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Parental participation in efforts to reduce the African-American math readiness gap at Timber Middle School: an evaluation study

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Parental participation in efforts to reduce the African-American math readiness gap at Timber Middle School: an evaluation study

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Content Running head: AFRICAN-AMERICAN MATH READINESS GAP 1

PARENTAL PARTICIPATION IN EFFORTS TO REDUCE THE AFRICAN-AMERICAN
MATH READINESS GAP AT TIMBER MIDDLE SCHOOL:
AN EVALUATION STUDY

by
Dean Andal

_____________________________________________________________________________

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 2019

Copyright 2019 Dean Andal

AFRICAN-AMERICAN MATH READINESS GAP 2

ABSTRACT
This evaluation study seeks to understand the beliefs and attitudes of African-American
parents towards math proficiency and readiness for high school college preparatory mathematics
at Timber Middle School. Specifically, the inquiry probes these parents’ potential acceptance of
an additional math instructional period for students that are performing below grade level
proficiency. An explanatory mixed-methods design combined a survey of all parents (N=532,
RR=47) at Timber Middle School with interviews of African-American parents (N=7) to explore
their beliefs in depth (Creswell, 2014). The study was structured with a (Clark and Estes, 2008)
gap analysis model to make six findings categorized by assumed knowledge, motivation, and
organizational influences. The knowledge influence findings are: 1) a gap was identified
between African American parent’s beliefs towards their children’s math mastery and actual
student math proficiency; 2) African American parents at Timber Middle overwhelmingly
believe math is central to college, career, and income opportunities for their children; and, 3) a
gap was identified between African American parents’ beliefs that their children will attend
college and actual student readiness for college prep math pathway. The findings with motivation
influences are: 1) African-American parents overwhelmingly attribute more math practice and an
extra math instructional period to improved math proficiency, and, 2) parents at Timber Middle
are evenly split on whether the teacher has the primary responsibility for their child’s math
education, but if their children are struggling in mathematics a majority rely on the teacher to
take responsibility. Finally, one organizational influence was found in that African-American
parents feel frustration with past attempts to engage the school in an effort to improve their
child’s math performance.

AFRICAN-AMERICAN MATH READINESS GAP 3

ACKNOWLEDGEMENTS
No dissertation can be considered a solitary effort and this study is no exception. As with
anything of value that I have attempted since we married over 32 years ago, I’m grateful to my
wife Kari Lyn (Bauer) Andal who positively impacted this study as its first editor, partner in data
collection, and a loyal motivator. The invaluable assistance of the Redwood Unified family, the
outstanding Principal of Timber Middle School, and its five dedicated math teachers, made this
study possible. They are committed educators who welcomed this study and are unfailingly
dedicated to their students’ welfare. Timber Middle School is a happy place where the students
are the focus of the very best that professional educators have to offer. During the data
collection, I met 532 Timber Middle School students and was reminded of their limitless
potential and precious opportunities to learn. The loving African-American parent interviewees
spent time generously sharing with me their challenges of raising their children and making sure
they are advancing in their math mastery. The dissertation committee chair was Dr. Angela
Hasan who proved invaluable with her excellent research guidance and this paper also benefited
from the tireless editing of Dr. Susanne Foulk through many drafts. Dr. Steven Lowder and Dr.
Lawrence O. Picus generously offered their considerable expertise as members of the
dissertation committee. My son, Patrick Andal, a certified public accountant, provided valuable
advice on the study’s data analysis and presentation of tables. Finally, I’d like to thank my
parents, Gene and Carolyn Andal, that have showed me by their own example the importance of
a curiosity toward understanding society’s challenges and a lifetime commitment to continuing
education. All of the positive aspects of this paper were because of these many selfless
contributors and any shortcomings are mine alone.

AFRICAN-AMERICAN MATH READINESS GAP 4

TABLE OF CONTENTS
Acknowledgements………………………………………………………………………………..3
List of Tables……………………………………………………………………………………...7
List of Figures……………………………………………………………………………………..9
Introduction………………………………………………………………………………………10
Organizational Context and Mission………………………………………………...…..............12
Organizational Goal…………………………………………………………………….………..13
Related Literature………………………………………………………………………………...15
Importance of the Evaluation…………………………………………………………………….16
Description of Stakeholder Groups……………………………………………………………....17
Stakeholder Groups’ Performance Goals……………………………….…………..…………....17
Stakeholder Group for the Study..……………………………………………………………….18
Purpose of the Project and Research Questions………………….……………………………....19
Methodological Framework……………………………………………………………………...20
Definitions…………………………………………………………………………...…………...21
Organization of the Research Project……………………………………………….…………...21
Review of the Literature…………………………………………………………………………23
Influences on the Problem of Practice…………………………………………………………...24
Effects of Math Proficiency……………………………………………...………........................24
African-American Student Math Performance Variables……………………...………………...31
Successful African-American Math Interventions…………………..……..………………….…35
Impact of Parent Involvement…………………………....………......…………………………..37
Alternative Math Courses During and After School……………………………………………..42
AFRICAN-AMERICAN MATH READINESS GAP 5

Impact of Practice...……………………………………………………...……………………....45
Impact of Instructional Time.………………………………………………....…………………47
Role of Stakeholder Group of Focus…………………………………………………………….48
Clark and Estes’ Gap Analysis Framework……………………………………………………...51
Knowledge, Motivation, and Organizational Influences…………………………...…………....52
Knowledge Influences…………………………………………………………………………...54
Motivation Influences…………………………………………………………………………....57
Organizational Influences………………………………………………………………………..62
Conceptual Framework………………….……………………………………………………….63
Knowledge, Motivation, and Organizational Factors…………………………………………....64
Methods…………………………………………………………………………………….........70
Participating Stakeholders …………………………………………………….……...………....73
Survey Sampling Criteria and Rationale………………………………………………………...73
Interview Sampling Criteria and Rationale…..…………………………………………………..75
Interview Sampling and Recruitment Strategy and Rationale…...………………………………76
Data Collection and Instrumentation………….…………………………………….…………...76
Survey Instrument and Procedures……………………………………………………………....76
Interview Protocol and Procedures………………………………………………........................77
Data Analysis…...……………………………………………………………….….....................78
Credibility and Trustworthiness………………………………………………………………….78
Validity and Reliability…………………………………………………………………………..79
Ethics……………………………………………………………………………………..............80
Limitations and Delimitations…………………………………………………………………....82
AFRICAN-AMERICAN MATH READINESS GAP 6

Results and Findings………………….………………………………………………….............83
Participating Stakeholders…..……………………………………….……………....…………..84
Findings………………………………………….………………...…...………….…………….86
Knowledge Findings……………………………………………………………………………..86
Motivation Findings……………………………………………………………………………...90
Organizational Finding…………………………………………………………………………..95
Solutions, Implementation, and Evaluation...…………………………………………….…….100
Knowledge Recommendations…………..…………………………………………....………..105
Motivation Recommendations…………………...………………………………….………….108
Organizational Recommendations……………………...……………………………...……….111
Integrated Implementation and Evaluation Plan………………………………………………..116
Strengths and Weaknesses of the Approach……………………………………………………128
Recommendations for Future Research…………………………………………………….......130
References………………………………………………………………………………...…….132
Appendix A: Parent Survey……………………………………………………………………160
Appendix B: Informed Consent/Information Sheet..……………………………………….….161
Appendix C: Interview Protocol………………………………….…………………………....162
Appendix D: Immediate Evaluation (Levels 1 & 2)……………………………………….…..166
Appendix E: Delayed Evaluation (Levels 1, 2, 3, & 4)………………………………...……...168
Appendix F: Data Analysis Chart……….…………………………………………..…………170
AFRICAN-AMERICAN MATH READINESS GAP 7

LIST OF TABLES
Table 1 CAASPP Math Results for African-American Students at Timber Middle School….…14
Table 2 Organizational Mission, Global, and Stakeholder Goals………………………......18, 103
Table 3 Timber Middle School Math Proficiency by Ethnic sub-group (2017-18)......................48
Table 4 Redwood Unified Math Proficiency by Ethnic sub-group (2004-09)…………..............50
Table 5 Knowledge, Motivation, and Organizational Influences in Redwood Unified…….…...53
Table 6 Potential Redwood High School Math Pathways………………………...…………..…54
Table 7 Comparison Between Survey Question 4 and Actual CAASPP Math Results…….…...87
Table 8 Parent Survey Results: Questions 5 and 6………………………………………....……90
Table 9 Parent Survey Results: Questions 2, 3, and 8………………………………...…………88
Table 10 Comparison Between Survey Question 7 and African-American Math Proficiency….89
Table 11 Parent Survey Results For Question 1……………………………………..……..……94
Table 12 Summary of Knowledge Recommendations………....……….………………….......105
Table 13 Summary of Motivation Recommendations………...……………..………………....108
Table 14 Summary of Organizational Recommendations………...………....………………....111
Table 15 Outcomes, Metrics, and Methods for External and Internal Outcomes…...………….117
Table 16 Critical Behaviors, Metrics, Methods, and Timing for New Reviewers…....……......118
Table 17 Required Drivers to Support Critical Behaviors…………………………………...…119
Table 18 Components of Learning for the Program….………………………………………...122
Table 19 Components to Measure Reactions to the Program……………………………..........123
Table 20 Demographic Background of Survey Sample…………………………………………85
Table 21 African-American Parent Interview Participants……………...…………………….…85

AFRICAN-AMERICAN MATH READINESS GAP 8

Table 22 Relationships between Survey Items, Influences, and Research Questions..……….…73

AFRICAN-AMERICAN MATH READINESS GAP 9

LIST OF FIGURES
Figure 1 African-American Income by Educational Level……………………………………....30
Figure 2 Redwood Unified - Math Proficiency by Ethnic Subgroup (2004-09)...........................49
Figure 3 Conceptual Framework for African-American Parent Stakeholders…………………...69
Figure 4 Mock-up of Infographic for Formative Level 1 and 2 Data………………………..…126

AFRICAN-AMERICAN MATH READINESS GAP 10

CHAPTER ONE: INTRODUCTION
This paper addresses the problem of low readiness rates of African-American students at
Timber Middle School (Timber Middle)
1
in the Redwood Unified School District (Redwood
Unified)
2
for enrollment in high school college preparatory (college prep) mathematics courses.
Specifically, African-American parental beliefs towards math and support for an additional math
instructional period at Timber Middle are explored. Eighty-eight percent (88%) of Timber
Middle’s students are not grade-level proficient in mathematics (CAASPP, 2016) and are not
qualified to begin the college preparatory math sequence in the ninth grade (Lincoln High School
Course Catalog, 2017). African-American students have a math achievement gap (NAEP 2007-
2018); this math proficiency gap leads to a high school math readiness gap at Timber Middle
(Lincoln Unified Course Catalog, 2017); when fewer African-Americans take advanced high
school math courses they are less interested in STEM (Sadler, Sonnert, Hazari, and Tai, 2012);
and the resulting STEM degree gap contributes to a lifetime African-American earnings, wages,
and household income gap (Downs, 2016).
Although mathematics test scores for all students have increased since the 1960s,
African-American students have a continuing and persistent mathematics achievement gap with
white students. The U.S. Civil Rights Act of 1964 mandated the first academic effort to compile
educational outcome data and segment it by demographic group (Coleman, 1966). In a survey of
achievement test data from over 3,000 public schools (N=600,000), 87% of white students in
1966 scored higher on mathematics achievement tests than the average African-American
twelfth grader (SD=1.1). The eighth-grade African-American student mathematics achievement
gap persisted on the 2007 National Assessment of Educational Progress (N=147,000) with a

1
Timber Middle School is a pseudonym
2
Redwood Unified School District is a pseudonym
AFRICAN-AMERICAN MATH READINESS GAP 11

differential of 31 points (NAEP, 2007). By the eighth-grade, 91% of African-American students
are not proficient in mathematics compared to 63% of white students (NAEP, 2013, Haycock,
2006). This demonstrated mathematics achievement gap leads African-Americans to take fewer
advanced high school mathematics courses, more remedial classes, and score much lower on
mathematics assessments (NSF, 1999).
The AP program, a non-profit organization operated by the College Board, offers high
school students the opportunity to take college-level courses at their local high schools (College
Board, 2009). In AP courses, students typically read more demanding college-level textbooks
and spend more time on homework (Kohli, 2015). For students who obtain high scores on AP
subject matter examinations, (usually at least 3 on a 5-point scale), many colleges grant course
credit (Tugend, 2017). Completion of AP courses strongly correlates with admission to and
successful graduation from college (College Board, 2009; Klopfenstein, 2004). Although
African-American and Latino high school students make up 37% of high school students
nationwide, they constitute only 27% of AP course enrollment and just 18% of students scoring a
3 or higher on at least one AP exam (U.S. Department of Education, 2014).
The lack of college prep high school mathematics correlates with less interest in STEM
(Science, Technology, Engineering, and Mathematics) college degrees (Sadler, Sonnert, Hazari,
& Tai, 2012). Disproportionately low levels of African-American STEM degree attainment is a
factor in the African-American household income gap (Downs, 2016). Thus, poor mathematics
readiness for advanced high school mathematics has lifelong consequences for the overwhelming
majority of African-American students.
Racial disparities in the pursuit of STEM degrees occur because African-American
students are disproportionately unprepared for STEM in high school (Burkam & Lee, 2003).
AFRICAN-AMERICAN MATH READINESS GAP 12

African-American college students are then underrepresented in higher-paying STEM degree
pathways and overrepresented in lower-paying non-STEM majors. African-American students
complete fewer advanced high school mathematics courses and have less interest in STEM
careers, inferring fewer STEM careers and lower household incomes for African-American
households. While African-Americans make up 10.8 percent of employed workers, they
comprise only 6.4 % of employees in STEM occupations (Landivar, 2013). This disparate
propensity for African American college students to choose non-STEM college degrees and
occupations results in lower household incomes for college African-American college graduates.
Thus, a journey that begins with poor mathematics readiness in the eighth-grade ends with lower
lifetime household incomes for African-Americans.
Organizational Context and Mission
Timber Middle School enrolls approximately 650 seventh and eighth-grade students in
Redwood Unified (LCAP, 2018). Redwood Unified is a K-12 public school system located in
Central Valley of California. Approximately one-half of Redwood Unified’s seventh and eighth-
grade students attend Timber Middle. The district serves more than 9,400 students at 13 schools
including a comprehensive high school, alternative high school, middle school, nine K-8
elementary schools, and a district dependent STEM charter school (CALPADS, 2017).
Redwood Unified has an ethnically diverse student population that includes Latino (46.9%),
white (22.7%), African-American (12.4%), and Asian (9.5%) students (CALPADS, 2017). Less
than a majority of Redwood Unified students met grade-level standards in Mathematics (32.1%)
in the 2016-17 school year (CAASPP, 2017). Over 58% of Timber Middle’s students participate
in the free or reduced lunch program (California Department of Education, 2018). At Redwood
AFRICAN-AMERICAN MATH READINESS GAP 13

Unified’s only comprehensive high school, the African-American graduation rate is 90%
(California Department of Education, 2018).
A five-member Board of Trustees elected by the registered voters from evenly divided
trustee areas and a Superintendent appointed by them govern the district. The district employs
404 certificated teachers and has an average student/teacher ratio of 23.2 (California Department
of Education, 2015). Like all public school districts in California, Redwood Unified is governed
by laws adopted by the State of California. Both the California Board of Education and
Redwood Unified have mission statements that commit themselves to providing a quality
education for all students under their care (California Board of Education, 2016, Redwood
Unified School District, 2018):
“to educate all students to achieve their maximum potential (Redwood Unified School
District, 2018).”
“ensure that all students are performing at grade level or higher (California Board of
Education, 2018).”
Reviewing the two mission statements yields an important difference: the lack of a pledge
by Redwood Unified to the California Board emphasis on a measurable student-achievement
accountability system.
Organizational Goal
Timber Middle’s organizational goal is to increase the percentage of eighth-grade African-
American students that meet or exceed the state mathematics standard for each of the next three
school years (Redwood Unified LCAP, 2017). Redwood Unified Board of Trustees approved
the 2017-18 Local Control Accountability Plan and Annual Update (LCAP) and submitted the
plan to the State Department of Education. The California Assessment of Student Performance
AFRICAN-AMERICAN MATH READINESS GAP 14

and Progress (CAASPP) measures the expected outcome of the LCAP annually. Currently, only
18 percent of Redwood Unified’s eighth-grade African-American students meet or exceed the
state standards for mathematics on the annual standardized test (CAASPP, 2017). Only 13% of
Timber Middle’s African-American students are proficient in math. Table 1 shows the
proficiency rates for African-American students have not improved since the institution of the
CAASPP in California schools in the 2014-15 school year.
Table 1
CAASPP Math Results for African-Americans at Timber Middle School
Achievement Levels 2014-15 2015-16 2016-17 2017-18

Standard Exceeded Level 4 4% 5% 4% 3%
Standard Met Level 3 10% 14% 10% 10%
Standard Nearly Met Level 2 39% 32% 20% 25%
Standard Not Met Level 1 47% 49% 66% 62%

Source: CAASPP (2018).

It is critical to evaluate Timber Middle’s and Redwood Unified’s progress towards
increasing mathematics proficiency for eighth-grade African-American students to ensure a
larger share of this cohort of students can enter the pathway leading to the college prep math in
high school. Since Timber Middle’s students represent almost half of all eighth-graders in
Redwood Unified and their African-American proficiency rates are lower, any meaningful
improvement Redwood Unified’s proficiency rates will need to address Timber Middle’s math
proficiency rates.

AFRICAN-AMERICAN MATH READINESS GAP 15

Related Literature
African-American students have a mathematics achievement gap when compared to their
white contemporaries (NAEP, 2018). When high school students take advanced high school
mathematics courses it increases interest in STEM and college STEM degree attainment (Sadler,
Sonnert, Hazari, & Tai, 2014). The resulting African-American college STEM degree gap
contributes to a cap with whites in lifetime earnings, wages, and household income (Downs,
2016).
Although national mathematics test scores for all students have increased since the 1960s,
African-American students have a continuing and persistent mathematics achievement gap with
white students (NAEP, 2018). The U.S. Civil Rights Act of 1964 mandated the first academic
effort to compile educational outcome data and segment it by demographic group (Coleman et
al., 1966). In a survey of achievement test data from over 3,000 public schools (N=600,000),
87% of white students in 1966 scored higher on mathematics achievement tests than the average
African-American twelfth grader (SD=1.1) (Coleman, 1966) The eighth-grade African-
American student mathematics achievement gap persisted on the 2007 National Assessment of
Educational Progress (N=147,000) with a differential of 31 points (NAEP, 2007). As recently as
2013, only 91% of African-American eighth-graders were not proficient in mathematics
compared to 63% of white students (NAEP, 2013). This demonstrated mathematics achievement
gap leads African-Americans to take fewer advanced high school mathematics courses, more
remedial classes, and score much lower on mathematics assessments (NSF, 1999).
Racial disparities in the pursuit of STEM degrees occur because African-American and
Hispanic students are disproportionately unprepared for STEM in high school (Burkam & Lee,
2003). African American college students are then underrepresented in higher-paying STEM
AFRICAN-AMERICAN MATH READINESS GAP 16

degree pathways and overrepresented in lower-paying non-STEM majors. When African-
American students complete fewer advanced high school mathematics courses and have less
interest in STEM careers, it leads directly to lower household incomes for African-American
households. While African-Americans make up 10.8 percent of employed workers, they
comprise only 6.4 % of employees in STEM occupations (Landivar, 2013). This disparate
propensity for African-American college students to choose non-STEM college degrees and
occupations results in lower household incomes for college African-American college graduates.
In summary, an educational journey that begins with poor mathematics readiness in the eighth-
grade ends with lower lifetime household income.
Importance of the Evaluation
It is important to address the problem of low African-American ninth grade math
readiness at Timber Middle because it: 1) impairs the California Board of Education’s goal of
all students performing at grade-level standards in mathematics; 2) exacerbates the achievement
gap between African-Americans and other students; 3) leaves African-American students
unprepared and ineligible for the sequence of courses leading to AP Calculus and AP Statistics
courses; 4) reduces post-secondary opportunities for graduating Redwood Unified African-
American students; and 5) ultimately leads to much lower lifetime household incomes for
Redwood Unified’s African-American students.
AFRICAN-AMERICAN MATH READINESS GAP 17

Description of Stakeholder Groups
Redwood Unified is a K-12 public school system located in the northwestern section of
Stockton, California. It has several stakeholder groups. First, the district serves an ethnically
diverse population of 9,400 students, which includes Latino (46.9%), white (22.7%), African-
American (12.4%), and Asian (9.5%) sub-groups (CALPADS, 2017). Second, the parent
stakeholder groups include a few of the wealthiest Californians and many of the poorest, with an
active Parent Teacher Association at all 13 schools. Third, a five-member Board of Trustees
elected by the registered voters from evenly divided trustee areas governs the district. Fourth,
the administration of the district includes a Superintendent, Associate Superintendent for
Education Services, and principals at each school. Fifth, the district employs 404 certificated
teachers and has an average student/teacher ratio of 23.2 (California Department of Education,
2015).
Stakeholder Groups’ Performance Goals
Redwood Unified’s organizational mission, performance goal, and stakeholder
performance goals are aligned. These goals are all articulated in the annual local control and
accountability plan for Timber Middle (LCAP, 2018). Table 2 illustrates the connection between
Redwood Unified’s mission statement and Timber Middle’s stakeholder goal for African-
American student math proficiency.

AFRICAN-AMERICAN MATH READINESS GAP 18

Table 2
Organizational Mission, Global, and Stakeholder Goals
Organization Mission

To educate all students to their maximum potential and to prepare them to be responsible citizens.

Organizational Global Goal

Student math proficiency shall increase by 10% by the end of the 2019-20 school year.

Superintendent Goal Principal Goal
African-American
Student/Parent Goal

All district students shall either
be math proficient or increase
math proficiency by 10% by the
end of the 2019-20 school year.
All Timber Middle students shall
either be math proficient or
increase math proficiency by 10%
by the end of the 2019-20 school
year.
African-American students at
Timber Middle shall either be
math proficient or increase math
proficiency by 10% by the end of
the 2019-20 school year.

Stakeholder Goal

African-American 8th-grade student math proficiency shall increase by 10% by the end of the 2019-20
school year.

