External Influences as the Primary Contributor to ELL Student Success
The data below supports the finding that teachers do not attribute student success or
failures to the Math teacher’s instruction or effort. The interview data found that while teachers
expressed interest in acquiring knowledge about how to support ELLs in Math, they listed
primarily external causes as the cause of student success or lack thereof. The external causes
identified represented perceived assets and deficits in the students.
Student Success is Often Attributed to Character Traits or Behaviors of Students.
When asked to think of a student who is an ELL who was successful or struggled in their class,
all seven teachers attributed student success or difficulties to behaviors or personality traits of the
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students. Teachers attributed success and failure to something other than teacher effort or the
impact of teacher instruction. This is important because learners experience increased motivation
when they attribute success or failure to their own effort rather than ability (Anderman &
Anderman, 2009). T3 said:
I think of [student name] because he works really, really hard and he responds really well
in class. He is just really open to asking questions. I think it has to do with his confidence
and comfort level.”
This student was described as hardworking, participatory and confident which highlights T3
doesn’t have control over the student’s personality and therefore has little control over the
conditions that make the student successful. Other teachers also expressed similar ideas and said
students are successful because they are “able to participate and share and just raise their hand so
enthusiastically” while another teacher said, “ELLs who are successful in class tend to be hard
workers.” All three administrators also attributed student success to their external traits. An
administrator said: “[Student Name] was successful and they worked really hard. They came in
barely speaking English and made a lot of progress. They were a really hard worker and they did
everything they were asked to.” This shows that student success is attributed to student behavior
and behaviors external to the teacher. Potentially teachers have less knowledge about success for
English Language learners and need accurate feedback that identifies the teacher skill or
knowledge that teachers can use to support ELLs (Pintrich, 2009). This was also true when
teachers described students who were unsuccessful: teachers related it to student behavior rather
than instruction. T2 described a student who “had great social skill, but his academic confidence
was lacking so he wouldn’t participate in class and take risks so he couldn’t progress.” This
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shows that Teachers do not explicitly connect student success or barriers to instruction, but rather
the students' feelings or behaviors.
Two teachers further identified a student’s disability as the barrier to student progress
rather than instruction which highlights a lack of control of the outcomes on the teacher’s behalf.
Teachers said, “the disabilities students have impact how successful they are”, “they might be an
ELL, but also have all these other struggles or challenges from what their IEP says” and
“Students come in multiple grade levels behind and it feels like until that gap is filled we cannot
focus on supporting their language.” This highlights that prior academic gaps impact the success
of students, but does not reflect on what part of that is within teacher control. Two teachers and
one administrator also mentioned that the lack of service or support students receive in grade K-4
also impacts student success. A2 stated, “I wish there was a clear plan for providing support in
grades K-4. By the time students get to middle school their gaps are big so that presents a
challenge to teach them grade level content and fill gaps.”
On the survey between 70-80% of all 50 participants interviewed agreed that when
students who are ELLs achieve poorly it is due to internal problems in the classroom or school.
Potentially teachers know that they control instruction and can impact learning for ELLs, but
lack exposure to feedback and opportunities to reflect on how teachers contribute or control
success or barriers for ELL students. T2 received coaching from an ELL specialist and her
answer addresses the connection between teacher knowledge, self-efficacy, feedback and
attribution theory.
Last year I used to feel overwhelmed how far behind kids were with English and with
Math. I struggled to think beyond the gaps. But as I learned about new strategies and tried
them and got weekly feedback from my coach, I saw that they worked. Students may
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have still had gaps and might not know English perfectly, but they were participating so
once I saw this I realized that my instruction was able to create success even in the
presence of gaps in knowledge.
T2’s ability to see the positive impact her instruction can make shows the impact that knowledge,
feedback and reflection have on a teacher's attribution of success.
While some teachers struggled to clearly link student success or misunderstanding with
their teaching, all teachers expressed the fact that they do feel responsible to teach language
development. They saw language instruction as their responsibility. Teachers said, “technically
everybody is an ELD teacher”, “I want to get to the point where I am teaching language through
Math”, “I know students should be learning language and Math in my classroom.”
Expectancy Value Theory
Expectancy value theory also known as task value, refers to the importance one feels
towards a certain task (Rueda, 2011). Expectancy Value theory helps people answer the
question, “Why does this matter?” There are four different components of task or value theory:
attainment or importance value, intrinsic value, utility value and cost value (Rueda, 2011). This
motivational influence was not part of the assumed knowledge influences as presented in
Chapter 2 therefore there was no question specifically targeting it on the survey or in the
interview protocol. However, nine out of ten participants referenced either attainment value,
intrinsic value or utility value as it pertains to Math teacher motivation and progress towards the
performance goal. Table 18 shows the finding in relation to value theory in response to research
question one. The finding in Table 18 will be referenced in relation to the data from the study
throughout Chapter 4 and 5.

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Table 18

Value Theory Findings and Sub Findings

Research Question KMO Type Finding Sub Finding
What are teachers’
knowledge and
motivation in relation
to reaching the
organizational
performance goal of
85% of ELL students
meeting or exceeding
the standard on the
state Math assessment
through differentiated
instruction?
Motivation
Expectancy
Value
Theory and
Goal Theory
Teacher Investment and
Motivation increased
through a connection and
understanding of both the
performance data as well
as larger rationale
Increased Teacher
Investment through goal
setting and a connection
to the larger purpose
also bright spot of
collective responsibility
Teacher Motivation Increased Through a Connection to Data and Rationale
The data below supports the finding that teachers experience increased motivation related
to supporting ELLs in the Math classroom when they see value. The finding focuses on three
aspects of Task Value Theory. The focus is on the value teachers place on doing a task well
(attainment), the interest teachers express about a task (intrinsic) and how useful teachers believe
ELL supports are in accomplishing a goal (utility). Teachers in the study described how their
increased intrinsic and attainment value supports an increased motivation.
Increased Teacher Investment Through Goal Setting. When asked what goal they
knew of related to ELLs and what motivated them, All 10 participants interviewed mentioned the
importance of the ELPAC and Reclassification. When they described why the ELPAC and
Reclassification mattered to them all participants connected the measures to the larger goal of
improving life outcomes for their students who are ELLs which shows the inclusion of the
importance and utility value of a task increases motivation (Pintrich, 2003). T4 talked about a
time she spoke to students and motivated them to finish their work for their ELD class after they
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completed their Math work: “I think if just one teacher says it then it only seems important to
one teacher, but if all of us teachers make it a priority to talk about it then we can help reinforce
the importance.”
The use of reclassification as a motivator shows the teacher has an understanding of how
that goal impacts the larger why and contributes to students living a choice-filled life. Other
teachers said, “I know we use the ELPAC to create goals for ourselves and our kids”, “I’ve
learned a lot more this year than any other year in terms of how our special education kiddos are
evaluated and why it matters” and 5 teachers said, “I want them to do well on the ELPAC and I
want them to be reclassified”. Teachers wanted students to “feel more confident” and have more
“doors opened for success for them”. Teachers referenced a training session conducted by the EL
Specialist that increased their knowledge about the importance of EL Supports. At the training
teachers said they “saw a bunch of statistics about language development” like “how students
who have been reclassified actually perform better on all the standardized tests than students who
are English Only” and reported feeling more motivated to support ELLs. This shows the value
placed on the task, increased teacher commitment and intrinsic motivation to learn new strategies
to support students who are ELLs in the Math classroom. Teachers wanted to know that their
effort would yield results for students in the classroom. Teachers said, “I want to know it works,
but it seems we don’t get enough time to try” and “I know it's important, but I want to see that I
can do it.” One teacher described the impact that utility value and seeing positive results had on
their classroom. T2 stated:
So last year I started to focus on ELD in my Math classroom and even if it was just things
like increasing student talk or using sentence frames, I did that. And I’m still doing it and
sticking with it because I got a lot of bang for my buck because it worked. More students
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were taking than ever. They were using complex Math terms. It was effective for me and
my kids and I saw how important it was.
T2 saw strategies to increase student talk like sentence frames as valuable in achieving her
performance goals because she got to see them work in her classroom. Therefore, she showed
motivation and persisted in her use of the strategies and ultimately utility value encouraged her
as she acquired new knowledge. As teachers described that students mimicked their motivation.
Teachers said, “Students are always asking me how they can improve their grades because they
want to be reclassified and even during a worldwide pandemic parents are asking me about the
ELPAC” and that they will “hear students discussing their progress towards reclassification”.
While this motivation influence focuses on teacher motivation, the teachers at Éxtio Academy
noticed that their increased motivation affected students and their families.
Organizational Findings
The assumed organizational influences first referenced in Chapter 2 includes cultural
settings such as an organizational belief in the achievement of ELLs as well as a comprehensive
mission and vision of how the organization supports ELL students. The assumed cultural models
included the need for competent role models and experts in EL Strategies as well as quality
professional development that ultimately lead to results in the Math classroom. Below the sub
findings and findings related to the interaction between teacher knowledge, motivation and
organizational context are presented.

Administrators and Teachers have Similar Knowledge and Motivation Gaps
The administrator interviews reflected a similar knowledge gap and motivation gap as
the teachers interviewed. This is important because leaders play a crucial role in organizational
change and the increase in knowledge and motivation (Schneider, Brief & Guzzo, 1996). A1,
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the administrator focused on Special Education said: “I don’t really know about differentiation
tailored to English Language Learners, but I just recognize strategies for different learners in
general. For example, teachers will slow down on certain examples or emphasize a key
vocabulary word.” This shows that similar to the teachers interviewed, administrators listed
strategies that do not specifically target ELLs and do not bridge the language and the content.
Teachers who identified with some level of knowledge of the student’s primary language also
overly relied on that knowledge. An administrator who served as a teacher at the school site
before becoming an administrator, expressed similar use of translation.
When a teacher asks for help for a student who doesn’t speak English, I’ll usually suggest
providing additional support like giving the text in Spanish or having them answer in
Spanish. I have a basic level of Spanish so I’ve found that I can provide a very specific
level of translation, but like absent from my knowledge of Spanish my ability to support
ELLs would be less than novice.
Here the administrator clearly states that their reliance on Spanish is due to a lack of knowledge
of other ways to support ELs. A3 even adds that as an administrator she doesn’t see the
organization use strategies. She says, “Sometimes I’ll see the organization translate a paper or
flyer and it seems like we’ve accepted that as enough.” A3 makes the point that the actions of the
organization send a message to the rest of the organization about what is an acceptable amount of
support. Here we see that the organization at large, teachers and administrators have a tendency
to over rely on translation which fails to actually develop the English of their students.
Teachers mentioned skills like small group work that could be transferred to support
language development, but teachers did not use them to explicitly develop language in relation to
Math content. A2, who has served as an administrator at the school for over five years, said:
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“Some of the ways I’ve seen teachers differentiate is by pulling small groups. Now I wouldn’t
say that I’ve seen people differentiate specifically for English Language Learners because our
school is not at that place yet. I need to learn what that would look like.” A2 can identify that the
teachers are not specifically targeting language development, but needs more support in how and
when to apply that strategy to support ELLs. 82% of administrators surveyed expressed that they
do not receive training that is EL specific. 75% of administrators felt that the strategies used in
their school do not result in improved achievement for students who are ELLs. 92% of
administrators surveyed expressed a desire for more training that specifically addressed their role
in supporting ELLs. The survey data shows that administrators are aware of their knowledge gap,
but are not receiving organizational support to close those gaps and ultimately improve student
achievement.
Administrators Identified Similar Motivational Gaps pertaining to Self-Efficacy
Teachers identified low self- efficacy in relation to supporting ELLs and identified a lack
of feedback and reflection as one of the factors impeding their self- efficacy. Similarly, teachers
mentioned they received a lot of feedback, but the feedback did not relate to their instruction of
ELL students. All teachers interviewed rated their skills at novice or intermediate. Similarly,
administrators were asked to rate their ability when it came to coaching to support the needs of
ELLs. All three administrators chose a rating of novice. A2 replied with, “Definitely novice. I
am just starting to learn about ELD and what it means.” A2 makes a reference to her need to
acquire more knowledge and that relation to her beliefs about her self-efficacy as a coach. A3
also rated herself as a novice.
I’d say novice plus...maybe that’s cheating. I feel more comfortable than I did when I was
a classroom teacher because last year I got more professional development and I’ve been
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able to observe the Designated ELD class to get some ideas of what that might look
like….that being said I still rely on Spanish as I’m not quite in a place where I can reflect
on what I saw and go apply it in all these contexts.
While A3 acknowledged her recent growth she also stated she needed more reflection in relation
to building metacognitive knowledge so she would know when and how to use these strategies.
This shows that Administrator self-efficacy and belief in abilities was low due to the need for
more knowledge and reflection. Survey data from administrators also identifies a knowledge and
motivation gap. Nearly 67% of administrators surveyed did not feel confident in their ability to
give feedback that specifically targeted ELL support.
Administrators identified similar gaps in their knowledge and motivation from when they
were teachers and identified that the gaps persisted. 25% of Administrators surveyed said they
were somewhat confident in their abilities to support ELLs when they were teachers while 75%
of administrators said they were not confident about their abilities to support ELLs as a teacher.
Senge (1990) stated that in learning organizations, development of the leaders is equally as
important as the development of other members. This aligned with the interview responses from
administrators. All three administrators rated themselves as novice when they were teachers in
regard to supporting ELL students and highlighted that they lead in different demographic and
educational settings than where they taught. Administrators said “I only had one ELL in my class
each year”, “I didn’t receive a lot of support or guidance” and “I do think that like the nature of
teaching I would modify for that student, but it wasn’t with intentionality” The administrators
described the adjustment to the context where they lead: “When I was a teacher I taught in low
income communities, but not a high EL population so when I came here that was an adjustment”
and “As a teacher I didn’t have to focus on it so it is harder to focus on it now”. This shows that
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the administrator’s knowledge gap as a teacher impacted their ability to focus and lead for
change in regard to supporting ELLs.
Cultural Models
Cultural models refer to the shared understandings of how the world works or ought to
work and are useful in characterizing organizations and even individuals (Gallimore &
Goldenberg, 2001). Cultural models create a shared way of being that can evolve over time
however they are often invisible and unnoticed by the organization as a whole (Rueda, 2011).
Table 19 shows the sub findings and findings in relation to cultural models in response to
research question two. These sub findings and findings in Table 19 will be referenced in relation
to the data from the study throughout Chapter 4 and 5.
Table 19

Cultural Models Findings and Sub Findings

Research Question KMO Type Finding Sub Finding
How do teachers'
knowledge and
motivation
interact with the
organizational
culture and
context in
supporting
students who are
ELLs in meeting
or exceeding the
standard on state
Math
assessments?
Cultural
Models

The organization
lacks a clear and
explicit belief that
is unique to the
abilities of ELLs
Lack of Explicit Beliefs Around ELLs
Creates Invisibility
The Absence of Beliefs Creates
Conversations about Deficit as opposed
to Asset

The organization lacks a clear and
explicit belief that is unique to the
abilities of ELLs.
The organization
lacks a
comprehensive
approach to
support ELLs that
includes a mission,
vision and shared
actions.
The organization has a reactive rather
than proactive approach to supporting
ELLs.
The organization sees ELD as separate
rather than integrated.

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The Organization Lacks Clear and Explicit Beliefs About ELLs
Beliefs are often reflected in the way an organization enacts policies and in the day to day
behaviors (Rueda, 2011). The sub findings below support the finding that organizations must
have a clear and explicit belief that is unique to the abilities of ELLs. This finding focuses on the
creation of a shared mental schema connected to the shared values the members of the
organization hold about educating ELLs. Multiple teachers mentioned that their school site had
more values, but that was not reflected in the larger organization. 10 out of 11 interviewees
stated well “All children can learn”, but failed to mention any belief specific to ELLs.
Lack of Explicit Beliefs Around ELLs Creates Invisibility. 78.95 of teachers and 75%
of administrators agreed with the statement “My organization believes that ELLs can achieve at
high levels.” The 10 interview participants were asked to describe any beliefs they felt their
organization holds about ELLs. Ten out of ten participants replied with identical answers by
saying my organization believes “All kids can learn and achieve” which highlights that cultural
models are often invisible but represent the shared way of thinking or perceiving (Gallimore &
Goldenberg, 2011). It is important to note that Éxito Academies is an organization of schools
committed to serving low income students and aspire to high results. While participants stated
that “all kids can learn”, additional answers revealed hesitation as “that doesn’t really mention
ELLs though.” T1 commented:
I think about the action behind ‘All kids can learn’ and I don’t think the priorities align
with it. Like I don’t know what we do or believe about ELLs unless they are only a part
of ‘All kids’.
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This highlights that there is not a perceived differentiation or explicit action about the beliefs of
supporting ELLs even though the organization holds a value to support “all kids.” Other
teachers said, “ My organization thinks all kids can learn”, “I don’t really know about ELLs
though because when I think of the organization I’ve never heard anything from them about it”
and “I kinda don’t think it’s a priority as the larger organization took control it got lost”. English
language learners have diverse needs (Echevarria, 2008).
The needs of low-income students cannot be seen as synonymous with the needs of
ELLs. Therefore, the organization’s sole focus on low income students creates a sort of
invisibility to the intersectionality of identity that is experienced by the students who are ELLs.
Administrators also said, “we talk a lot about how “All kids can learn '' however, I don’t think
that belief spurs any action”, “I’ve never heard it specifically addressed in relation to ELLs”. To
refer back to the survey data where more than 70% of teachers and administrators said their
organization believes in ELLs’ achievement, there is a possibility based on interview data that
survey participants equated the organization’s belief that “All students can learn” to include
ELLs, but as expressed in nine out of ten interviews the beliefs do not explicitly state the unique
needs of ELLs. Belief spur action (Rueda, 2001) and therefore, the invisibility of ELLs in the
organization’s beliefs may spur the invisibility seen in the knowledge and motivation sub
findings and findings. Teachers identified knowledge gaps in seeing, hearing and supporting
ELLs appropriately which could be a manifestation of the invisibility in the beliefs.
The Absence of Beliefs Creates Conversations about Deficit as Opposed to Asset.
Each interview participant was asked to describe the last conversation they had in their
organization that pertained to ELL students. 8 participants (7 teachers and 1 administrator) all
referred to preparation meetings for an IEP meeting where they were trying to figure out why a
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student wasn’t growing. Two administrators reflected on a conversation about planning for the
ELPAC and how to do it as quickly as possible, so students weren’t fatigued for the Math and
ELA state testing. These conversations are based on gaps or areas of lack which relates to
cultural models or shared way of being in an organization. T5 described the conversation about
the IEP by saying “the IEP team couldn’t figure out what supports the student needed or why
they weren’t meeting their goals.”
Teachers described the same meeting and said, “I don’t know it didn’t even occur to us to
think about language development and how that impacted their ability or even how they might
need different supports” and “After we had exhausted all our options it popped up to us like
maybe the need is language.” Both quotes show an initial invisibility of the student’s
identification as an ELL. It also appears that only in the presence of a gap in student ability was
their identity as an ELL considered. The invisibility stemming from a lack of clear and specific
beliefs about ELLs is also seen in the conversations and daily actions of school staff members.
The organization Lacks a Mission, Vision and Set of Practices for ELL Support. The
culture of an organization can be defined using concepts of structural stability, depth, breadth or
patterns of integration (Schein, 2004). The sub findings below support the finding that the
organization lacks a comprehensive approach to support ELLs that includes a mission, vision and
shared actions. The finding focuses on the gap in the shared beliefs and actions of the
organization in regard to supporting ELLs. Teachers and administrators unanimously reflected
that they do not know the approach, actions, practices or goals the organization has in supporting
ELLs. Survey data affirmed these responses.

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The Organization has a Reactive Approach as Opposed to Proactive for ELD
Six teachers and administrators discussed that the organization has made small
movements only when confronted with data. This connects with the notion that an organization’s
beliefs inform their actions and the actions impact the day to day behaviors and reflect the
organizational culture (Rueda, 2011). Teachers described that when “our kids were not doing
well on the standardized tests the organization looked at data” and when the “organization
wanted better EL data they considered giving more support to schools.” This highlights that ELD
was not a priority in comparison to the Math and ELA data and the organization waited to
respond to data about EL progress as opposed to proactively supporting it. Teachers also talked
about the organization’s reactive approach. T1 said:
It feels like it's never a priority. We all know it's there, but maybe we can focus on it once
we get good ELA data or once our Math scores are higher or once we close the reading
gaps. Now that the state is monitoring the ELPAC it seems like they are more open to
talking about it.
The organization’s focus on ELA and Math and a reactivity to the state’s monitoring of ELPAC
data further supports a lack of a proactive approach. Teachers also mentioned they “either need
to prove that ELD and a lack of support is the root of low-test scores or we have to give them
ELD support and prove that to the organization that it works”. This further demonstrates that the
organization is not prioritizing the need for shared beliefs and actions around the support of
ELLs, but responds to data points or situations. Similar to the previous finding the absence of
clarity creates a sort of invisibility.
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Teachers and administrators were asked what best practices the organization has or any
strategic plans pertaining to ELD or ELLs. Ten out of ten participants could list goals pertaining
to the ELPAC and Reclassification, but added that it was based on the school’s work with the EL
specialist one year prior and was not a reflection of the organization. T4 said, ‘I can’t tell you
any goals that the organization has because I’ve never heard them.” Six participants commented
on the organization’s silence about how students who are ELLs are impacted by COVID and the
pandemic as well as the switch to virtual learning. Ten out of ten teachers said that their
organization does not have a set of best practices. T2 said, “there are no specific practices
pertaining to ELD, we have a few for reading like our reading block, but nothing for ELLS.” A3,
who has been an administrator and teacher in the organization said:
I’ve been asking for years for a set of best practices about what makes Éxito Academy
Éxito Academy. That would include best practices for ELLs. Like I think about our work
last year with sentence frames and student talk and I think like if those were listed as best
practices in all the classrooms what would the impact be on students.
There is not a shared understanding or shared beliefs about the organization’s support of ELLs.
The absence of best practice demonstrates a lack of teacher knowledge about instructional
strategies for ELLs therefore there is an absence of support for ELLs in the classroom. Teachers
added “ [they’ve] seen best practices in a few classrooms, but nothing school wide”, “I wish we
had a list, but to me it is bigger than just best practices like what do we want and do for our kids
who are ELLs”. One teacher hypothesized the absence to the fact that “maybe the organizational
leaders don’t have the expertise.”44% of Administrators surveyed agreed that their organization
sets achievement goals for students who are ELLs while only 8% of administrators said their
organization meets the goals they set for ELLs. 25% of administrators said their organization has
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a vision of what excellent instruction looks like for ELLs. That number dropped when only 6%
of administrators said that their organization addresses a vision of what the Math classroom
should look like for ELLs.
The Organization sees ELD as Separate Rather than Integrated. Seven out of ten
interview participants mentioned that they feel the organization viewed ELD as something
“extra” on top of their other duties and as “separate” from academic achievement. However, the
teachers advocated that in order to increase teacher knowledge and motivation in relation to the
performance goal, the organization should integrate EL support in all processes and systems.
Teachers said, “It feels like EL supports are always something extra that is nice to have”, “It
feels like we can’t work on EL supports until we have good data” and “EL Supports are things
experienced teachers work on”. The organization sees ELL support as separate from getting
“good data” rather than one of the necessary conditions that produces “good data.” Teachers
perceived that the organization does not believe that EL supports are necessary in order to run
good classrooms. Teachers advocated that, “using EL supports is just good teaching and we need
it.”
As part of the interview process teachers were asked to name actions that the organization
could take that they believed would increase teacher knowledge and ultimately motivation in
relation to the performance goal. All teachers and administrators mentioned at least one example
of an EL focus being added to a pre-existing system or process. Therefore, Math teachers wanted
ELL Supports to be integrated into the shard way of being as opposed to separate. T6 mentioned
the weekly grade level meetings that happen at school. T6 said:
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“It would be nice if there was a portion of our grade level meeting where we could
choose a few students who are ELLs and talk about what is working well for them or their
struggles. People could share out what they’ve tried or where they need help.”
T6’s example presents a clear set of actions that can be incorporated into grade level
meetings. Teachers also talked about incorporating ELL supports into weekly data meetings and
said, “the Organization should just incorporate thinking about ELLs in everything we do”. This
shows there are strong systems at the organization like data meetings, but there currently are no
explicit actions to support ELLs. While a set of best practices specifically supporting ELLs is
needed, it is also necessary that the experience of ELLs is accounted for in all systems and
procedures to create a model here. The organization lacks a plan for ELD that encompasses all
contents, systems, processes and stakeholders.
Cultural Settings
Cultural settings are social contexts where organizational policies and procedures are
enacted (Rueda, 2011). Cultural settings are more visible aspects of the organization as
compared with cultural models and specific settings are where these models are enacted. As
Rueda (2011) stated, cultural settings can be seen as the “who, what, when, where, why and how
of the routines that constitute everyday life [in the organization].” Table 20 shows the sub
findings and findings in relation to cultural settings in response to research question two. These
sub findings and findings in Table 20 will be referenced in relation to the data from the study
throughout Chapter 4 and 5.
Table 20 Cultural Settings Finding and Sub findings.

Research Question KMO Type Finding Sub Finding
How do teachers'
knowledge and
Cultural Settings Access to experts in
Supporting ELLs increases
Gaps in Instructional
Coaching
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motivation interact
with the
organizational
culture and context
in supporting
students who are
ELLs in meeting or
exceeding the
standard on state
Math assessments?
teacher knowledge and
motivation in relation to the
organizational performance
goal

The Positive Potential Impact
of Instructional Coaching

Professional Development
does not ensure that Theory
and Pedagogy translates
into Application, Action
and Reflection.

There is an absence of quality
PD supporting Math teachers and
support for ELLs.
There are barriers to PD such
as time, priorities and expertise

Access to Experts Increases Teacher Knowledge and Motivation
The sub findings below support the finding that teachers need access to experts in
supporting ELLs as a means to increase teacher knowledge and motivation in relation to the
organizational performance goal. More specifically, teachers need access to instructional coaches
that are experts in supporting ELLs. Access to these experts through instructional coaching will
provide increased opportunity for reflection and learning around supporting ELLs.
Gaps in Instructional Coaching. 41.67% of Administrators agreed that their
organization has experts in EL strategies while only 16% of Administrators somewhat agreed
that the expert has knowledge of how to support ELLs in Math. This connects to the
metacognitive and factual knowledge gap identified in teacher interviews for research question
one. Teachers need knowledge of how EL Supports explicitly connect to Math skills and
sociocultural theory (Scott & Pallinscar, 2006) and Self-Efficacy Theory (Pajares, 2006) both
state that learners acquire new knowledge through interactions with others. 33% of
Administrators agreed with the phrase “I frequently give instructional feedback to Math teachers
pertaining to the needs of students learning English.” 25% of Administrators said that a majority
of their coaching sessions address the language proficiency of students in Math. 16% of
Administrators said they gather weekly data on how ELL students are performing in Math. This
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connects to the motivation influences presented in the findings and sub findings for research
question two. Teacher motivation specifically self-efficacy could be improved through feedback
and reflection. However, the data from the administrator survey reveals that this is a gap. A2,
who primarily leads the Math team reflected on the absence of feedback explicitly targeting the
support of ELLs.
I can’t remember a time this year that I gave feedback to a Math teacher about their
ELLs. I have given general feedback about alignment to their objective mostly and the
types of questions they use for their exit tickets, but when we talk about that I’m realizing
that I don’t ask about ELLs. Last year I gave some feedback on sentence frames, but only
because that was our focus as a whole school.
This shows the absence of feedback and reflection specifically pertaining to ELL success in
Math. When A2 states that she gave feedback when it was the focus of the whole school she
revealed a dependency upon training led the EL Specialist to guide that feedback which supports
the knowledge gap that administrators have as presented in the earlier organizational sub
findings. Teachers also acknowledged a lack of feedback and said, “EL Supports are not in
lesson plans” and they’d “be surprised if anyone ever received lesson plan feedback on
supporting ELLs specifically” and another teacher said “I know I personally haven’t received
feedback on supporting ELLs. Five out of seven teachers stated they had never received
feedback addressing ELL needs. The absence of ELLs from the lesson planning template
highlights the invisibility of ELL needs in the feedback systems. This references the need to
integrate a lens of ELL support into all processes as was discussed in the sub findings about the
cultural models.
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The Positive Potential Impact of Instructional Coaching. Throughout the teacher
interviews two teachers reflected an increased knowledge and gradual increased self-efficacy.
Both T2 and T5 were coached by the administrator that also served as the EL Specialist which
shows teacher knowledge and self-efficacy increases through self-regulation and feedback
aligned with goals (Pajares, 2006). This Administrator had increased knowledge and self-
efficacy pertaining to supporting ELLs and in turn was able to support and develop the
knowledge and motivation of Math teachers in relation to the organizational performance goal.
In this sub finding we will look at how T2 and T5 describe the feedback they received from their
coach and also how that feedback changed their knowledge, motivation and ultimately student
achievement. They expressed an increase in their metalinguistic awareness and ability to “be
aware of the language choices [they’re] making and why”. T2 and T5 then said they “share
those small details with students and “see [students] really grasp how to use language in Math.”
Students were supposed to say, “If you ____ then ___” but students were just saying
“The answer would be____.” My coach told me to really explain what the “If you ____”
means and how it changes the purpose and language we use If I want students to really
understand and compare how math would change based on the operations. Once I did that
students started to use it and even use it outside our class.
T5 noted that she saw students using the language and ultimately using it outside of just this
lesson. This highlights that teacher knowledge was enhanced through their reflection with an
expert in EL strategies and learning how to share the purpose and use of language with students.
T2 reflected on a similar experience when her and her coach were working on Math word
problems. T2 mentioned in the past they relied on strategies like “underline the keywords, circle
the word that is the operation, and highlight the question”, but last year her coach told her to
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“take the Math out”. T2 put post it’s over all the numbers so students wouldn’t focus on
calculations and with the coaches support began to act out, draw, visualize and even connect
reading strategies to the Math problems and that with a focus on the language and not the Math
students “got it”.T2 and her coach determined if the root cause of the misunderstanding was the
Math or the language and then selected an appropriate strategy. T2’s coach was able to model
and guide T2 through strategies that specifically targeted ELLs which in turn increased her self-
efficacy, “I used to rely on a teacher who spoke Spanish and I was always wishing that I knew
Spanish to translate and now I don’t really feel that way.” Through T2’s reflection on her process
and her successes she increased her self-efficacy and student misconception decreased. It was
previously identified that administrators have a knowledge gap and will need explicit knowledge,
but they may also need access to a competent role model themselves that can model what it looks
like for an administrator to coach, give feedback and lead using knowledge of math and language
development.
Professional Development Does not Close Knowledge and Motivation Gaps
The sub findings below support the finding that the organization does not provide
professional development that ensures pedagogy and theory translates to application, action and
reflection for teachers. The finding focuses on the cultural setting created by professional
learning communities and professional development. Teachers in the study described limited
participation in professional development that targeted supporting ELLs. Teachers and
administrators stated that there have always been barriers in the organization to a focus on ELD.
As T7 put it, “It is always a priority yet never a priority.”
Absence of PD Related to Supporting ELLs in Math. 84.21% of teachers who took the
survey stated that they wanted more PD about how to specifically support ELLs which highlights
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that teachers need practice, guidance and feedback in order to make meaningful connections to
new knowledge (Mayer, 2011). 26% of teachers felt like the PD they have attended has made a
positive impact on their classroom which means that 74% of teachers felt it did not positively
impact their classroom. 39% of teachers said that they have attended at least one PD from their
organization about supporting ELLs since they joined the organization. Meanwhile 21% said that
the training gave Math samples or examples while 79% stated an absence of Math. Administrator
responses reflected similar sentiments. 100% of Administrators surveyed said their organizations
do not spend enough time talking about how to support ELLs. 16% of Administrators said their
organizations offer PD about how to support ELLs while only 8.33% referenced Math specific
PD. 0% of Administrators had attended a PD specifically for administrators on how to support
teacher knowledge and motivation in relation to EL Support. 92% of Administrators said the PD
does not make an impact on their ability to lead a school for their ELL students nor do they see a
positive impact in the classrooms at their schools. The preceding data highlights that there is a
lack of professional development for both teachers and administrators to support their acquisition
of knowledge in relation to serving ELL students. Furthermore, the PD does not specifically
address Math instruction and does not have a visibly positive impact on their classrooms which
ultimately impacts teacher and administrator self- efficacy.
Barriers to Quality PD Supporting ELLs. Teachers mentioned only one series of PD
that focused on EL Supports and that it did not remain a priority. Teachers presented a variety of
barriers to having consistent PD. Five teachers mentioned that maybe it felt like an extra
responsibility. The organization's ability to be adaptive, flexible and generative in response to
these barriers is an important quality of a learning organization (Senge, 1990). Teachers said,
“Maybe people feel like it is an extra additional thing on our plates” and “It feels like there are so
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many different levels and like until students can read at grade level we can’t focus on ELD.”
Four teachers and two administrators mentioned pacing and curriculum maps as a barrier and
said, “With our pacing calendars we have no time to slow down or rearrange”, “We have to stick
to them to prepare for testing” and “I want to slow down and listen to student language and
actually listen to where the language becomes confusing then I want to take time to model my
language and understanding, but I just don’t feel I can take that time.” In addition to the pressure
and barrier presented by testing and pacing; Administrators also mentioned that it required a shift
from silent and compliance-based schooling.
I’d walk into classrooms and there would be so much talking. Usually we are always
talking about voice volume and quiet voices and it took a shift to say like okay now we
want there to be more and louder voices.
Another barrier for administrators was struggling to see the whole in order to create
comprehensive PD. Administrators said, “I feel like people get the ELD teacher and what she
does, but what would a full ELD program look like”, “Without seeing the whole it's hard to plan
and get there” and “[they’d] be excited for a comprehensive plan that was research based and had
clear behaviors and measures for all stakeholders.” When asked why they don’t have this all
three administrators mentioned that they “just don’t have enough people with the knowledge.” In
interviews, a participant shared that both the EL Specialist and the ELD class was the first to go
with a set of budget cuts.
Summary
This chapter includes the findings from qualitative interviews and quantitative surveys
that were conducted to identify KMO influences that have an impact on Math teacher instruction
for ELLs in relation to the Teacher performance goal. Responses from both the quantitative and
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qualitative instruments were coded to deduce sub findings that supported findings (Creswell &
Creswell, 2018; Merriam & Tisdell, 2016). To support sub findings and findings, triangulation of
data was used to reference prior research on knowledge, motivation and organizational theories.
The needs of English Language learners are diverse and different than their peers who do
not identify as ELLs (Echevarria, 2008). A majority of teachers interviewed identified a need for
more knowledge about supporting ELLs. Evidence showed that teachers needed factual
knowledge about strategies and specifically how to use them to bridge language development
and math. The lack of knowledge caused some teachers to be reliant on their ability to speak the
student's primary language therefore not developing English at all. Teachers identified the need
for building procedural knowledge about how to create a classroom culture that supports ELL
success. While teachers identified common goals, they were unclear about a unified way to build
the values in the school culture. Evidence also shows a gap in the procedures for building a
community of collaboration that ultimately supports both teacher knowledge of serving ELLs as
well as ELL achievement. Teachers also talked about the impact that building a relationship
with families had on student success. The relationships were rooted in empowerment through
information and advocacy. Based on the interview responses, teachers lacked the metacognitive
knowledge to make choices about strategies pertaining to language and Math. Specifically
teachers lacked metalinguistic awareness and the ability to reflect on language use. Although a
majority of teachers had knowledge gaps, two teachers showed improved factual, procedural,
metacognitive and metalinguistic awareness. Both of these teachers described their experience
being coached by an EL Specialist and how it impacted their acquisition of new knowledge and
ultimately their students.
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Motivation increases when teachers believe they are able to accomplish a goal, attribute
success or failures to their own effort or when they find value in the task at hand (Clark & Estes,
2008). There is a reciprocal relationship between teacher’s knowledge and motivation (Rueda,
2011). Teachers identified low self-efficacy as they did not rate themselves proficient in
supporting ELLs. Teachers also stated that they do not get specific feedback on supporting ELLS
nor did they get many opportunities for reflection. Teachers rarely attributed ELL success or
failure to their ability to teach. Teachers saw student behavior and character as one factor to
which success or failure could be attributed. When students struggled with language, there was a
connection to students' disability as stated in their IEP. Teachers who had increased knowledge,
had an increased self of self and more commonly attributed student success to their actions.
Teachers stated investment in reclassification and the ELPAC test because they knew how it
impacted a student’s life trajectory. Teachers’ confidence grew in the case that they had exposure
to an instructional coach who was an EL Expert. This was the case for two teachers who
participated. Learners must believe that their efforts will have an impact on the outcome
(Grossman & Salas, 2011). Teachers also saw that their increased commitment to goals caused
an increased commitment and investment from their students.
Learning organizations develop both the leaders and those whom the leaders serve
(Schein, 2004). Teacher knowledge and motivation interacts with organizational models and
settings. Administrators often served as a liaison between the larger organization and the
teachers. Administrators had similar knowledge and motivation needs as did the teachers.
Administrators also expressed low self-efficacy in their ability to serve ELLs from when they
were teachers and the self-efficacy gap persisted. The cultural models explored in the study were
the beliefs the organization held about ELLs as well as the mission, vision and actions that the
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organization held as central in their support of ELLs. Through both teacher and administrator
surveys and interviews, evidence showed that there are no specific beliefs about ELLs. The
organization focuses on their desire to serve low income students however a failure to recognize
the intersectionality of students who are low income and also ELLs creates a certain invisibility
in the beliefs and behaviors at the organization. There was not a mission, vision or set of best
practices for how the organization would support ELLs. The organization took a reactive
approach rather than a proactive approach to supporting ELLs. They also did not view EL
Supports as necessary to student achievement and treated it as something “extra” or separate. As
one teacher put it, “it (ELD) is always a priority yet never a priority.”
The cultural settings show how the shared beliefs come alive in policies, procedures and
everyday actions (Rueda, 2011). The two settings that were focused on in relation to
organizational impact teacher knowledge and motivation were: instructional coaching and
professional development. Based on the interview results teachers did not receive instructional
coaching that offered them specific support in EL strategies. Administrators also stated that they
did not give feedback or collect data on language development in the Math classroom. Two
teachers had access to an instructional coach who was able to provide specific feedback on both
Math content and support for ELLs. These teachers expressed an increase in their knowledge and
self-efficacy. Teachers and administrators identified little to no PD to support ELLs. This
number decreased even more when they were asked about PD that was specific for Math
teachers. However, five teachers and two administrators all mentioned one specific PD that made
a positive impact on their knowledge and self- efficacy. The factors that made this PD helpful
were explained via the interview responses.