Stakeholder Group for the Study
Although a complete analysis involving all the stakeholders would be desirable, this
study will focus on the parents of the sub-group of African-American students at Timber Middle.
Of all ethnic subgroups in Redwood Unified, African-American students have the lowest level of
readiness for eighth-grade mathematics. Only 18% of the district’s entering ninth grade African-
American students are grade-level proficient in mathematics (CAASPP, 2016) and
approximately half of this cohort graduates from Timber Middle. The CAASPP annual
achievement reports provide the necessary measurement to evaluate progress and are consistent
with the district’s LCAP annual measurable outcome. If there is no improvement in eighth-grade
AFRICAN-AMERICAN MATH READINESS GAP 19

mathematics readiness among African-American students, the district risks not providing a
quality education for “all students” as articulated in its mission statement. African-American
parental support is critical for the success of interventions designed to improve math proficiency
and readiness.
Purpose of the Project and Research Questions
The purpose of this project is to conduct an evaluation study of the African American
parents’ perception of eighth-grade African-American student readiness for advanced high
school mathematics at Timber Middle. Specifically, the project goal is to gauge African-
American parental support for establishing an additional instructional period of mathematics for
students who are below proficiency entering the eighth-grade. Consistent with the Clark and
Estes (2008) gap analysis model, this study will identify deficiencies in the areas of knowledge
and skill, motivation, and organization necessary to reach the performance goal of reducing the
eighth-grade African-American math achievement gap. Because the additional math period
could come at some opportunity cost to the students (through either an additional period in the
school day or substitution for an elective course), evaluating the attitudes and beliefs of the
African-American parents is critical to understanding the viability of the project.
The initial inquiry research questions are:
1. To what extent is Redwood Unified meeting its math proficiency goals?
2. What is the extent of African-American parents’ knowledge and motivation related to
Redwood Unified’s math proficiency goals?
3. What is the interaction between Redwood Unified culture and context and African-
American parents’ knowledge and motivation?
AFRICAN-AMERICAN MATH READINESS GAP 20

4. What are the recommendations for organizational practices in the areas of knowledge,
motivation, and Redwood Unified resources?
Methodological Framework
Central to the design of this study’s methodology is a KMO gap analysis that seeks to
understand the potential obstacles to implementation of a second mathematics period for students
that are less than proficient (Creswell, 2014). Because assessing parental support for the extra
mathematics period was critical, particularly for the African-American parent stakeholder group,
this study used an explanatory sequential mixed-methods model (Creswell, 2014) to test both
groups. Two distinct phases of data collection were pursued. In phase one, a survey of all
parents at Timber Middle School was conducted to assess their view of the importance of math
proficiency, readiness for high school college preparatory mathematics, and the relationship
between practice and math performance. During phase two, seven African-American parents
participated in interviews to provide a deeper understanding of their family’s situation, its effect
on their student’s math performance, and relative support for an additional instructional
mathematics lab period.
The survey data produced in the first phase quantitative study was then used to inform the
development of the parent interviews conducted in the second phase qualitative study. The
parental survey explored four themes: 1) demographic information on parent ethnicity, gender,
and educational attainment; 2) attitudes towards school, parent, and student roles in the
educational process; 3) an assessment of how the parents value advanced mathematics in terms
of their child’s post-secondary and career prospects; and 4) whether they would consent to an
extra hour in the school day for a mathematics lab.

AFRICAN-AMERICAN MATH READINESS GAP 21

Definitions
Math proficiency: Grade-level mathematics mastery of state standards as demonstrated
on annual state standardized test.
Math readiness: Qualified and ready to enter the next sequential mathematics course at
grade-level as defined by state standards.
Real-world math connection: Mathematics instruction that uses math applications useful
in the daily life of students to teach math concepts.
SES: An acronym for socio-economic status.
STEM: An acronym for science, technology, engineering, and mathematics. In an
educational context, a sequential program designed to prepare primary and secondary students
for college study and careers in science, technology, engineering, and mathematics.
Complementing subject-specific learning, STEM focuses on scientific inquiry, reasoning, and
collaboration skill development.
Organization of the Research Project
This study is organized into five chapters. This chapter provides key concepts and
definitions relevant to the African-American student math achievement gap. Also introduced
were Redwood Unified School District’s mission, goals, and stakeholders and the framework for
this evaluation. Chapter Two offers a review of current literature covering: 1) the relationship
of African-American math achievement gap to the related gaps in STEM careers and household
income; 2) the impact of parents on student math performance; 3) African-American student
math performance variables and successful interventions; 4) alternative math courses during and
after the school day; and 5) the impact of practice and extra instructional time on math
achievement. Chapter Three advances the methodology to choose the participants and data
AFRICAN-AMERICAN MATH READINESS GAP 22

collection strategy used to analyze specific knowledge, motivation, and organizational
influences. Data and results are reported and analyzed in Chapter Four. Chapter Five provides
solutions to the African-American math readiness gap at Timber Middle and Redwood Unified,
based upon data and literature, and action plan with recommendations to reduce the gap.

AFRICAN-AMERICAN MATH READINESS GAP 23

CHAPTER TWO: REVIEW OF THE LITERATURE
This research addresses the inadequate preparation of African-American students for
college prep mathematics courses. The demonstrated mathematics achievement gap leads
African-Americans to take fewer advanced high school mathematics courses, more remedial
classes, and score much lower on mathematics assessments (NSF, 1997). Chapter two begins
with a review that is divided into two foundational sections. In the first section, the progression
of the African-American math achievement through its ultimate destination of lower African-
American household incomes is explored. Section one has four parts: 1) a short review of the
mathematics achievement gap for African American students; 2) advanced high school
mathematics courses increase STEM interest; 3) advanced high school mathematics coursework
improves the rate of college STEM degree attainment; and 4) the African-American STEM gap
leads to a nation-wide household income gap between African-Americans and whites. Section
two reviews the literature on variables that affect African-American math performance and some
successful intervention programs. In section three of the literature review, parental self-efficacy
and participation literature are outlined. Section four addresses the research on alternative math
courses during and after the school day. Section five reviews relevant literature on the effect of
practice and additional instructional time on math performance. Finally, the general literature
review is then followed by a methodological framework including knowledge, motivation, and
organizational influences with a strategic scheme by which to understand African-American
students’ impediments to success in mathematics.

AFRICAN-AMERICAN MATH READINESS GAP 24

Influences on the Problem of Practice
African-American students have a mathematics achievement gap when compared to their
white contemporaries; when high school students take advanced high school mathematics
courses it increases interest in STEM and college STEM degree attainment; and the African-
American STEM gap contributes to a gap with whites in lifetime earnings, wages, and household
income.
Effects of Math Proficiency
The African-American mathematics achievement gap. Although mathematics test
scores for all students have increased since the 1960s, California African-American students
have a continuing and persistent mathematics achievement gap with white students (CAASPP,
2016). The U.S. Civil Rights Act of 1964 mandated the first academic effort to compile
educational outcome data and segment it by demographic group. Before 1966, most studies of
educational equity concentrated on educational inputs such as teacher preparedness or school
funding. Congress mandated that the U.S. Department of Education publish a report within two
years of enactment that outlined the disparities in educational opportunities in elementary and
secondary public schools. The Coleman Report provided the first comprehensive nationwide
review of academic performance achievement in public schools (Coleman, 1966). The Coleman
Report was a one-time project and, thus, did not have the capability of annual assessment.
Nonetheless, this report spotlighted the African-American achievement gap for the first time and
provided a benchmark to measure subsequent improvement.
In 1969, the National Assessment of Educational Progress (NAEP) began measuring what
students know and can do in mathematics. Every other year, eighth-grade students use their
knowledge of mathematical concepts and skills to solve problems. NAEP mathematics
AFRICAN-AMERICAN MATH READINESS GAP 25

assessments are valuable to researchers because they use uniform test booklets and collect
student demographic information over many years. NAEP data provides insight into long-term
academic progress by ethnic group. The African-American eighth-grade achievement gap in
mathematics measured 33 points on a 500-point scale in the inaugural National Assessment of
Educational Progress (NAEP, 1990). Compared to the inaugural 1990 NAEP, actual
mathematics assessment scores in 2007 were higher for both African-American and white
students (Vanneman, Hamilton, Baldwin- Anderson, and Rahman, 2009). Nonetheless, the
eighth-grade African-American student mathematics achievement gap persisted on the 2007
NAEP (N=147,000) with a differential of 31 points (NAEP, 2007). By the eighth-grade, 91% of
African-American students are not proficient in mathematics compared to 63% of white students
(NAEP, 2013, Haycock, 2006).
The eighth-grade African-American mathematics achievement gap is also confirmed by
the only national longitudinal study of low and high-level mathematics skills in eighth, tenth, and
twelfth-grade students: The National Education Longitudinal Study of 1988 (NELS:88).
NELS:88 uses long-term trend data to identify transition moments on a student’s academic
journey leaving middle school, attending high school, and, later, work, or college. African-
American and Hispanic students were less likely than white or Asian students to show advanced
proficiency on the NELS:88 (N=24,599) mathematics examinations (Green, Dugoni, Ingels, &
Camburn, 1995). This demonstrated mathematics achievement gap leads African-Americans to
take fewer advanced high school mathematics courses, more remedial classes, and score much
lower on mathematics assessments (NSF, 1999). In 1999, 70% of whites, but only 27% of
African-American 17-year-olds scored the 300 or more necessary to meet the New Basic Skills
(Murname & Levy, 1996) that are needed to secure a middle-class job (NAEP, 1999). Thus,
AFRICAN-AMERICAN MATH READINESS GAP 26

while all ethnic groups have experienced modest mathematics achievement gains, the African-
American achievement gap persists.
Advanced high school mathematics courses increase STEM interest. Research
abounds as to what increases student interest in entering and completing a STEM field pathway
(Blickenstaff, 2005; Mitchell & Hoff, 2006; Riegle-Crumb, Moore, & Ramos-Wada, 2011).
Some students are attracted to STEM fields from activities outside of formal coursework
including parents, science museums outings, or student clubs (Dabney et. al., 2012). However,
most students receive their primary motivation for STEM opportunities from formal school
coursework (Jones, Howe & Rua, 2000; Hazari, Sandler & Tai, 2008).
High schools offer advanced STEM coursework, including mathematics, to students for
three primary reasons: 1) to reduce the time required to obtain a college degree (National
Research Council, 2002); 2) to better prepare students for college STEM courses (Sadler & Tai,
2007); and 3) to increase interest in STEM careers (Tyson, Lee, Borman, & Hanson, 2007). In a
retroactive cohort study of students taking mandatory college English courses (N=4,691), an
attempt was made to isolate factors correlating to the pursuit of a STEM career (Sadler, Sonnert,
Hazari, & Tai, 2014). College students took a fifty-question survey to ascertain the
characteristics and high school courses that related to an interest in STEM careers. Students who
took at least one year of calculus in high school were found to have much higher odds of having
an interest in a STEM career (R=1.75:1.00).
Advanced coursework improves college STEM degree attainment. Fewer African-
American students take advanced high school mathematics, but when African-American students
complete a college preparatory math pathway they attain college STEM degrees at the same
percentage as white students. Burkam & Lee (2003) developed STEM-related course categories
AFRICAN-AMERICAN MATH READINESS GAP 27

using national data sets and then categorized high school mathematics into three academic levels:
low, middle, and advanced. The low academic level included pre-Algebra, Algebra 1 – Part 1,
Algebra 1 – Part 2, and informal Geometry. The middle academic level included many classes
associated with a college preparatory math track: Algebra 1, Algebra 2, Plane and Solid
Geometry, and unified Math 1, 2, and 3. The advanced level had the following courses:
Algebra, Trigonometry, Analytic Geometry, Introductory Analysis, Linear Algebra, AP and
general Statistics, AP and general Calculus. These categories provided the structure in
multivariate regression models to determine the relationship between high school mathematics
course taking, the demographic background of the students, and its relationship to mathematics
achievement. The study concluded that African-American and Hispanic students who attempt
advanced high school mathematics courses pursue college STEM degrees at the same rate as
white students. Racial disparities in the pursuit of STEM degrees occurred because African-
American students are disproportionately unprepared for STEM in high school (U. S.
Department of Education, 2003). As a result, course-taking has a strong relationship to eighth-
grade to twelfth-grade mathematics achievement and twelfth-grade mathematics proficiency.
Earlier academic achievement also does not diminish the effect of course taking on achievement
(Madigan, 1997). More rigorous high school mathematics course work correlates to higher
achievement on the Scholastic Aptitude Test (SAT) (Riegle & Crumb, 2006).
African-American and Hispanic students have the lowest percentage of advanced high
school mathematics course taking (Tyson, W., Lee, R., Borman, K. M., & Hanson, M.A., 2009).
Tyson et al. used a longitudinal dataset (N=94,078) collected from over 350 Florida public high
schools to analyze high school and college course taking and post-education employment.
African-American student’s complete baccalaureate degrees in Florida (11.4%) at a lower rate
AFRICAN-AMERICAN MATH READINESS GAP 28

than whites (27.1%) do. However, there was no perceptible difference between the percentage
of African-American and white students who obtained a baccalaureate degree in a STEM major.
Tyson (2007) posits that the attrition rate of African-American students on the high school
mathematics pathway, before advanced courses, is largely responsible for the STEM degree
attainment gap between African-American and white college students. High school students
who take at least one year of calculus have a higher interest in STEM careers (Sadler, 2014). A
retrospective cohort study compared college students planning to enter a STEM career with those
who were not to determine the effect of advanced high school coursework had on this
orientation. Students completed questionnaires choosing their career goals from a list of five
occupational groups, two from STEM fields. While African-American students complete fewer
advanced high school mathematics courses and have less interest in STEM careers; this leads
directly to lower household incomes for African-American households.
African-American STEM gap leads to an income gap. Despite extraordinary efforts to
attract women, men continue to dominate STEM professions (Hill, 2015). Within the cohort of
male STEM professionals, African-American men remain the most underrepresented ethnic
minority (Landivar, 2013), an increase of 45% (N=12,484 to 18,102) from 2002 to 2012 (NSF,
2013). While African-Americans make up 10.8 percent of employed workers, they comprise
only 6.4 % of employees in STEM occupations (Landivar, 2013). According to the U.S.
News/Raytheon STEM Index, there has been no significant progress since 2000 in closing the
racial gap for interest in STEM. “Though the Bachelor's degrees earned by black college
students rose 60 percent from 2000 to 2014, it made up a smaller share of the overall number of
bachelor's degrees earned by black students during the same time (Escobar, 2016).” This
AFRICAN-AMERICAN MATH READINESS GAP 29

suggests more African-Americans are attending college, but they are under-represented in high
paying college majors.
The four highest-paying occupations in the United States are all STEM dominated with
average annual earnings for Architecture and Engineering ($66,206); Computers, Statistics, and
Mathematics ($61,998); Health ($61,868); and Business ($51,861). African-Americans are
disproportionately attracted to the lowest-paying professions with average annual earnings of
Industrial Arts, Consumer Services, and Recreation ($42,107); Psychology and Social Work
($42,107); and Arts ($43,034). The disproportionate percentage of African-American students in
STEM occupations foreshadowed their low representation among STEM majors in college.
African-American students represented only eight percent of engineering, seven percent of
mathematics, and five percent of computer science majors (Carnevale, Smith, & Melton, 2016).
An example of the economic impact of earning a STEM degree is the “$4 million lifetime
earnings difference between a four-year degree in early childhood education and petroleum
engineering (Downs, 2016).” African American college students, then, are underrepresented in
higher-paying STEM degree pathways and overrepresented in lower-paying non-STEM majors.
This disparate propensity for African-American college students to choose non-STEM
college degrees and occupations leads to significantly lower lifetime household incomes. This
STEM educational gap explains part of the overall gap in wages between African Americans and
whites. As shown by Figure 1, African-Americans have a wage gap at all levels of educational
attainment. Counterintuitively, the gap is widest among African Americans who have advanced
degrees.

AFRICAN-AMERICAN MATH READINESS GAP 30

Figure 1
African-American Income by Educational Level

AFRICAN-AMERICAN MATH READINESS GAP 31

African-American Math Performance Variables
Isolating the variables that explain disproportionately low math proficiency outcomes for
African-American students has occupied researchers since the achievement gap was first
identified. Three significant potential reasons identified in relevant research are: 1) family
influences; 2) an African-American math identity; 3) teacher subject matter competence; and 4)
culturally relevant instruction. This section summarizes current research on these four
approaches as possible explanations for the current math achievement gap for African-
Americans.
Family influences. A significant, if not primary, explanation for the persistent African-
American achievement gap is parent and other family influences on school participation. The
genesis of the poor reading and mathematics performance is the family unit (Armor, 2006;
Glassman and Roelle, 2007). A gap in academic performance presents itself during
kindergarten when the school has not yet had the opportunity to impact student learning (Armor,
2006). Armor (2006) posits many family variables affect academic achievement including
academic encouragement, emotional support, parent education attainment, socio-economic
status, age of mother, nutritional levels, and birth weight. Because African-American students
are disproportionately from households below the poverty line, the lack of books, computers, and
other educational resources may affect academic pursuits (Steptoe, 2004). Finally, parental
education attainment reduces participation and self-efficacy as children confront a more
demanding curriculum in the secondary school years (Gonzalez-DeHass & Williams, 2003).
This study seeks to better understand how African-American parental participation can usefully
improve student math proficiency.
AFRICAN-AMERICAN MATH READINESS GAP 32

African American Math Identity. Many recent researchers posit that successful math
interventions directed at African-American achievement gap must be informed by need for
African American students to develop math and science identities during the early stages of their
K-12 education (McGee & Pearman, 2014). Factors in building a strong math identity in the
primary years include: computational fluency by the third grade, math engagement, extrinsic
recognition, and relational connections between teachers, families, and out of school activities
(Berry, Thunder, & McClain, 2011). In relation to improving STEM outcomes, developing
successful science identities may prove challenging for many African-American males because
of systemic bias and discrimination in some classroom settings (Boykin & Noguera, 2011).
These collective African American identities may prevent them from seeing themselves as
mathematicians and scientists (Aschbacker, Li, & Roth, 2010).
Teacher Subject Matter Competence. Another explanation for the African-American
achievement gap is the established teacher competence in mathematics (Aaronson, Barrow, &
Sanders, 2003; Jencks & Phillips, 1998). Nationwide, students in high poverty school districts
with large African-American student populations are disproportionately taught mathematics by
teachers without even at least a college minor in math (Haycock, 2001; Darling-Hammond,
2006). Smith, Desimone, & Ueno (2005) established a link between the teacher’s level of
content knowledge and student achievement. Smith et al (2005) also found that teachers who
had at least a minor in mathematics and subject matter certification were more effective math
instructors.
Darling-Hammond (2006) found a teacher’s subject matter mastery and knowledge of
pedagogy have a strong impact on student learning. Research comparing teacher subject matter
examinations across three states has confirmed that knowledge of the subject is a strong factor in
AFRICAN-AMERICAN MATH READINESS GAP 33

student mathematics success (Ferguson, 1991; Sanders & Horn, 1996, Johnson, 2005). Teacher
scores on the Texas Examination of Current Administrators and Teachers (TECAT) were found
to be the most significant teacher input on African-American math and reading achievement
(Ferguson, 1991). These results were confirmed in a similar study in Tennessee using research
findings from the Tennessee Value-Added Assessment System (TVAAS) database (Sanders &
Horn, 1996). Finally, a study by Johnson (2005) compared eighth-grade student math test scores
(N=1995) on the Alaska Benchmark Exam (ABE) to various forms of certifications of their math
teachers (N=204). A logistic regression analysis found that “students who had teachers with a 7-
12 math certification for two years were twice as likely to pass the ABE in math.” (Johnson,
2005). Although the research strongly points to a lack of math teachers with content competence
as a significant contributing factor to low African-American math achievement, this variable is
difficult for a middle school principal to overcome due to a dearth of certificated math teachers
seeking employment in California schools (Darling-Hammond, Sutcher, & Carver-Thomas,
2018).
Culturally relevant teaching. Significant research has posited the lack of mathematics
instruction targeted to specific aspects of the African-American cultural experience as an
explanation for poor performance (Orey & Rosa, 2007; Burns, Keyes, & Kusimo, 2005). In a
review of the potential disconnect between traditional mathematics education and the reality of
many African-American students’ lives, white (2012) identified three foundational case studies
that argue the need for culturally relevant math instruction. First, Murell (1994) identified a
specific recommended standard, math curriculum presented through discourse to improve
conceptual understanding and conducted an ethnographic inquiry into two middle school
classrooms that implemented the standard. He found that although African-American students
AFRICAN-AMERICAN MATH READINESS GAP 34

participated in math concept discussions, there was a reluctance to share a lack of understanding
with their classmates.
Secondly, Tate (1995) posits that conventional math teaching methods are a “foreign
pedagogy” for many African-American students. For African-American students to thrive in this
type of math classroom, he found that they would need to have the same household experience as
white students. To change that dynamic, African-American students would have to bring their
home life and other cultural experiences into the math classroom. Finally, Tate (1990) witnessed
students in his daughter’s eight grade math class had difficulty understanding abstract math
concepts. He found that by connecting mathematical concepts to cultural experiences, students
were better able to master algebraic concepts. These three studies are representative of a school
of thought that advocates mathematics instruction specifically tailored to the relevant ethnic sub-
group of students.
But, implementing culturally responsive instruction on a scale necessary to change math
achievement for African-American students could be problematic. Viewed through the lens of a
middle school principal seeking to narrow the African-American achievement gap in
mathematics, this is a difficult variable to influence. Certificated math teachers, especially
African-American teachers, are very difficult to hire due to chronically scarce high pools in
California (Darling-Hammond, Sutcher, & Carver-Thomas, 2018). Hiring any math teacher,
much less those schooled in culturally relevant teaching techniques, is a challenging exercise.
Adding to that burden is the very diverse nature of Timber Middle School’s student body. All
classrooms contain statistically significant sub-groups of African-American, Asian-American,
Latino, and white students. Offering culturally relevant instruction in a meaningful way to all
AFRICAN-AMERICAN MATH READINESS GAP 35

these groups in a daily one-period mathematics class is a tall order for even the most
accomplished teacher.
Successful African-American Math Interventions
Given the persistent African-American math achievement gap since it was first identified
in the Coleman Report (1966), it is not surprising that a conclusive “magic pill” program has not
been found to narrow the gap. In California, African-American students who are both college
aspirational and unprepared for college-level mathematics usually enter the community college
system. In this brief review of three programs, some modest success at increasing African-
American measures of math success are found. The three programs are: 1) an effort by Los
Angeles Community Colleges to focus on specific attributes designed to improve African-
American performance in development math courses (Gebru, 2009); 2) a review of the
performance of African-American students participating in a suite of federal initiatives known as
the “TRIO” programs at four Southern California school sites (Polee, 2017); and 3) an analysis
of a math boot camp for students not yet qualified for college-level math courses at Cosumnes
River College in Sacramento, California (Powell, 2017).
Gebru (2009) used data collected from African-American students participating in math
development programs at three different community colleges in Los Angeles County. The study
found specific components that were used to improve participation in the program and successful
completion of the developmental math program. Assessment and placement were employed in
two ways: to identify individual skill levels at the starting point and to ensure a successful
outcome. Boylan (2002) found that it was critical to know specific skill levels to serve
underprepared students. Students subject to mandatory assessment and placement have
improved academic performance (McCabe, 2000). A correlation was also found between
AFRICAN-AMERICAN MATH READINESS GAP 36

counseling and academic advisement services and success in the developmental courses. Finally,
individual tutoring was present, consistent with its common use in assisting students unprepared
for college mathematics (Boylan & Bonham, 2007). African-American students who were
successful in completing the developmental math program participated in academic advisement
and counseling (91.9%); learning communities (86%); supplemental instruction (71.2%); and
tutoring (67%) services (Gebru, 2009).
Upward Bound, Talent Search, and Student Support Services, collectively known as
“TRIO,” are a group of federal programs designed to decrease school dropout rates, reduce the
need for remedial education, and provide information on the benefits of post-secondary
education (US Department of Education, 2015.) TRIO now includes additional federal programs
that provide academic tutoring, personal counseling, mentoring, and other supports to increase
access and retention for underserved populations. In a study of four TRIO sites and three
different Los Angeles area community colleges, Polee (2017) found that the college-going rate
for African-American program participants increased.
Cosumnes River College, a community college in Sacramento, California, conducts a
“Math Boot Camp,” a developmental math program for students not prepared for college
mathematics. African-American students were the cohort most likely to enroll in math camp
(Powell, 2017). Math Camp participation was strongly correlated to persistence in completing
the developmental math sequence within four semesters. These three programs illustrate the
need for more focus on middle school mathematics. The African-American program participants
in all three studies are students who aspire to a college education but graduated from high school
without preparation for advanced mathematics. Academic advisement focused learning
AFRICAN-AMERICAN MATH READINESS GAP 37