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CHAPTER FIVE: DISCUSSION AND RECOMMENDATIONS
Chapter 5 includes recommendations for practice that align with the findings of the study
and support the organization in reaching the organizational performance goal. The chapter first
includes a brief discussion of the findings as it relates to the conceptual framework and the
literature reviewed in Chapter 2. The findings and recommendations are organized in alignment
with the KMO framework which serves as the basis for the research questions. Following the brief
discussion of the findings, recommendations for practice are made organized by knowledge,
motivation and organizational influences. As findings are presented, data from the study and
connections to the findings will be made. Following the recommendations, a discussion of the
training program and the data collection methods will conclude the recommendations section. The
training program is grounded in the New World Kirkpatrick Model (Kirkpatrick & Kirkpatrick,
2016) and is based on the four levels of learning. Program implementation begins with level four
as organizations consider the goals they need to attain then plan the behaviors (level 3), learning
required (level 2) and desired reactions (level 1) in order to positively impact the desired results.
The training focuses on developing the behaviors related to the knowledge and motivational
influences in order to support the organizational culture in relation to the organizational
performance goal. Chapter 5 concludes with a discussion of the limitations of the study as well as
recommendations for future research.
Discussion of Findings
The literature in Chapter 2 discussed the diverse needs of students who are ELLs,
language development and teacher implementation of strategies to support ELLs. Students
learning English must not only learn informal English, but they must also acquire the formal
academic language needed to navigate academia. While formal English is a challenge,
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researchers have indicated that formal academic English may require more time and support
(Collier, 1987; Cummins, 1981; Mitchell, Destino & Karam, 1997). Cummins (1981), and
Mitchell, Destino and Karam (1997) estimated it may take up to ten years before students
learning English are fully competitive in the academic uses of English as compared with their
FEP counterparts. The evidence highlights that the instructional needs of English Language
Learners are diverse from their English Only peers (Krashen & Terrell 1983; Menken 2010,
Gersten & Russel 1996, Chang (2008). The diverse needs of English Language Learners require
diverse practices in the classroom that are unique to English Language Learners (Gersten &
Russel, 1996). Teachers need knowledge, strategies and preparation for working with English
Language Learners in the field of Mathematics (Turkan, de Jong; 2018). This literature
influenced the knowledge, motivation and organizational influences for the study as well as the
creation of the conceptual framework and the design of the mixed methods study.
Following the interviews and surveys, knowledge, motivation and organizational findings
were delineated in alignment with the assumed influences. Teachers need factual knowledge of
strategies that support development of Math skills and language development while also being
developmentally appropriate. Teachers expressed a need for procedural knowledge about how to
collaborate to best support ELLs as well as the importance of the process of building
relationships in and outside of the classroom that support language development. The
metacognitive language needs highlighted a need to use factual knowledge about instructional
practices as well as knowledge of language proficiency to make self-aware instructional choices
that support ELLs in the Math classroom. Teachers and administrators expressed low self-
efficacy in relation to supporting ELLs and highlighted a lack of opportunity for feedback and
reflection that specifically targeted ELD. Furthermore, teachers struggled to attribute ELL
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success to teacher instructional practice. However, teachers expressed that motivation increased
in relation to goal setting and investment in the largest importance of reaching the organizational
performance goal. In alignment with the conceptual framework, the influence of organizational
models and settings on teacher knowledge and motivation was a focus of the interviews and
surveys. The findings supported that the organization needs a clear strategic plan for supporting
ELLs as well as a clear set of beliefs, goals and instructional practices that address the unique
development of ELLs and also make explicit reference to Math achievement. Math teachers need
training that targets the findings presented in the knowledge section and teaches strategies that
explicitly link Math content with knowledge of language development in order to choose
strategies that are developmentally appropriate in supporting ELLs in Math. Organizations also
need to provide teachers access to instructional coaches that provide targeted observations,
feedback and support that specifically targets the skills needed to support ELLs in the Math
classroom. These findings support the problem of practice as increased knowledge, motivation
and organizational support ultimately supports Math teachers in supporting the academic
achievement and language development of ELLs.
Recommendations for Practice
Knowledge Recommendations
The table below includes the assumed knowledge influence as well as the data validation
through the qualitative and quantitative data. Table 21 highlights the validation based on the
qualitative and quantitative data of the mixed methods research as well as the most frequently
mentioned knowledge influences to achieving the stakeholders’ goal. Using Krathwohl's (2008)
four knowledge influences (factual, procedural, conceptual and metacognitive), the study
narrowly focuses on the factual, procedural and metacognitive influence that support Math
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teacher’s instruction of students learning English. Behavior that is reinforced is strengthened
(Daly, 2009) and the knowledge influences that impact the stakeholder group can be
strengthened through reinforcement. The reinforcement and strengthening of the knowledge
influences support goal attainment (Rueda, 2011). As indicated in Table 21, these three
knowledge influences are validated and have a high priority for achieving the stakeholders’ goal.
During the data collection and analysis process a new knowledge influence was validated that
you will see reflected in the table below. The recommendations for these validated influences
based on theoretical principles are also included in the table. These recommendations use the
New World Kirkpatrick Model (2016) with an emphasis on level 2 of the model that includes the
knowledge, skills, attitudes, confidence and commitment of Math teachers towards supporting
students who are learning English.

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Table 21
Summary of Knowledge Influences and Recommendations
Assumed Knowledge
Influence

Validated as a
Gap?
Yes, High
Probability or
No
Priority
Yes, No
(Y, N)
Principle and Citation Context-Specific
Recommendation
Teachers need to know
a variety of strategies to
teach students who are
English Language
Learners in Math.
(Factual)
Y Y To develop mastery,
individuals must acquire
component skills, practice
integrating them, and know
when to apply what they have
learned (Schraw &
McCrudden, 2006).
Provide training that focuses
on a set of instructional best
practices for English
Language Learners that
support Math teachers.

Provide a job aid that has
samples of what these
strategies look like, how to
plan the strategies and a
rubric of criteria for success
that can be accessed by
teachers as needed.
Teachers need to know
how to build
relationships resulting
in partnerships that
support students who
are ELLs. (Procedural)
Y Y Procedural knowledge
includes strategic knowledge
(Anderson & Krathwohl,
2001).

Provide training that shares
the best practices for
creating a culturally
responsive classroom that
creates an active experience
for students learning English
and their families.
Teachers need self-
awareness about using
proficiency and content
knowledge to
appropriately
differentiate.
(Metacognitive)
Y Y The use of metacognitive
strategies facilitates learning
(Baker, 2006).
Provide a job aide that
supports teachers in how to
plan for language supports
in their Math lesson plan.
The job aide would address
metacognitive skills.

Provide training on how to
incorporate metacognitive
and metalinguistic
awareness into the lesson
cycle.
NEW INFLUENCE
Math teachers need
knowledge of the
defining features of the
continuum of language
development (Factual)
Y Y To develop mastery,
individuals must acquire
component skills, practice
integrating them, and know
when to apply what they have
learned (Schraw &
McCrudden, 2006).
Provide targeted and
specific training on the
components of language and
language development.

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Increasing Math Teacher Knowledge of Strategies to Support ELL Students
The results and findings of this study indicated that Math teachers need more in-depth
factual knowledge about the strategies that can be used to support ELL students specifically
pertaining to Math. The results of the administrator and teacher survey indicated that more than
90% of participants need more training on strategies used in the Math classroom to support
ELLs. In interviews 100% of teachers and administrators listed strategies for ELLs but could not
identify what that would look like in the context of a Math lesson. Therefore, the
recommendation should address the gap between the language demands and the context of the
Math content. A recommendation rooted in information processing theory has been selected to
close this factual knowledge gap. Schraw and McCrudden (2006) found that how individuals
organize knowledge influences and develop mastery is strengthened by modeling of effective
strategy use, including “how” and “when” to use particular strategies. This would suggest that
providing training that allows teachers/administrators to develop mastery through acquiring
component skills, practicing those skills, integrating them and knowing when to apply those
skills would increase teacher knowledge.
The recommendation is to provide teachers and administrators with a series of training.
The training would include strategies to support ELLs that are taught in the context of the Math
standard and would also align with language proficiency and students’ developmental needs. An
example is a series of training on increasing student talk through the use of sentence frames. This
training would teach the skill of planning and executing sentence frames. The training would
align the ELL strategy with the Math standard as well as the language proficiency of students in
the class. As participants transfer and apply the factual knowledge from the training, a job aid
that highlights key features of the strategies, language development/proficiency levels and the
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Math content can reinforce the knowledge acquired throughout the application process (Mayer,
2001).
The job aid is the second of two recommendations for this influence with the training
being the first. This recommendation rooted in Cognitive Load Theory aims to increase germane
load by providing adequate guidance via scaffolding (Mayer, 2001). An example of the job aid is
a chart that includes each language proficiency level and a quick summary of what students can
do at that level as well as what key features of language they are developing. In addition, the
study found a need for teachers and administrators to have training on language proficiency and
development. While this was not an assumed knowledge influence, the data validated it as a gap
as explained in the findings in chapter 4 and this will be specifically addressed in the
recommendations and implementation plan.
The goal of teacher development should be an increase in teacher knowledge that is
applied to the classroom and in turn increases student achievement for all student subgroups
including Math achievement as well as language development (Yoon, Duncan, Lee, Scarloss &
Shapley, 2007). When planning and executing the training a focus on implementation as opposed
to memorization is central while also allowing participants to make connections between new
knowledge and prior knowledge (Schraw & McCrudden, 2006). As participants gain new
knowledge, training should highlight effective use of the strategy that includes the “how” and
“when” (Schraw & McCrudden, 2006). The recommendation includes a series of training as a
response to the findings and the research indicating that frequent practice spread out over shorter
targeted learning sessions is more effective for learning (Mayer, 2011). In order to support the
development of the factual knowledge of teachers, key features of the training include
opportunities to practice and transfer the skill, worked examples (Mayer, 2011). One key
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component that interview participants unanimously mentioned that is also confirmed by research
is the need for follow up on the training in the form of feedback (Mayer 2011; Shute, 2008).
Feedback should be timely and relate the strategy to improved student achievement (Shute,
2008). As training participants transition into application of the acquired knowledge, a job aid
would be helpful in transferring the skill (Mayer, 2011). This represents the second of two
recommendations which will be discussed in detail in the implementation plan. The job aid will
be introduced as part of the training but will extend into other areas of the organization therefore
the job aid serves as the second recommendation.
Increasing ELL Student Achievement Through Stakeholder Relationship Building
The results and findings of this study indicated that more than 80% of teachers expressed
they have procedural knowledge about building relationships with key stakeholders including
ELL students however, building relationships centered on data with families of students learning
English was identified as a gap. Teachers who spoke the home language of the students reported
strong relationships with students learning English. Ten out of ten Teachers and Administrators
interviewed indicated that while they had amicable relationships with students, there was a desire
for strategies to create relationships that empowered students and families in topics such as
learning and language proficiency. A recommendation rooted in social cognitive theory has been
selected to close this procedural knowledge gap. Denler, Wolters and Benzon (2009) found that
individuals acquire new behaviors through demonstration and modeling. This would suggest that
providing learners with training in culturally responsive practices as well as strategies to
strengthen key stakeholder relationships (students and families) can improve
teacher/administrator knowledge.
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The recommendation then is to provide Math teachers and school administrators with
training that gives strategies and clear steps for implementation on how to create relationships
with students and families that support academic growth. An example is a series of training on
how to invest students and families in why language learning and proficiency is important and
how it impacts a student’s life trajectory. Another example would include procedural strategies
to invest students in goal setting on reclassification, language development, and Math
achievement.
Building relationships can be a nebulous and large task that may impact a participant’s
extraneous load and germane load (Kirshner et al., 2006). When crafting training that teaches the
skills associated with how to build relationships with ELL students and families, the complex
material should be segmented into simpler parts (Kirshner et al., 2006). Building relationships is
a behavior, therefore the training is informed by Social Cognitive Theory (Denler et al., 2009).
Teachers should first get an opportunity to observe the procedural knowledge then rehearse the
modeled behavior before enacting them overtly (Mayer, 2011). As preparation for the desired
procedural behavior, teachers should set productive goals that are challenging, plan for self-
evaluation and learn strategies to manage their time and environment as part of the training
(Denler et al., 2009; Dembo & Eaton, 2000).
Increasing Teacher Self Awareness About Student’s Language Proficiency
The results and findings of this study indicated that teachers need more in-depth
metacognitive knowledge about their self-awareness in using language proficiency coupled with
content knowledge to appropriately differentiate for ELL students. Participants could identify a
few strategies for supporting language development and a few for Math instruction but struggled
to bridge the two to support ELL student learning in the Math classroom. A recommendation
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rooted in information processing theory has been selected to close this metacognitive knowledge
gap. Baker (2006) found that when individuals have the opportunity to both watch a model of the
metacognitive process as well as participate in metacognitive reflection their use of new
knowledge is strengthened. This suggests that providing learners with training that gives them
exposure to metacognitive modeling that incorporates knowledge of the strategies to support
ELLs, knowledge of language development and knowledge of Math content will promote
metacognitive knowledge (Baker, 2006).
The recommendation then is to provide training to teachers that focuses on the
metacognitive process of planning Math instruction that supports both the language needs as well
as the Math content. In order to increase application and transfer of metacognitive knowledge
after the training, a second recommendation stemming from Cognitive Load theory is indicated
in table 21. A job aid that reminds Math teachers of the metacognitive processes to implement
when planning would support self-reflection and assessment (Mayer, 2011; Baker, 2006). An
example of the job aid would include questions that teachers can ask themselves to ensure the
strategy to support ELL students aligns with the rigor called for by the Math content and the
language developmental needs.
Metacognitive knowledge impacts the choices Math teachers make in planning, executing
and reflecting on lessons (Echevarria, 2008). Training should not only focus on seeing the
strategy in action, but also an equal focus on seeing a model of the metacognitive process that
bridges language proficiency with Math content (Baker, 2006). As teachers bridge the gap, the
identification of prior knowledge (what they do and do not know about a task) sets a foundation
for metacognitive learning (Baker, 2006). When modeling metacognitive knowledge, the
training facilitator should include a reflection on the choices made and an assessment on the
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strengths and weaknesses of the choice (Baker, 2006). After seeing the ELL strategies in the
context of the Math content and observing the metacognitive model, teacher participants should
then debrief the thinking process they experienced before they begin practicing the strategy with
opportunities for self-monitoring and self-assessment (Baker, 2006). As teachers and
administrators take the metacognitive skills learned in the training, they will have a job aid that
walks them through implementation of the metacognitive skills in lesson plans and lesson
execution in order to support transfer of the skill (Mayer, 2011). The job aid is the second of two
recommendations and will be discussed in the recommendations and implementation plan
section in detail.
Motivation Recommendations
The table below includes the assumed motivation influences. Table 22 highlights the
validation based on the qualitative and quantitative data of the mixed methods research. Clark
and Estes (2008) propose three facets of motivation that influence performance within an
organization which include active choice, persistence and mental effort. While there are many
motivational influences, the assumed motivation influences for this study are self- efficacy
(Pajares, 206) and attribution theory (Anderman & Anderman, 2009). Self-efficacy reinforces
that individuals are capable of learning what is being taught or are capable of performing a task
(Pajares, 2006) while attribution theory means individuals relate success or failures to effort
(Anderman & Anderman, 2009). As indicated in Table 22, both of the motivation influences
were validated as a gap by the research. The recommendations pertaining to motivational
influences are based on theoretical principles. These recommendations use the New World
Kirkpatrick Model ( 2016) with an emphasis on level 2 of the model that includes the
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knowledge, skills, attitudes, confidence and commitment of Math teachers towards supporting
students who are learning English.
Table 22
Summary of Motivation Influences and Recommendations
Assumed Motivation Influence*

Validated as
a Gap
Yes, High
Probability,
No
(V, HP, N)
Priority
Yes, No
(Y, N)
Principle and
Citation
Context-Specific
Recommendation
Self-Efficacy
Math Teachers need to
believe they are capable of
effectively differentiating
instruction for students who
are ELL.
Y Y
Feedback and
modeling
increases self-
efficacy and
high self-
efficacy can
positively
influence
motivation
(Pajares, 2006).
Provide
instructional
support for Math
teachers that
centers on
reflection,
consistent
feedback and
modeling as
needed.
Attributions
Math Teachers should feel
the achievement of ELLs is
due to the actions of math
teachers, rather than a deficit
in the student themselves.
Y Y
Learning and
motivation are
enhanced when
individuals
attribute success
or failures to
effort rather
than ability.
(Anderman &
Anderman,
2009).
Provide accurate
feedback through
instructional
coaching that
identifies the
skills or
knowledge the
teachers lack,
along with
communication
that skills and
knowledge can be
learned, followed
with teaching of
these skills and
knowledge to the
teachers
(Anderman &
Anderman, 2009)

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Increase Self-Efficacy of Teachers and Administrators
Nine out of ten teachers and administrators reported that they would not rate themselves
proficient in terms of supporting students learning English. This data was reinforced when 90%
of administrators identified that they are not confident in their school’s ability to adequately
support students learning English in mastering Math. In interviews, all administrators said they
would feel more confident if they had more knowledge. Similar findings were reflected in the
administrator responses on the survey.
A recommendation rooted in self-efficacy theory has been selected to close this factual
knowledge gap. Pajares (2006) found that modeling and feedback increases self-efficacy. This
would suggest that providing teachers with modeling of what they need to do and then providing
feedback on their application would increase their self-efficacy. The recommendation is for the
organization to provide instructional support that centers on reflection, consistent feedback and
modeling as needed. This combination of modeling, practice, and frequent targeted feedback
would include multiple opportunities for practice and gradual release as well as opportunities for
teachers to self-monitor their implementation of strategies. This feedback can take place across a
variety of formal and informal activities within the organization such as lesson planning,
instructional coaching, data meetings, goal setting, observations, professional development and
training. The targeted feedback, modeling and reflection will strengthen teacher (and
administrator) self-efficacy.
Pajares (2006) states that high self-efficacy can have a positive impact on motivation.
This suggests that when individuals have confidence about their ability to do something they are
more likely to pursue the goal and increase performance. Beliefs about one’s self-efficacy come
from mastery experiences, vicarious experiences (observing others), social persuasions (reading
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social cues) and physiological reactions (awareness of environment) (Pajares, 2006). Ross (2014)
found that teachers had a low self-efficacy when asked about their impact on positively
impacting the student achievement of ELLs. Teachers in the study experienced reduced self-
efficacy when working with students who are ELLs relative to non-ELLs (Ross, 2014). Teachers
identified high quality professional development and targeted feedback aimed at supporting
students who are ELLs as a strategy for improving their self-efficacy (Ross, 2014). Pajares
(2006) further states that learning and motivation are strengthened when learners have positive
belief about their success. From a theoretical perspective, then, it would appear that increasing
self-efficacy through instructional support for Math teachers that centers on reflection, consistent
feedback and modeling would have a positive impact on ELL student success.
Self-Reflection and Teacher Attribution of ELL Student Success
100% of participants interviewed mentioned the specific ELD teacher as responsible for
supporting students. Out of ten interviews nine participants cited student personality or character
as either a barrier to success or a support. A recommendation rooted in attribute theory has been
selected to close this motivation gap. Anderman & Anderman (2009) found that learning and
motivation are enhanced when individuals attribute success or failures to effort rather than
ability. This would suggest that providing learners with accurate feedback through instructional
coaching that identifies the skills or knowledge the individual lacks, along with communication
that skills and knowledge can be learned, followed with the teaching of these skills and
knowledge would increase their motivation and value. The recommendation is for the
organization to provide Math teachers with strategic instructional coaching with opportunities for
practice, reflection and feedback that identifies the knowledge lacking, but also provides
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strategic support in acquiring the knowledge needed. This combination of feedback, reflection
and support strengthens the reflection and attribution of success.
Anderman and Anderman (2009) state that Attribution theory “examines individuals'
beliefs about why certain events occur and correlates those beliefs to subsequent motivation” or
to “specific things such as the lack of ability, lack of effort, and poor instruction”. This suggests
that contributing success or failures to effort rather than ability can create productive attribution
and achievement orientation (Anderman & Anderman, 2009). Research found that when teachers
analyzed low performance outcomes for ELLs, teachers focused on the student’s label as an ELL
while for other student subgroups teachers attributed student performance to teacher instruction
(Bertrand & Marsh, 2015). Furthermore, in a study by Gutiérres and Orellana (2006), teachers
primarily attributed low ELL achievement to student native language, lack of English acquisition
and teacher perceptions of a student’s home life. Providing teachers with accurate feedback that
identifies the skills or knowledge the teacher lacks, along with communication that skills and
knowledge can be learned coupled with the teaching of these skills and knowledge can increase
teacher motivation as well as self-responsibility (Anderman & Anderman, 2009). From a
theoretical perspective, then, it would appear that increasing teacher self-responsibility and
motivation in the instruction of students who are ELLs would increase performance and
ultimately student achievement.

Organization Recommendations
The table below includes the assumed cultural models and settings. Table 23 highlights
the validation based on the qualitative and quantitative data of the mixed methods research.
While there are many cultural models and settings that impact the organizational performance
this study focused on 4. The assumed cultural models include the need of a vision and strategic
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plan for what constitutes excellent instruction for students who are ELLs as well as an
organizational belief and commitment that students who are ELLs are capable of achieving at
high levels. In addition there two cultural settings which included a need for instructional
leaders with expertise in supporting students who are ELLs as well as strategic and quality
professional development for teachers. As indicated in Table 23, three of the cultural models and
settings were validated as a gap by the research while the other influence was not validated as a
gap. The organizational conditions that contributed to one of influences not being validated will
be discussed briefly in this section and was also highlighted in the findings in Chapter 4. The
recommendations pertaining to motivational influences are based on principles of organizational
leadership (Schein, 2009). These recommendations use the New World Kirkpatrick Model (cite
year) with an emphasis on level 4 of the model that includes the planning, goal setting and vision
of organizational learning and strategizing their models and settings towards supporting students
who are learning English.

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Table 23
Summary of Organization Influences and Recommendations
Assumed
Organization
Influence*

Validated
as a Gap
Priority
Yes, No
(Y, N)
Principle and Citation Context-Specific
Recommendation
Cultural Models
The organization
needs a vision and
strategic plan for
what constitutes
excellent
instruction for
students who are
ELLs.
Y Y Organizational change can
take root and produce
intended results when
leaders focus on the climate
of their organizations
(Schneider, Brief, & Guzzo,
1996)
Create a research based strategic
plan for supporting English
Language Learners that includes
designated ELD, Integrated
ELD, best practices and
stakeholder goals.

Host a series of focus groups
with key stakeholders to discuss
the current experience around
EL Education. Stakeholders
would include students, staff,
families and community
members.
Cultural Models
The organization
needs a culture of
belief and
commitment that
students who are
ELLs are capable
of achieving at
high levels.
N N (Moran & Brightman, 2000)
Change is not about
managing change it is about
managing people and
affecting the PURPOSE,
IDENTITY, and
MASTERY of workers.
Not a priority
Cultural Settings
The organization
needs
instructional
leaders with
expertise in
supporting
students who are
ELLs.
Y Y (Langley et al., 2009) The
five central principles of
improvement: 1. Knowing
why you need to improve 2.
having a way to get
feedback to understand if
improvement is happening.
3. develop a change that you
think will result in
improvement 4. test the
change before any attempts
to implement 5. implement
the change
Create a framework for
instructional equity coaching for
students who are ELLs. This
framework would identify

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Cultural Settings
The organization
needs strategic
and quality
professional
development for
teachers.
Y Y (Senge, 1990) Building an
organization that is adaptive
and generative is an
important aspect of a
learning organization.
(Creative tension principle).
IT IS IMPORTANT TO
Develop leaders as well as
the learning organization.
This leads to CHANGE that
is sustainable.
Using the goals outlined in the
strategic plan create an
organization wide goal and
provide targeted training that is
differentiated for administrators,
teachers and content level.