communities, supplemental instruction, and individually paced tutoring might also inform a
middle school math intervention.
Impact of parent involvement
Parent self-efficacy. Relevant to this study is the step-by-step link between African-
American parents’ confidence, their involvement in their child’s school, and student academic
outcomes. Collins (1990) reported that parents have a significant role in affecting the positive
development of their adolescent children. Whether parents believe they can positively affect
student outcomes can be defined as parent efficacy (Bandura, 1976, 1986). A parent’s
confidence in their ability to affect their student’s school performance increases parental school
involvement (Eccles & Harold, 1996). Finally, greater school participation among African-
American parents leads to parental efficacy and positive student academic outcomes (Hoover-
Dempsey et al, 1992, 1997).
In a study of the parents of kindergarten through fourth-grade children in an urban public
school district (N=390) and their teachers (N=50), several indicators of parental involvement
were measured (Hoover-Dempsey, Bassler, & Bressie, 1992). Hoover-Dempsey, et al (1992)
found a statistically significant relationship between parent self-efficacy and time spent by
parents on: 1) classroom volunteering; and, 2) educational activities with their children.
Although parental self-efficacy has a clear link to parental involvement in their child’s school,
this correlation becomes more fragile when the socio-economic status of the parent is considered.
Existing research has identified three parental behaviors that are foretold by parental self-
efficacy: 1) parental involvement; 2) parental monitoring; and 3) parent-child communication
(Steinberg, Lamborn, Dornbusch, & Darling, 1992). Shumow and Lomax (2002) used a social
cognitive model to investigate whether the socio-economic status (SES) of parents predicted the
AFRICAN-AMERICAN MATH READINESS GAP 38

three behaviors commonly associated with parental self-efficacy. Their study reviewed a
stratified random sample (N=929) of parents and their children to determine if this model
successfully predicted parental efficacy. The Shumow and Lomax (2002) model was tested on
each of the three different ethnic subgroups: African-American (N=259); Latin-American
(N=283); and European-American (N=387) parents. For African-American and European-
American parents, the model found that socio-economic status predicted parental efficacy, which
correlated with the three desired parental behaviors (parental involvement, parental monitoring,
and parent-child communication). If low African-American parental participation is explained
by the disproportional low SES, what factors could increase involvement in school activities and
decisions?
Different perceptions of parent involvement in math education. Research into the
value attributed parental involvement in math education illustrates perception differences among
parents and teachers. At a basic level, researchers disagree on what comprises parental
involvement (Lewis & Forman, 2002). Parent involvement can be defined as a wide range of
activities that can: improve achievement, produce lower dropout rates, foster positive attitudes
towards learning and school, increase parent-child communication, promote positive student
behaviors, enhance educational experiences for students from low socio-economic families,
increase home and community support for schools, and be a basic right of all parents (Peressini,
1998, p. 557). In mathematics education, there is a paucity of systemic efforts to involve parents
in math learning (Peressini, 1998). Some research portrays parental beliefs about learning
contributing to their children’s failure in math (Peressini, 1998, p. 567). Recent research
challenges the idea that parents are problems to overcome (Barton, Drake, Perez, St. Louis, &
George, 2004). But in earlier research, parents can be depicted as: 1) not understanding math; 2)
AFRICAN-AMERICAN MATH READINESS GAP 39

not understanding their children’s math and characterizing their children’s math work as
incorrect; 3) not interested in their children’s math work; or 4) resistant to change. These
counter-narratives provide useful insight in successful implementation of math interventions,
where parental support could be the sustaining influence (Jackson & Remillard, 2005).
Available research then strongly suggests that a successful math intervention should start with a
clear focus on the type of parental involvement that is successful and is also consistent with
parent beliefs.
Parental Participation. Parents are more likely to become involved in their child’s
school if they believe they have the requisite knowledge and skills needed to help their children
succeed (Bandura, 1997). If parents believe that their actions will facilitate learning
improvements and academic performance for their children, they will engage (Hoover-Dempsey,
Bassler, & Brissie, 1992; Stevenson, Chen, & Uttal, 1990). Parents are more willing to
participate in the school decision-making process and have higher self-efficacy when they are
more knowledgeable (McCrudden, Schraw, & Hartley, 2006; Bandura, 2000). In sum, parental
self-efficacy, knowledge, and participation are tightly linked.
Relevant to the middle school African-American students of interest in this inquiry,
parental involvement and support are particularly challenging at the secondary level.
Parental motivation to participate in school matters related to their children sharply declines as
children enter high school (Desplandes & Bertrand, 2005; Freedman-Doan, Arbreton, Harold, &
Eccles, 1993). This decline in parent involvement during the high school years suggests their
belief in being able to help their children is in doubt. A possible reason for this decline in parent
participation during the secondary years is the sophisticated courses that students navigate in
high school. Gonzalez-DeHass and Willems (2003) found that the more complex the curriculum
AFRICAN-AMERICAN MATH READINESS GAP 40

at the high school level reduces parental involvement and self-efficacy. A predictor of parent
participation at the secondary level is the parent’s ability to navigate the complicated curriculum
(Simon, 2001). This study seeks to better understand whether greater knowledge of the
importance of math proficiency and the high school math pathway could increase African-
American parental interest and support of an additional math instruction period.
Parent relationship to academic achievement. Academic literature has identified clear
positive student outcomes from parental involvement in school work. In their meta-study of the
effect of parental involvement on student achievement (Hill & Tyson, 2009), a positive
relationship was found with three types of parent activity. First, when parent interaction with
students and teachers creates an understanding of the purpose, goals, and meaning of academic
performance, student performance can improve. Second, parental communication of
expectations for students has a positive impact on student learning. Finally, academic
socialization by parents offering students strategies they can use to improve results were found to
have a positive effect (Hill & Tyson, 2009).
Counterintuitively, Hill and Tyson (2009) found no identifiable relationship to student
outcomes for only one common type of parental interaction with students: supervising and
grading homework. But, research on the effect of parent involvement in direct homework
assistance is mixed. Zelkowski (2011) found a positive relationship for parental homework
assistance and (O’Sullivan, et al., 2014) found no effect on student academic outcomes. The
lack of a strong relationship to academic achievement between parent involvement and
homework assistance has important implications for this study.
Parent relationship to math performance. Specifically, parental impacts on student
math performance are also supported by the literature. Partnerships between parents and
AFRICAN-AMERICAN MATH READINESS GAP 41

teachers could impact teaching strategies and student math outcomes (Martin, 2012; Reece, et
al., 2013). The positive effects of certain parental participation on student math performance has
been found across all socio-economic subgroups. Shaver and Walls (1998) examined the impact
of parental participation by grade level on mathematics achievement of Title I students in grades
2-8. They analyzed data from a sample of students and their parents (N=335) to measure the
effect of socio-economic and gender variables on student success. They found that parent
involvement, notwithstanding socio-economic status, is impactful on student mathematics
outcomes (Shaver & Walls, 1998). In a caution for some types of math interventions, Zelkowski
(2011) found that parents must have the technical competence to meaningfully impact student
mathematics homework.
African-American parent relationship to math performance. The differences and
ramifications of our stakeholder group in focus, African-American parents, on student math
achievement was also explored. Research support has found significant variation for African-
Americans in parent: involvement (Kim, 2015; Latunde, 2017), beliefs (Lareau, 1987; Barg,
2019), and relationship to academic outcomes (Hill & Craft, 2003). In contrast to direct
homework assistance, encouraging African-American parents of the benefits of their
involvement in mathematics learning by providing structure and information to complete
mathematics work and improve student performance could show positive results on academic
outcomes (O’Sullivan et al., 2014; Zelkowski, 2011). When parents are a motivational source
for students, their involvement makes an impact on African-American student gains in
mathematics proficiency (Noble & Morton, 2012).
Of interest to African-American parent participation in math achievement is the
relationship with their student’s teacher. Parent and teacher collaboration build the relationships
AFRICAN-AMERICAN MATH READINESS GAP 42

necessary to adjust educational practices that increase African-American student engagement in
math (Cousins & Mickelson, 2011; Ishimaru, 2014). When schools have fostered these positive
parent/teacher collaborations, middle-class African-American parents had the same levels of
engagement as white parents (Cousins & Mickelson, 2011). While one of the answers to
improving African-American student math proficiency is likely more parent involvement in
specific aspects of the educational process, African-American parents and students might not
have relationships with the school that support student achievement (Louque & Latunde, 2014).
Fostering African-American parental participation in a Timber Middle School math intervention
program appears supported by the relevant literature.
Alternative Math Courses During and After School
After school programs. Colloquially known as “after school programs,” efforts to
improve academic performance after the regularly scheduled school day are also referenced by
researchers: out of school time or “OST” (After School Alliance, 2011; Beckett, et al., 2009:
Hall and Gruber, 2007). Both the No Child Left Behind Act (NCLB) and its successor federal
program Every Student Succeeds Act (ESSA) emphasize after school programs. While after
school programs have had a variety of recreational and social objectives in the past, they are
increasingly viewed as an opportunity to improve academic achievement for underperforming
students (After School Alliance, 2011; James-Burdumy et al., 2005).
A study of elementary and middle school students, including 35 after-school programs,
found modest positive impacts on math performance and that low-income students had more
improvement than middle-income students (Vandell et al., 2007). A meta-analysis of K-8 after-
school programs found a statistically significant impact on math achievement (Crawford, 2011).
Crawford (2011) also confirmed that more time to learn the curriculum was a key component of
AFRICAN-AMERICAN MATH READINESS GAP 43

this increase in math performance. Beckett et al. (2009) posited five recommendations for
academic improvement focused after school programs: 1) after-school programs are
academically aligned with the school day curriculum; 2) high levels of student attendance; 3)
instruction at both the individual and small group setting; 4) interactive student learning
opportunities; and 5) continual program review using results to improve quality. Many schools
have adopted these recommendations to facilitate academic achievement gains (Stonehill, et al.,
2009). The research, although limited, has confirmed that after-school programs can improve
math achievement for less than proficient students but may require high levels of participation to
meaningfully impact the achievement gap.
“Double Dose Math.” At the other end of the spectrum of interventions including
additional math instruction time are two periods of Algebra instruction or a “double dose.”
Double dose math is typically offered to high school freshmen who are having difficulty passing
Algebra. Since Algebra is a high school graduation requirement in California, its importance is
not limited to the college-bound, but to those whose objective is secondary school graduation.
Double dose math has a mixed history in the relevant research. The Chicago Public Schools
implemented a version of double dose math and saw an increase in test scores, but a decline in
passage rates in Algebra courses (Durwood, Krone, Mazzeo, 2010). Since less proficient
students were assigned two periods of math, the remaining proficient students were left in single
period Algebra courses. This sorting by ability resulted in both groups, single and double dose
math, increasing student assessment scores (Nomi and Allensworth, 2009). Long term benefits
of double dose math included increases in college entrance exam scores, high school graduation
rates, and college enrollment rates (Cortes, Goodman and Nomi, 2013).
AFRICAN-AMERICAN MATH READINESS GAP 44

Middle school double math programs have found that doubling of math periods may
diminish over time (Heitin, 2014). Taylor (2014) reported that sixth-grade students enrolled in
double math courses were assessed higher while in the intervention, but lost half of the gain
when they were returned to single math periods in later grades. Relevant to the implementation
of a successful double math program is that students testing just below proficiency improved
more than students far below proficiency (Heitin, 2014; Taylor, 2014). One important difference
between the Chicago Public Schools’ high school double dose program and the referenced
middle school program was the use of the second period. In the Chicago Public Schools
program, one period was used for grade-level curriculum and the other was used for remedial
math skill development. This infers that a second math period dedicated to math skill
development at the developmental level of the individual student could be most effective.
Computer and Team Assisted Mathematics Acceleration (CATAMA) Lab. Balfanz,
Ruby, and MacIver (2008) conducted a three-year evaluation of the Computer and Team
Assisted Mathematical Acceleration (CATAMA) Lab a math intervention designed by the
Center for Social Organization of Schools at Johns Hopkins University. Although the CATAMA
Lab could be adapted as a supplement to all math learning levels, it was targeted to
underperforming students at low socio-economic schools in urban areas. The Lab was conducted
by a single experienced and credentialed math teacher and used several different instructional
methods. Individualized computer instruction, direct instruction, small group learning, and
individual tutoring are used to teach both skills and concepts depending on the needs of the
students. The Lab period features 20 to 30 minutes of individualized computer instruction that
takes advantage of individualized supplemental capabilities of computer-based instruction
(MacNab & Fitzsimmons, 1999; Abidin & Hartley, 1998). The Lab is designed to be in place of
AFRICAN-AMERICAN MATH READINESS GAP 45

an elective course and allows the student to continue with their regular grade-level course during
a different period of the day.
The CATAMA lab program was found to have a significant positive impact on Lab
students’ math proficiency, with Lab students achieving double the results on a pre-algebra test
compared to students that did not participate in the study (Balfanz, Ruby, & McIver, 2008).
Balfanz, Ruby, and McIver also found that the gain in math proficiency for the students that
participated in the Lab was larger than would have been expected from the same students
spending more time in their regular math class.
Because of the difficulties with scaling a voluntary after school remediation program to
include many less than proficient students that decline to participate, this option as limited use in
Timber Middle’s goal of reducing the math achievement gap. At the same time, a double dose
math program that only increases direct instruction at grade level does not address the pre-
algebra math skills deficiencies of the less than proficient students. This study, then, focuses on
a second math lab period similar in design to the CATAMA lab as the intervention with the most
promise.
Impact of Practice
Many researchers have found that practice has a clear impact on learning. Substantial
percentile gains in the following studies indicate the strong positive learning effect associated
with practice: Ross (1988) found a 40% percentile gain in learning effects; Bloom (1976) saw
gains from 21 to 42% in various sub-groups, and; Kumar (1991) documented a 44% increase.
Regular practice bolsters automaticity and requires less working memory capacity (Schraw &
McCrudden, 2006).
AFRICAN-AMERICAN MATH READINESS GAP 46

If practice produces such positive learning outcomes, how much practice is useful and
effective to produce better learning outcomes? Anderson (1995) and Newell & Rosenbloom
(1981) explored the number of practice sessions needed for competence, when the most
significant gains occurred in the practice cycle, and at what point future practice sessions
diminish in value. A summary table of the Anderson (1995) and Newell & Rosenbloom (1981)
work in Marzano, Gaddy & Dean (2000) suggests that 24 practice sessions on a particular skill
are required on average to achieve 80% competence. The most substantial gains come from the
initial practice opportunities, with a 22% increase in learning after the first practice session. But
after 17 practice sessions, each new practice opportunity provides diminishing results with
increases in learning of less than 1%.
While a critical component of the learning experience, the practice of skills and processes
is not a substitute for deep conceptual learning (Mathematical Science Education Board, 1990).
Clement, Lockhead, and Mink (1979) have shown that even a sound grounding in the steps of
algebraic math does not correspond to a conceptual understanding. Students who are most able
to solve mathematical problems have learned how at the conceptual level first (Davis, 1984;
Romberg & Carpenter, 1986). So while practice cannot replace initial conceptual learning, for
some students it may be a critical supplement necessary for mastery (Marzano, Gaddy & Dean,
2000). The intervention of interest in this study, an extra instructional period for students that
are less than proficient in mathematics, assumes this additional instructional time will provide
practice opportunities that supplement the direct classroom conceptual instruction.

AFRICAN-AMERICAN MATH READINESS GAP 47

Impact of Instructional Time
An additional math period to permit individualized math practice for less than proficient
students is the proposed intervention of this study. Instructional time allows for understanding,
prediction, and control (Berliner, 1990). Past research on instructional time as an intervention
has been criticized for either being without academic rigor (McNamara, 1981) or, if measured
reliably, not a powerful variable (Karweit, 1983; Levin, Glass, & Meiser, 1984; Levin & Tsang,
1987). Nevertheless, in a foundational study on instructional time, Berliner (1990) explains that
instructional time is complex and must be differentiated among allocated time, engaged time,
time-on-task, academic learning time, transition time, and waiting time to accurately measure
effectiveness.
Based on a large scale, cluster-randomized sample of Danish fourth-grade students
(N=1931), Anderson, Humlum, and Nandrup (2015) found that increasing instructional time in
school increased learning (SD=0.15). Counterintuitively, they also found that a general increase
in instruction time is at least as effective as an expert developed, detailed teaching program that
increases instruction with the same amount of time. School officials increasing instructional
time often face a choice between highly regulated direct instruction and a differentiated program
attuned to individual skills and needs (Anderson, Humlum, & Nandrup, 2015).
Battisin and Meroni (2016) studied the short-term effects of a large-scale intervention
targeting low achieving secondary schools (6th to eighth-grade). The Quality and Merit Project,
funded by the European Union, funded extra instructional time for schools in southern Italy with
academic performance much lower than the rest of the nation. They found that extra
instructional time improved mathematics achievement (Battisan & Meroni, 2016).
AFRICAN-AMERICAN MATH READINESS GAP 48

In sum, research on increased instructional time as an intervention was found to 1) be
benign as an intervention conceptually (McNamara, 1981); 2) be complex and require more
focus on the actual use of the additional time (Berliner, 1990); 3) to improve math performance
in underperforming student populations (Battistin & Meroni, 2016); 4) as useful on
individualized student time as for increased direct instruction (Anderson, Humlum, & Nandrup,
2015); and 5) could result in declining persistence after short-term gains (Taylor, 2014).
Role of Stakeholder Group of Focus
The key stakeholder group of focus in this study is African-American parents at Timber
Middle. Although all ethnic subgroups at Timber Middle trail California averages in math
proficiency scores, the persistent achievement gap among African-American students has been a
particular focus of Redwood Unified. Recommendations for improvement in African-American
student math proficiency would also likely improve other sub-groups with challenging
proficiency rates. Table 4 illustrates the ethnic sub-group by percentage at Timber Middle as
compared to the State of California.
Table 3
Timber Middle School Math Proficiency by Ethnic Sub-Group (2017-18)
Ethnic Sub-Group Timber Middle School California

African-American 13.04% 19.74%
Asian-American 45.46% 73.54%
Latino 27.24% 26.65%
white 42.37% 53.57%
Source: CAASPP, 2017-18.

Over the past twenty years, many interventions have been attempted by Redwood Unified
to increase math proficiency including voluntary after-school programs, integrated mathematics
curriculum, teacher professional development, math software programs, and new textbooks.
AFRICAN-AMERICAN MATH READINESS GAP 49

Most of these reforms have not improved mathematics proficiency as measured by state
assessment tests (CAASPP, 2017). One reform that did increase mathematics proficiency in
Redwood Unified as measured by state assessment tests was the institution of extra math
instructional time for less than proficient students from 2005-2009. As illustrated by Figure 3
and Table 4, proficiency measurably increased across all ethnic subgroups. African-American
student math performance almost doubled over the five-year period, increasing from 19%
proficient in 2004 to 37% proficient in 2009 (Redwood Unified, 2009).
Figure 2
Redwood Unified - Math Proficiency by Ethnic sub-group (2004-09)

AFRICAN-AMERICAN MATH READINESS GAP 50

Table 4
Redwood Unified - Math Proficiency by Ethnic sub-group (2004-09)
Ethnic Sub-Group 2004 2005 2006 2007 2008 2009
African-American 19% 26% 29% 32% 35% 37%
Asian-American 45% 56% 60% 63% 66% 62%
Latino 30% 36% 42% 43% 45% 47%
White 47% 54% 56% 59% 59% 58%
Source: Redwood Unified (2009).

By 2014, a new statewide assessment system (CAASPP) began measuring student math
performance in California and Redwood Unified had discontinued the extra math instructional
time. Currently Timber Middle offers one instructional period for math and a voluntary after-
school intervention program. Many explanations for the discontinuation of the extra math
instructional time for less than proficient students are possible: no statewide assessment to draw
attention to results; new school boards; installation of the new common-core math standards are
just a few. This study assumes one reason for the end of the additional math instructional time
was a lack of parental support. Parents may not have been aware of the improvement math skills
under the additional math instruction time or perhaps objected to their children being singled out
for additional math instruction during the school day. Regardless, to attempt the reintroduction
of the additional math period for students with low math proficiency would benefit from a
significant effort to communicate the rationale of the program to African American parents in
particular.

AFRICAN-AMERICAN MATH READINESS GAP 51

Clark and Estes’ Gap Analysis Framework
This study used the Clark and Estes (2008) gap analysis conceptual model to isolate the
gap between articulated organization and stakeholder groups’ performance goals and their actual
performance level. If a gap exists, the next step in this process is to scrutinize the stakeholder
knowledge, motivation, and organization influences that may prevent the organization from
reaching its performance goals (Clark and Estes, 2008). First, knowledge and skills are split into
the four types defined by Krathwohl (2002): 1) factual; 2) conceptual; 3) procedural, and; 4)
metacognitive. These four types of knowledge types are designed to understand whether the
stakeholders have particular knowledge to meet the performance goal. Next, motivational
influences are identified using the principles identified by (Rueda, 2011), specifically attributions
and utility value. Finally, models and settings are considered as organizational influences,
including processes, resources, and culture (Clark & Estes, 2008).
The components of the Clark and Estes (2008) gap analysis were employed to catalog
Redwood Unified School District’s possible knowledge, motivation, and organizational
deficiencies in meeting their goal of reducing the math proficiency achievement gap for African-
American eighth-graders. The first section reviews assumed influences on disproportionately
low African-American eighth-grade math proficiency from a knowledge and skills lens.
Secondly, assumed motivational influences are identified and examined. Finally, assumed
organizational influences on eighth-grade African-American math proficiency and readiness for
advanced high school mathematics was explored. The assumed stakeholder knowledge,
motivation, and organizational influences were tested using the methodology described in
Chapter 3.

AFRICAN-AMERICAN MATH READINESS GAP 52

Knowledge, Motivation, and Organizational Influences
There is a considerable amount of research related to parental knowledge and motivation
and their participation in their children’s school. However, this study focuses on factors that
would lead African-American parents at Timber Middle to support a single intervention
program: an additional math instructional period. Table 22 in Chapter 3 summarizes each
question on the survey, the knowledge and motivation influence that is being probed, and
whether it is a knowledge or motivation influence. This section is a brief description of those
knowledge, motivational, and organizational influences.
The study will focus on two conceptual knowledge influences that might negatively
affect parental participation in the effort to improve the eighth-grade math readiness of African-
American students. First, is the importance of the traditional high school mathematics pathway.
Second, is the importance of core mathematics proficiency to post-secondary career and college
opportunities. Then two motivational influences are reviewed: 1) the role of self-efficacy in
student mathematics proficiency and 2) the need for real-world applications of math. Finally,
two organizational influences are outlined: 1) budgetary and scheduling resources and the lack
of a parent communication plan, and 2) a sense of helplessness from past failure. Table 5
integrates the organizational mission and goals with the knowledge, motivation, and
organizational influences.

AFRICAN-AMERICAN MATH READINESS GAP 53

Table 5
Knowledge, Motivation, and Organizational Influences in Redwood Unified
Organization Mission

To educate all students to their maximum potential and to prepare them to be responsible citizens.

Organizational Global Goal

Student math proficiency shall increase by 10% by the 2019-20 school year.

Stakeholder Goal

African-American 8th-grade student math proficiency shall increase by 10% by the 2019-20 school year.

Knowledge Influences Motivational Influences Organizational Influences

Parents need to understand the
importance of the articulated
high school math pathway to
college and career opportunities.
Parents need to attribute extra work
to improved student math
proficiency.
Lack of budgetary resources,
scheduling, and parental
communications plan to support
an extra math instructional
period.
Parents need to understand the
importance of maintaining
grade level math proficiency to
readiness for advanced high
school mathematics.
Parents need real world applications
of math concepts.
Sense of helplessness from past
reform failures.