Increase Organizational Performance Through Strategic Plan, Mission, Vision for Supporting
ELLs
44% of Administrators surveyed agreed that their organization sets achievement goals for
students who are ELLs while only 8% of administrators said their organization meets the goals
they set for ELLs. 25% of administrators said their organization has a vision of what excellent
instruction looks like for ELLs. That number dropped when only 6% of administrators said that
their organization addresses a vision of what the Math classroom should look like for ELLs. The
lack of a mission, vision and unified set of actions contributes to the knowledge and motivation
gap in relation to the realization of the organizational performance goal.
A recommendation rooted in the study of the New World Kirkpatrick Model has been
selected to close this organizational gap. Clark and Estes (2008) indicate that organizational
performance increases when individuals communicate constantly around a shared plan including
shared processes. This suggests that the organization should provide teachers with a strategic
plan that is specific to the instruction of students who are ELLs . The recommendation is for the
organization to develop a strategic plan that includes a mission, vision, goal and set of behaviors
that is uniform across the organization. For example, the organization may include a list and
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description of best practices of strategies for Math teachers (and all teachers to use) to
differentiate instruction for ELLs.
Clark and Estes (2008) state that when policies and procedures are aligned and
communicated from the top with all stakeholders, organizational performance increases. Waters,
Marzano and McNulty (2003) found that focusing the work on a school’s vision correlated with
improved outcome in student achievement and performance as measured by state standardized
tests. Kluger and DeNisi (1996) also indicate that learning, motivation and performance will be
enhanced if participants have clear, current and challenging goals. This mirrors the position of
Schein (2004) who also found that organizational effectiveness increases when leaders help the
organization set strategic and measurable goals that align with the vision, mission and ultimately
behaviors of the organization. Nine out of ten teachers and administrators interviewed identified
that there was a disconnect between the organization’s beliefs and actions. Given this
organizational gap, it appears that the literature would support the necessity for a strategic plan
that includes a mission, vision and set of behaviors specific to ELL instruction.
Increase Equitable Outcomes and Belief that ELLs can Achieve at High Levels
100% of interview participants and 89% of survey participants indicated that the
organization has a belief that “All students can learn.” While this belief does not specifically
address ELL achievement and participants mentioned gaps in the organization’s action
supporting ELLs, there is evidence that this is not a high priority gap. This finding is not a high
priority finding therefore there is not a recommendation to the organization for this finding.
Teachers and administrators did not identify a gap in the organization’s belief that ELLs can
achieve while there was no specificity that focused on ELL achievement, teachers unanimously
stated “All children can learn.” The need for specificity pertaining to ELLs is mentioned in the
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recommendation for the first assumed organizational influence accounts for the need for
specificity in the strategic plan.
Increase Teacher Knowledge and Motivation through Competent Role Models and Coaching

33% of Administrators agreed with the phrase “I frequently give instructional feedback to
Math teachers pertaining to the needs of students learning English.” 25% of Administrators said that
a majority of their coaching sessions address the language proficiency of students in Math. 16% of
Administrators said they gather weekly data on how ELL students are performing Math. Five out of
seven teachers reported no feedback specifically targeting ELLs in Math while the two teachers who
did report frequent feedback targeting EL support were both coached by the EL specialist at the
school. A recommendation rooted in sociocultural learning theory has been selected to close this
organizational gap. Sociocultural theory (Scott & Pallinscar, 2006) state that learners acquire
new knowledge through interactions with others. This suggests that Math teachers need feedback
and reflection focusing on their support of ELLs from their coaches. In order to accomplish this,
Administrators who serve as coaches also need support to develop their self-efficacy and
knowledge in relation to supporting ELLs. The recommendation is for the organization to
develop a framework for instructional coaching that focuses on equity for ELLs. For example,
one aspect of the framework may be a list of reflection questions to use to give feedback and
reflect on lesson planning or lesson execution.
Mayer (2011) states that learners increase their knowledge and motivation when they
engage in reflection and receive feedback from competent role models. In the case of Math
teachers, that increased learning ultimately impacts student outcomes. This mirrors the position
that Pincus (2006) took when they indicated that effective communication and support from a
supervisor correlated with job satisfaction and performance. Kluger and DeNisi (1996) also
suggest that feedback that is timely and focused on the task or goal enhances learning,
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motivation and ultimately performance of participants. As such, it appears that the literature
would support the necessity for the organization to create a framework for instructional coaching
around educational equity for ELLs that empowers both administrators and Math teachers to
increase their knowledge and motivation.
Increase Teacher Participation in Formal and Informal Organizational Development
Opportunities
84.21% of Math teachers who took the survey stated that they wanted more PD about
how to specifically support ELLs. 26% of teachers felt like the PD they have attended has made
a positive impact on their classrooms on their classroom which means that 74% of teachers felt it
did not positively impact their classroom. A recommendation rooted in organizational learning
theory is suggested. Teachers need practice, guidance and feedback in order to make meaningful
connections to new knowledge (Mayer, 2011). This suggests that organizations need to provide
quality professional development to Math teachers that positively impacts their instruction. The
recommendation is for the organization to provide targeted training that is differentiated for
administrators, teachers and includes information that is specific to the content and grade level of
the teachers. For example, the organization may create a series of PDs that support
administrators in understanding language supports or a PD that teaches Math teachers how to
increase student talk about their Mathematical thinking.
Knowledge and motivation are increased through timely feedback, guided support and a
clear focus on outcomes (Mayer, 2011). This mirrors the position of Pajares (2006) in their
indication that new learning is increased through reflection and guidance that highlights how and
when to apply the newly acquired skills. Furthermore, Learning organizations develop both the
leaders and those whom the leaders serve (Schein, 2004). As such, it appears that the literature
would support the necessity for the organization to provide professional development that
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supports administrators and (Math) teachers with the knowledge needed to support student
learning English and progress towards the organizational performance goal.
Elements of a Successful PD Experience Supporting ELLs. There were seven teachers
interviewed who had been at the specific school site for more than one year. When asked about
professional development that targeted EL Supports all teachers said there wasn’t enough and
that up until the prior year they hadn’t attended any. However, all seven mentioned a series of
PD on sentence frames and increasing students talk that was planned and facilitated by the EL
Specialist. All seven teachers stated that this training increased their knowledge about how to
support ELLs and for five participants also increased their self-efficacy. Here we will discuss
what teachers identified as helpful about this PD as potential recommendations for consistent and
large-scale PD for the organization at large.
Teachers mentioned that a lot of their credential courses and master’s courses focused on
theory or pedagogy, but did not leave them with application as to how to use it in the classroom.
Teachers noted that the specific focus on one strategy allowed them to gain depth of knowledge.
Teachers also described a positive impact from seeing the strategies modeled in their classes,
with their content and their kids. Teachers said, “the facilitator would show us a video of her
doing it in one of our classrooms” or “the facilitator would pre teach a teacher to do it and then
then they would show it off.” Teachers responded to these facilitation moves by saying “that was
great because usually I see strategies with kinder students and I’m like how will this look in fifth
grade or eighth grade.” In the PD sessions, teachers would get a chance to practice both the
strategy as well as the planning that went along with the strategy. Each week teachers would
receive feedback in alignment with the strategy. Five out of five teachers reported receiving
feedback as a result of this initiative and for three of the teachers this was the only time they
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received feedback specific to their ELL Support. Administrators gathered data both as a reason
for why the initiative mattered also to provide reflection on school wide progress. This is an
example of bridging the knowledge gap between Math and language development that is
mentioned in the knowledge findings for research question one. Administrators participated in
the training alongside the teachers. This also increased the knowledge and bridged the
knowledge gap that the administrators had while also teaching them how to use the knowledge in
coaching. Teacher self -efficacy increased and so did the perception of student self-efficacy.
Integrated Implementation and Evaluation Plan
Implementation and Evaluation Framework
The following implementation and evaluation plan is created in alignment with the New
World Kirkpatrick Model (2016) which creates a model for evaluating training programs and
implementation plans in order to maximize the value for the organization. The Model centers on
creating effective training programs that ultimately lead to improved job performance and
positively contributes to organizational results. The original Kirkpatrick model created in the
1950’s by Dr. Don Kirkpatrick included four levels: reaction, learning, behavior and results. In
2010 the model became the New World Kirkpatrick Model addressing the levels in reverse to
create more positive impact when organizations plan with the results in mind first. By using the
levels in reverse and starting with level 4 organizations consider the behaviors (3), learning
required (2) and desired reactions (1) in order to positively impact the desired results. For the
purpose of this study, the organizational performance goal and the teacher knowledge and
motivation needed in relation to accomplishing it will serve as the basis for the suggested
implementation plan for effective training.

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Organizational Purpose, Need and Expectations
The organization had an overall score of 64% meeting or exceeding the standard on the
state Math assessments in 2019. 11 % of ELLs met or exceeded the standard while 72 % of
English proficient students met or exceeded the standards. This represents a gap of 61%.
In previous years a similar trend existed while there has been growth in schools. For
example, in 2019, Éxito Academy increased ELL Math proficiency from 13% to 32% as
measured by the CA Math assessment. In 2018, the largest grade level gap was 56% while in
2019 the largest gap was 41% (in only one classroom). In 11 classrooms, the gap between ELLs
and fluent English proficient students was cut in half and overall proficiency increased by 10-
13%. The organization’s data aligns with national trends as a similar gap persists across the state
of CA as well as Nationally.
The current performance impacts the organization’s ability to live out their mission. They
exist to prepare historically underserved communities for college and to ‘prove the possible’
through excellent student results. The Math data shows that students who are learning English
are not getting excellent results on the state Math assessment. The gap in proficiency shows a
lack of mastery of math content needed to be college ready.
The Organizational Performance Goal is that by 2023, 85% of English Language
Learners will meet or exceed the standard as measured by the CA state math assessments. In
order to increase student achievement on the state math exam, the performance gap between
ELL, EO and RFEP students will decrease from the 56% gap that exists in the 2017-2018 school
year to 15% gap. This goal was established by the Instructional Leadership Team at Éxito
Academy after reviewing the results from the 2017-2018 state math exams. The Stakeholder goal
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for teachers mirrors the Organizational Performance Goal: By 2023, 85% of students who are
ELLs will meet or exceed the standard as measured by the CA State Math assessment.
The desired results for the recommendations and implementation plan are to increase
teacher knowledge and motivation in relation to supporting ELLs which would support progress
towards realization of the Teacher performance goal. The recommendation plan also aims to
create effective cultural models and settings that also support positive progress towards
achieving both the teacher performance goals as well as the organizational performance goal.
Level 4: Results and Leading Indicators
Table 24 shows the proposed Level 4: Results and Leading Indicators in the form of
outcomes, metrics, and methods for both external and internal outcomes for Éxito Academy. If
the internal outcomes are met as expected as a result of the training and organizational support
for teachers and administrators, then there should also be a positive correlation with the
realization of the external outcomes.

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Table 24
Outcomes, Metrics, and Methods for External and Internal Outcomes

Outcome Metric(s) Method(s)
External Outcomes
Increased Performance by
ELL Subgroup as measured by
the State Math Assessment
The number or percent of students who
are ELLs that are meeting or exceeding
the standard.
Solicit data and comparison of
student subgroup data
Improved teacher knowledge
and motivation pertaining to
supporting ELLs in Math
The rating that teachers and
administrators give about the
development of their knowledge and
motivation
Semester check ins with a coach or
administrative team member
specifically about the development
around supporting ELLs.
Increased Student Participation
in Math Classes and
Development of Academic
English
The amount of students engaging in
reading, writing, listening or speaking
in Math class.
Track frequency of participation and
opportunities for student engagement
with listening, reading, writing or
speaking as part of Math class.
Increased satisfaction and
involvement of families and
key stakeholders in the
education of students who are
ELLs
The rating that families and community
members give about the organization’s
mission, vision and plan to support
ELLs.
Quarterly check ins with families and
community members pertaining to
the support and academic program
for ELLs.
Increase in Student
Development of English.
The percent of students reclassified
each year or the percent of students
making progress as measured by the
ELPAC Language Assessment
Track progress and supports
pertaining to student progress on the
ELPAC
Internal Outcomes
Increased Use of Strategies to
Support ELLs
The frequency of use of strategies to
support ELLs that align to the language
needs as well as the mathematical
content
Collect and Aggregate data on
teacher use of strategies to support
ELLs.
Increased Performance of ELL
subgroup in formative and
summative assessments
% of student proficiency or increasing
in mastery on all formative and
summative assessments administered
as part of classroom instruction.
Collect and Aggregate data on a
weekly and daily basis
Increased quality of coaching,
feedback and training to
support teacher knowledge and
motivation
Positive/Negative feedback from
teachers and administrators
Set aside time for regular 1:1
conversations, administer input
surveys, compare survey and
feedback results
Increased opportunities for
collaboration and reflection
pertaining to supporting ELLs
in Math
The number of opportunities for
reflection and collaboration to support
and the positive or negative impact on
teacher and student performance.
Set aside time for regular 1:1
conversations, administer input
surveys, compare survey and
feedback results
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Level 3: Behavior
Critical Behaviors
The stakeholders of focus for this study are Math teachers who serve students learning
English. The first critical behavior is that Math teachers need to implement instructional
strategies that support student acquisition of Math concepts and language development while
also being developmentally appropriate. The implementation of strategies in the classroom
implies behaviors pertaining to lesson planning and strategy choice. The second critical behavior
is that teachers must engage in reflection, feedback cycles and coaching with administrators that
facilitates the development of teacher knowledge and motivation. The third critical behavior is
that teachers and administrators can identify the specific language levels and needs of students in
their classroom in order to select appropriate strategies. The critical behaviors are outcomes
based on the findings from the data.
Training Should Include Developmentally Appropriate Strategies that Align to the
Math Content and Language Demands. In the qualitative interviews, four teachers mentioned
that they often do not see EL strategies applied in a way that is both age appropriate, content
appropriate and addressing the emerging language needs of their students who are ELLs. In
2018, 70.2% of California’s total ELL enrollment was in elementary grades K-5 with only 29.8%
enrolled in grades 6-12 (CDE, 2018). Much of the training and resources pertaining to the
instruction of English language learners pertains to students in younger grades most likely due to
the fact that students in grade K-5 make up 70.2% of the total EL enrollment in California.
Teachers interviewed identified that they are often given a strategy that doesn’t align to their
context and do not receive guidance on how to adapt it to their classroom. In the survey given to
35 teachers only 21.05% of teachers strongly or somewhat agreed with the statement “The PD
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specifically talks about how to support students learning English in the Math classroom.” This
supports that teachers desire a connection specifically to the Math as well as the context of the
students in their classroom. In addition, 26% of teachers identified that the training offered made
a positive impact on the students learning English in my classroom. While 89% of teachers
surveyed expressed that they can identify strategies to support ELLs only 47% identified that
they can match a Math strategy for differentiation with a student’s language proficiency. The
needs of LTEL students is different from the needs of younger EL students due to the language
demands of the content, complexity of Math content as well as their developmental age. When
acquiring the factual knowledge of strategies to differentiate for ELLs, the teachers expressed a
desire to see the strategies in their context including age appropriate and connected to their
specific content.
Teachers have Transferable Skills, but Need Explicit Knowledge to Make the
Connection to Language Supports. All teachers interviewed mentioned the use of small groups
as a strategy. While sub finding one revealed a lack of connection to explicit language, small
groups could be explicitly used to support ELLs. Teachers can transfer their knowledge of and
experience with small groups to better support specific language needs. Connecting new
knowledge with prior knowledge supports meaningful learning and allows learners to think in
strategic ways about new learning (Schraw & McCrudden, 2006).
All teachers mentioned vocabulary instruction. However, the teachers’ ability to
recognize content specific vocabulary is a transferable skill that can be used to explicitly support
the language development of students who are learning English. Five out of seven teachers
discussed the use of visuals to support ELL and teacher knowledge of visuals can be transferred
to explicitly connect the language students need to master in order to demonstrate the Math
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skills. Two other transferable strategies that were mentioned by a majority of the teachers were
word banks and opportunities to talk. Teachers have factual knowledge of some strategies that
could be used to specifically target the needs of ELLs even if they do not currently use them to
do so in their classrooms.
Teachers Need Knowledge to Distinguish Between Language Needs and the Needs
Stated in a Student’s IEP. Similar to how teachers used factual knowledge about language
development to identify supports for ELL students, there was a gap in knowledge for special
education teachers. Special education teachers struggled to identify if student need or
performance was due to the student’s disability as written in their Individualized Education Plan
(IEP) or language needs. Two Special Education Math teachers interviewed both mentioned this
misconception and a need for factual knowledge as a solution. In addition to the perspectives
expressed by the Special Education teachers; three teachers also mentioned a part of
conversations where a team of educators were trying to decide if a student needed language
support or if it was related to their disability. A need emerged for factual knowledge including
facts and definitions that can support educators in distinguishing between language development
and the different abilities students have written in their IEPs. All teachers need factual
knowledge about the specifics of language development and there is an extra need to distinguish
between the facts of language development and the facts and manifestations of a student’s
disability.

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Table 25
Critical Behaviors, Metrics, Methods, and Timing for Evaluation
Critical Behavior Metric(s) Method(s) Timing
1.implement
instructional
strategies that
support student
acquisition of
Math concepts
and language
development.
The number of
strategies
implemented in Math
classrooms to support
students learning
English.
School Administrators
shall track the strategies
used, frequency and
impact on student
outcomes
Collect data on a
weekly basis
2.engage in
reflection,
feedback cycles
and coaching with
administrators that
facilitates the
development of
teacher
knowledge and
motivation.
The number of
opportunities for
reflection, feedback
and collaboration that
teachers and
administrators have on
a weekly basis.
School administrators
shall track the reflection,
feedback and coaching
opportunities that
support teacher
knowledge and
motivation pertaining to
supporting students
learning English
Teachers will
receive feedback at
least once a week
that specifically
addresses the
support of ELLs
through one of the
following: lesson
plan feedback, data
meeting feedback,
lesson observation
feedback, coaching
feedback
conversation or
feedback as part of a
training.
3.identify the
specific language
levels and needs
of students in their
classroom in order
to select
appropriate
strategies.
The number of
strategies or
instructional choices
that address individual
student language
needs.
School Administrators
shall track the number of
instructional choices that
teachers make pertaining
to language needs.
Coaches and
teachers shall
monitor the use of
strategies to support
ELLs.