AFRICAN-AMERICAN MATH READINESS GAP 54

Knowledge Influences
The importance of the math pathway. The first proposed knowledge influence is that
parents need to understand the importance of the articulated high school math pathway to college
and career opportunities. This understanding needs to come well before their students enter high
school. Unfortunately, if students are not already prepared and sufficiently proficient in
mathematics by the eighth-grade, they will be unable to complete the advanced math pathway
(Figure 1). This important gateway to high school and post-secondary opportunities for students
could be in conflict with their parents’ expectations because of a critical lack of knowledge.
Table 6
Potential Redwood High School Math Pathways
Pathway 8th Grade 9th Grade 10th Grade 11th Grade 12th Grade

Remedial

General Math I General Math II
Math 9
(Bridge)
May 10
(Bridge)

College Prep

Math 9
(Algebra)
Math 10
(Geometry)
Math 11
(Trigonometry
/Algebra 2)
AP Statistics

Honors
Math 9H (Algebra
Honors)
Math 10H
(Geometry
Honors)
Math 11H
(Trigonometry/
Algebra 2
Honors)
Analysis
Honors
AP Calculus
Source: Redwood High School Course Catalog (2018).

Valuable long-term student academic planning is compromised because of a lack of
access to information (Cabrera & La Nasa, 2008; Hrabowski, 1998). Students often have little
knowledge about the high school courses that are required to attend college (Choy, Horn, Nunez,
& Chen, 2000; Hrabowski, Maton, Greene, & Grief, 2002). Parents, particularly those who are
not college graduates, often don’t know fundamental planning steps to prepare for college
AFRICAN-AMERICAN MATH READINESS GAP 55

admission (Institute for Higher Policy, 1998). For many high school students, college planning
doesn’t begin until the junior or senior year of high school, too late to align with college
admissions realities (Immerwahr, 2003; Noeth & Wimberly, 2002). This parent information gap
may represent a negative knowledge influence on math readiness.
The achievement gap between African-American students and white students in English
and mathematics was first identified by Coleman (1966). Reigle-Crumb (2006) documented the
disproportionate percentage of African-American students who do not keep pace with the math
pathway leading to the advanced mathematics sequence in high school. This lack of preparation
for high school mathematics later evidences itself as African-American students fall further
behind as they progress through high school (Green, Dugoni, Ingels & Camburn, 1995).
Parents who have attained a college degree have knowledge of the mathematics
progression prior to their entering and throughout high school. This access to basic, factual
knowledge is central to preparation for the advanced high school mathematics track, which needs
to begin by the eighth-grade. Basic math skills (i.e. addition, subtraction, multiplication, and
division) need to be mastered before the California eighth-grade math standard of Algebra 1 can
be successfully navigated.
Parents of less than proficient math students in the primary grades (K-6) are certainly
informed their children are not up to grade level standard through report cards and annual
standardized test reports (CAASPP, 2018). But, if a parent does not have the experience of
successfully navigating the high school college preparatory math pathway, they are unlikely to
understand the importance of maintaining grade level proficiency in mathematics. Not
understanding the relationship between the advanced high school math pathway prerequisites
and post-secondary opportunities is a negative knowledge influence. Along with a lack of math
AFRICAN-AMERICAN MATH READINESS GAP 56

pathway knowledge, many parents don’t understand the critical role of maintaining grade-level
proficiency in mathematics.
The importance of math proficiency. The second proposed knowledge influence is
parents’ need to understand the importance of students’ maintaining grade-level math
proficiency for their readiness for advanced high school mathematics. It is a reality that, unlike
other academic subjects, students must maintain grade-level proficiency in kindergarten through
eighth-grade or they will most likely fall permanently behind. Throughout the primary grade,
mathematics builds from one skill and concept to another. Once a student falls behind,
attempting to master both the missed math concept and the next sequential subject can overload
the limited capacity to process new information (Miller, 1956). Falling further behind in math
proficiency during the primary grades can have a compounding effect as students fall further
behind with each successive year. If an incoming eighth-grade student is not ready for Algebra
1, the California eighth-grade math standard, they have no conceivable path to Advanced
Placement Calculus during their senior year in high school. This connection between math
proficiency and readiness for advanced high school mathematics is likely difficult for parents
who have not followed the path from high school to college admissions.
Interpreting standardized test scores can be a challenge for all parents, even those who
are college-educated. Understanding and acting on below proficiency math assessments may be
a challenge for some parents. Low socio-economic African-American parents face significant
obstacles to involvement in their children’s education (Halle, Kurtz-Costes, & Mahoney, 1997;
Koonce & Harper, 2005; Trotman, 2001; Williams & Sanchez, 2013). Moles (1993) identified a
modest parental educational background as a potential hindrance to their support for the
student’s schoolwork. For example, students from families with low parental educational
AFRICAN-AMERICAN MATH READINESS GAP 57

attainment receive less help on their homework because their parents’ education did not equip
them to assist (Carrasquillo & London, 1993). Also, parents can be discouraged from asking
questions about student performance by the “educational jargon” often used at school (Hoover-
Dempsey, Bassler & Brissie, 1992). The second knowledge influence, the importance of
maintaining grade-level math proficiency, is informed by the unique barriers faced by some
African-American parents in reviewing math proficiency reports. A longitudinal study tracking
the progression and performance of high school seniors, (Green, Dugoni, Ingels, & Camburn,
1995) found African-American students falling further behind in mathematics as they progressed
through their academic careers. This gap between actual math proficiency before the eighth-
grade and its relationship to readiness for the advanced mathematics pathway beginning with
Algebra 1 in eighth-grade is a critical knowledge influence.
Motivation Influences
One of the most challenging issues in teaching less than proficient students is a clear
understanding of parent motivation to assist their students in the learning process. Unmotivated
students cannot learn at maximal levels. Retaining information or even participation in learning
activities become obstacles to proficiency. Motivation is part of the knowledge, motivation, and
organization (KMO) gap analysis used to organize this study (Clark & Estes, 2008). It can be
defined as the general desire to do something. This study focuses on two assumed motivational
influences affecting parent interest in improving the mathematics performance of African-
American students: 1) parents need to attribute extra work as a necessary element in overcoming
their students’ lack of mathematics proficiency, and 2) parents need to find connections to real-
world applications of math concepts to create utility value in math proficiency.
AFRICAN-AMERICAN MATH READINESS GAP 58

Self-efficacy in mathematics proficiency. The first proposed motivational influence in
this study is that parents need to attribute their extra work to the ability of their students to
become math proficient. The attributional weight given parents between extra work and higher
performance is informed by how they emphasize the importance of ability versus effort. Parental
attitudes can then shape student beliefs toward the relationship between work and success in
academic pursuits. In a study of elementary school students, Ames and Archer (1987), found
that students who envisioned effort leading to success were more willing to view master of a
subject as a function of hard work. In a meta-analysis of one hundred and twenty-five studies
found that students who envisioned effort leading to success were more willing to view mastery
of a subject as a function of hard work. Their study showed that Japanese eighth-grade students
achieved higher mathematics rankings (5
th
out of 57) than in the United States (14
th
of 57)
eighth-graders (TIMSS, 2015). Holloway (1988) found that Japanese children subscribed higher
academic achievement to effort, while American children attributed academic success to innate
ability. In another example of the importance of work attributions for success, Chinese and
Chinese-American mothers ascribed low academic performance to a lack of effort, while
American Caucasian mothers attributed poor results to the school and ability of the student
(Hess, Chang, & McDevitt (1987). In a meta-analysis of one hundred and twenty-five studies
(N=61,456), Huang (2016) found a connection between student self-efficacy and achievement
goals.
Motivational influences affecting African-American male student’s mathematics
performance have been widely researched. Riegle-Crumb, Moore, and Ramos-Wada (2011)
reviewed data collected from an eighth-grade student cohort to compare ethnic subgroups to
white males regarding their interest in science and math careers. Differences in the importance
AFRICAN-AMERICAN MATH READINESS GAP 59

of enjoyment, self-concept, and achievement were isolated to determine if there was a
disproportionate impact on interest in STEM (Science, Technology, Engineering, and
Mathematics) careers. The study found that, in spite of a vast achievement gap between the two
groups, African-American and Hispanic male students had very similar science and math career
ambitions to white male students. While their interests and ambitions in STEM are similar to
white students, the African-American student cohort has a gap in primary grade math
proficiency.
If African-American students in the primary years (K-6) consistently fail to reach
proficiency as defined by California grade-level standards (CAASPP), they are likely to continue
falling short of proficiency in succeeding years. Motivating students behind the proficiency
curve to invest themselves in more time on task, would necessarily require the students to
attribute potential math proficiency to hard work. It is likely that not all students can maintain
this extra mathematics work and will continue to struggle with proficiency. But students that
assign a high utility value to the necessary work increase their expectancy of a successful result
(Eccles, 2006, Pintrich, 2003). African-American students have an interest in mathematics, but
are disproportionately not proficient at math. This study proposes the parents’ attributional value
of extra work to math proficiency is a motivational influence.
As an example of the link between the emphasis on hard work and parent self-efficacy,
mothers from Japan and the United States who have high parenting self-efficacy attribute that
characteristic to different personal backgrounds. Japanese mothers who were treated harshly as
children believed they developed personal strengths and competencies that increased their
parenting efficacy with their own children (Holloway and Behrens, 2002). Japanese mothers are
also held strongly accountable for their children’s actions by educators, media, and politicians
AFRICAN-AMERICAN MATH READINESS GAP 60

(Holloway 2000). Many researchers, then, focus on Japanese parents’ effectiveness in
motivating their children to study hard (Rothbaum, 2000b; Smith and Wiswell, 1982; Vogel,
1996). In a parenting survey of Japanese (N=309) and Korean mothers (N=372), Japanese
mothers’ education and self-efficacy related directly with their school related competence;
whereas Korean mothers’ household income affected both their self-efficacy and school related
competence. In contrast, mothers with higher efficacy in the United States are disproportionately
well educated, have strong social support infrastructure, and have children that are not difficult
(Cutrona and Troutman, 1986).
According to attributional value theory, it is assumed human beings will naturally attempt
to define the world in a manner that allows for a positive self-image (Heider, 1958). People
attribute their success or failure by assigning causes to events (Heider, 1958). To understand this
attributional causality, Heider (1958) identified three categories of attributes: internal or
external; stable or unstable; and controllable or uncontrollable. An example of an internal factor
would be when a child assigns blame for not being intelligent enough to understand a math
problem. By contrast, the same child might assign blame to an external factor by others, such as
poor teaching. If an attribute is stable, the person believes that, no matter what, the same
outcome is likely. For instance, a parent who views their student’s poor math performance as
stable could conclude it “doesn’t matter if the student studies harder, the child will still get a bad
grade.” But, if the cause of the poor result is due to an unstable attribute, the parent may believe
that more effort could result in better performance. Finally, part of the causation assigned to
poor performance can be viewed by the parent as controllable or uncontrollable. A controllable
attribute would be if a parent is convinced hard work could produce a better math performance.
But a parent who attributes their student’s academic performance as completely reliant on a bad
AFRICAN-AMERICAN MATH READINESS GAP 61

teacher would assign blame to that uncontrollable factor. Uncontrollable factors are someone
else’s fault; after all, most parents cannot choose who will be their child’s teacher.
The need for real-world applications. The second proposed motivational influence of
this study is that parents need real-world applications to math concepts. To improve parents’
views of mathematics tangible utility value, many teachers and researchers have stressed the
importance of real-world applications to math concepts. Gainsburg (2008) surveyed 62
secondary mathematics teachers as to how they make connections between math concepts and
real-world situations. Although conceptual agreement existed among the teachers for the use of
real-world examples in mathematics instruction, little empirical evidence exists to confirm its
actual use. This potential link between math concepts and the real lives of students is not limited
to a traditional classroom setting. Student participation in out-of-school math activities,
sometimes organized by their parents, foreshadowed their expectancies and values, leading to
more high school math courses attempted (Simpkins, Davis-Kean, & Eccles, 2006). In addition
to the high impact of real-world examples in the classroom and out-of-school math activities,
participation in science activities outside of the classroom increased interest in STEM (Dabney,
et al, 2012). Exploring the link between real-world applications of math concepts to parent
acknowledgment of the utility value of math instruction is embedded in this study.
The belief of a person that a particular goal will result in a desirable achievement is the
essence of expectancy-value theory (Eccles & Wigfield, 2006). Expectancy value theory has
three main assumptions: 1) individuals react to new information about an item or action by
developing a belief; 2) each attribute that contributes to this belief is designated a value; and 3)
from this belief and value attributed to the new information an expectation is developed (Eccles
& Wigfield, 2006). This research focuses on a particular utility value as an assumed
AFRICAN-AMERICAN MATH READINESS GAP 62

motivational influence. Eccles and Wigfield (2006) found that the value an individual assign to a
particular goal will strongly influence their willingness to start an activity, persist, and ultimately
finish a task. For instance, parents can be motivated to assist their children with math homework
by assigning: 1) intrinsic value, or how positive the experience is expected to be; 2) attainment
value, or whether the work fits the aspired self-image; 3) utility value or the likelihood that the
homework will achieve a goal; and 4) cost value or the assessment of the amount of time or
resources completion of the homework will cost (Eccles & Wigfield, 2006).
Organizational Influences
General theory. Cultural settings and models provide an understanding of influences on
an organization’s receptiveness to change (Gallimore & Goldenberg, 2001). Cultural settings
can provide visible and concrete evidence of an organization’s cultural norms and its effect on
employees. Employee tasks, whether or not specific organizational directives are effectuated,
and levels of employee turnover are all examples of cultural settings. In contrast, cultural
models are generally invisible and reflect values, beliefs, and attitudes that permeate the
organization (Gallimore & Goldenberg, 2001).
Budgetary resources and parental communication plan. Cultural settings can have a
decisive effect on a school reform initiative. For example, Odden and Archibald (2001) found a
key commonality of schools that successfully narrowed the achievement gap is the reallocation
of budgetary resources to achieve the most meaningful impact on student achievement. Viewed
through the lens of the cultural setting, two specific factors may prevent the Redwood Unified
eighth-grade mathematics readiness gap from closing: (a) an extra instructional period that
would facilitate individualized practice at the math concept level for less than proficient students
AFRICAN-AMERICAN MATH READINESS GAP 63

has not been budgeted and (b) a long-term communication plan has not been developed to
emphasize the importance of math proficiency to a student’s college and career trajectory.
Sense of helplessness from past failure. Organizational cultural models are deeply
embedded in schools (Schoen & Teddlie, 2008) and encompass the consensus belief, attitudes,
and principles of school members (Maslowski, 2001). One such cultural model is a sense of
helplessness among members of an organization after persistent failure to achieve a goal.
Learned helplessness can be defined as a sense of powerlessness after persistent failure to
succeed (Seligman, Meier, & Geer, 1968). In a school setting, if teachers, parents, and students
have repeatedly failed in efforts to improve math proficiency it could influence the
organization’s ability to tackle future math challenges. For instance, if a school repeatedly has
poor average math proficiency rates, parents, teachers, and students may begin to believe that
nothing can be done to improve math performance. In Redwood Unified, a sense of helplessness
in the organization due to the failure of previous math achievement gap improvement initiatives
may provide a specific cultural model factor that explains the hesitancy to attempt a math lab
period.
Conceptual Framework
A conceptual framework is a theory and a speculative basis for a study (Merriam &
Tisdell, 2016). It is a combination of concepts, beliefs, and assumptions. The conceptual
framework highlights the interaction between these concepts and guides a study’s research
(Merriam & Tisdell, 2016). It can include terms, concepts, models, thoughts, and ideas
(Merriam & Tisdell, 2016). Knowledge, motivation, and organizational influences are used to
understand the gap between the stakeholder goals and current performance when constructing a
conceptual framework. This conceptual framework is presented in two parts. First, is a narrative
AFRICAN-AMERICAN MATH READINESS GAP 64

of the knowledge, motivation, and organizational influences, and the second is a graphic
portrayal of how this relationship influences the gap in performance.
Knowledge, Motivation, and Organizational Factors
Knowledge, motivation, and organizational (KMO) influences are all central to the gap
analysis used to organize this study (Clark & Estes, 2008). This conceptual framework considers
the interrelationship between two knowledge and two motivational influences and their
connection to three related organizational influences present in Redwood Unified.
Knowledge factors. Conceptual knowledge represents the ability to use prior knowledge
to understand the relationships between multiple units of information (Krathwohl, 2002). Two
conceptual knowledge influences are contemplated in the study: (1) parents need to understand
the importance of the articulated high school math pathway to college and career opportunities,
and (2) parents need to understand the importance of maintaining grade level math proficiency to
student readiness for advanced high school mathematics. Riegle-Crumb (2006) documented the
disproportionate percentage of African-American students who do not keep pace with the math
pathway leading to the advanced mathematics sequence in high school. Progressing along this
critical math pathway requires grade level proficiency each year.
Motivational factors. The first of two assumed motivational influences is that parents
need to attribute their support for extra practice by their students to higher math proficiency.
According to attributional value theory, it is assumed that human beings will naturally attempt to
define the world in a manner that allows for a positive self-image (Heider, 1958). The
attributional weight given by parents between extra practice and higher performance is informed
by how they emphasize the importance of ability versus effort (Ames and Archer, 1987).
The second assumed motivational influence on eighth-grade math readiness is the parent's need
AFRICAN-AMERICAN MATH READINESS GAP 65

for real-world applications of math concepts. Eccles & Wigfield (2006) found that the value an
individual assigns to a particular goal will strongly influence their willingness to start an activity,
persist, and ultimately finish a task. To improve perceptions of mathematics tangible utility
value, many teachers and researchers have stressed the importance of real-world applications to
math concepts (Gainsburg, 2008). Next, this framework associates these four knowledge and
motivational influences with their corresponding organizational influences.
Organizational Cultural Settings. Organizational cultural settings and models provide
an understanding of influences on a receptiveness to change (Gallimore & Goldenberg, 2001).
Cultural settings can provide visible and concrete evidence of an organization’s cultural norms
and its effect on employees (Gallimore & Goldenberg, 2001). This study considers two cultural
settings that are assumed to affect disproportionately low math proficiency among eighth-grade
African-American students. First, Redwood Unified needs to reallocate budgetary resources and
provide changes to course scheduling to facilitate an extra instructional period for a mathematics
lab. The need for a math instructional lab directly impacts all four of the assumed knowledge
and motivational influences in this study. In convincing the parents of less than proficient math
students that proficiency and the math pathway are critical to their future success, Redwood
Unified’s lack of a funding source and scheduling for the math lab sends a signal that math
achievement is not a high priority. The lack of budgetary resources and scheduling for a math
lab also affects the two motivational influences considered in this study. First, it is difficult for
the parents of low proficiency math students to attribute more practice to a better outcome when
practice opportunities are not provided by Redwood Unified. Second, the utility-value of real-
world math applications would be better envisioned through math instructional software that can
provide many tangible examples at the proficiency level of an individual student.
AFRICAN-AMERICAN MATH READINESS GAP 66

The second organizational cultural setting of this study, the need for a parental
communications plan is also impactful on all four of our knowledge and motivational influences.
A central assumption of this inquiry is that the parents of low math proficiency African-
American students need to know both why math is important to their student’s future and how
their child’s math performance could be improved. A communications plan that stresses the
importance of math proficiency and the math pathway, attributes increased practice to
proficiency and shows the utility value of real-world math applications, may have a direct impact
on parent support for an extra math instructional period.
Organizational cultural model. Organizational cultural models are deeply embedded in
schools (Schoen & Teddlie, 2008) and encompass the consensus belief, attitudes, and principles
of school members (Maslowski, 2001). One such cultural model assumed in this study is a sense
of helplessness among teachers, students, parents, and other organization participants after
repeated failure of previous math interventions. This sense of helplessness by school officials
may impact African-American parents’ willingness to consider their student’s participation in an
extra math instructional period. Certainly, to secure their commitment, Redwood Unified will
need to convince parents that the math lab can be successful in increasing math proficiency when
other programs failed.
In summary, three organizational influences assumed in this study (budgetary and
scheduling resources, communications plan, sense of helplessness) interact directly with the
corresponding four knowledge and motivational influences (math proficiency, math pathway,
practice attribution, and real-world applications). The central focus of this study is Redwood
Unified’s goal of increasing African-American eighth-grade student math proficiency ten percent
by the 2019-20 school year.
AFRICAN-AMERICAN MATH READINESS GAP 67

Conclusion
The purpose of this study is to address parent participation in improving the low rates of
eighth-grade African-American student math readiness for college preparatory high school math
pathway. African-American students with low math readiness are affected by knowledge,
motivation, and organizational influences. Two conceptual knowledge influences are assumed
in this study. First, parents need to understand the importance of the link between the articulated
high school math pathway and college and career opportunities. Second, parents need to
understand the important relationship between maintaining grade level math proficiency through
the eighth-grade and their subsequent readiness for advanced high school mathematics.
Conceptual knowledge represents the ability to use prior knowledge to understand the
relationships between multiple units of information (Krathwohl, 2002). This research explores
parental knowledge of the importance of math proficiency and the high school advanced math
pathway.
This study also assumes two motivational influences. First, parents need to attribute their
support for extra work or practice to their students’ ability to become more proficient in
mathematics. People attribute their success or failure to a given task by assigning causes to
events (Heider, 1958). Second, parents need real-world applications of math concepts to assign
utility value in their increased participation. Gainsburg (2008) found that although conceptual
agreement exists among math teachers for the link between math concept understanding and
real-world examples, little empirical evidence exists. This study will explore this potential link
between real-world applications of math concepts and increased motivation to learn
mathematics.
AFRICAN-AMERICAN MATH READINESS GAP 68

Finally, cultural settings and models provide an understanding of influences on an
organization’s receptiveness to change (Gallimore & Goldenberg, 2001). This inquiry assumes
one cultural model and two cultural setting influences. First, a sense of helplessness fostered by
past failed math reform efforts is an assumed cultural model. Organizational cultural models are
deeply embedded in schools (Schoen & Teddlie, 2008) and encompass the consensus belief,
attitudes, and principles of school members (Maslowski, 2001). Second, an assumed cultural
setting influence is that an extra instructional period that would facilitate individualized practice
at the math concept level for less than proficient students has not been budgeted or scheduled.
Third, an assumed cultural setting influence is the lack of a long-term parent communication
plan to emphasize the importance of math proficiency to a student’s college and career
trajectory.
These knowledge, motivation, and organizational influences are assumed to explain the
gap present in low African-American student math readiness. During the methodology section, a
validation process is more fully described. For this study, African-American parents and the
organization were distinguished from each other since parents are not formally an actor internal
to the organization, but a key external stakeholder. Notwithstanding this separation, many
school resources are directed towards parents and they are impacted by Timber Middle’s culture,
student achievement goals, and success or failure. The stakeholder goal, then, corresponds to
both parents and the organization since both groups are focused on improved African-American
student math proficiency. Figure 3 illustrates the interaction between parental knowledge and
motivation with the organizational context of Timber Middle and Redwood Unified.

AFRICAN-AMERICAN MATH READINESS GAP 69

Figure 3
Conceptual Framework for African-American Parent Stakeholders

AFRICAN-AMERICAN MATH READINESS GAP 70

CHAPTER THREE: METHODS
This evaluation study seeks to understand the beliefs and attitudes of African-American
parents towards math proficiency and readiness for high school college preparatory mathematics.
Specifically, the inquiry probes these parents’ potential acceptance of an additional math
instructional period for students that are performing below grade level proficiency. The study is
structured using a gap analysis framework. A mixed-methods design combines quantitative and
qualitative data within the larger research design (Creswell, 2014). This chapter summarizes the
research design and methodology, data collection and instrumentation, and data analysis used in
the inquiry.
Under a sequential explanatory design, quantitative data is collected before the collection
and analysis of qualitative data (Creswell, 2014, Maxwell, 2013, Merriam & Tisdell, 2016). The
purpose of this sequence is to examine in more depth, help explain, interpret and contextualize
the quantitative findings (CIRT, 2018). In this study, the primary purpose of the quantitative
first phase was to inform the development of interviews of African-American parents in the
second phase. The parent survey preceded the qualitative second phase for two reasons: 1) to
allow for a comparison between all parents and the sub-group of African-American parents, and;
2) to identify appropriate African-American parents for the second phase interviews. In a
research context, interviews are conducted to secure evidence that describes, predicts or explains
the research questions (Cohen & Manion, 2007). In this study, distinct cultural differences
unique to African-American parents were also explored during the parent interviews. Specific
topics discussed in the interviews were: 1) why 87% of Timber Middle’s African-American
students are not ready for Algebra 1 in eighth-grade, 2) what they have observed to be home-
based cultural norms hindering the students’ academic performance, and 3) whether they believe
AFRICAN-AMERICAN MATH READINESS GAP 71

mathematics labs that emphasize practice of math skills and concepts would improve math
proficiency. After the interviews were completed, the two data collection methods provided a
form of triangulation that tests the validity of the findings and allows for the use of different data
sources to establish credible themes (Creswell, 2014).
The sequential explanatory design was chosen to make certain the interviews were
attentive to potential parent attitudinal differences toward math achievement and to reduce the
inherent vulnerabilities of the two data collection methods used in the study. The weakness of
the parent survey was that a quantitative study will not produce the family-specific insights and
deeper understanding of the students needed to proceed to implementation. The deficiency of
the interviews is the small group of parents (N=7) cannot be credibly projected to include all
African-American parents. The parental surveys (quantitative) and interviews (qualitative)
neatly double-check these potential weaknesses.
This chapter includes both a description of the participating stakeholders and a summary
of the methods and sampling criteria for both the quantitative and qualitative phases of the
inquiry. The quantitative survey results were used to identify potential African-American
parents to participate in the interviews that followed. Table 22 represents survey items and an
analysis plan for the inquiry. In Table 22, each of the eight survey items are linked to one of the
four knowledge and motivation influences of interest in this study. The survey items and
influences are then paired with the three research questions listed above. The survey will also
include two demographic questions on the ethnicity and educational attainment of the parental
respondents.
AFRICAN-AMERICAN MATH READINESS GAP 72

Table 22
Relationships between Survey Items, Influences, and Research Questions
Item Survey Item Influences Research Questions
1
My student's math education
is primarily the teacher's
responsibility. (strongly
disagree, disagree, agree,
strongly agree)
Parents need to attribute extra work to
their student's ability to become
proficient at math. (M)
What is the interaction between
Redwood Unified culture and context
and African-American parents’
knowledge and motivation?
2
Math is important for success
in everyday life. (strongly
disagree, disagree, agree,
strongly agree)
Parents need real-world application of
math concepts. (M)
What is the extent of African-
American parents’ knowledge and
motivation related to Redwood
Unified’s math proficiency goals?
3
Math is critical to my child's
adult job opportunities.
(strongly disagree, disagree,
agree, strongly agree)
Parents need to understand the
importance of the articulated high
school math pathway to college and
career opportunities. (K)
What is the extent of African-
American parents’ knowledge and
motivation related to Redwood
Unified’s math proficiency goals?
4
My child struggles to
understand math concepts.
(strongly disagree, disagree,
agree, strongly agree)
Parents need to understand the
importance of maintaining grade level
math proficiency to their readiness for
advanced high school mathematics.
(K)
What is the interaction between
Redwood Unified culture and context
and African-American parents’
knowledge and motivation?
5
If my child had an extra math
instructional period at school,
it would improve math
proficiency. (strongly
disagree, disagree, agree,
strongly agree)
Parents need to attribute extra work to
their student's ability to become
proficient at math. (M)
What are the recommendations for
organizational practices in the areas
of knowledge, motivation, and
Redwood Unified resources?
6
More practice would improve
my child's math proficiency.
(strongly disagree, disagree,
agree, strongly agree)
Parents need to attribute extra work to
their student's ability to become
proficient at math. (M)
What are the recommendations for
organizational practices in the areas
of knowledge, motivation, and
Redwood Unified resources?
7
After leaving high school, my
child is likely to attend
college. (strongly disagree,
disagree, agree, strongly
agree)
Parents need to understand the
importance of the articulated high
school math pathway to college and
career opportunities. (K)
What is the extent of African-
American parents’ knowledge and
motivation related to Redwood
Unified’s math proficiency goals?
8
Advanced math skills will
qualify my child for a higher
paying job after school?
(strongly disagree, disagree,
agree, strongly agree)
Parents need to understand the
importance of the articulated high
school math pathway to college and
career opportunities. (K)
What is the extent of African-
American parents’ knowledge and
motivation related to Redwood
Unified’s math proficiency goals?
KMO = Knowledge, Motivation, Organizational Influences.

AFRICAN-AMERICAN MATH READINESS GAP 73

Participating Stakeholders
Only 13% of African-American eighth-grade students attending Timber Middle are
grade-level proficient in math and ready for the college preparatory math track upon entering
high school (CAASPP, 2018). Similarly, a majority of every major ethnic subgroup at Timber
Middle is not proficient. Only the Latino sub-group at Timber Middle exceeds their statewide
cohort in math achievement (by less than 1%). This study focuses on Timber Middle’s parents
and their beliefs about math education. As part of this study, the researcher made presentations
to 532 Timber Middle students during their regularly scheduled math period. The students
participated in the study by taking home the surveys and bringing back their parents’ responses
the next day. The five math teachers at Timber allowed access to their classroom and
encouraged parent response. The principal at Timber Middle secured Redwood Unified’s
consent for the study and assisted in the recruitment of parents for the interview phase of the
inquiry. The Associate Superintendent of Education Services at Redwood Unified reviewed the
survey and interview guide before authorizing the contact with students and parents. Although
all of these stakeholders were participants in the study, parents at Timber Middle were the focus.
The study sought to ascertain the support of parents in general and African-American parents
specifically for an extra math instructional period.
Survey Sampling Criteria and Rationale
The survey of parents is the quantitative research portion of this mixed-methods
study. The survey of the parents of all Timber Middle School students sought to achieve two
objectives. First, it provided a method to identify the interview participants for the qualitative
part of this study by collecting the ethnicity and educational attainment levels of the parents.
Second, the survey allows a comparison between the parental beliefs regarding math
AFRICAN-AMERICAN MATH READINESS GAP 74

instruction by parental ethnicity and educational attainment. It is a quantitative research method
that seeks to generalize the results for the entire population of parents (Merrium & Tisdell,
2016). Because it seeks a sound statistical basis for this projection of results, it is a probability
form of sampling (Merrium & Tisdell, 2016). Probability sampling allows a statistical projection
of the results and is necessary in a quantitative study (Merrium & Tisdell, 2016).
This survey is a census of one parent for each of the 532 students present at
Timber Middle School on the day of the survey distribution. A census is a survey conducted on
an entire population (OECD, 2008). A census contrasts with a sample of a population selected to
represent an entire group (Salant & Dillman, 1995). This survey of the parents of all Timber
Middle school parents was designed to employ all of the characteristics commonly applied to a
quantitative method approach because it is a large, representative, and random observation of the
entire population (Creswell, 2014). Quantitative research has its roots in positivism in that it
seeks certain truth based upon verifiable data (Macionis & Gerber, 2010). The quantitative
method often uses an instrument with “closed-ended questions” where results are numerically
summarized (Creswell, 2014). Since this survey solicited responses from all of the parents of the
entire Timber Middle School population, it is not a sample. Instead, it is explicitly designed to
assist in the selection of a sample for the second observation in this study, which is interviews of
African-American parents.
Criterion. Parents. There are over 650 students at Timber Middle School and the
survey sought one parent response from each student. On the day of the survey, 530 students
were present, and each was asked to deliver a survey to their parents.

AFRICAN-AMERICAN MATH READINESS GAP 75

Interview Sampling Criteria and Rationale
The interview portion of this study is a qualitative research method. Sampling can be
placed into two types: probability and nonprobability (Merrium & Tisdell, 2016). Because the
goal of these interviews did not emphasize statistical generalization of results over an entire
population, non-probability sampling is appropriate (Honigmann, 1982). The interviews were
formed by criterion-based selection (LeCompte & Schensul, 2010) to determine the population
eligible to participate. As a qualitative study, the interviews provided the benefit of seeking
information in a direct single case (Maxwell, 2012) by allowing African-American parents to
weigh in on school instructional methods and the proposed extra instructional period.
The criterion-based selection for the interviews cascaded from the quantitative
stage of this inquiry in that participants must be African-American parents who participated in
the parental survey. This is an example of typical purposeful sampling because the selection
process seeks to focus on the average person of interest (Patton, 2015), in this case, African-
American parents. Because the interview criterion directly focuses on African-American parents
it is a non-random form of sampling.
The interviews are specifically targeted to two of this study’s four research
questions: 1) What is the extent of African-American parents’ knowledge and motivation related
to Redwood Unified’s math proficiency goals? and 2) What is the interaction between Redwood
Unified culture and context and African-American parents’ knowledge and motivation. The
ultimate objective of the interviews was to learn what operational steps could be taken to
encourage African-American parental support for an additional math instructional period.
Criterion. African-American Parents. African-American parents who have a child that
attends Timber Middle were recruited to participate in the interviews.
AFRICAN-AMERICAN MATH READINESS GAP 76

Interview Sampling and Recruitment Strategy and Rationale
The interview participants were purposefully selected and designed to seek a deeper
understanding of the beliefs of African-American parents. The survey sample (from which the
interview participants were selected) was selected by the census method. Thus, the survey
sample remained random to reduce selection bias (Krueger & Casey, 2009) and representative of
the population of parents at Timber Middle School (Johnson & Christenson, 2014). The
researcher, then, utilized simple random sampling in the first phase of the data collection. In the
second phase, the parents eligible for the interviews are a homogenous group of African-
American parents and had an equal chance of participation (Fink, 2013). The interviews of
African-American parents followed the quantitative survey of parents within a few weeks.
Interview participants were offered a $20 Starbucks gift card as a token of appreciation.
Data Collection and Instrumentation
Survey Instrument and Procedures
The survey instrument for this inquiry includes ten closed-answer questions designed to
provide a generalized reflection of all of the parents of students attending Timber Middle school.
These ten questions directly assess parental beliefs on knowledge and motivational influences
that are of interest in the conceptual framework of this study. The two knowledge influences are
parental understanding the importance of 1) grade-level math proficiency to readiness for
college preparatory mathematics, and 2) the high school math pathway to college and career
STEM opportunities. The two motivational influences are parental need: 1) for real-world
applications of math concepts, and 2) to attribute extra practice to math achievement. For
example, the following question seeks to understand the extent to which parents attribute
additional practice to math proficiency: Do you think an extra math period with the opportunity
AFRICAN-AMERICAN MATH READINESS GAP 77

to practice every day would improve your child’s math proficiency? Each of the ten questions
addresses at least one of these four knowledge or motivational influences.
The survey was conducted on May 6-7, 2019. These two days were without holidays and
in the middle of the spring semester. After the survey results were available, they were used to
select the parent participants for the interview phase of the study. The scheduling of the survey
was designed to allow for the survey and parent interviews to be completed before the last day of
the 2018-19 school year.
Interview Protocol and Procedures
Interviews help understand the participant’s life story and how it intersects with their
experiences. Interviews can explore research questions in more depth and follow-up on
responses to survey questions. (McNamara,1999) The interviews in this inquiry followed the
survey of all parents at Timber Middle School and specifically sought a deeper understanding of
the attitudes and beliefs of African-American parents. It was centered on what information could
be decisive in African-American parents supporting an extra instructional period for their
students. The interviews were divided into four sections, each exploring the four knowledge and
motivational influences of this study. During the interviews an “interview guide” of topics
covering all topics was used (Rubin & Rubin, 2012). This guide prompted an open discussion
with the interview participants.
The interviews were scheduled to avoid school holidays and the end of the semester. The
timing of the interviews was designed to be flexible to the parents’ work schedules and occurred
at school, on the phone, in restaurants, and in their homes for their convenience. Interviews were
also scheduled with a reasonable interval from the survey part of this inquiry. The time allowed
for the recruitment of interview participants identified in the survey demographic data. The
AFRICAN-AMERICAN MATH READINESS GAP 78

interviews were conducted with seven African-American parents and each lasted less than one
hour. Although the interviews were divided into four sections with prompting questions, the
sessions were informal to allow for full exploration of the parents’ views.
Data Analysis
An explanatory data research design was facilitated by the use of both a survey of 532
parents and interviews with seven African-American parents recruited from the survey
respondents. First, the surveys were collected, and data was entered on an Excel spreadsheet.
The data was cleaned, and incomplete or illegible responses were removed. Responses to each
question were then evaluated with a frequency score calculated for each of the eight questions.
Cross tabulation was also calculated between the eight questions and the two demographic
questions: ethnic sub-group and educational attainment. The African-American sub-group
respondents were identified for recruitment for the interview phase. Next, data from the seven
parent interviews was analyzed. The data collected from each interview was transcribed by a
service and then coded to assist in answering this study’s research questions. Analytical memos
were used to document initial reflections of the data. Open coding and axial coding were used
to organize the data into relevant categories (Merriam & Tisdell, 2015). Open coding apportions
data into key points to correspond to the conceptual framework and research questions. Axial
coding is designed to create categories from a synthesis of interview data. The interview data
was then compared to the survey results to determine the findings.
Credibility and Trustworthiness
To maintain confidence that the qualitative phase of this inquiry is trustworthy,
the interviews must be credible. Credibility is the researcher’s confidence that the data and
findings are true and accurate. To establish credibility and trustworthiness in the data collected
AFRICAN-AMERICAN MATH READINESS GAP 79

from the interviews, three strategies were employed. First, data collected from African-
American parents in the survey phase of this inquiry was compared to the information derived
from the interviews. This comparison will employ the process of triangulation or reviewing a
research question from multiple lenses. This process of triangulating the survey with the
interviews results assisted the evaluation of the consistency of the information. Triangulation is
inherent in the mixed methods methodology used in this study (Merriam & Tisdell, 2016).
Second, once findings are developed from the interviews, some members were asked to review
and provide comments.
The selection of interview participants from a survey of all parents improved credibility.
Before an invitation to participate in the interviews, the participants were identified as African-
American parents of students at Timber Middle School. Since the study seeks to understand
their beliefs and views, member checking is an appropriate method to provide credibility to the
findings (Creswell, 2008). Finally, a self-reflection of researcher bias was included. Since I am
not an African-American parent, my interpretation is subject to a different cultural background
and that was identified. Comments by researchers about how their own experiences might shape
their inquiry improves qualitative research (Creswell, 2008).
Validity and Reliability
The quantitative phase of this inquiry was a ten-question survey of one parent of
530 students present on May 6, 2019, at Timber Middle School. The use of a census method
provides a uniform approach and an assumption that the sample of all parents was an accurate
generalization of parents’ views at Timber Middle School. Further, the study had a target of a
10% response rate or approximately 65 responses to the survey from the parents of all students at
the school. In sum, the combination of a uniform survey instrument, a census sample of all
AFRICAN-AMERICAN MATH READINESS GAP 80

parents, and at least a 10% response rate satisfy the validity of the quantitative portion of this
study.
Ethics
This study stresses the researcher’s obligation to act ethically throughout the inquiry.
This imperative takes precedence over the study’s primary objective of seeking useful new
knowledge (Glesne, 2011). Among those responsibilities are informed consent, data handling,
and confidentiality.
Central to academic studies, informed consent is also a part of the Institutional
Review Board (IRB) process (Rubin & Rubin, 2012). Researchers are responsible for
safeguarding participants and not harming them during the study (Glesne, 2011). Since this
study’s participants are human subjects, all participants must be covered by informed
consent. The researcher gave notice to study participants of their coverage under the University
of Southern California Human Subjects Protection Program (HSPP). The researcher also
recorded Informed Consent for Non-Medical Research from each interview participant
and survey respondents received an Information Fact Sheet for Exempt Non-Medical Research.
Informed consent assures that participants in both the survey and the interviews had awareness
that their involvement is completely voluntary and identifies any potential risks (Glesne, 2011).
Specifically, all participants were informed at each step of the study that their input is
confidential and no information was shared with school district personnel. Further, it was
emphasized with interview participants that they have a responsibility to not share discussions
outside of the meeting. All participants could discontinue taking part in either
the survey or interviews at any time. At the beginning of the survey and orally before the
AFRICAN-AMERICAN MATH READINESS GAP 81

interviews began, the researcher declared that no opportunities within the school district
would be affected by the participant’s decision not to participate in the inquiry.
At the beginning of the interviews, the researcher sought permission to
record the session. All interview participants agreed to the recording. After the interviews, the
following steps were taken: 1) service was contracted to transcribe the session verbatim; 2)
transcriptions were coded with pseudonyms to ensure confidentiality; and 3) all files were
destroyed following the availability of the transcription.
The following assumptions were made during the study:
● Parents want their children to achieve math proficiency.
● Parents will answer the survey and interview questions honestly and according to their
sincerely held beliefs.
The researcher has the following inherent biases that must be considered during the
study:
● The researcher is a former member of the Redwood Unified School District Board of
Trustees.
● The researcher has been active in education reform as a state legislator, certificated
teacher, and charter school founder.
● The researcher knows the principal and some teachers at the school.
While the school principal was extremely supportive and facilitated contact with the
parents, confidentiality was maintained, and school officials did not have access to identifiable
responses. To make sure the research is viewed as ethically structured, the confidential nature of
the project was emphasized. The researcher has been active as a school board member in
advancing various interventions for students performing below proficiency in math, including an
AFRICAN-AMERICAN MATH READINESS GAP 82

extra math instructional period. It is in this previous role that the researcher could have been
identified as a “reformer” and “advocate.” Glesne (2011) describes a reformer as wishing to fix
an unjust effect and an advocate taking a stand on an issue. The remedy for these potential
biases is confidentiality. The participants had assurances of anonymity, which has been found to
encourage sincere answers to survey and interview questions (Creswell, 2014). Being aware of
these potential biases and speaking to them directly, makes it more likely to lead to a credible
analysis of the data (Glesne, 2011).
Limitations and Delimitations
A researcher must have a clear understanding of the limitations and delimitations of the
study. Limitations are factors beyond the control of the researcher. Some limitations that are
present in this study are:
● The study relies on the truthfulness of the respondents to both the survey and
interview phases.
● The parents that responded to the survey and agreed to participate in the interviews
may tend to be more attentive to school matters.

AFRICAN-AMERICAN MATH READINESS GAP 83

CHAPTER FOUR: RESULTS AND FINDINGS
This study was pursued to better understand the beliefs of African-American parents
towards their children's math studies and how that affects efforts to reduce the gap in student
readiness for the high school college preparatory math pathway. The project is focused on
determining knowledge, motivation, and organizational (KMO) obstacles and resources to
African-American parent participation and support for needed math interventions. The KMO
framework by Clark and Estes (2008) was used to organize the barriers to parent participation.
The results will also be presented in the KMO format. Survey data and seven African-American
parent interviews were collected over two months and provided both a baseline of all parents’
views and a deeper dive into the beliefs of African-American parents. The parent survey
questions were evenly paired with four questions connected to knowledge influences and four
questions related to motivation influences. The research questions used to guide the data
collection were:
1. To what extent is Redwood Unified meeting its math proficiency goals?
2. What is the extent of African-American parents’ knowledge and motivation related to
Redwood Unified’s math proficiency goals?
3. What is the interaction between Redwood Unified culture and context and African-
American parents’ knowledge and motivation?
4. What are the recommendations for organizational practices in the areas of knowledge,
motivation, and Redwood Unified resources?
This study was focused on the African-American parents at Timber Middle School. A
survey of all parents was first conducted with two demographic and eight Likert questions. The
survey enabled a comparison between all parents and the discrete group of African-American
AFRICAN-AMERICAN MATH READINESS GAP 84

parents on each question. The survey also helped identify, through the demographic questions,
African-American parents that would qualify and be willing to participate in interviews for the
qualitative phase of these mixed-methods study.
Each of the eight Likert questions in the survey were designed to probe the assumed
knowledge and motivation influences of this study. Likewise, the assumed knowledge and
motivation influences are directly targeted at the research questions. Each of the survey
questions then is designed to collect parent beliefs and opinions relevant to the research
questions of this study.
Participating Stakeholders
Table 20 shows the demographic characteristics of the parents who participated in the ten-
question survey. Data for this research came from the parents who returned the survey (N=251)
the day after it was delivered to all of the students present (N=532) at Timber Middle School on
May 6, 2019. This represented a 47% response rate (RR=47). Each parent response included
two demographic questions: 1) educational background, and 2) ethnic sub-group. African-
American parents encompassed 8% of the survey respondents.
AFRICAN-AMERICAN MATH READINESS GAP 85

Table 20
Demographic Background of Survey Sample
N %

Ethnic Sub-Group

African-American 19 8%
Latino 75 30%
White 79 31%
Other 66 26%
Decline to State 12 5%

Educational Attainment

Some High School 16 6%
High School Graduate 39 16%
Some College 69 27%
College Graduate 115 46%
Decline to State 11 4%

Table 21 provides limited demographic information on the seven African-American
parents who participated in the interviews. Each of these parents had at least one child attending
Timber Middle School during the 2018-19 school year.
Table 21
African-American Parent Interview Participants
Gender Educational Background Occupation

Parent 1 female college graduate Nurse
Parent 2 female some college Bank Operations
Parent 3 male some college Not Known
Parent 4 male college graduate Charter School Teacher
Parent 5 female some college Nursing Student
Parent 6 female college graduate School Librarian
Parent 7 female some college Preschool Teacher

AFRICAN-AMERICAN MATH READINESS GAP 86

Findings
The six findings of the study are presented below by knowledge or motivation influences
and include outtakes from the African-American parent interviews follow the survey results to
convey a deeper understanding.
Knowledge Findings
Finding 1: Gap identified between African American parent’s beliefs towards their
children’s math mastery and actual student math proficiency. A starting point for engaging
parents in their children’s math education is understanding the current reality of math
performance. Middle school parents have complicated lives full of responsibility and varying
levels of academic interest. The survey identified a significant gap between parent beliefs
regarding student understanding of math concepts and the actual performance of students at
Timber Middle School. This gap was slightly more pronounced for African American parents.
Question 4 of the survey asks parents to respond to the statement “my child struggles to
understand math concepts.” The responses from African American parents were split evenly on
the question, with 48% disagreeing with the statement. Among all parents, 60% did not believe
their child was struggling with math concepts. At 13%, the African American student
proficiency is the lowest of all ethnic subgroups. The difference between the 13% African
American student proficiency rate and the 48% of parents who believe their children are not
struggling at math creates a 35% gap between parental views of student math mastery and their
actual math performance. This gap in parental understanding of current student math mastery is
no less telling at 27% for all students at Timber Middle. Table 7 illustrates this gap with a
comparison between the responses to Question 4 on this study’s survey and CAASPP math
proficiency results at Timber Middle (CAASPP, 2017-18).
AFRICAN-AMERICAN MATH READINESS GAP 87

Table 7
Comparison between Survey Question 4 and Actual CAASPP Math Results
My child struggles to understand math concepts.
Strongly
Disagree
Disagree Agree
Strongly
Agree
All parents 20% 40% 31% 9%
African American parents 16% 32% 42% 11%
Timber Middle Math Proficiency Standard.
Exceeded Met
Nearly
Met
Not Met
All students 13% 20% 30% 37%
African American students 3% 10% 25% 62%
Source: CAASPP (2017-18).