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Required Drivers
Teachers require the support of administrators and instructional leaders as well as
colleagues in acquiring key knowledge and motivational skills that contribute to support for
ELLs in the Math classroom. Support may come in the form of a job aid to reinforce newly
acquired knowledge. Rewards and public recognition should be established for teachers who use
the newly acquired knowledge and in turn see a positive impact on student achievement. Table
26 shows the recommended drivers to support critical behaviors of Math teachers.

Table 26
Required Drivers to Support Critical Behaviors
Method(s) Timing
Critical Behaviors Supported
1, 2, 3 Etc.
Reinforcing
Job Aid including steps to
implement strategies to
support ELLs
Weekly or Daily (as needed) 1,2,3
Job Aid including steps to take
for lesson planning.
Weekly or Daily (as needed) 1,2,3
Weekly Coaching Meetings
that include opportunities for
feedback and reflection on
strategies to support ELLs
Weekly 1,2,3
Content Specific Team
Meeting to provide specific
support
Weekly 1,2,3
Encouraging
Feedback from an instructional
leader and instructional
observations
Weekly 1,2,3
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Collaboration and Peer
Modeling as part of trainings
Weekly 1,2,3
Rewarding
Public Acknowledgement of
teachers implementing
strategies and seeing a positive
impact on student achievement
Weekly 1,2,3
Monitoring
Instructional Coaches and
Administrators gather data on
use of strategies
Weekly 1,2,3
Instructional Coaches and
Administrators gather data on
student achievement and
language development
Weekly 1,2,3

Organizational Support. Resource and time will need to be allocated in order to
implement the organizational change plan. School leadership, including instructional coaches,
will need to ensure time is built into weekly coaching, observations and data meetings to ensure
there is a focus on developing teacher knowledge and motivation in relation to supporting ELLs.
In addition, administrators need support in acquiring the knowledge and skills in order to better
support teachers. Additional resources like content specific training may be needed to provide
specific support in the acquisition of knowledge and motivation. Furthermore, the organization
will need to support teacher knowledge and motivation by developing a culture, mission, vision
and strategic plan that supports teachers and administrators in the development of knowledge and
motivation necessary to support ELLs. The organizational support is based on the findings that
emerged from the data presented in Chapter 4 that supports a need for collaboration and
instructional support (see below).
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Relationship Building and Collaboration Amongst Staff Supports both Teacher and
Student Achievement. All participants interviewed mentioned the need for procedural
knowledge about the steps they can take to build collaborative relationships that center on
practices supporting ELLs. Sociocultural Theory states that learners learn in relation and
collaboration with others (Scott & Palinscar, 2006). The sub findings below support the finding
that teachers need procedural knowledge about building a culture of collaboration amongst staff
members. Collaboration involves a certain set of procedures and behaviors within the school
culture and system. Systems for collaboration support both the knowledge development of the
staff in relation to the performance goal as well as the learning of students. This finding
specifically focuses on how teachers see the procedures of collaboration while research question
2 addresses the larger organization. Following the presentation of the data for each of the sub
findings the finding will be discussed in relation to the sub findings and procedural knowledge
influence.
The Procedures of Collaboration Support Teacher Knowledge. All seven teachers
were asked what could be done to support them in their acquisition of new knowledge. While
teachers mentioned a variety of ideas that will be further discussed in the organizational
literature, all seven referred to building the skill and procedure of collaboration amongst teachers
which supports Sociocultural Theory that having learners occasionally perform difficult or new
tasks in partnership with others supports the acquisition of new knowledge ( Scoot & Palincsar,
2006). T3 said “We spend time talking about Math, but it would be nice to work together on
lesson planning and brainstorm on differentiation for ELLs like actually to go in and watch how
others are supporting ELLs.” The systems that T3 mentioned will be addressed in the
organizational culture and settings, but T3 mentions a need for shared procedural knowledge on
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how to collaborate to support ELLs. Teachers mentioned that their knowledge could be increased
from collaboration with the ELD teacher to be able to “sit and co plan with the ELD teacher like
hear what they are working on [in ELD] so I can support it in the Math classroom or even just
bounce ideas off of each other” and overall advocated for “more connection”. The ELD teacher
mentioned that she would like to invite teachers to come in and observe their students during the
teacher’s prep period so they can see the language students are working on in hopes that “Math
teachers and students can make connections to it outside of ELD in the Math classroom.” This
shows that collaboration allows teachers to acquire new knowledge through a specific set of
behaviors and builds collective responsibility which will be highlighted as a gap in the
motivational attribute theory below. Teachers mentioned a desire to lesson plan together, share
weekly data on ELL progress and “look at the posters and listen to how other teachers support
ELLs.” Teachers mentioned a variety of ways they would like to collaborate with each other, but
a common procedure for collaboration is missing.
Organizations Must Have a Clear and Explicit Belief in the Abilities of ELLs.
Interview data revealed that teachers and administrators did not recognize shared beliefs that the
organization held related to supporting ELLs. Interview participants did recognize that the
organization has a belief that “All students can learn'' and focuses on the achievement of low
income students. However, the needs of ELLs are diverse (Echevarria, 2008) and a lack of
beliefs about ELLs creates an invisibility to the organization’s support of ELLs. This element of
organizational culture interacts with teacher knowledge because we see that teachers could not
recognize the individual language needs of students and teachers also chose strategies that did
not address language. There were similar elements of invisibility as teachers discussed their
classroom instruction. A lack of a clear set of beliefs about what the organization believes to be
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true creates a lack of clarity on how the daily action of the organization pertaining to ELLs is
carried out. Organizational change can take root and produce desired results when leaders focus
on the climate of their organizations (Schneider, Brief & Guzzo, 1996)
Level 2: Learning
Learning Goals
Following completion of the recommended solutions, specifically the content specific
training and instructional coaching, Math teachers will be able to:

1. Identify key strategies to support ELLs that are developmentally
appropriate (F)
2. Identify Strategies that support both the Language demands and Math
skills of the Math Standards. (F)
3. Identify the specific language development levels as well as common
features of that level for each of their students identified as ELL.(F)
4. Create relationships with family members and students that are
empowering and specific to the needs of ELLs. (P)
5. Plan and monitor their use of instructional strategies to determine progress
towards performance goals (P, M)
6. Recognize and participate in structures for collaboration that support
knowledge acquisition (P)
7. Correctly use self-awareness developed through feedback and reflection
to choose an appropriate strategy to support ELLs in both lesson planning
and lesson execution (M)
8. Identify goals pertaining to the instruction of ELLs and value attaining
those goals (Value Theory)
9. Indicate confidence (developed through feedback, reflection, coaching and
training) in supporting students who are ELLs
10. Identify the organization’s mission, vision, values and strategic plan to
support ELLs

Description of the Training Program

The learning goals listed in the previous section will be achieved with a training program
that explores the knowledge and motivation needed to support ELLs in Math. The program will
consist of training, coaching, feedback, data analysis and collaboration. The primary learners,
Math teachers, will study a variety of instructional strategies to implement in the Math classroom
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to support students learning English. While the primary learners are Math teachers, School
Administrators will also participate in a series of targeted training sessions in order to prepare
them to support teachers. The program will consist of weekly lesson plan feedback, weekly
observation and instructional coaching sessions, weekly data meetings and collaborative
meetings with peers. In addition to these elements the coaching will consist of 11 sessions. Two
sessions will focus on goal setting and an overview of data and components of ELD. Following
those two sessions there will be one strategic training a month for the whole school staff. The
monthly training session will include a focus on lesson planning as well as execution of the
strategy in the classroom. Each session will focus on one strategy that is developmentally
appropriate and will include modeling of both execution and the metacognitive processes of
lesson planning, feedback, practice lesson planning, execution and teacher reflection.
Evaluation of the Components of Learning
Acquisition and demonstration of declarative knowledge is a prerequisite to applying
knowledge and demonstrating procedural and metacognitive knowledge. Therefore, it is crucial
to evaluate the procedural, metacognitive and factual knowledge being taught in order to gauge
teacher ability to apply new knowledge to improve teacher practice. In addition to the
importance of knowledge, it is foundational that teachers and participants value the training and
feel a connection to the purpose and goals in relation to the training. However, teachers must also
experience confidence and increased self-efficacy so that they can apply the knowledge acquired
to lesson planning and instruction. As such, Table 27 exhibits the evaluation method(s) and
timing for these components of learning.

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Table 27
Evaluation of the Components of Learning for the Program
Method(s) or Activity(ies) Timing
Declarative Knowledge “I know it.”
Knowledge checks using observation of
strategies and models of the strategies (call out
key features)
In the asynchronous portions of the
course during and after video
demonstrations or live modeling.

Knowledge checks using teacher practice of
implementing the strategies
In the asynchronous portions of the
course during and after video
demonstrations or live modeling.

Knowledge checks to call out what language
students need and use in a lesson depending on
the Math content and the language demands
During the workshop and at the end as
part of a knowledge check
Procedural Skills “I can do it right now.”
Checklist of strategies and how to implement
them
During and After the workshops.

Checklist for lesson planning During and After the workshops.

Demonstration (using job aids) of planning the
strategy
During the workshop.
Demonstration of how to execute the strategies
from lesson plans
During the workshop.
Individual Implementation of Strategies to
support ELLs in Math in lesson plans and daily
instruction.
During and After the workshops.
Quality of feedback form instructional coaches
on lesson plans and observations.
During and After the workshops.

Attitude “I believe this is worthwhile.”
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Facilitator and Administrator/Instructional Coach
feedback and observation on the statements and
actions demonstrating that they see the benefit of
the strategies they are being asked to do.
Before, during and after the training.
Discussions of the value and purpose of what
they are being asked to do.
Before, during and after the training.
Reflection and goal setting centering on
supporting ELLs and ELL achievement in Math
Before, during and after the training.
Participation in reflection on strengths and
weaknesses in relation to their use of the
knowledge presented.
During and After the course.

Confidence “I think I can do it on the job.”
Survey items using scaled items After the training.
Discussions following practice and feedback Before, during and after the training.
1:1 reflection with an administrator about their
confidence in applying new learning.
Before, during and after the training.
Commitment “I will do it on the job.”
Creation of an individual goal Before, during and after the training.
Commitment to implement strategies from the
training as part of a weekly observation
During and After the training.
Discussions following practice and feedback Before, during and after the training.

Level 1: Reaction
Acquisition of new knowledge is impacted, either positively or negatively, by a
participant’s engagement, relevance and satisfaction with the training. Engagement refers to the
active involvement of participants in the learning or training experience that ultimately results
relates to their level of attainment of knowledge. Relevance refers to the extent that participants
will be able to apply new learning from the training on the job. While the facilitation of the
training is important, if participants do not see the relevance then the value of the training is
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lowered. Evaluation of customer satisfaction occurs during and after a training and is purposeful
as a formative measure to identify and remove any barriers to learning during the program.
Table 28 shows the methods and timing for evaluation of teacher engagement, relevance and
satisfaction in relation to the training and acquisition of new knowledge.

Table 28

Components to Measure Reactions to the Program
Method(s) or Tool(s) Timing
Engagement
Asks meaningful questions During the session.
Completion of practice scenarios During the session.
Participation in reflection, group talk and
scenarios
During the session.
Participation on goal setting for the session Before and At Start of Session.
Exit Ticket to check for understanding of the
material that is the focus of the training
End of Session.
Follow Up Observations to view the
implementation of the strategies in the week
after the training.
After the session.
Relevance
Pulse check via survey or discussion During the session.
Anonymous Survey After the session.
1:1 Check in with an administrator or
instructional coach as follow up within the next
week
After the session.
Customer Satisfaction
Dedicated observer who gives feedback to the
facilitator on participant body language and use
of new knowledge
During the session.
Anonymous Survey After the session.
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Evaluation Tools
Immediately Following the Program Implementation
Surveys will be administered immediately following the training. The surveys will be
administered digitally and will contain questions about level 1 reactions to the training. In
addition,, the surveys will also contain questions about the relation to the participant’s job and
the perceived newly acquired knowledge from the training. The surveys will be used to plan
future training and inform the coaching conversations and feedback that happen weekly between
school administrators and teachers. Figure 2 shows a sample of the data acquired from the
survey.
Figure 2
Evaluation Immediately Following Training or Professional Development (PD)

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What could be done in the future to make similar PDs more impactful for you?
More sample videos
I would like to see videos or lesson samples from my current unit not just my grade level.
Examples of one content at different proficiency levels so we can discuss the nuances.
What questions do you have? What follow up or support do you need if any?
I want to know what to do if there are outliers and the frame is too easy or too hard for 1-2 students.
I'd like a planning session with my coach to review how I will use this
How do I know if a student is emergent or bridging?
What is your action step based on today's PD?
I will use a sentence frame that aligns to the lesson's objective each day.
Deconstruct my Math standards with language in mind.
Use one turn and talk with sentence frames during my modeling time to hear student misconceptions.

In addition to surveys, rubrics will be created for each strategy presented as part of the
nine training sessions. In addition to the strategy specific rubrics there will be another rubric that
is universal for lesson planning and lesson execution. The rubrics will be referenced in coaching
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sessions, content team meetings, data meetings and other collaborative structures. These rubrics
will be introduced at the training sessions so that Math teachers and Administrators build shared
knowledge around the criteria and end goals.
The rubrics will also be used to increase engagement and motivation as teachers can
select specific intentions or areas of focus on the rubrics for training sessions, coaching or
feedback. These rubrics primarily address Level 2 behaviors. The rubrics are used before, during,
immediately after and delayed after the training.
Figure 3 shows the rubric that can be used before to provide opportunities for self -
reflection assessment. During the training it can provide a focus for the teacher’s work. It will
also be used as an observation tool by Administrators that is then referenced in the weekly
instructional coaching sessions. The rubrics can be modified to address specific nuances of the
training.

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Figure 3

Rubrics for Coaching Around ELD and Language Supports

Name: _____________ Date: ____________________ Subject: __________________
Administrator Name: _________________
Teacher Students Environment/Materials
Time
In:

Time
Out:
Open the Lesson
❏ State the Content
Objective
❏ State the Language
focus/objective
❏ Bring it to life through
background knowledge
Model and Practice
❏ T explicitly states the
vocabulary words as
well as the grammatical
forms and language
functions for the lesson
❏ T adjusts the
pace/complexity of
language to meet
student proficiency
❏ T practices and models
the above

Practice the Language
❏ The task or activity
include opportunities for
language (reading,
writing, listening and
speaking)
❏ T monitors student
practice
❏ T gives feedback on
language objective and
content objective
Close the Lesson
❏ Reviews the objective,
criteria for success,
connections to life
❏ T stamps how the
language is ‘portable’ to
other situations
Precursor Conditions
❏ Engaged
❏ Actively Listening
❏ Materials ready
❏ Participation
Language Practice (note the
opportunities that apply)
❏ Writing:____________
❏ Reading:___________
❏ Listening: __________
❏ Speaking: __________
❏ Whole Group________
❏ Small Group:________
❏ Partners: __________
❏ Individual:__________
Behaviors of Language Use:
❏ Responds in complete
sentences
❏ Successfully practices
language stated in objective
❏ Language use stretches
beyond current ability
❏ Flexibility of language
❏ Self-assess language and
content mastery

❏ Objective is posted
along with target
language
❏ Age appropriate
visuals
❏ Connection to first
language
❏ Resources for
topic specific
vocabulary
❏ Resources for
language patterns
❏ Co-created
resources
❏ Students can use
resources for
learning and
practice

Resources for Four
Domains:
❏ Reading
❏ Writing
❏ Listening
❏ Speaking
Com
ment
s

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Focus Student Content Alignment Analysis
Student Name

Content
Standard/Objective

ELD Level

ELD Standard/
Language Objective

Oral Language
Notes: Record
student
speaking or
listening
What language is used
to demonstrate
mastery of the Math
Content?
*Craft an exemplar
response*

Written
Language
Notes: Record
student writing
or reading

What language can
students already do?

What can they
do? Where do
they need
support?

What language
requires support?

Data Check:
Fill in the
student’s
latest mastery
score from
this lesson or
the most
recent lesson.