Finding 2: African American parents at Timber Middle overwhelmingly believe
math is central to college, career, and income opportunities for their children. The
connection between math skills and adult economic success is very strong in Timber Middle’s
parents. African American parents believe their student’s math skills will increase their child’s
success in everyday life (100%), adult job opportunities (89%), and result in a higher paying job
(84%). African American parents do not differ from the parents of all students in their belief that
math is integral to a financially secure future. Strong support for the benefits of learning math
augur well for parental backing for math interventions like an extra instructional math period.
Table 9 illustrates the responses to questions 2, 3, and 8 on the parental survey.
The African-American parents who were interviewed recognized the more prominent role
that math skills are playing in college and career opportunities. A representative opinion came
from Katelyn
3
, when she said:
The STEM jobs will require more math because you want to go into coding and

3
Aliyah, Claire, Emma, Jalen, Karem, Katelyn, and Tiara are pseudonyms
AFRICAN-AMERICAN MATH READINESS GAP 88

different things. Then all of that is tied to mathematics, when you’re building codes.
And we are definitely a society that is moving towards more occupations using these
different types of technologies in the workforce. If you’re a mechanic, you’re going
be using some type of mathematics because you are working on all these different
kinds of computers. So with it being technology driven, then there is opportunity to
make more money in that arena.
Table 9
Parent Survey Results for Questions 2, 3, and 8
Math is important for success in everyday life.
Strongly
Disagree
Disagree Agree
Strongly
Agree
All parents 0% 3% 38% 59%
African American parents 0% 0% 47% 53%
Math is critical to my child's adult job opportunities.
All parents 1% 5% 41% 52%
African American parents 5% 0% 26% 63%
Advanced math skills will qualify my child for a higher
paying job after school graduation.

All parents 0% 9% 46% 44%
African American parents 5% 11% 26% 58%

Finding 3: Gap identified between African American parents’ beliefs that their
children will attend college and actual student readiness for college prep math pathway.
The key to understanding the missing cultural and learning components that result in the African
American math achievement gap may be the difference between parental expectations for their
children and the student readiness to meet those aspirations. The survey identified a significant
gap between parent expectations that their middle school children are college-bound and the
actual student readiness to begin high school college preparatory math pathway in the ninth
AFRICAN-AMERICAN MATH READINESS GAP 89

grade. Responses to Question 7 of the survey indicate that all parents (98%), including African
American parents (95%), believe their children are likely to attend college.
But the math readiness rate for the high school college prep math pathway beginning with
Algebra 1 is not met for most students. Students at Timber Middle who are not proficient in
math as defined by the California State Standard are not ready for Algebra 1. Only 13% of
African American students at Timber Middle are proficient and eligible for the college
preparatory math pathway as they begin high school. A majority of all students (67%) are also
not ready for the high school college prep math pathway. A severe expectation gap presents
itself between African American parents who believe their children are likely to attend college
(95%) and those who are prepared to do college prep math as they enter high school (13%); an
82% expectation gap. This expectation gap also occurs among the parents of all students that
believe their children will attend college (98%) and those on track for advanced high school
mathematics (33%); a difference of 65%. Table 10 illustrates the parent expectation gap with a
comparison between the responses to Question 7 on this study’s survey and CAASPP math
proficiency results at Timber Middle (CAASPP, 2017-18).
Table 10
Comparison Between Survey Question 7 and African-American 8th Grade Math Proficiency
After leaving high school, my child is likely to
attend college.
Strongly
Disagree
Disagree Agree
Strongly
Agree
All parents 1% 1% 27% 71%
African American parents 5% 0% 32% 63%
Timber Middle 8th Grade Math Proficiency. Exceeded Met Nearly Met Not Met
All students 13% 20% 30% 37%
African American students 3% 10% 25% 62%

AFRICAN-AMERICAN MATH READINESS GAP 90

Motivation Findings
Finding 4: African-American parents overwhelmingly attribute more math practice
and an extra math instructional period to improved math proficiency. Two questions in the
survey were directed at the roles of practice and instructional time in improving math
performance. African American parents (90%) and all parents (95%) believe that more practice
would improve their child’s math proficiency. Similarly, African American parents (76%) and
all parents (84%) agree that if their child had an additional instructional period in math during
the school day, it would improve math proficiency. Although African American parents agree
with all parents on the efficacy of practice and additional math instruction time, they differ in
intensity.
African American parents “strongly agreed” that more practice (53%) and an extra
instructional period (47%) would meaningfully improve their child’s math proficiency. This
intensity difference between African American parents and all parents was significant for both
practice (21%) and an extra instructional period for math (24%). Table 8 details the parent
survey responses to the practice and extra instructional time.
Table 8
Parent Survey Results for Questions 5 and 6
More practice would improve my child's math proficiency.
Strongly
Disagree
Disagree Agree
Strongly
Agree
All parents 2% 8% 58% 32%
African American parents 5% 0% 42% 53%
If my child had an extra math instructional period at
school, it would improve math proficiency.

All students 5% 19% 53% 23%
African American students 5% 11% 37% 47%

AFRICAN-AMERICAN MATH READINESS GAP 91

The African-American parent participants in the interviews uniformly supported an extra
instructional period during the school day dedicated to a math lab. During the interviews they
were asked to specifically comment on three options: 1) an extra period during the school
instead of one elective course, 2) a longer school day, or 3) a voluntary after school program.
The parents preferred during the school day math lab for a variety of strategic, practical, and
emotional reasons. Some believed a longer school day would result in a parent scheduling
challenge. Different work schedules and other parent obligations might cause resistance to
changing school drop-off and pick-up times. Others thought the voluntary nature of the after-
school program would mean light attendance. Finally, a few of the parents were concerned
about any stigma that might attach to being singled out for math after school hours because of
low proficiency. Here are a representative sample of comments from the parents who were
interviewed:
Katelyn said:
I definitely think having...the math lab option is really good and you’re not
extending the day because, lets face it, they are seventh and eighth-graders. By the
time they get out already they want to eat and there’s not time. They can’t eat in the
after school program, which is one of the reasons they didn’t want to stay. But I do
like the idea of having a math lab for extra support.
Jalen said:
(Having an extra instructional period) during the school day, which I think
would be the best option. Yep, you get pulled out of your non-core class and you
go in there. Because of course, you don’t want to get into the after-school stuff.
Hey, can this parent afford to be off work? During the school (day), let's get you
AFRICAN-AMERICAN MATH READINESS GAP 92

the math tradeoff for an elective. I would weigh in on the elective option (math lab
period instead of one elective). I do think a double or extended math period would
be beneficial. I felt that during (my daughter’s) time at Timber Middle, she needed
more time to grasp math concepts.
Tiara said:
I’m supportive of it. I would probably do the math lab first, because if you
want them to be in the after school programs..if he’s not signing in, then he’s not
getting anything done. If they are doing math lab during school time, then I know
you’re actually going there.
Claire said:
I always thought there’s got to be a grow class for these kids who are not
ready. Instead of taking like a craft class or cooking put them in another math class.
So, they can be ready to go back into the other (math) class. Yeah, they need that or
even a mandatory after school class which I wanted for myself.
The African-American parents expressed, both in the survey and interviews,
overwhelming support more practice, more in school math instructional time, and an extra period
of math instead of an elective course for those students below proficiency.
Finding 5: Parents at Timber Middle are evenly split on whether the teacher has
the primary responsibility for their child’s math education, but if their children are
struggling in mathematics a majority rely on the teacher to take responsibility. The survey
question with the least consensus was whether parents believed that their child’s math education
is primarily the responsibility of the math teacher. The inferred alternative was that the parent
and/or student was primarily responsible for math achievement. The all parent’s cohort in the
AFRICAN-AMERICAN MATH READINESS GAP 93

survey was evenly divided in their response, with 50% say the teacher had lead responsibility
and 49% believing the teacher was secondary to a student’s math education. Counterintuitively,
African American parents were much more strongly opposed to the idea that their child’s math
education was the teacher’s responsibility, with 69% disagreeing with that statement. But these
parental views of the role of the teacher may depend on whether they believe their child is
having difficulty in math class. Table 11 illustrates the parental differences in the role of the
teacher in math.
AFRICAN-AMERICAN MATH READINESS GAP 94

Table 11
Parent Survey results for Question 1
My child's math education is primarily the
teacher's responsibility.
Strongly
Disagree Disagree Agree
Strongly
Agree
All parents 8% 42% 39% 10%
African American parents 16% 53% 21% 11%
All Parents/Child Struggles at Math (Q4) 7% 38% 45% 9%

Given the even split of parents on who was primarily responsible for a child’s math
education, further analysis was performed by matching the responses from survey Question 1
(role of teacher) to Question 4 (child struggles at math). A clear shift in parent beliefs was
revealed with 54% of parents who believed their children were struggling at math counting on
the teacher as the person primarily responsible for their child’s math education. In contrast, only
46% of parents who don’t believe their children struggle at math identified the teacher as
primarily responsible for the child’s math education. Although African-American parents’ view
of the teacher’s responsibility also varied depending on whether they believed their child was
struggling at math, the sample size did not permit meaningful review. If parents of children who
are struggling at math disproportionately look to the teacher as the solution, it may imply support
for school-based interventions are warranted to improve math achievement. These parents may
not feel qualified to help their children or for other reasons need their children to engage in
longer math practice sessions at school.
AFRICAN-AMERICAN MATH READINESS GAP 95

Organizational Finding
Finding 6: African-American parents feel frustration with past attempts to engage
the school in an effort to improve their child’s math performance. The parent survey was
completed by 19 African-American parents and represented 8% of the respondents. Of the 19
African-American survey respondents, 7 agreed to interviews. None of the eight survey
questions was specifically focused on the parent’s efforts to provide interventions when their
child had less than proficient results on the yearly CAASPP report. However, two prompts in the
interview protocol engendered responses that showed widespread frustration from the parents
who attempted to help their child improve at math. Those two prompts were 1) has your
student’s attitude towards math changed in the 7th and 8th grade? and 2) do you feel comfortable
or capable of helping your student with their homework? Since these seven parents had all
attended some college, they would be expected to be more able than most to assist their children.
Nevertheless, the difficulties they faced are vivid and their responses are unequivocal.
Katelyn is a pre-school teacher at a non-profit organization serving victims of child abuse.
She has a son at Timber Middle who just finished seventh-grade. After finishing his elementary
school years mostly proficient in math, the school reported he was now testing below
proficiency. She described her effort to help her son:
I did notice this year in particular, as he was..getting acclimated to seventh-grade
life..with multiple classes and multiple teachers, I would ask him like, do you have
any questions? Did you understand it? And he would tell me yes, but when the test
scores were low or we double checked the homework, then he was missing
(problems). With seventh-grade math there’s like (the) usual multiple steps and
if you miss one step then that throws you off the rest of your problems. He would
AFRICAN-AMERICAN MATH READINESS GAP 96

miss like one step and throw his whole answer off. The school did offer like an
after-school program, we tried that route. That wasn’t helping.
Several parents expressed that math instruction had changed dramatically since they were
students, making it difficult to help their students. Aliyah, a nurse, described her and her
husband’s challenges in helping their three sons in math:
Math is totally different than when my husband and I were in math. Getting to the
functionality of solving a problem. It’s completely different. The way we used to
solve a problem, it was easier. Now, ...it’s more steps, it’s more ways and you have
to do it that way. My husband literally had to go back and study. They send links
home, so he had to go check it out to see exactly what it was that they were doing
different and why we couldn’t at home show them how to solve the problem the way
we were taught versus how they wanted them to learn it.
Aliyaha described paying tutors to help their sons maintain math proficiency:
I’ve had them in tutoring for math through the years and everything.
Emma also hired tutors for her daughter in elementary school. When Emma was asked
how her daughter felt about math, she said:
She absolutely hates math. But in elementary school they would go back and reteach
and spend more time, come in at recess. I hired a tutor. That happened in
elementary school. But when she got to (Timber Middle), it’s just keep marching
ahead. No stopping, no reteaching or come to Math Infusion or see me before class.
I even met with one math teacher who admitted that much of her class didn’t get a
particular concept but curriculum required her to move on to keep pace instead.
AFRICAN-AMERICAN MATH READINESS GAP 97

Like Katelyn and Aliyah, Emma expressed frustration with the current emphasis on
teaching how to solve problems using multiple methods when she said:
I think it (math instruction) is almost like a language she doesn’t understand and
she is expected to understand it. Like automatically understand it, is my feeling.
And she doesn’t. They teach you 13 ways to do this problem. That’s too many
ways for her. She just needs to know one way. It all becomes overwhelming.
So with that much information, you’re just like, “I can’t,” and I “hate this.”
Jalen echoed the other parents’ views on the pace of instruction being too fast to practice
the concepts before moving on to the next lesson. He also noted a difference between the
question asking skills of his daughter and son when he said:
The way they do it now is kind of like going from the high level to the low level.
They’re taking big numbers and they want the kids to break it down into your order,
thousands, hundreds, tens, and ones. So that’s how they want them to break the
questions down. Well you know when we were told that it was one plus one.
So it comes down from the fact that when I try to show my kids...a math problem,
they’ll be like, “Well that’s not how they show us doing (it) at school.”
Jalen reflected the views of many of the parents on their difficulty helping their children
keep up with the math instructional pace when he states:
The next day, it’s something new. It’s like you get this (this) day, homework on
it. The next day you come in, you’re not even working on that anymore. You’re
working on something else. You’re working on the next level. And then the day
after that you’re working on the next level because Monday you got the first part
of it. Homework. The next day you get the second part of it. Homework. Third
AFRICAN-AMERICAN MATH READINESS GAP 98

day, third part of it. Homework. Fourth day, fourth part of it. Homework. Friday,
test.
These parents, then, are reflecting the squeeze they and their middle school children are
facing on their journey to math proficiency. The teachers must keep an instructional pace
necessary to prepare their students for the high school math pathways and only have one period a
day to teach the concepts. This leaves no practice time or reteaching before the student is
exposed to the next concept. These parents, with the advantage of some college, are finding it
difficult to teach math using methods that are unfamiliar. This finding shows the need to address
two parental concerns: 1) the need for more at school math practice and instructional time, and
2) the imperative to help parents overcome the sense of helplessness caused by past efforts to
help their child improve at math.
Conclusion
The results and findings of the parent survey and interviews of African-American parents
address two of this study’s four research questions. First, research question two asks “what is the
extent of African-American parents’ knowledge and motivation related to Redwood Unified’s
math proficiency goals?” Two assumed knowledge motivations were validated by the survey
results: 1) African-American parent beliefs their children struggle in math (53%) contrasts with
the actual student proficiency (13%), showing a knowledge gap on proficiency, and 2) a
knowledge gap exists between African-American parents who believe their children will attend
college (95%) and those who are ready for the college prep math pathway necessary to achieve
that goal. A key motivational influence was also validated as an asset: African American parents
believe extra work will lead to improved math proficiency when they responded to the survey
AFRICAN-AMERICAN MATH READINESS GAP 99

questions that an extra math instructional period (84%) and practice (95%) would improve
proficiency.
In research question 3, the study seeks to find out “what is the interaction between
Redwood Unified culture and context and African-American parents’ knowledge and
motivation?” Finding 6, based upon parent interviews, was that African-American parents feel
frustration with past attempts to improve their child’s math performance. This validates one of a
key assumed organization influence: a sense of helplessness from past reform efforts. The
validated findings will support the recommendations in Chapter 5.

AFRICAN-AMERICAN MATH READINESS GAP 100

CHAPTER FIVE: SOLUTIONS, IMPLEMENTATION AND EVALUATION PLAN
The assumed influences of this study are: 1) parents need to understand the importance
of the articulated high school math pathway to college and career opportunities; 2) parents need
to understand the importance of maintaining grade level math proficiency to their readiness for
advanced high school mathematics; 3) parents need to attribute extra work to their ability to
improve their student’s math proficiency; and, 4) parents need real world applications of math
concepts. In the Chapter 4 findings, the parental survey’s eight question responses and African-
American interview transcripts were used to validate the assumed influences. These validations
resulted in six findings. This chapter will provide solutions to the articulated gaps in the form of
an implementation and evaluation plan. The recommendations are presented in the categories of
validated influences. These categories will use the Kirkpatrick and Kirkpatrick (2016) approach
following the knowledge, motivation, and organization (KMO) design. What follows is a
restatement of the organizational context of Timber Middle School.
Organizational Context and Mission
Timber Middle School enrolls approximately 650 seventh and eighth-grade students in
Redwood Unified (LCAP, 2017-18). Redwood Unified is a K-12 public school system located
in Stockton, California. Approximately one-half of Redwood Unified’s seventh and eighth-
grade students attend Timber Middle. The district serves more than 9,400 students at 13 schools
including a comprehensive high school, alternative high school, middle school, nine K-8
elementary schools, and a district dependent STEM charter school (CALPADS, 2017).
Redwood Unified has an ethnically diverse student population that includes Latino (46.9%),
white (22.7%), African-American (12.4%), and Asian (9.5%) students (CALPADS, 2017). Less
AFRICAN-AMERICAN MATH READINESS GAP 101

than a majority of Redwood Unified students met grade-level standards in English Language
Arts/Literacy (47.3%) or Mathematics (32.1%) in the 2016-17 school year (CAASPP, 2017).
A five-member Board of Trustees elected by the registered voters from evenly divided
trustee areas and a Superintendent appointed by them govern the district. The district employs
404 certificated teachers and has an average student/teacher ratio of 23.2 (California Department
of Education, 2015). Like all public-school districts in California, Redwood Unified shares the
mandate of laws adopted by the State of California. Both the California Board of Education and
Redwood Unified have mission statements that commit themselves to providing a quality
education for all students under their care (California Board of Education, 2016, Redwood
Unified School District, 2018):
“to educate all students to achieve their maximum potential (Redwood Unified School
District, 2018).”
“ensure that all students are performing at grade level or higher (California Board of
Education, 2018).
Reviewing the two mission statements yields an important difference: the lack of a pledge
by Redwood Unified to the California Board emphasis on a measurable student-achievement
accountability system.
Organizational Performance Goal
Timber Middle’s organizational goal is to increase the percentage of eighth-grade African-
American students that meet or exceed the state mathematics standard for each of the next three
school years (Redwood Unified LCAP, 2017). Redwood Unified Board of Trustees approved
the 2017-18 Local Control Accountability Plan and Annual Update (LCAP) and submitted the
plan to the State Department of Education. The California Assessment of Student Performance
AFRICAN-AMERICAN MATH READINESS GAP 102

and Progress (CAASPP) measures the expected outcome of the LCAP annually. Currently, only
18 percent of Redwood Unified’s eighth-grade African-American students meet or exceed the
state standards for mathematics on the annual standardized test (CAASPP, 2017). It is critical to
evaluate Redwood Unified’s progress towards increasing mathematics proficiency for eighth-
grade African-American students to ensure a larger share of this cohort of students can enter the
pathway leading to AP Calculus or Statistics by their senior year.
Description of Stakeholder Groups
Redwood Unified is a K-12 public school system located in the northwestern section of
Stockton, California. It has several stakeholder groups. First, the district serves an ethnically
diverse population of 9,400 students, which includes Latino (46.9%), white (22.7%), African-
American (12.4%), and Asian (9.5%) sub-groups (CALPADS, 2017). Second, the parent
stakeholder groups include a few of the wealthiest Californians and many of the poorest, with an
active Parent Teacher Association at all 13 schools. Third, a five-member Board of Trustees
elected by the registered voters from evenly divided trustee areas governs the district. Fourth,
the administration of the district includes a Superintendent, Associate Superintendent for
Education Services, and principals at each school. Fifth, the district employs 404 certificated
teachers and has an average student/teacher ratio of 23.2 (California Department of Education,
2015).

AFRICAN-AMERICAN MATH READINESS GAP 103

Stakeholder Groups’ Performance Goals
Table 2
Organizational Mission, Global and Stakeholder Goals
Organization Mission

To educate all students to their maximum potential and to prepare them to be responsible citizens.

Organizational Global Goal

Student math proficiency shall increase by 10% by the end of the 2019-20 school year.

Superintendent Goal Principal Goal
African-American
Student/Parent Goal

All district students shall either
be math proficient or increase
math proficiency by 10% by the
end of the 2019-20 school year.
All Timber Middle students shall
either be math proficient or
increase math proficiency by 10%
by the end of the 2019-20 school
year.
African-American students at
Timber Middle shall either be
math proficient or increase math
proficiency by 10% by the end of
the 2019-20 school year.

Stakeholder Goal

African-American 8th-grade student math proficiency shall increase by 10% by the end of the 2019-20
school year.

Stakeholder Group for the Study
Although a complete analysis involving all of the stakeholders would be desirable, this
study will focus on the parents of the sub-group of African-American students. Of all ethnic
subgroups in Redwood Unified, African-American students have the lowest level of readiness
for eighth-grade mathematics. Only 18% of the district’s entering ninth grade African-American
students are grade-level proficient in mathematics (CAASPP, 2016). The CAASPP annual
achievement reports provide the necessary measurement to evaluate progress and are consistent
with the district’s LCAP annual measurable outcome. If there is no improvement in eighth-grade
AFRICAN-AMERICAN MATH READINESS GAP 104

mathematics readiness among African-American students, the district risks not providing a
quality education for “all students” as articulated in its mission statement. African-American
parental support is critical for the success of interventions designed to improve math proficiency
and readiness. The goal of the African-American parents is symmetrical with the District’s goal,
for the African-American students to close the math achievement gap.
Purpose of the Project and Research Questions
The purpose of this project is to conduct an evaluation study of the eighth-grade African-
American student readiness for advanced high school mathematics at Timber Middle.
Specifically, the project goal is to gauge African-American parental support for establishing an
additional instructional period of mathematics for students who are below proficiency entering
the eighth-grade. Consistent with the Clark and Estes (2008) gap analysis model, this study will
identify deficiencies in the areas of knowledge and skill, motivation, and organization necessary
to reach the performance goal of reducing the eighth-grade African-American math achievement
gap. Because the additional math period could come at some cost to the students (through either
an additional period in the school day or substitution for an elective), evaluating the attitudes of
the African-American parents is critical to understanding the viability of the project.
The initial inquiry research questions are:
1. To what extent is Redwood Unified meeting its math proficiency goals?
2. What is the extent of African-American parents’ knowledge and motivation related to
Redwood Unified’s math proficiency goals?
3. What is the interaction between Redwood Unified culture and context and African-
American parents’ knowledge and motivation.
AFRICAN-AMERICAN MATH READINESS GAP 105

4. What are the recommendations for organizational practices in the areas of knowledge,
motivation, and Redwood Unified resources?
Knowledge Recommendations
Table 12 provides a summary of the assumed knowledge influences, whether they were
validated in the findings and recommendations to address them.
Table 12
Summary of Knowledge Recommendations
Assumed Knowledge Influences
Validated
as a Gap?
Principle and Citation
Content Specific
Recommendation

Parents need to understand the
importance of the articulated high
school math pathway to college and
career opportunities. (D)
Y
How individuals
organize knowledge
influences how they
learn and apply what
they know (Schraw &
McCrudden, 2006).
Provide parents an annual
in-person presentation
(training) on back-to-school
night that explains the math
pathway through high
school and its connection to
post-secondary college and
career opportunities.

Parents need to understand the
importance of maintaining grade
level math proficiency to readiness
for advanced high school
mathematics. (D)
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 parents an
informational brochure
(study aid) that clearly
articulates the connection of
math proficiency to the
math pathway. The parent
brochure would be provided
in concert with the annual
state assessment reports.
AFRICAN-AMERICAN MATH READINESS GAP 106

Increasing parent knowledge of the importance of grade-level math proficiency.
The results and findings of this study indicated that there is a 35% gap between African-
American parental of their student’s math mastery and actual math performance on standardized
tests (CAASPP, 2018). A recommendation rooted in information processing theory has been
selected to close this declarative knowledge gap. Schraw and McCrudden (2006) found that to
develop mastery, individuals must acquire component skills, practice integrating them, and know
when to apply what they have learned. This would suggest that providing parents a study aid
that connects math proficiency to the high school math pathway would support their learning.
The recommendation then is to provide parents an informational brochure (study aid) that clearly
articulates the connection of math proficiency to the math pathway. The parent brochure would
be provided in concert with the annual state assessment reports.
Parents are more likely to become involved in their child’s school if they believe they
have the requisite knowledge and skills needed to help their children succeed (Bandura, 1997).
Most, if not all, training programs are characterized by a less than adequate information transfer
(Ford & Weissbein, 1997). To improve on the transfer of key points in a training program, one
strategy is to ensure that the knowledge and skills taught are in a form that can be applied (Clark
& Estes, 2008, pg. 135). A useful complement to training is a study aid that articulates specific
information to perform a task (Clark & Estes, 2006, page 58). Training aids can enhance the
learning of knowledge from training by providing reminders about how to integrate the
knowledge into the performance of the designated skills (Clark & Estes, 2008, pg. 58).
AFRICAN-AMERICAN MATH READINESS GAP 107

Increase parent knowledge of high school math pathway importance. The results
and findings of this study indicated that an 82% African-American parent expectations gap exists
between their belief that their children will attend college and their student’s actual readiness for
the high school college preparatory math pathway that leads to college admission. This suggests
a need to increase parent knowledge of the importance of student readiness for the high school
math pathway. A recommendation rooted in information processing theory has been selected to
close this declarative knowledge gap. Schraw and McCrudden (2006) found that how
individuals organize knowledge influences how they learn and apply what they know. This
would suggest that providing parents with training that explains the importance of the math
pathway and its connection to post-secondary college and career opportunities would support
their learning. The recommendation then is to provide parents an annual in-person presentation
at back-to-school night that explains the math pathway through high school and its connection to
post-secondary college and career opportunities.
Gonzalez-DeHas and Willems (2003) found that the more complex the curriculum at the
high school level reduces parent involvement and self-efficacy. Parental motivation to
participate in school matters related to their children sharply declines during the child’s high
school years (Desplandes & Bertrand, 2005; Freedman-Doan, Arbreton, Harold & Eccles, 1993).
However, if parents believe that their actions will improve their child’s academic performance,
they will engage (Hoover-Dempsey, Bassler & Brissie, 1992; Stevenson, Chen & Uttal, 1990).
A predictor of parent participation at the secondary level is the parent’s ability to navigate the
complicated curriculum (Simon, 2001). This suggests that providing training that increases
parental knowledge of the high school math pathway would heighten their interest in critical
math education decisions. Training can be defined as an effort to provide the “how-to”
AFRICAN-AMERICAN MATH READINESS GAP 108

knowledge and skills, some guided practice, and corrective feedback (Clark & Estes, 2008, pg.
58). Clark and Estes (2008) articulate four types of knowledge and skill enhancement:
information, study aids, training, and education. Training can be envisioned as the sum of
information, study aids, guided practice, and corrective feedback (Clark & Estes, 2008).
Motivation Recommendations
Table 13
Summary of Motivation Recommendations
Assumed
Motivation
Influences
Validated
as a Gap?
Priority Principle and Citation
Content-Specific
Recommendation

Parents need to
attribute extra work
to their student's
ability to become
proficient at math.
(Attributions)
Y Y Adaptive attributions and
control beliefs motivate
individuals (Pintrich,
2003)

Provide feedback that
stresses the process of
learning, including the
importance of effort,
strategies, and potential
self-control of learning
(Anderman & Anderman,
2009).
Provide parents attributional
retraining related their own
capability to assist their students
in becoming proficient in math
before high school.

Provide feedback to parents that
reports the extra practice time
and progress of their students.

Parents need to view
the usefulness to
themselves of real-
world application of
math concepts. (UV)
Y N Rationales that include a
discussion of the
importance and utility
value of the work or
learning can help learners
develop positive values
(Eccles, 2006; Pintrich,
2003).
Provide parents rationales as
well as targeted inputs by peer
models who view the usefulness
to themselves of real-world
application of math concepts.

Increasing parent attribution of hard work to student math performance. The
results and findings of this study indicated that African-American parents believe that more
AFRICAN-AMERICAN MATH READINESS GAP 109

practice (76%) and an extra math instructional period (84%) would improve their child’s math
proficiency. Parents, then, already attribute student success in mathematics to the hard work
involved in more practice of math concepts and skills. But, a majority of parents who believe
their child struggles in math, believe the teacher has the primary responsibility for their child’s
math education. This creates a gap in parent expectations for their role. Critical to encouraging
students to do the extra work necessary to improve math performance is their parents’ belief that
investing time in motivating their students will be rewarded with higher levels of math
proficiency. A recommendation rooted in both utility value and self-efficacy theories has been
selected to close this utility value gap.
When individuals attribute success or failure on a given task to effort rather than ability,
learning and motivation are enhanced (Anderman and Anderman, 2009). An individual’s
adaptive attributions and beliefs provide motivation to persist (Pintrich, 2003). Borgogni (2011)
found that feedback, in additional actual learning achievement, can improve learning and
motivation. Feedback that stresses the importance of effort is an important strategy to improve
attributional value (Pintrich, 2003). This would suggest that providing parents attributional
retraining on the importance of math proficiency and regular feedback on the progress of their
students would increase attributional value. The recommendation is two-fold: 1) provide
parents attributional retraining related to their capability to assist their students in becoming math
proficient before high school, and; 2) provide feedback to parents that reports the extra practice
time and progress of their students.
Improving the attributional value African-American parents attach to the relationship
between extra work and results is central to this inquiry. If these parents are motivated to assist
their child by assigning an attributional value to their effort, parental participation may increase.
AFRICAN-AMERICAN MATH READINESS GAP 110

Collins (1990) reported that parents have a significant role in effecting the positive development
of their adolescent children. Whether parents believe they can positively affect student outcomes
can be defined as parent efficacy (Bandura, 1976, 1986). A parent’s confidence in their ability to
affect their student’s school performance increases parental school involvement (Eccles &
Harold, 1996). Finally, greater school participation among African-American parents leads to
parental efficacy and positive student academic outcomes (Hoover-Dempsey et al, 1992, 1987).
Increasing parent understanding of real-world application of math concepts.
The results and findings of this study indicated that African-American parents believe math skills
will increase their child’s success in everyday life (100%), adult job opportunities (89%), and
result in a higher paying job (84%). Providing a link between these strong supportive parental
views on the benefits of math and everyday examples of the applications of math could improve
both student motivation to engage in math studies and their parents to help provide the daily
motivation. A recommendation rooted in utility value theory has been selected to close this gap.
The rationalization of utility value assigned with the recommended learning can help students
develop a positive relationship to their studies (Eccles 20006; Pintrich, 2003). Learning and
motivation are enhanced if the learner values the task (Eccles, 2006). This would suggest that
providing parents a link between the math concepts their students are studying, and real-world
applications would improve parental self-efficacy and support. The recommendation then is to
provide parents targeted inputs by peer models who view the usefulness to themselves of real-
world application of math concepts.
By providing parents this link between math concepts and real-world applications, they
can be better armed with examples and motivated to encourage their children. Eccles and
Wigfield (2006) found that the value an individual assigns to a particular goal will strongly
AFRICAN-AMERICAN MATH READINESS GAP 111

influence their willingness to start an activity, persist, and ultimately finish a task. Both parents
and, through them, students can be motivated if they assign a higher utility value to the work
(Eccles & Wigfield, 2006). Although teachers have wide conceptual agreement for the use of
real-world application in math instruction, little empirical evidence exists to confirm its actual
use in regular classroom activities or communication with parents (Gainsburg, 2008). This study
explored the connection between real-world math applications and parental motivation to support
more time spent on math instruction.
Organizational Recommendations
Table 14 provides a summary of assumed organizational influences, whether they were
validated by the findings, and the proposed recommendation.
Table 14.
Summary of Organizational Recommendations
Assumed Organization
Influence
Validated? Principle and Citation
Context Specific
Recommendation
Parents feel a sense of
helplessness from past
efforts to help their
students improve math
outcomes. (CM)
Y Leaders who espoused
values are not in sync with
the organization's culture
will have difficulty leading
(Schein, 2004).
Be able to explain why the extra
instructional period will work in
90 seconds or less.
Communicate the math lab
vision every time there is parent
attended event.

There is a lack of a parent
communication plan to
explain the importance of
grade-level math
proficiency to post-
secondary college and
career opportunities. (CS)
Y Effective leaders are
knowledgeable of
communication processes
and how to use them for
effective organizational
change (Lewis, L.K., 2001;
Denning, Stephen, 2005).
Develop and implement a parent
communications plan to
illustrate the connection
between: math proficiency, high
school math pathway, college
and career entry, and higher
adult household income.

AFRICAN-AMERICAN MATH READINESS GAP 112

Course scheduling
calendars do not currently
accommodate an extra
math instructional period.
(Process)
HP Organizational performance
increases when processes
and resources are aligned
with goals established
collaboratively (Clark &
Estes, 2008)
Hold collaborative meetings
with parents, teachers, and
administrators to change the
course schedule to permit an
extra math instructional period
for less than proficient students.

Processes
Course scheduling calendars to accommodate an extra math instructional period.
The results and findings of this study indicated that 76% of African American parents and 84%
of all parents at Timber Middle strongly support the addition of an extra math instructional
period. Currently, Timber Middle students do not have the option of taking a second period
during the school day. A recommendation rooted in organizational theory is proposed to narrow
this gap. Organizational performance increases when processes and resources are aligned with
goals established collaboratively (Clark & Estes, 2008). The recommendation is to hold
collaborative meetings with parents, teachers, and administrators to change the course schedule
to permit an extra math instructional period for less than proficient students.
Consistent with research on additional math instructional periods, the extra period should
be structured differently than the direct teacher instruction in the regularly scheduled math
course. The extra period should be used to learn and practice math skills at the current level of
proficiency of each student. The course should emphasize all instructional methods other than
direct instruction, including: computer-based learning, small group instruction, and tutoring.
This approach tracks the successful CATAMA math intervention lab implemented successfully
by the Center for Social Organization of Schools at John Hopkins University (Balfanz, Ruby,
and MacIver (2008).
AFRICAN-AMERICAN MATH READINESS GAP 113

Organizational cultural settings provide an understanding of influences on a receptiveness
to change (Gallimore & Goldenberg, 2001). These cultural settings can provide visible and
concrete evidence of an organization’s cultural norms and its affect its members (Gallimore &
Goldenberg, 2001). The lack of an additional math instructional period for less than proficient
students may send an unwitting signal to parents and students alike that one period of math is
sufficient for student success.
Cultural settings
A parent communication plan to explain the importance of student readiness for the
high school college preparatory math pathway. The results and findings of this study
indicated most of Timber Middle’s African-American parents (95%) believe their children will
attend college. This overwhelming belief or aspiration was registered for parents of all ethnic
groups including whites (98%) and Latinos (98%). But less than 34% of Timber Middle students
and only 13% of African-American students, graduate from Timber Middle prepared to begin
high school college preparatory math pathway that leads to college admission (CAASPP, 2018).
A recommendation rooted in leadership theory is proposed to narrow this gap. Effective leaders
are knowledgeable of communication processes and how to use them for effective organizational
change (Lewis, L.K., 2001; Denning, Stephen, 2005). The recommendation is to implement a
parent communications plan to illustrate the connection between math proficiency, high school
math pathways, college and career entry, and higher adult household income.
The emphasis of this recommendation is on parental motivational support, rather than
direct homework assistance. The literature review supported parental participation, but was
inconclusive in homework support. Support that children receive from parents demonstrably
declines as they enter middle school (Winquist-Nord, 1998). However, in a meta-analysis of
AFRICAN-AMERICAN MATH READINESS GAP 114

research (N=50) related to parental involvement in middle school (Hill & Tyson, 2009) found
that parental involvement was positively associated with student achievement. Apart from
homework, parental involvement focused on academic socialization had the strongest impact on
student academic success. Parents are interested in what their children are doing at school and
how they can help them achieve success (Morrison, 1988; Quinton & Rutter, 2018). In a field
experiment (Harackiewicz, Rozek, and Hulleman, 2012) tested an intervention to assist parents
of high school students in articulating the importance of math to find whether it would lead the
students to take more math and science courses. The three-part intervention, two brochures and
a website, found that the group of students took approximately one semester more of math and
science courses.
Cultural model
Overcoming a sense of helplessness from past efforts to help students improve math
outcomes. In the interview phase of this study, several African-American parents expressed
challenges with past attempts to improve their child’s math performance. Part of a program to
encourage parents to support math interventions, including an extra instructional period, should
include an effort to link the intervention to student success. A recommendation rooted in
organizational change theory has been selected to close this gap. An organization’s leaders will
have difficulty leading change if their espoused values are not in sync with the organization’s
culture (Schein, 2004). Timber Middle’s sense of past failure to improve math achievement
manifested itself in the African-American parent interviews and needs to be addressed. A person
who values a task and believes they are likely to succeed at it will be more motivated to do it
(Wigfield & Eccles, 2000. The recommendation is to prepare a job aid that includes a review of
AFRICAN-AMERICAN MATH READINESS GAP 115

academic literature, including Redwood Unified's experience, that shows that the use of targeted
extra instructional time has increased math achievement.
A key finding of this study is that many parents at Timber Middle need math
interventions to succeed a math. However, parents have witnessed their children try various
math improvement strategies in the past unsuccessfully. Organizational cultural beliefs are
deeply embedded in schools (Schoen & Teddie, 2008) and encompass the consensus belief,
attitudes, and principles of school members (Maslowski, 2001). Although in recent years Timber
Middle School has been unsuccessful in improving math achievement, during the 2004-09
school years, the implementation of extra math instructional period increased African-American
student math assessment results by 18% (Redwood Unified, 2009). Providing evidence of past
success may help overcome the sense of helplessness and encourage parental support for the
proposed intervention of an extra math instructional period.
AFRICAN-AMERICAN MATH READINESS GAP 116

Integrated Implementation and Evaluation Plan
Implementation and Evaluation Framework
To create an integrated implementation and evaluation plan, the New World Kirkpatrick
model was used (Kirkpatrick & Kirkpatrick, 2016). This model articulates the original Four-
Level Model of Evaluation (Kirkpatrick & Kirkpatrick, 2006) which envisions evaluation plans
beginning with the goals of an organization and working in reverse. In this way, the “leading
indicators” connect the proposed solutions to the organization’s goals. By using this inverse
method, the New World Kirkpatrick model begins the following sequence: 1) reviewing work
behaviors informs the solution outcomes; 2) indicators of actual learning during implementation
are developed; and 3) indicators of organizational member satisfaction with implementation
strategies are identified. Drafting the implementation and evaluation plan using this model
compels a link between the proposed solutions and the organizational goal. Finally, the model
encourages the support of key stakeholders to ensure ultimate success (Kirkpatrick and
Kirkpatrick, 2016).
Organizational Purpose, Need, and Expectations
The purpose of Redwood Unified School District and Timber Middle school is “to educate
all students to achieve their maximum potential (Redwood Unified School District, 2018).” The
stakeholder group of focus in this study is the parents of African-American students at Timber
Middle School. African-American parents were chosen after a review of Timber Middle
School’s state assessment results showed that African-American students had the lowest math
proficiency scores (CAASPP, 2018). African-American parents, Timber Middle School, and
Redwood Unified School District have an aligned goal to increase the math proficiency of the
African-American students and their readiness for Algebra 1 when they begin high school.
AFRICAN-AMERICAN MATH READINESS GAP 117

Level 4: Results and Leading Indicators
Table 15 shows the proposed Level 4: Results and Leading Indicators in the form of
outcomes, metrics, and methods for both external and internal outcomes for Timber Middle
School. If the parent external outcomes occur, it is likely to support the internal organization
outcomes tied to better student math performance.
Table 15
Outcomes, Metrics, and Methods for External and Internal Outcomes
Outcome Metrics Methods

Internal Outcomes

Increased African-American parent
self-efficacy in assisting their
children in math achievement.
The number of African-
American parents who report
that they are able to assist their
children in math.
Conduct a quarterly parental
survey.

Improved African-American parent
knowledge of student mastery of
math skills and concepts.
The number of African-
American parents who sign and
return to the school the weekly
formative math assessment
generated from the math lab.
Send home current
formative math
assessment results to
parents weekly and ask
them to sign and return
them.

External Outcomes

Increased African-American math
grade-level proficiency by 10%.
The % of African-American
students proficient in grade
level math on the annual
CAASPP.
Compare the annual
CAASPP results from
year to year.

Increased 9th grade African
American student enrollment in
Algebra 1.
The number of 9th grade
African-American students
enrolled in Algebra 1.
High school counselors
prepare a report that
segments 9th-grade
former Timber Middle
School students by their
math course assignment.

AFRICAN-AMERICAN MATH READINESS GAP 118

Level 3: Behaviors
Critical behaviors. The stakeholders of focus are the parents of African-American
students at Timber Middle School. The first critical behavior is that the parents must receive and
review the weekly formative assessments of their students' math mastery. The second critical
behavior is that they contact their student’s teacher if progress is not being made. The third
critical behavior is for the parents to encourage their students to apply themselves in the daily
math lab sessions. The specific metrics, methods, and timing for each of these outcome
behaviors appear in Table 16.
Table 16
Critical Behaviors, Metrics, Methods, and Timing for New Reviewers
Critical Behavior Metrics Methods Timing

Parents review
weekly formative
assessments.
The number of signed and
returned parent reports on
formative assessments.
Math lab instructor will
track and record the
signed parent reports.
Weekly

Parents contact
teachers if progress
is not being made.
The number of parent
contacts received by
teachers.
Math teachers will
track and record parent
contacts.

Math lab instructor will
collect and consolidate
parent contacts.
End of school
year

Parents encouraged
their students to
apply themselves in
math lab practice
sessions.
The number of parental
encouragement comments to
engage in math lab session
reported by students.
Math lab instructor will
produce a summary of
parental comments
reported by the
students.
Weekly

Required drivers. Parents of math lab participants require the support of the math lab
instructor, math teachers, and principal of Timber Middle School to reinforce the importance of
AFRICAN-AMERICAN MATH READINESS GAP 119

the math lab with their students. Rewards should be established for the achievement of the
performance goal: the improvement of math mastery and proficiency. Table 17 shows the
recommended drivers to support the critical behaviors of African-American parents.
Table 17
Required Drivers to Support Critical Behaviors
Methods Timing
Critical Behaviors
Supported
Reinforcing
Provide parents an annual in-
person presentation (training)
on back-to-school night that
explains the math pathway
through high school and its
connection to post-secondary
college and career
opportunities.
Once, at parents back-to-
school night at the beginning
of the school year.
1, 4
Provide parents an
informational brochure (study
aid) that clearly articulates the
connection of math proficiency
to the math pathway. The
parent brochure would be
provided in concert with the
annual state assessment
reports.
Twice, once in the "Notice of
Assessment" that is sent to
parents before the annual state
assessment and again before
the annual state with the
"Smarter Balanced
Summative Assessment."
4
Provide parents attributional
retraining related to their own
capability to assist their
students in becoming proficient
in math before high school.
Once a semester, during
parent teacher conferences.
1, 3. 4
Provide feedback to parents
that reports the extra practice
time and progress of their
students.
Weekly 2, 3, 4
Provide parents rationales and
targeted inputs by peer models
who view the usefulness to
themselves of real-world
application of math concepts.
Weekly 1, 2, 3, 4
AFRICAN-AMERICAN MATH READINESS GAP 120

Rewarding
Schedule end of semester pizza
party with math lab students
and their parents to celebrate
the gains in math proficiency.
Monthly 1, 2, 3, 4
Monitoring
Principal conducts targeted
parent phone calls to African-
American parents of students
in math labs to solicit input.
Monthly 1, 2, 3, 4

Organizational Support. The critical behaviors and drivers targeted for performance
improvement above also require implementation of recommendations at the organizational level.
For our stakeholder group of focus (African-American parents) to achieve their goal of
improving math proficiency for their children, Timber Middle School would need to: 1) Create a
job aid that includes a review of academic literature, including Redwood Unified's experience,
on the use of targeted extra instructional time to increase student math outcomes to inform staff
and parents; 2) Develop and implement a parent communications plan to illustrate the
connection between math proficiency, high school math pathways, college and career entry, and
higher adult household income; and 3) Hold collaborative meetings with parents, teachers, and
administrators to change the course schedule to permit an extra math instructional period for less
than proficient students.
Level 2: Learning
Learning goals. Following completion of the recommended solutions, Timber Middle
School parents will be able to:
1. Recognize the importance of their student’s grade level math proficiency and will
be able to monitor key components of their student’s weekly math formative
assessment.
AFRICAN-AMERICAN MATH READINESS GAP 121

2. Recognize the importance of readiness for college preparatory math pathway and
their student’s progress toward eligibility for Algebra 1.
3. Attribute extra math and instructional time to improve math proficiency.
4. Parents will increase their self-efficacy in assisting their children in math.
5. Parents will better understand the utility value of math concepts.

Program. Evaluation of the components of learning. Applying knowledge to solve
problems often requires the demonstration of declarative knowledge. It is then important to
evaluate learning as it occurs for evidence that declarative and procedural knowledge has been
taught successfully. It is equally important for learners to value their training as a precursor to
applying the newly learned knowledge and skills to the job. Finally, the learners must be
confident that application of their knowledge and skills will positively affect their job
performance and be committed to using them. Table 18 lists the evaluation methods and timing
for these components of learning.
AFRICAN-AMERICAN MATH READINESS GAP 122

Table 18
Components of Learning for the Program
Methods or Activities Timing

Declarative Knowledge

Parent brochure outlining the importance of math proficiency,
high school math pathway, and potential benefits from the extra
math instructional lab period.
Beginning of school year.