Where are there
opportunities for this
in the lesson?

For Level 1, during the in-person training or coaching sessions, the facilitator will
conduct periodic pulse checks where participants are polled to assess the relevance to their work,
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delivery, organization, understanding and needs. There will also be opportunities for more
formal Level 1 checks at the end of each training in order to provide valuable information to the
facilitator to support new learning from teachers.

Delayed for a Period After the Program Implementation
Administrators will gather weekly data on implementation of knowledge from the
training material and its impact on student achievement. They will gather data that is aligned
with the rubrics. This will allow aligned data to be collected for the entire school and the
organization can make conclusions on positive and negative trends. The rubrics and spreadsheets
will also include categories for student achievement data so that ultimately teacher practice is
linked to student support. Administrators will share this data with staff members once a month
and the administrators will review the information weekly in their own meeting. Administrators
may also gather video or artifacts like lesson plans that reinforce desired behaviors and serve as
examples for other teachers.
Figure 4 shows a sample of the administrator facing rubric that they may use to plan and
evaluate teacher progress. The rubric mentions a variety of strategies, but organizations can
focus on the strategies of focus during the training. The rubric also includes management items
for classroom culture and procedures as well as rigor which focus on the instructional use.

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Figure 4
Sample Rubric for Administrators and Teachers Following or Delayed After the PD

Figure 3 highlights one of the rubrics that focuses on one specific strategy developed as
part of the training program. This can be used in classroom observations and may also be used by
teachers to reflect on progress and areas of growth. These rubrics will be given at the time of
training so participants know what the vision and goal is for the use of the strategy.
Data Analysis and Reporting
The Level 4 goal of improving student performance through increased teacher knowledge,
motivation and organizational culture is measured by student performance on the State
Standardized Math assessments because that is a common measure that can be used to measure
how students use language to demonstrate their Math knowledge. Each week, teachers and
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administrators will measure recent formative and summative internal assessments against the prior
year’s data on the state assessment as well as the benchmark of the stakeholder performance goal.
Connection to level 2 and 3 behaviors will be ultimately linked to the impact (positive or negative)
on Level 4 goals. The Weekly dashboard will be stored in the same spreadsheet as the weekly data
collected from the rubrics. The dashboard will compare overall performance to subgroup
performance. The dashboard images below is an example of the data collected, monitored and
shared as part of the accountability tool. It is important to note that the dashboard accounts for the
specific performance levels based on language development levels.
Figure 5 shows a sample of the weekly data dashboard for one class. It compares the weekly
data to the yearlong data and can be used to measure progress towards the Organizational
Performance goal and stakeholder performance goals.
Figure 5
Data Dashboard to Measure Progress Towards Performance Goal

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Summary
The New World Kirkpatrick Model served as the basis to plan, implement and evaluate
the recommendations for the organization in order to optimize achieving the stakeholder goal
and the organizational goal. The advantage of using the New World Kirkpatrick Model is that the
focus on data driven decisions ensures that organizations are consistently measuring progress
against the desired level 4 goals and are also ensuring that the level 1,2,3 components support
progress towards the performance goal. Data analysis will include asking if the desired behaviors
meet expectations. If it does, then analyze why it was successful or how it can be multiplied. If it
does not meet expectations, then an analysis about why it doesn't meet expectations and what can
be done differently will ultimately allow the organization to ensure they progress towards the
organizational performance goals.
The suggested training follow-up and data analysis will result in higher teacher self-
efficacy in supporting students who are learning English in Math. Teachers will have increased
factual knowledge about strategies to support language development in the Math classroom and
will also develop the metacognitive knowledge to plan strategies that align with the individual's
language needs of ELL students in their class. The training will create a framework for
instructional coaching that allows administrators to give targeted feedback to teachers and
engage in reflection with teachers around their practices to support ELLs. Through an increase in
knowledge and motivation there will be a positive impact on student achievement, language
development and overall feelings of support.
Support for Other Key Stakeholders
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The stakeholder of focus for the study is teachers therefore, the recommendations
primarily focus on the development of teacher knowledge and motivation in relation to
supporting ELLs in Math. However, the data presented in Chapter 4 supported the importance
that relationship building with students and families have on student achievement. Teachers
mentioned a relationship with families that empowered them through understanding the data and
what it means to be an ELL. This was also referenced as a critical behavior in Table 21.
Following are two samples of how schools can increase the knowledge and motivation of family
partners in supporting students who are ELLs. These two forms are completed in a 1:1 setting on
a yearly basis with the family of each ELL.

189

Figure 6
Forms to Increase Key Stakeholder Participation
Student Name: _________________ Grade: ___________ Homeroom: _______________
Teachers: As you conduct the data chart, have students mark each statement that applies to them. Students may
identify in more than one category (ie: exiting Emerging and entering Expanding). Students must meet all the
criteria in the English Proficient. Column in order to be considered for reclassification.
Emerging Expanding Bridging English Proficient
I am able to:
❏ Participate in
simple
conversations
with
peers and others
❏ Understand
words and phrases
learned from
previously taught
content areas
❏ Read brief
texts with
simple
sentences
and
familiar
vocabulary
supported by graphics
or pictures
❏ Write or use
familiar
words and
phrases
related to
everyday and
academic
topics ❏
ELPAC score
is 1 or 2
❏ Report Card
grades are C’s
or below
❏ Writing is
beginning or
developing
❏ SBAC is not a 4 or 3
I am able to:
❏ Participate in
simple
conversation on
social and
academic topics
❏
Comprehe
nd basic
concepts
in content
areas
❏ Read more
complex texts
supported by
graphics or pictures
❏ Write and express
ideas to meet social
and academic needs
using new vocabulary
❏ ELPAC score
is score 2 or
3
❏ Report Card
grades may
be C’s or
better
❏ Writing is
developing
❏ SBAC is not
a 4 or 3
I am able to:
❏ Participate in
discussions on a
variety of academic
and social topics
❏ Begin to
interpret the
meaning of
words and
phrases in the context
that they are used
❏ Read and
understand a
variety of grade
level
texts supported by
graphics or pictures
❏ Write and express
ideas to meet more
complex academic
demands
❏ ELPAC
score is 3
or 4
❏ ❏ Report
Card
grades are
C’s or
better
❏ Writing is
developing or
proficient
❏ SBAC is not a 3 or
4
I am able to:
❏ Participate fully in
collaborative
conversations in all
content areas
Interpret the meaning
of words and phrases
in the context that they
are used
❏ Read and
comprehend a
variety of texts in
all
content areas
❏ Write and express
ideas to meet a variety
of social and
academic
demands
I may still be learning
formal language and
need extra support in
academic language
Language Assessment
❏ ELPAC score is 4
Report Card
❏ C or better in ELA
❏ C or better in
other
content areas
Writing
❏ SBAC is a 3 or
4
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Student Name: _____________ Grade:________ Homeroom: _____________ Teacher:
Talking points/affirmations to share with the students
● I am an English Language Learner because my first language is a language other than English.
● I am learning the skills to fully participate in English in an academic setting appropriate for my grade level and
purpose.
● I know a lot about English even though I am still learning.
● I understand and speak two (or more) languages!
Why is it important to understand my assessment data?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
What are my strengths?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
What are my goals? What do I want to improve on and what steps will I take in order to accomplish my goals?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
In what areas have I made progress towards my goal?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
What are my new goals? What do I still need to work on and what steps will I take in order to accomplish
my goals?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
I understand that putting my best effort when I take the ELPAC will help me reach my goals to become English
proficient.
ELPAC Date:
Overall: _________
Written:_________
Oral: __________
Grades in ELA
Q1: ________
Q2: ________
Grades in Math
Q1: _________
Q2:____________

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Limitations and Delimitations
The research questions for this study focused on the knowledge and motivation of Math
teachers in relation to reaching the organizational performance goal of 85% of ELLs meeting or
exceeding the standard on the state Math assessments. The study uniquely focused on language
development in the Math classroom, but is limited in the sense that the perspective focused on
students in grades four through eight because the needs of long term ELLs is unique however the
limited grade levels represented limits the ability to analyze the root causes in the K-12 system.
Furthermore there may be gaps in knowledge and motivation that overlap between the
experience of Math teachers and other content areas. The study intentionally included the
perspective of Math teachers only, however inclusion of other content areas may create findings
that connect to the larger systemic needs.
Administrators were also asked about their behaviors in relation to the development of
teacher knowledge and motivation. While this study focused on the Math teacher stakeholder
group the findings revealed that the organization lacked a comprehensive approach to language
development and supporting ELLs. The study is limited in understanding the larger systems and
school wide initiatives that impact ELL success. The key behaviors of administrators in relation
to development of teacher knowledge and motivation is the focus however questions that target
the unique behaviors and skills of administrators related to school leadership is not a focus of the
study.
Teachers mentioned a variety of existing school systems like data meetings, grade level
meetings, parent meetings and content team/planning meetings as areas where teacher
knowledge and motivation in relation to language development can be grown. While teachers
mentioned some key elements and opportunities that can be implemented to support knowledge
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and motivation development; the study did not ask teachers to focus on these elements. Teachers
identified them; however, the level of detail needed to truly understand the areas for
improvement, target behaviors and elements that provide support was limited due to the
interview protocols.
The study focused on the key stakeholder group of teachers; however students and
families are also key stakeholders that support progress on the organizational performance goal.
The study did not include the perspective of students nor families, but did include teacher
perception of the experience of students and families. The focus on teacher stakeholder groups
creates a limited understanding of the comprehensive experience for all key stakeholders in
relation to the organizational performance goal.
Recommendations for Future Research
Throughout this study, both teachers and administrators were interviewed or surveyed.
Through those interviews data emerged that demonstrated that administrators had similar
knowledge and motivation gaps pertaining to teaching ELLs. While there is overlap between the
instructional knowledge that administrators need to support the development of teacher
knowledge and motivation; further research about the skills and behaviors unique to
administrators would support further progress towards the organizational performance goal.
Specific research on instructional coaching and what leader behaviors support ELL
achievement through the development of teacher knowledge and motivation would provide
behaviors specific to programs for administrators. Two teachers in the study referenced a
positive coaching experience with an administrator who was an EL Specialist and noted positive
growth in their knowledge about instructional supports as well as increased self-efficacy through
reflection and feedback. Further research about the unique behaviors that support ELLs and the
193

features unique to targeted instructional coaching for language development in Math would
support organizations in refining and crafting a model of coaching uniquely fit to support
teachers of ELLs and ELLs.
Teachers discussed the perceived impact and response that ELLs had in response to
instructional supports like sentence frames, goal setting and use of home language. However,
further research that studies the impact from the perspective of the student would strengthen the
teacher's experience from the study. In addition, parent involvement was mentioned from
various teachers in this study. Further research that focuses on parent knowledge, motivation and
how the organization facilitates that growth would support the development of key stakeholders
outside of teachers that impact the realization of the organizational performance goal.
Finally, a variety of teachers and administrators mentioned elements outside the Math
classroom like Designated ELD classes, small group support, literacy intervention and
reclassification. Further research about how the different organizational elements interact to
create comprehensive support for ELLs would strengthen the creation of intentional school
systems that support widespread achievement of ELLs.
Conclusion
As one teacher said during the interviews, “ELLs can become invisible.” The needs and
experiences of ELLs can become invisible and furthermore the unique experience of Math
teachers in relation to supporting ELLs can also be overlooked and invisible. The findings of this
study make visible the needs of Math teachers in developing the knowledge and motivation
needed to effectively support ELLs in the Math classroom as well as the organizational elements
needed to develop support for teacher growth. The performance and achievement gaps are
widening between English Fluent Proficient and ELL students as measured by the state Math
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assessments (CDE, 2015-2019). Addressing the language needs of English Language Learners as
well as the support needed by students who are English Language Learners is becoming
increasingly important as state data shows that the percent of Long-Term English Language
Learners (LTELs) who are “at risk” is increasing (CDE, 2018). In the 2017-2018 school year in
California there were currently 218,135 students who were LTELs and 144,146 students who
have five years of schooling and are at risk for becoming LTELs. This study introduced the
organizational performance status, stakeholder goal, related literature and methods of research
for the mixed methods design all in alignment with the KMO framework. Chapter 4 reviewed
the findings based on the data from the survey and interviews while Chapter 5 presented a series
of recommendations in alignment with the KMO framework, findings of the study and the New
World Kirkpatrick Model (Kirkpatrick & Kirkpatrick, 2016).

195

References

Banse, H. W., Palacios, N. A., Merritt, E. G., & Rimm-Kaufman, S. (2017). Scaffolding
English language learners' mathematical talk in the context of calendar math. Journal of
Educational Research, 110(2), 199-208. doi:10.1080/00220671.2015.1075187

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203

APPENDIX A
Survey Items and KMO Alignment
Stakeholder Group: Teachers
DemographicQuestions:
Years Teaching: 0-1, 2-5, 6-10, 11-15, 15+
Credential Held: type in response
Estimate of percent of students in class identified as ELLs: 0-25%, 26-50, 51-75, 76-100

Scale for all questions is strongly agree, agree, disagree, strongly disagree
1. The strategies that I use in my classroom to differentiate for ELLs close or significantly
lessen the achievement gap. K-F
2. I know a variety of different strategies to differentiate the math content for students who
are learning English. K-F
3. I use a variety of different strategies to differentiate the math content for students who are
learning English. K-F
4. I know a variety of different strategies to differentiate the math content for students who
are learning English based on their individual proficiency level. K-F
5. I know the specific proficiency levels and needs of the students who are ELLs in my
class. K-F
6. What resources do you use to support students who are ELLs. Check all that apply with
the option to add some responses. K-F
7. I know how to create strong relationships with students learning English. K-P
8. I have specific strategies to create inclusive and safe space for students learning English.
K-P
9. My relationships with students learning English are equally strong as my relationships
with students considered English fluent. K-P
10. My relationships with families of students learning English are equally strong as my
relationships with families of students considered English fluent. K-P
11. I can choose a specific strategy that best supports a student’s proficiency level. K-M
12. I modify my lessons daily to meet student proficiency levels. K-M
13. I modify assessments to meet student proficiency levels. K-M
14. I know what revision to make to my curriculum based on student proficiency levels that
support student achievement. K-M
15. I feel confident about my ability to build relationships with students who are ELLs. M-SE
16. I feel confident about my ability to build relationships with families of students who are
ELLs. M-SE
17. I feel confident about my ability to modify and differentiate instruction for students who
are ELLs. M-SE
18. I feel confident about my ability to adequately meet the needs of students who are ELLs.
M-SE
19. I feel confident about the idea that your ELL students can outperform or perform equally
to your EO students. M-SE
204

20. When an ELL doesn’t understand a lesson or concept it is usually because I didn’t
adequately differentiate the lesson. M-AT
21. When my students who are ELLs achieve poorly I believe it is due to my instruction and
knowledge. M-AT
22. The success of my students who are English language learners is most impacted by
factors inside the classroom. M-AT
23. The success of my students who are English language learners is most impacted by
factors outside the classroom.M-AT
24. My organization values equity for students learning English. O-CM
25. My organization sets achievement goals for students learning English. O-CM
26. My organization meets the goals set for students learning English. O-CM
27. My organization has a vision of what excellent instruction to students learning English
looks like in the classroom. O-CM
28. I believe my organization sets high expectations for students who are ELLs. O-CM
29. My organization believes that ELLs are capable of achieving at high levels. O-CM
30. ELLs in my organization achieve high levels. O-CM
31. My organization has experts in EL strategies and education. O-CS
32. There is a teacher who is an expert in EL strategies that I can learn from. O-CS
33. There is an admin who is an expert in EL strategies that I can learn from. O-CS
34. My organization offers PD specifically focused on EL support. O-CS
35. The PD and support offered makes a positive impact on the students learning English in
my classroom. O-CS
36. The PD provided allows me to lead positive change in the classroom for students who are
learning English. O-CS
37. My teacher preparation or credentialing program prepared me to support students
learning English in the Math classroom.
K-F=Knowledge-Factual, K-M=Knowledge Metacognitive, K-P= Knowledge Procedural, M-
A=Motivation-Attribute, M-SE= Motivation Self- Efficacy, O-CM=Cultural Models, O-
CS=Cultural Settings.