Formative weekly assessments signed and returned by parents. weekly

Procedural Skills

Formative weekly assessments signed and returned by parents. weekly

Math lab teacher's observation of student's statement and actions
demonstrating that their parents have emphasized specific skills
identified in the weekly formative assessment.
ongoing

Attitude

Math lab teacher's observation of student's statements and
actions demonstrating that their parents have emphasized the
importance of doing well in math lab.
ongoing

Parent Likert survey. end of school year

Level 1: Reaction
Components to measure parent reactions to learning events during and after the school
year has been developed. Table 19 lists these components and their timing.
AFRICAN-AMERICAN MATH READINESS GAP 123

Table 19
Components to Measure Reactions to the Program
Methods or Tools Timing

Engagement

Attendance at Back to School night & parent conferences end of semester
Recorded contacts to math teachers following formative math assessment
reports end of semester
Data analytics by the math lab instructor ongoing
Observation by math teachers and math lab instructor ongoing
End of school year parent survey end of school year
Formative weekly assessments signed and returned by parents. weekly

Relevance

Observation by math teachers and math lab instructor ongoing
End of school parent survey end of school year

Customer Satisfaction

Observation by math teachers and math lab instructor ongoing
End of school parent survey end of school year

Evaluation Tools
Immediately following the program implementation. At the end of the fall semester
(approximately 18 weeks after program implementation), the parents will receive a Likert survey
(Appendix D). The parent survey will gauge parental reactions to 1) the math lab instructional
period; 2) weekly student math assessment report; and 3) parental math brochure, and; 4)
interactions between parents and teachers. The evaluation tool will feature five questions that
cover all categories of Level 1 and 2 outlined above.
Delayed for a period after the program implementation. At the end of the school
year, a final Likert parent survey will be conducted. This survey will feature 10 items designed
AFRICAN-AMERICAN MATH READINESS GAP 124

to evaluate all four levels of learning outlined above (Appendix B). The parent survey will focus
on an evaluation of the program for the current school year and inform any alteration of the
program in the next school year.
Data Analysis and Reporting
Critical to the current program effectiveness is a robust measurement system focusing on
parental commitment to the extra math instructional period. Without these measurements,
program participants are more likely to get lost in the challenging confusion of everyday middle
school life. Math teachers, the math lab coordinator, administrators, parents, and students have
many competing demands on their attention. The implied objective of the math instructional
period is to have these stakeholders focus more of their time and intellectual energy on math
proficiency. To that end, employing the straight-forward evaluation tools described in previous
sections (Appendices A, B) will ensure the daily steps towards closing the math achievement gap
are achieved. These include consistent stakeholder feedback, transfers of knowledge, and
persistent behavioral changes. Formative and summative measurements will be used not only to
keep on track during the school year, but also improve the program before the beginning of school
the next year.
To be effective and encourage stakeholder participation, data analysis must be based upon
an assessment that the data collected is directly associated with organizational goals and
expectations (Kirkpatrick & Kirkpatrick, 2016). The instructional math program seeks to directly
impact the math achievement of less than proficient students, but also requires the ongoing support
and interest of their parents. The recommended intervention, an extra math instructional period,
is built on increasing parent knowledge of the importance of math proficiency; the high school
math pathway link to college and career opportunities; and the link of additional math practice to
AFRICAN-AMERICAN MATH READINESS GAP 125

better academic outcomes. Also of interest, is the ongoing parent self-efficacy in their belief that
by actively participating in the math lab program, they can improve their child’s math proficiency.
The data collected will be used by the math teachers, the math lab coordinator, the principal, and
central office administrators to “fine-tune” the program as it proceeds and incrementally improve
the program for future school years. The results will then be used to attract and retain the active
support and participation of parents.
The learning goals described earlier are directly associated with the stakeholder goal of
improving math proficiency for their children and the organizational goal of narrowing the math
achievement gap for African-American students. The metrics collected inform both declarative
and procedural knowledge related to parent: 1) knowledge of the weekly improvement in their
child’s math mastery; 2) self-efficacy; 3) relevance to everyday life application; and 4)
commitment to their student’s participation in the math instructional lab. Two different methods
will be used to present data to the stakeholders. The first method, an infographic, will emphasize
immediate level 1 and 2 feedback. A summary of the end of each semester parent survey will
report the long-term data collection of the project.
As part of this Integrated Plan, parents will have interactions with school personnel through
the back to school night, parent/teacher conferences, and reactions to the weekly formative math
assessments. Following each of these encounters, brief exit ticket evaluation forms will be
collected. Summary information from the exit ticket evaluation forms will then be distributed to
other stakeholders including the math teachers, math instructional lab coordinator, and
administrators. This data can be analyzed and shared to make mid-term course corrections. The
exit ticket evaluations also offer insight into how parents are reacting to the program during its
implementation phase. This data will be shared with stakeholders in an infographic that outlines
AFRICAN-AMERICAN MATH READINESS GAP 126

attendance statistics, responses by parents to exit ticket questions, and program activities. All
information available information will be presented, regardless of outcome, to ensure that any
concerns will be addressed transparently. The data in the infographic pictured in Figure 4
represents the first part of presenting Integrated Plan information to organizational stakeholders.
Figure 4
Mock-up of Infographic for Formative Level 1 and 2 Data

In the second part of the data analysis reporting for the integrated plan, more long-term data
will be gathered and analyzed at the end of each school semester. The first-semester parent survey
will focus on level 1 and 2 learning objectives consisting of five questions and an open-ended
feedback opportunity. The first parent survey will focus on parental attitudes towards the
instructional math lab and their interaction with the program. The results of the parent survey will
AFRICAN-AMERICAN MATH READINESS GAP 127

also be presented in an infographic and presented to the stakeholders during the first school week
in January. Parents and students will be invited to a pizza party where positive results from the
parent survey and actual summative assessment results are presented. The second-semester parent
survey (Appendix E) will have survey items representing all four levels of training and evaluation
objectives. Again, an open-ended feedback space will be provided. The second semester survey
results will be summarized in a chart and sent to all stakeholder groups. A sample of the end of
the school year parent survey results chart is included as Appendix F.
Summary
The integrated plan for supporting an extra instructional period for a math lab at Timber
Middle School was prepared using Kirkpatrick and Kirkpatrick’s New World Model (2016).
The first step was to identify the gap between Timber Middle School’s organizational goal (math
proficiency for all students) and the math achievement of African-American students (13%
proficiency). Using an explanatory mixed method, parents from all ethnic subgroups were
surveyed (N=250, RR=47%). The survey was followed by interviews with African-American
parents (N=7) to explore their knowledge and motivational influences affecting their child’s
math education. These influences then informed the recommendations consistent with research
and other successful interventions.
The Kirkpatrick and Kirkpatrick model (2016) articulates four levels of training and
evaluation: reaction, learning, behavior, and results. A key characteristic of the model is a
training and evaluation plan author plans the steps with the end result in view. This method then
uses metrics that would indicate ultimate success, in the study present that African-American
student math performance would increase by 10% annually. The recommended intervention
requires parental support for maximum effectiveness. Parental behaviors that could student
AFRICAN-AMERICAN MATH READINESS GAP 128

results were then identified. To improve parental participation, their self-efficacy and math
knowledge were improved by: back to school night workshops, parent-teacher conferences, a
parent brochure, and weekly formative student math assessments. All four levels of the
Kirkpatrick model were integrated into the plan.
Parental support will be necessary to sustain long-term viability of the math instruction
lab period. To develop this support in the Timber Middle School, specific programmatic
elements are embedded in the program. These include parent evaluations at the end of each
semester to assist in persistent improvement. Timber Middle School educates approximately
half of the 7th and 8th grade students in the Redwood Unified School District. The successful
use of the Kirkpatrick model could then be expanded to the district as a whole in the future.
Strengths and Weaknesses of the Approach
Among several strengths to the approach used in this study, the KMO approach provided
significant structural support to the project. It provided discipline in evaluating a wide range of
knowledge, motivation, and organizational influences at work in African-American parental
support for efforts to reduce the math readiness gap. Parental participation in the survey portion
of the study was far greater than expected with almost half of all parents returning the 10-
question survey. This provides some evidence of strong parental concern and opinion regarding
the way math instruction is delivered to their children. Both a strength and a weakness of the
project was the African-American parent interviews. The parents who participated in these
interviews were, without exception, caring, forthright, and generous in sharing their individual
struggles with the math education of their students. Two unavoidable weaknesses must be
identified: 1) the seven African-American parents that participated are relatively modest group
of parents that do not allow statistical projections of their entire ethnic sub-group, and 2) the
AFRICAN-AMERICAN MATH READINESS GAP 129

seven African-American parents, with one exception, had attended or graduated from college.
The views of African-American parents with a high school diploma or less, then, were not fully
explored. Finally, during the survey distribution, significant interaction was possible with the
five dedicated math teachers at Timber Middle. Their beliefs on what would work to improve
math achievement surely are very important to this question, but not in the scope of this study.
Limitations and Delimitations
Given the time and resources available for this inquiry, there were some limitations and
delimitations. First, only seven interviews were conducted with African-American parents and
those parents who did participate had relatively high levels of educational attainment. Although
the parents that were interviewed all identified relevant struggles with their children’s’ math
education, the possibly different experiences of African-American parents with a non-college
background could have offered more insight. Second, the study did not seek the beliefs of the
math teachers at Timber Middle. Asking similar questions to the teachers would have provided
invaluable insight. Finally, since this was a review of the parents at a single middle school, it
would have provided a richer study to do a comparison with a similar school with different
demographics.
This study examined just of Redwood Unified’s stakeholder groups, African-American
parents and the performance goal related to their involvement. Many other stakeholder groups
certainly have an impact on parent involvement. The school board, central office administrators,
teachers, parent leaders, and classified staff all participate in the complex operation of a public
school. All of these stakeholders could potentially impact a parent’s view of the school and their
willingness to participate in math intervention programs. Finally, the stakeholder group most
AFRICAN-AMERICAN MATH READINESS GAP 130

central to performance, the student themselves could provide very useful information. These
limitations and delimitations are a consequence of having a limited scope to the inquiry.
Recommendations for Future Research
This study explored the parent beliefs with respect to their challenges with their students’
math education and potential participation in the intervention of an extra math instructional
period. Because of its organizational structure, Redwood Unified has a unique opportunity to
conduct a potential experiment. Approximately half of all seventh and eighth-grade students in
Redwood Unified attend Timber Middle. The other half of the middle school students are
distributed at the district’s K-8 elementary schools. If Redwood Unified did adopt an extra
instructional period at Timber Middle on a one-year pilot project basis, it would allow a
comparison between schools that did not have the extra math instructional period by comparing
CAASPP results at the end of the year. In addition, future research should be conducted to
deeply understand the views towards interventions of the math teachers at Timber Middle.
These educators attempt to teach students to grade level proficiency in math with less than an
hour a day of instruction time and wide variety of achievement levels in their classrooms.
Having lengthy interviews with these teachers would add much context to the best way forward
to improve math readiness.
Conclusion
Having conducted this inquiry into the knowledge, motivation, and organizational
influences affecting parental participation on the issue improving math achievement, it is
recommended that an extra math instructional period be scheduled for students that are less than
proficient. Further, to increase parental participation and support, a comprehensive parent
communications plan is recommended that includes weekly formative student reports,
AFRICAN-AMERICAN MATH READINESS GAP 131

explanations of the importance of the high school math path and math proficiency, and frequent
updates on student progress. Finally, it would be desirable for the extra math period to be used
for a math lab featuring individually tailored computer-based instruction and tutoring with a
dedicated certificated math teacher. This math lab teacher would then support the instruction of
the math teachers in the traditional classes with a constant flow of information on the progress of
individual students.

AFRICAN-AMERICAN MATH READINESS GAP 132

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APPENDIX A
Parent Math Education Survey
Survey
Item
Strongly
Disagree
Disagree Agree
Strongly
Agree
1
My child's math education is
primarily the teacher's
responsibility.
2
Math is important for success
in everyday life.
3
Math is critical to my child's
adult job opportunities.
4
My child struggles to
understand math concepts.
5
If my child had an extra math
instructional period at school, it
would improve math
proficiency.
6
More practice would improve
my child's math proficiency.
7
After leaving high school, my
child is likely to attend college.
8
Advanced math skills will
qualify my child for a higher
paying job after school
graduation.

Parent Demographic Information

Some
High
School
High School
Graduate
Some College College
Graduate
Decline
to State
9 Educational Background

African-
American
Latino White Other
Decline
to State
10 Ethnic Sub-Group
Parent Survey Disclosure
This voluntary survey is part of a research project being conducted by a University of Southern California
graduate student. The survey is not affiliated with Lincoln Unified School District. All survey responses
will be kept confidential and aggregated to inform the study's purpose of better understanding parental
beliefs about middle school math education.
Parent Signature:
Print Name:
If you are interested in being part of a voluntary interview, please add your email:
Parent Email:

AFRICAN-AMERICAN MATH READINESS GAP 161

APPENDIX B
Informed Consent/Information Sheet
University of Southern California
Research Information Sheet
You are invited to participate in a research study conducted by Dean Andal at the University of Southern
California. This study is part of a dissertation project to receive a Doctor of Education. Please read
through this form and ask any questions you might have before deciding whether or not you want to
participate.
Purpose of the Study
This study seeks to understand parent knowledge, beliefs, and experiences related to their child’s math
education and support for extra math instructional time.
Participation Involvement
If you agree to take part in this study, you will be asked to complete a one-hour interview with a small
number of other parents. The interview will include questions and a discussion about your child’s math
experience and some demographic questions. You do not have to answer any questions you don’t want
to.
Compensation for Participation
You will receive a $20 Starbucks gift card as a token of appreciation.
Confidentiality for Participation
Any identifiable information obtained in connection with this study will remain confidential. At the
completion of the study, direct identifiers will be destroyed, and the de-identified data may be used for
future research studies.
Dean Andal, Dr. Angela Hasan (his chair), and the University of Southern California’s Human Subjects
Protection Program (HSPP) may access the data. The HSPP reviews and monitors research studies to
protect the rights and welfare of research participants like yourself.
Investigator Contact Information
If you have any questions or concerns about the research, please feel free to contact Dean Andal at
dandal@usc.edu or Angela Hasan at ahasan@usc.edu.
IRB Contact Information
If you have questions, concerns, or complaints about your rights as a research participant or the research
in general and are unable to contact the research team, or if you want to talk to someone independent of
the research team, please contact the University Park Institutional Review Board (UPIRB), 3720 South
Flower Street #301, Los Angeles, CA 90089-0702, (213) 821-5272, or upirb@usc.edu.

AFRICAN-AMERICAN MATH READINESS GAP 162

APPENDIX C
Interview Protocol
Section 1. Introduction (Purpose, Confidentiality, Consent, Permission)
Thank you for participating in this doctoral study on African-American student readiness for
college prep math at Timber Middle School. The time that you have set aside for this research
study is greatly appreciated. As I mentioned, this interview should take about a half hour. Does
that work for you? (If yes, we move forward; if no, we reschedule)
Before getting started, I want to give you a brief overview of this study and give you the
opportunity to ask any questions that you may have. As a component of my doctoral program, I
am developing a dissertation on the readiness of 7
th
and 8
th
grade students for the college
preparatory math pathway at the high school. All of your responses will be confidential and no
personally identifying information will be shared outside of this discussion. If at any time during
the interview you wish to stop, please just let me know.
At this time, do any of you have any questions that I may answer?
Do I have your permission to begin the interview?
So that I may accurately capture your responses to the following questions, may I record the
audio of our discussion? Only my dissertation advisor and I will have access to the recording,
and they will be destroyed after the completion of this study.
Section 2. Interview Questions
To start this interview, I am going to ask you some questions to ensure I am speaking with a
representative group of parents. If you are not comfortable with any of the questions, let me
know and we can skip them.
How many children do you have that currently attend a school in the district?
What are their grade level(s) and which schools do they attend?
AFRICAN-AMERICAN MATH READINESS GAP 163

Does your student think math is important?
Do you think your student will attend college?
The following questions focus your student’s feelings and experiences with math at school.
Would your student say that is one of their favorite classes or one of their least favorite classes at
school?
Does your student generally keep up with the pace of math instruction or sometimes feel like
they are falling behind?
Has your student’s attitude towards math changed in the 7
th
and 8
th
grade? If so, how?
If your student feels negatively towards math, why do you think that is?
Do you feel like your math knowledge has helped or harmed your job opportunities as an adult?
Do you wish that you had taken more advanced math classes when you were in high school?
Do you feel comfortable or capable of helping your student with their math homework?
Now, I’d like to ask you some questions about your math experiences when you were in high
school.
When you attended high school did you have a mostly positive or mostly negative experiences in
your math courses?
Tell me more about what caused you to feel that way?
Did you take Algebra 1?
Would you feel comfortable helping your student with their Algebra homework?
Next, we are going to talk about math grade level proficiency and its relationship to the high
school math pathway. Before we get started on this section, I’d like to explain what I mean by
math proficiency and pathway. The State of California has adopted standards spelling out what
students should know at the end of each grade level. Every year by state law, all students take
the California Assessment of Student Performance and Progress (CAASPP). Students that are
proficient have learned the grade level standard and are ready for the next year’s instruction.
The high school math pathway starts with Algebra 1 in either the 8
th
or 9
th
grade. Depending on
where a student starts in the first year of high school determines whether they are on a non-
college, college, or advanced pathway before high school graduation.
After each year’s assessment, a student score report is then sent to their parents showing whether
a student is below standard, near standard, or above standard in math. Above standard means the
child is grade level proficient. Do you remember receiving and reading these annual reports?
AFRICAN-AMERICAN MATH READINESS GAP 164

After reading your student’s annual report, did you feel like they were ready for the next year’s
math instruction or did you feel like they were falling behind?
Do you feel like your student will be ready to complete Algebra 1 in the 8
th
or 9
th
grade?
Are you aware of what math classes are offered at the high school and what your student will be
qualified to take in the 9
th
grade?
Do you know what the math pathway that leads to the University of California entrance
standards by high school graduation?
I’d now like to discuss with you the relationship between the high school math pathway and
STEM college degrees and jobs. STEM means Science, Technology, Engineering, and
Mathematics.
Do you think your student will get into a better college or technical program if they take more
advanced math classes in high school?
Do you think getting a STEM college degree requires more advanced math?
Do you think that STEM jobs pay more?
One possible intervention program to help students who are not yet ready for Algebra 1 is an
extra instructional period at school to provide more practice and help for daily math lessons.
I’d like to ask you how you feel about this.
If your student is not ready for Algebra 1, would you support an extra math period to help them
get ready?
If yes, would you be willing to have your student attend school for an extra period in the school
day?
If yes, would you be willing for your student to forgo an elective class during the existing regular
school day to make time for an extra math instructional period?
Section III. Closing
Is there anything else anyone would like to add that we may not have covered? Thank you for
your time today. Everything you have shared was really helpful for my research study.
Section IV. Thanks
As a thank you for your time today, please accept this gift card as a token of my appreciation.
Section V. Clarification
AFRICAN-AMERICAN MATH READINESS GAP 165

(Note: to ensure clarity and understanding use phrases such as “to ensure I am understanding
you, could you tell me more about …”and could you walk me through it.”
AFRICAN-AMERICAN MATH READINESS GAP 166

APPENDIX D
Appendix D: Immediate Evaluations (Levels 1 &2)
Parent Survey - Math Instructional Lab - Fall Semester

Directions: Thank you for your support of Timber Middle School's math instructional lab. Our school community
appreciates your commitment to the extra math instructional period and the focus on improving readiness for high
school math pathway beginning in the ninth grade. To help ensure the lab is doing everything possible to help
parents in assisting their student, please truthfully respond to the following five survey items. You will also have
the opportunity to provide additional feedback at the conclusion of this feedback form. The feedback forms are
confidential. However, if you would like to provide additional one-on-one feedback, please contact the math lab
instructor directly.

Number 1: I am satisfied that my child is benefiting from the extra math lab instructional period.
1 2 3 4 5
Strongly Disagree Disagree Neutral Agree Strongly Agree

Number 2: The weekly math assessment reports you receive are helpful in understanding your student's
progress in math.
1 2 3 4 5
Strongly Disagree Disagree Neutral Agree Strongly Agree

Number 3: I feel comfortable contacting my student's math teacher and the math lab instructor to discuss my
student's math progress.
1 2 3 4 5
Strongly Disagree Disagree Neutral Agree Strongly Agree

Number 4: Parent events like Back to School Night and parent/teacher conferences explain the reasons for the
math instructional lab period in clear terms.
1 2 3 4 5
Strongly Disagree Disagree Neutral Agree Strongly Agree

AFRICAN-AMERICAN MATH READINESS GAP 167

Number 5: The parent brochure on math at Timber Middle School clearly explains the importance of the high
school math pathway and its relationship to good college and career opportunities for my student.
1 2 3 4 5
Strongly Disagree Disagree Neutral Agree Strongly Agree

Additional Feedback:

AFRICAN-AMERICAN MATH READINESS GAP 168

APPENDIX E
Appendix E: Delayed Evaluation (Levels 1, 2, 3, & 4)
Parent Evaluation Survey - Math Instructional Lab - Spring Semester

Directions: Thank you for your support of Timber Middle School's math instructional lab this year. Our school
community appreciates your commitment to the extra math instructional period and the focus on improving
readiness for high school math pathway beginning in the ninth grade. To help ensure the lab is doing everything
possible to help parents in assisting their student, please truthfully respond to the following five survey items. You
will also have the opportunity to provide additional feedback at the conclusion of this feedback form. The feedback
forms are confidential. However, if you would like to provide additional one-on-one feedback, please contact the
math lab instructor directly.

Number 1: The information provided at parent conferences, in the parent math brochure, and other interaction
with school staff was helpful in understanding the purpose of the math instructional lab period. (L1&2)
1 2 3 4 5
Strongly
Disagree
Disagree Neutral Agree Strongly Agree

Number 2: The weekly parent report from the math instructional lab instructor continues to assist me in helping
my student advance in math proficiency. (L1&2)
1 2 3 4 5
Strongly
Disagree
Disagree Neutral Agree Strongly Agree

Number 3: As a parent I feel that I was able to positively impact my student's math achievement this year.
(L3&4)
1 2 3 4 5
Strongly
Disagree
Disagree Neutral Agree Strongly Agree

Number 4: I believe I clearly understand the importance of the high school math pathway beginning with
Algebra 1 in the 9th grade. (L3&4)
1 2 3 4 5
Strongly
Disagree
Disagree Neutral Agree Strongly Agree

AFRICAN-AMERICAN MATH READINESS GAP 169

Number 5: The math instructional lab increased my student's math achievement this year. (L4)
1 2 3 4 5
Strongly
Disagree
Disagree Neutral Agree Strongly Agree

Additional Feedback:

AFRICAN-AMERICAN MATH READINESS GAP 170

APPENDIX F
Appendix F: Data Analysis Chart

Fall Semester Parent Survey Results

Number 1: I am satisfied that my child is benefiting from the extra math lab instructional period.
% % % % %
Strongly Disagree Disagree Neutral Agree Strongly Agree

Number 2: The weekly math assessment reports you receive are helpful in understanding your student's
progress in math.
% % % % %
Strongly Disagree Disagree Neutral Agree Strongly Agree

Number 3: I feel comfortable contacting my student's math teacher and the math lab instructor to
discuss my student's math progress.
% % % % %
Strongly Disagree Disagree Neutral Agree Strongly Agree

Number 4: Parent events like Back to School Night and parent/teacher conferences explain the reasons
for the math instructional lab period in clear terms.
% % % % %
Strongly Disagree Disagree Neutral Agree Strongly Agree

Number 5: The parent brochure on math at Timber Middle School clearly explains the importance of the
high school math pathway and its relationship to good college and career opportunities for my student.
% % % % %
Strongly Disagree Disagree Neutral Agree Strongly Agree

Abstract (if available)

Abstract This evaluation study seeks to understand the beliefs and attitudes of African-American parents towards math proficiency and readiness for high school college preparatory mathematics at Timber Middle School. Specifically, the inquiry probes these parents’ potential acceptance of an additional math instructional period for students that are performing below grade level proficiency. An explanatory mixed-methods design combined a survey of all parents (N=532, RR=47) at Timber Middle School with interviews of African-American parents (N=7) to explore their beliefs in depth (Creswell, 2014). The study was structured with a (Clark and Estes, 2008) gap analysis model to make six findings categorized by assumed knowledge, motivation, and organizational influences. The knowledge influence findings are: 1) a gap was identified between African American parent’s beliefs towards their children’s math mastery and actual student math proficiency

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Asset Metadata

Creator Andal, Dean Fredrick (author)

Core Title Parental participation in efforts to reduce the African-American math readiness gap at Timber Middle School: an evaluation study

School Rossier School of Education

Degree Doctor of Education

Degree Program Organizational Change and Leadership (On Line)

Publication Date 11/18/2019

Defense Date 10/14/2019

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

Tag achievement gap,African-American,California,instructional time,mathematics,middle school,OAI-PMH Harvest,Parents,readiness gap

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Hasan, Angela (committee chair), Lowder, Steven (committee member), Picus, Lawrence O. (committee member)

Creator Email dandal@usc.edu,deanandal@sbcglobal.net

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-237368

Unique identifier UC11673816

Identifier etd-AndalDeanF-7934.pdf (filename),usctheses-c89-237368 (legacy record id)

Legacy Identifier etd-AndalDeanF-7934.pdf

Dmrecord 237368

Document Type Dissertation

Rights Andal, Dean Fredrick

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