Stakeholder Group: Administrators
DemographicQuestions:
Years Teaching: 0-1, 2-5, 6-10, 11-15, 15+
Credential Held: type in response
Years as administrator: 0-1, 2-5, 6-10, 11-15, 15+
Estimate of percent of students in school identified as ELLs: 0-25%, 26-50, 51-75, 76-100
Scale for all questions is strongly agree, agree, disagree, strongly disagree
1. The strategies used in my school to differentiate for ELLs close or significantly lessen the
achievement gap. K-F
2. I know a variety of different strategies to differentiate the math content for students who
are learning English that I can teach to teachers. K-F
3. I see frequent use of different strategies to differentiate Math for students learning
English at my school. K-F
205

4. I know a variety of different strategies to differentiate the math content for students who
are learning English based on their individual proficiency level. K-F
5. I know the specific proficiency levels and needs of the students who are ELLs in my
school. K-F
6. What resources do you use to support students who are ELLs. Check all that apply with
the option to add some responses. K-F
7. I know how to create strong relationships with students learning English. K-P
8. I have specific strategies to create inclusive and safe space for students learning English.
K-P
9. My relationships with students learning English are equally strong as my relationships
with students considered English fluent. K-P
10. My relationships with families of students learning English are equally strong as my
relationships with families of students considered English fluent. K-P
11. I can choose a specific strategy that best supports a student’s proficiency level. K-M
12. I frequently give instructional feedback to teachers pertaining to the needs of students
learning English
13. In my instructional coaching a majority of the feedback I give targets the specific
language proficiency levels of students in the classroom.
14. A majority of the daily lessons at my school are modified to meet student proficiency
levels. K-M
15. A majority of the assessments at my school are modified to meet student proficiency
levels. K-M
16. My teachers know what revisions to make to their curriculum based on student language
proficiency levels. K-M
17. I feel confident about my ability to build relationships with students who are ELLs. M-SE
18. I feel confident about my ability to build relationships with families of students who are
ELLs. M-SE
19. I feel confident about my ability to coach teachers to modify and differentiate instruction
for students who are ELLs. M-SE
20. I feel confident about my school’s ability to adequately meet the needs of students who
are ELLs. M-SE
21. I feel confident about the idea that our ELL students can outperform or perform equally
to your EO students. M-SE
22. When an ELL doesn’t understand a lesson or concept it is usually because our school
staff didn’t adequately differentiate the lesson. M-AT
23. When my students who are ELLs achieve poorly I believe it is due to my school’s
instruction and knowledge. M-AT
24. The success of our students who are English language learners is most impacted by
factors inside the classroom. M-AT
25. The success of our students who are English language learners is most impacted by
factors outside the classroom.M-AT
26. My organization values equity for students learning English. O-CM
27. My organization sets achievement goals for students learning English. O-CM
28. My organization meets the goals set for students learning English. O-CM
29. My organization has a vision of what excellent instruction for students learning English
looks like in the classroom. O-CM
206

30. I believe my organization sets high expectations for students who are ELLs. O-CM
31. My organization believes that ELLs are capable of achieving at high levels. O-CM
32. ELLs in my organization achieve high levels. O-CM
33. My organization has experts in EL strategies and education. O-CS
34. There is an organizational leader who is an expert in EL strategies that I can learn from.
O-CS
35. My organization offers teacher PD specifically focused on EL support. O-CS
36. My organization offers school leader/administrator PD specifically focused on EL
support. O-CS
37. The PD and support offered makes a positive impact on the students learning English in
my school. O-CS
38. The PD provided allows me to lead positive change in my school for students who are
learning English. O-CS
39. Teacher preparation or credentialing programs prepare my teachers to support students
learning English in the Math classroom.
K-F=Knowledge-Factual, K-M=Knowledge Metacognitive, K-P= Knowledge Procedural, M-
A=Motivation-Attribute, M-SE= Motivation Self- Efficacy, O-CM=Cultural Models, O-
CS=Cultural Settings.

207

APPENDIX B
Interview Protocol and KMO Alignment Key
Stakeholder Interview: Teachers
1. Think about a time that represents how you differentiate for students who are English
Language Learners and describe that experience. (both planning and how it went in the
classroom). K-F What steps do you usually take when differentiating? And when you
____ how do you know that is what your ELL students need?
2. Describe the process you go through in lesson planning to differentiate for students who
are ELLs.K-F
3. Think about a time you used your knowledge of a student’s English proficiency level to
differentiate instruction. Describe the process you went through and the choices you
made. K-F Why did you make those choices?
4. Describe a time when an ELL student was successful in your class. What happened?
What did you do to make it that way? K-P How did you know those were the right moves
to make?
5. Describe a time an ELL student struggled. What happened? What did you do or want to
do to address it? K-P How did you know that was the right thing to do?
6. Describe your vision of excellent ELL instruction in your Math classroom. What would
we see? Hear? Feel? Do? What resources would you need to make this a reality? K-P
7. How would you describe yourself? Would you call yourself novice, intermediate or
proficient in teaching and supporting English Language Learners? Tell me about that. K-
P
8. Think about a time you made an instructional choice either in planning or execution that
was based on language proficiency level? Describe that. K-M Why did you make those
choices? How did you know those choices were the right ones?
9. What do you do well in supporting students who are ELLs? M-SE
10. What is challenging about teaching students who are English Language Learners? M-SE
11. What makes you feel confident or less confident about teaching students who are ELLs?
M-SE
12. Describe what you see as having the biggest impact on ELL success and achievement in
your Math classroom. Describe the biggest barrier M-AT
13. Describe the vision/beliefs that your organization has for supporting students learning
English. O-CM
14. Describe the instructional best practices that your organization has for supporting
students learning English. O-CM
15. Describe the goals and performance measures that your organization has for supporting
students learning English. O-CM
16. Describe what you would do if you needed help supporting a student in your class who is
an ELL. Who would you go to? Why?O- CS
17. When a teacher needs help supporting an English Language Learner how does your
organization respond? O-CS
18. Describe a time you received training or feedback on supporting ELLs in your classroom.
What happened? What was it like? Describe the impact it had on your classroom. O-CS
208

19. What impact did teacher training or preparation programs have on your ability to
differentiate for ELL students?
20. Think of the last time your organization talked about ELLs. Describe it including
what the topic was, who was involved and how you felt. O-CS
K-F=Knowledge-Factual, K-M=Knowledge Metacognitive, K-P= Knowledge
Procedural, M-A=Motivation-Attribute, M-SE= Motivation Self- Efficacy, O-
CM=Cultural Models, O-CS=Cultural Settings.

Organization Interview:Administrators
1. Think about a time or observation that represents how your school differentiates for
students who are English Language Learners and describe that experience. (both
planning and how it went in the classroom). K-F Allow any response, but then if admin
gives a non-Math example prompt: Can you give an example of a Math classroom?
2. Describe the process your teachers go through in lesson planning to differentiate for
students who are ELLs.K-F How do teachers know what to differentiate? How do they
know what modifications are best?
3. Think about a time you used your knowledge of a student’s English proficiency level to
differentiate instruction or teacher feedback. Describe the process you went through and
the choices you made. How did you know those were the right choices? K-F
4. Describe a time when an ELL student was successful in your school. What happened?
What did you do to make it that way? K-P Allow any response, but then if admin gives a
non-Math example prompt: Can you give an example of a Math classroom?
5. Describe the process your teacher go through in lesson planning to differentiate for
students who are ELLs.K-F
6. Describe a time an ELL student struggled. What happened? What did you do or want to
do to address it? K-P Allow any response, but then if admin gives a non-Math example
prompt: Can you give an example of a Math classroom?
7. Describe the process your teachers go through in lesson planning to differentiate for
students who are ELLs.K-F
8. Describe your vision of excellent ELL instruction in your Math classrooms. What would
we see? Hear? Feel? Do? What resources would you need to make this a reality? K-P
9. How would you describe yourself? Would you call yourself novice, intermediate or
proficient in teaching and supporting English Language Learners? Would you call
yourself novice, intermediate or proficient in coaching and supporting teachers in
practices for English Language Learners? Tell me about that. K-P
10. Think about a time you gave feedback to a teacher that was based on language
proficiency level? What was the feedback? How did you know that feedback was
appropriate? Describe that. K-M
11. What do you do well in supporting teachers in supporting ELL students? M-SE
12. What is challenging about supporting teachers in supporting ELL students? M-SE
13. What makes you feel confident or less confident about teaching students who are ELLs?
M-SE
14. Describe what you see as having the biggest impact on ELL success and achievement in
your school. organization. Describe the biggest barrier M-AT How do you know these
have the biggest impact?
209

15. Describe the vision/beliefs that your organization has for supporting students learning
English. O-CM
16. Describe the instructional best practices that your organization has for supporting
students learning English. O-CM
17. If you were to describe a lesson that you think is adequately scaffolded for ELL students
what would it include and why?
18. Describe the goals and performance measures that your organization has for supporting
students learning English. O-CM
19. Describe what you would do if you needed help supporting a student in your school who
is an ELL. Who would you go to? Why?O- CS
20. When a teacher needs help supporting an English Language Learner how does your
organization respond? O-CS
21. Describe a time you received training or feedback on supporting ELLs in your school.
What happened? What was it like? Describe the impact it had on your classrooms. O-CS
22. Think of the last time your organization talked about ELLs. Describe it including
what the topic was, who was involved and how you felt. O-CS
K-F=Knowledge-Factual, K-M=Knowledge Metacognitive, K-P= Knowledge
Procedural, M-A=Motivation-Attribute, M-SE= Motivation Self- Efficacy, O-
CM=Cultural Models, O-CS=Cultural Settings.

210

APPENDIX C

Rubric For Use Before, During and After Training Sessions
Name: _____________ Date: ____________________ Subject: __________________
Administrator Name: _________________Rubrics for Coaching Around ELD and Language Supports

Name: _____________ Date: ____________________ Subject: __________________
Administrator Name: _________________
Teacher Students Environment/Materials
Time
In:

Time
Out:
Open the Lesson
❏ State the Content
Objective
❏ State the Language
focus/objective
❏ Bring it to life through
background knowledge
Model and Practice
❏ T explicitly states the
vocabulary words as
well as the grammatical
forms and language
functions for the lesson
❏ T adjusts the
pace/complexity of
language to meet
student proficiency
❏ T practices and models
the above

Practice the Language
❏ The task or activity
include opportunities for
language (reading,
writing, listening and
speaking)
❏ T monitors student
practice
❏ T gives feedback on
language objective and
content objective
Close the Lesson
❏ Reviews the objective,
criteria for success,
connections to life
❏ T stamps how the
language is ‘portable’ to
other situations
Precursor Conditions
❏ Engaged
❏ Actively Listening
❏ Materials ready
❏ Participation
Language Practice (note the
opportunities that apply)
❏ Writing:____________
❏ Reading:___________
❏ Listening: __________
❏ Speaking: __________
❏ Whole Group________
❏ Small Group:________
❏ Partners: __________
❏ Individual:__________
Behaviors of Language Use:
❏ Responds in complete
sentences
❏ Successfully practices
language stated in objective
❏ Language use stretches
beyond current ability
❏ Flexibility of language
❏ Self-assess language and
content mastery

❏ Objective is posted
along with target
language
❏ Age appropriate
visuals
❏ Connection to first
language
❏ Resources for
topic specific
vocabulary
❏ Resources for
language patterns
❏ Co-created
resources
❏ Students can use
resources for
learning and
practice

Resources for Four
Domains:
❏ Reading
❏ Writing
❏ Listening
❏ Speaking
Com
ment
s

211

Focus Student Content Alignment Analysis
Student Name

Content
Standard/Objective

ELD Level

ELD Standard/
Language Objective

Oral Language
Notes: Record
student
speaking or
listening
What language is used
to demonstrate
mastery of the Math
Content?
*Craft an exemplar
response*

Written
Language
Notes: Record
student writing
or reading

What language can
students already do?

What can they
do? Where do
they need
support?

What language
requires support?

Data Check:
Fill in the
student’s
latest mastery
score from
this lesson or
the most
recent lesson.

Where are there
opportunities for this
in the lesson?

212

APPENDIX D
Rubric for Use Following or Delayed from Training

213

APPENDIX E

Sample Data Dashboard to Measure and Message Progress

214

APPENDIX F

Sample Forms to Increase Key Stakeholder Participation
Student Name: _________________ Grade: ___________ Homeroom: _______________
Teachers: As you conduct the data chart, have students mark each statement that applies to them. Students may
identify in more than one category (ie: exiting Emerging and entering Expanding). Students must meet all the
criteria in the English Proficient. Column in order to be considered for reclassification.
Emerging Expanding Bridging English Proficient
I am able to:
❏ Participate in
simple
conversations
with
peers and others
❏ Understand
words and phrases
learned from
previously taught
content areas
❏ Read brief
texts with
simple
sentences
and
familiar
vocabulary
supported by graphics
or pictures
❏ Write or use
familiar
words and
phrases
related to
everyday and
academic
topics ❏
ELPAC score
is 1 or 2
❏ Report Card
grades are C’s
or below
❏ Writing is
beginning or
developing
❏ SBAC is not a 4 or 3
I am able to:
❏ Participate in
simple
conversation on
social and
academic topics
❏
Comprehe
nd basic
concepts
in content
areas
❏ Read more
complex texts
supported by
graphics or pictures
❏ Write and express
ideas to meet social
and academic needs
using new vocabulary
❏ ELPAC score
is score 2 or
3
❏ Report Card
grades may
be C’s or
better
❏ Writing is
developing
❏ SBAC is not
a 4 or 3
I am able to:
❏ Participate in
discussions on a
variety of academic
and social topics
❏ Begin to
interpret the
meaning of
words and
phrases in the context
that they are used
❏ Read and
understand a
variety of grade
level
texts supported by
graphics or pictures
❏ Write and express
ideas to meet more
complex academic
demands
❏ ELPAC
score is 3
or 4
❏ ❏ Report
Card
grades are
C’s or
better
❏ Writing is
developing or
proficient
❏ SBAC is not a 3 or
4
I am able to:
❏ Participate fully in
collaborative
conversations in all
content areas
Interpret the meaning
of words and phrases
in the context that they
are used
❏ Read and
comprehend a
variety of texts in
all
content areas
❏ Write and express
ideas to meet a variety
of social and
academic
demands
I may still be learning
formal language and need
extra support in academic
language
Language Assessment
❏ ELPAC score is 4
Report Card
❏ C or better in ELA
❏ C or better in
other
content areas
Writing
❏ SBAC is a 3 or
4
215

Student Name: _____________ Grade:________ Homeroom: _____________ Teacher:
Talking points/affirmations to share with the students
● I am an English Language Learner because my first language is a language other than English. ● I am learning the
skills to fully participate in English in an academic setting appropriate for my grade level and purpose.
● I know a lot about English even though I am still learning.
● I understand and speak two (or more) languages!
Why is it important to understand my assessment data?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
What are my strengths?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
What are my goals? What do I want to improve on and what steps will I take in order to accomplish my goals?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
In what areas have I made progress towards my goal?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
What are my new goals? What do I still need to work on and what steps will I take in order to accomplish
my goals?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
______________________________________________
I understand that putting my best effort when I take the ELPAC will help me reach my goals to become English
proficient.
ELPAC Date:
Overall: _________
Written:_________
Oral: __________
Grades in ELA
Q1: ________
Q2: ________
Grades in Math
Q1: _________
Q2:____________

Abstract (if available)

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Asset Metadata

Creator Daley, Brittany (author)

Core Title Learning the language of math: supporting students who are learning English in acquiring math proficiency through language development

School Rossier School of Education

Degree Doctor of Education

Degree Program Organizational Change and Leadership (On Line)

Publication Date 12/01/2020

Defense Date 10/15/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag ELD,English Language Development,Language,language acquisition,language development,math,mathematics,OAI-PMH Harvest,proficiency,supporting students,teacher knowledge,teacher support

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Min, Emmy (committee chair), Hasan, Angela (committee member), Park, Jennifer (committee member)

Creator Email bdaley@usc.edu,daley3b@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-401121

Unique identifier UC11666500

Identifier etd-DaleyBritt-9172.pdf (filename),usctheses-c89-401121 (legacy record id)

Legacy Identifier etd-DaleyBritt-9172.pdf

Dmrecord 401121

Document Type Dissertation

Rights Daley, Brittany

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA