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Promising practices of California community college mathematics instructors teaching AB 705 accessible courses

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Promising Practices of California Community College Mathematics Instructors Teaching
AB 705 Accessible Courses

Shawn Michael Taylor

Rossier School of Education
University of Southern California
A dissertation submitted to the faculty
in partial fulfillment of the requirements for the degree of
Doctor of Education

May 2023

© Copyright by Shawn Michael Taylor 2023
All Rights Reserved

The Committee for Shawn Michael Taylor certifies the approval of this Dissertation

Angela Hasan
Alex Miranda
Robert Filback, Committee Chair

Rossier School of Education
University of Southern California
2023

iv
Abstract
Historically, California Community Colleges (CCCs) had broad discretion to determine which
students could enroll directly in transferable college-level courses and which students had to
begin with remedial prerequisites. These policies have disproportionately affected students of
color and low socioeconomic status by placing them into remedial classes. Remediation may also
impede graduation rates, particularly in math courses. AB 705 was passed to address this issue,
which aimed to improve student success by using multiple measures to determine course
placement. Since its passage, there has been an influx of academically underprepared students,
creating new challenges for instructors. However, little research has focused on the experiences
of math faculty in AB 705-affected courses. This study aimed to identify instructional practices
that address learning gaps while meeting the needs of a diverse student population. Qualitative
data were collected through conversations with community college math faculty. Findings
suggest the need for a more student-centered approach to teaching math, including inquiry-based
and personalized learning experiences. Additionally, professional development opportunities
must be funded and accessible for instructors to stay current with the latest research and best
practices. This study contributes to the development of effective strategies for closing learning
gaps while promoting equity in community college math education.
Keywords: AB 705, California community colleges, math remediation, instructional
strategies

v
Dedication
To my mother, Karen Taylor; my father, Thomas Taylor; my sister, Sharon Reynolds; my
brother, Mark Taylor; and my extended family, I love you and thank you for accepting, pushing,
loving, and helping me whenever I am in need. I am deeply grateful for your unwavering support
and encouragement throughout this journey. Your love, patience, and understanding have been
the bedrock of my success.

To my wife, Dr. Erin Craig, I would like to express my unbounded love and appreciation.
Without your wisdom, guidance, love, and support, I would not be a Trojan. You are the love of
my life and so much more.

To my friends, bandmates, and colleagues, thank you for your support, encouragement, and
camaraderie. Your belief in me has sustained me through the many challenges of this process. In
particular, I owe an enormous chunk of gratitude to my long-time friend Chloe Orizo who
always had my back—thick or thin—and for selflessly committing to transport me to and from
USC.

To my colleague Bobby Patsios, thank you for your unwavering accommodation, great
conversation, and life-long memories.

To my friend Philip Simpkin, you are my brother. We have bested this world in many ways,
from 5 to 45 years old, and I look forward to seeing your future doctoral experiences firsthand.
vi
To all my students, your enthusiasm, dedication, and hard work have been a constant source of
inspiration to me as a math teacher.

To all the educators and educational leaders who have inspired me throughout my life, I would
like to express my gratitude, especially Dr. Pierre Grimes, Christopher Drover, Bernie Gilpin,
Evan Williams, Tom Kubis, Dr. Mohammed Jamalodeen, Thomas Scardina, Dr. Joseph Bennish.
Their dedication, passion, and commitment to improving the lives of others have been a constant
source of inspiration and motivation for me.

To my daughter McKenzie Dean Taylor, I dedicate this work to you—Daddy loves you more
than words can express. But, whatever you do, as you grow older, please do not become a UCLA
Bruin =).

To the rest of you… FIGHT ON! �

vii
Acknowledgments
I am deeply grateful to have had the opportunity to pursue my doctoral degree in
educational leadership at the University of Southern California. I have wanted to be a Trojan
since I was a young boy. Back then, that dream was an impossibility, but as the years went on
and my educational experience grew, the road to Troy became a reality. Being a graduate student
at USC is still a surreal idea for me to comprehend. Knowing this journey is ending is
bittersweet, but as I continue onward, I will dawn the cardinal and gold with extreme pride,
flying the sign of victory.
I am indebted to the many individuals who have supported me throughout this journey.
Firstly, I would like to express my sincere gratitude to my dissertation advisor, Dr. Robert
Filback, for his guidance, encouragement, and unwavering support. Dr. Filback’s expertise and
insights were invaluable to the completion of this project. I would also like to thank the members
of my dissertation committee, Dr. Angela Hasan, and Dr. Alex Miranda, for their thoughtful
feedback and suggestions that helped me to improve my work. Moreover, I would like to extend
my appreciation to the faculty and staff of the Rossier School of Education, who provided me
with a stimulating and supportive environment in which to learn and grow. The resources,
opportunities, and mentorship provided by the Rossier community have been invaluable to my
professional development and success as a Trojan.

viii
Table of Contents
Abstract .......................................................................................................................................... iv
Dedication ....................................................................................................................................... v
Acknowledgments......................................................................................................................... vii
List of Figures ................................................................................................................................ iv
Chapter One: Introduction to the Study .......................................................................................... 1
Statement of the Problem .................................................................................................... 1
Purpose of the Study ........................................................................................................... 2
Importance of the Study ...................................................................................................... 3
Conceptual Framework ....................................................................................................... 4
Methodology ....................................................................................................................... 6
Limitations .......................................................................................................................... 6
Delineations ........................................................................................................................ 7
Assumptions ........................................................................................................................ 7
Definition of Terms............................................................................................................. 7
Organization of the Dissertation ......................................................................................... 9
Chapter Two: Literature Review .................................................................................................. 10
Recent California Legislation AB 705 .............................................................................. 11
High School Programs That Prepare Students for College Math ..................................... 23
The Transfer-level Math Approach in California Community Colleges .......................... 35
Student Diversity in California Community Colleges ...................................................... 41
Conceptual Framework ..................................................................................................... 49
Conclusion ........................................................................................................................ 60
Chapter Three: Methodology ........................................................................................................ 62
Research Questions ........................................................................................................... 62
ix
Purposeful Sample and Population ................................................................................... 63
Study Context.................................................................................................................... 63
Data Collection ................................................................................................................. 65
Recruitment ....................................................................................................................... 66
Data Analysis .................................................................................................................... 66
Ethical Considerations ...................................................................................................... 67
Trustworthiness Measures ................................................................................................ 68
Role of the Researcher ...................................................................................................... 69
Chapter Four: Findings ................................................................................................................. 72
Identified Instructional Challenges ................................................................................... 73
The Presence of Differentiated Instructional Strategies ................................................... 82
Additional Instructional Strategies ................................................................................... 95
Conclusion ...................................................................................................................... 115
Chapter Five: Discussion and Recommendations....................................................................... 117
Discussion ....................................................................................................................... 117
Recommendations ........................................................................................................... 126
Future Research .............................................................................................................. 130
Conclusion ...................................................................................................................... 133
References ................................................................................................................................... 136
Appendix A: Protocols ................................................................................................................ 165
Research Questions ......................................................................................................... 165
Introduction ..................................................................................................................... 165
Interview Questions ........................................................................................................ 167
Closing Statements .......................................................................................................... 168

iv
List of Figures
Figure 1: Model of the Conceptual Framework ............................................................................ 50
Figure 2: Tomlinson’s Model of Instructional Differentiation ..................................................... 52
Figure 3: Merril’s First Principles of Instruction .......................................................................... 53
Figure 4: Anderson and Krathwohl’s Revised Bloom’s taxonomy .............................................. 55
Figure 5: The Progress of Knowledge .......................................................................................... 58

1

Chapter One: Introduction to the Study
California Assembly Bill 705 (AB 705) allows community college students to enroll
directly in transfer-level math courses such as college algebra and introduction to statistics
without matriculation or prerequisite coursework. Since the passage of AB 705, an enormous
influx of academically underprepared students has enrolled in these transfer courses. Many
scholars and practitioners argue that removing remedial math requirements and allowing greater
access to college-level math courses is essential to eliminating systemic inequity, particularly for
historically underrepresented community college students (Bensimon, 2004). However, while
this argument may be valid, the new approach presents significant challenges for math educators
since they must now address a broader spectrum of learning needs in their classrooms while still
trying to fulfill rapidly evolving state curriculum requirements.
Statement of the Problem
Historically, California Community Colleges (CCCs) had broad discretion to determine
which students could enroll directly in transferable college-level courses and which students had
to begin with remedial prerequisites. Before AB 705, more than 75% of incoming students had to
take remedial math or English classes based solely on their performance on standardized
entrance exams and placement tests (Baily, 2009; Noel-Levitz, 2007; Rodriguez, 2017;
Schwartz, 2007). Over the past 2 decades, considerable attention has been devoted to the need
for low-skilled students to enroll in nontransferable developmental mathematics courses
(Bonham & Boylan, 2012; Rosin, 2012). Typically, students put into remediation are much less
likely to reach their educational goals than those who are not (California Community Colleges
Assessment & Placement, 2017). However, evidence suggests (Adelman 1999; Adelman 2004;
2

Chen 2016) that significantly more students would complete transfer requirements in math and
English if enrolled directly in transfer-level English and math courses.
College assessment instruments and placement policies have profound implications for
equity, as students of color and low socioeconomic strata are far more likely to be placed into
remedial courses (Kreysa, 2006). In addition, researchers (Attewell et al., 2006) argue that
completing math remediation courses may be the most significant barrier to increasing
graduation rates. Recognizing the student success deficiencies associated with developmental
education, lawmakers sought to enact legislation to address these shortcomings head-on. On
October 13, 2017, the governor of California signed Assembly Bill 705, taking effect on January
1, 2018. Instead of relying on traditional placement tests, AB 705 mandates that community
colleges use other metrics such as high school courses, grades, and GPAs as deciding factors for
the placement of incoming students into transfer math courses.
In the hope of repairing the harms done by more than 50 years of mainly consigning
racially minoritized students to remedial education courses, California policymakers set
aggressive postsecondary transformational goals such as AB 705 and dual enrollment programs.
Unfortunately, these novel programs and laws simultaneously create new instructional hurdles
and learning obstacles for community college instructors and students. This study centers on the
experiences and promising practices of community college math instructors who teach transfer-
level courses affected by AB 705. Identifying these academic hurdles and the innovative
solutions instructors use to overcome them is the primary goal of this study.
Purpose of the Study
This study wishes to determine the following: (a) the instructional strategies used to
address the diverse learning needs of all students in entry-level transfer math courses; (b) identify
3

the challenges community college math instructors encounter now that AB 705 has removed all
remediation and prerequisite barriers; (c) how community college math instructors differentiate
their lessons and curriculum to meet the diverse learning needs and skill gaps of their students
while covering all required course content within a semester; and (d) the deliberate planning
approaches used by community college mathematics instructors that guide their students through
the various knowledge and instructional levels as described by Anderson and Krathwohl (2001),
and Merrill (2002).
Three primary research questions guiding the investigations were:
• What challenges do community college math instructors face now that AB 705 has
removed all remediation into transfer-level math courses?
• How do community college math instructors differentiate the curriculum to meet
students’ diverse learning needs and skill gaps in AB 705 accessible math courses?
• What other instructional strategies are community college math instructors using with
their students that generate equitable outcomes in AB 705 accessible math courses?
Importance of the Study
This qualitative study presents an understanding of community college math instructors’
instructional challenges now that AB 705 has removed all remedial placement policies. The
study also wishes to understand what promising instructional practices these faculty members are
utilizing to close the learning gaps remediation traditionally attempted to address while
simultaneously meeting the educational needs of the diverse student population in their
classrooms. Although research on effective instructional strategies is abundant, the extant
literature has neglected teaching practices related to the instructional challenges AB 705 math
courses create. Furthermore, research centering on the firsthand experiences of mathematics
4

faculty teaching AB 705-affected math courses is lacking. This study helps to fill this research
gap. The significance of this study is twofold: It seeks to reveal how other community college
mathematics instructors perceive the challenges present in the post-AB 705 era and it benefits
California’s community colleges by identifying potential curricular reforms that make the
learning experiences and academic outcomes of entry-level transfer math students more fruitful.
This study also provides a foundation for further research.
Conceptual Framework
Effective instructors use learning theories in instructional planning and classroom
teaching to increase students’ knowledge and success. This study will analyze student learning
processes through the lens of Anderson and Krathwohl’s (2001) six stages of cognitive
dimensions, also known as the revised Bloom’s taxonomy (RBT). Anderson and Krathwohl
modify the six stages of Bloom’s taxonomy (1956). According to the revised version of Bloom’s
taxonomy (2001), there are six cognitive learning levels, each conceptually different and
mutually exclusive. The six levels are remembering, understanding, applying, analyzing,
evaluating, and creating.
Although Anderson and Krathwohl’s revised stages of cognitive dimension theorize how
students progress through the cognitive stages of learning, it lacks details regarding how teachers
are to facilitate instruction that guides students to the highest levels of the taxonomy. To augment
this, the author will utilize David Merrill’s (2002) first principles of instruction. Five core
principles center on task-based learning. Merrill suggests compelling learning experiences are
rooted in problem-solving (Merrill, 2002). Merrill’s principles are prescriptive (design-oriented)
rather than descriptive (learning-oriented) and draw from several instructional design theories
and models. Merrill’s five core principles are
5

1. Learning is promoted when learners are engaged in solving real-world problems.
2. Learning is promoted when existing knowledge (and skill) is activated as a
foundation for new knowledge (and skill).
3. Learning is promoted when new knowledge is demonstrated to the learner.
4. Learning is promoted when the learner applies new knowledge.
5. Learning is promoted when new knowledge is integrated into the learner’s world.
Community college math faculty serve diverse learners in their classes, including dual
enrollment students, adult learners returning to college after time away, English learners,
students with developmental and physical disabilities, recent high school graduates, students
seeking to transfer to a university, and students with extreme variance in math skill. These
populations coexist in the same classroom, requiring faculty to rethink and replan how they
previously taught these courses. To meet the diverse needs of students, math faculty should
utilize evidenced-based learning and instructional theories described by Anderson and
Krathwohl’s six stages of cognitive dimension (2001) and David Merrill’s first principles of
instruction that build students’ knowledge and comprehension systematically.
The two frameworks complement one another but lack a key component. Neither theory
recognizes the differences in students’ cognitive ability, readiness, and academic skills. To
address this shortcoming, the author will utilize Tomlinson’s method of instructional
differentiation (Tomlinson, 2017). In Tomlinson’s model, teachers adjust a lesson’s content,
process, and products to improve the likelihood of students’ engagement and achievement.
Emphasis is placed on demonstrating, scaffolding, and lesson design, for students to understand
and extend their knowledge of the subject. Differentiated instruction is a philosophy of teaching
purporting that students learn best when their teachers effectively address the variance in
6

students’ readiness levels and interests while remembering profile preferences (Tomlinson,
2005).
Methodology
A qualitative approach and methodology were selected to understand better the individual
challenges and experiences of community college math instructors who teach entry-level transfer
math courses. The implemented methods throughout the study were to collect qualitative data
related to faculty perceptions and firsthand accounts gathered from conversations with
community college math faculty.
The data collection method was a semi-structured interview comprised of banks of open-
ended questions. The duration of each interview lasted approximately 60 minutes. All
participants were interviewed via the video-conferencing application known as Zoom. After the
data collection phase was completed, audio and video recordings were transcribed. The data was
gathered during the Spring 2023 semester. Data analysis was conducted immediately following
each interview and verified for accuracy. Each interview recording was transcribed into a text
format. Each transcription was reviewed thoroughly and annotated, labeling relevant words,
phrases, sentences, or sections with codes. The data was then conceptualized by creating
categories and subcategories by grouping the codes created during the annotation process. Next,
the data was segmented. The segmentation of data is the process of positioning and connecting
categories. This allows the establishment of the data cohesively. Next, each segment was
analyzed to determine if there were hierarchies among categories. The final step of the analysis
was a presentation of the findings.
Limitations
The following limitations were present in the study:
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1. This study only interviewed faculty from the southern California region of the United
States, as defined in Chapter Three.
2. Other AB 705 affected disciplines like English and ELL (English Language
Learning) are not considered.
3. Although college algebra and introduction to statistics are courses offered at CSU and
UC institutions, only California Community College courses are investigated.
4. Qualitative data collection using interviews with community college math faculty
increases the potential for subjective interpretation of results.
Delineations
The following delineations are present in the study:
1. There is limited statewide generalizability due to the restriction of the study to the
southern California region of community colleges.
2. Only full-time tenured math faculty are considered in the participant pool. This study
does not consider the perspectives of students or other stakeholders.
3. For all AB 705 accessible math courses, only college algebra (C-ID 151) and
introduction to statistics (C-ID 110) are considered.
Assumptions
The following assumptions are made for this study:
• The methodology and procedure selected are congruent with the scope of the study.
• Faculty participants will be honest, forthcoming, and candid during their interviews.
Definition of Terms
This section identifies important definitions used throughout the study:
8

1AB 705 Accessible Math Courses are transfer-level math courses such as College
Algebra and Introduction to Statistics that students may enroll in directly without needing
remediation or placement exams.
Advanced Placement Courses (AP Courses) are 38 full and half-year courses across 20
subject areas offered to high school students. Students must take and pass the Advanced
Placement exam in the spring to receive college credit.
California Assembly Bill 705 (AB 705) is a law passed in 2017 giving community college
students the right to enroll directly in transfer-level math and English classes without needing to
take remedial courses first.
California common core state standards (CCCSS) are high-quality academic standards in
mathematics and English language arts literacy that outline what knowledge and academic skills
a student should possess and demonstrate at the end of each grade level.
Community colleges are publicly funded postsecondary educational institutions that offer
2-year programs leading to the Associate of Arts (AA), Associate of Science (AS) degree, and
other vocational certifications.
Developmental courses are designed to develop students reading, writing, or math skills
who are deemed underprepared for college-level courses—usually through standardized tests.
Dual enrollment programs are partnerships between high school districts and institutions
of higher education that allow high school students to enroll in college courses.
Non-traditional students are a growing population on community college campuses who
fall outside the traditional college ages of 18 to 22.
Remediation is a supplementary education program assigned to students to assist them in
achieving competencies in core academic skills such as literacy and numeracy.
9

Science, technology, engineering, and math (STEM) is an interdisciplinary approach that
helps students succeed in college and their future careers, focusing on hands-on, problem-based
learning.
Transfer-level courses are courses in which the units earned can be applied toward
specific bachelor’s degree requirements at 4-year institutions and universities.
A transfer student begins their bachelor’s degree at a community college and completes it
at a university.
Organization of the Dissertation
Chapter One presents the introduction, statement of the problem, the purpose of the
study, research questions, importance of the study, a summary of the methodology,
limitations, delimitations, assumptions, the definition of terms, and the organization of the
dissertation.
Chapter Two presents a review of the literature in the following areas: prior remediation
practices in California Community Colleges, California Assembly Bill 705, high school
programs that prepare students for college math, the transfer-level approach to math in California
Community Colleges, the diversity of community college student populations in California, and
the learning gaps of transfer math students.
Chapter Three presents the research methodology used, the data collection
process, and the methods used to perform the data analyses.
Chapter Four reports the findings from the study.
Chapter Five provides a summative discussion of the findings, research implications,
recommendations for policy practice, future research suggestions, and study conclusions.

10

Chapter Two: Literature Review
This qualitative study investigates promising practices and innovative instructional
strategies of math faculty who teach transfer-level courses at a California community college.
The need for this study arose due to the California Community Colleges System transitioning to
performance-based funding and enhanced accountability, emphasizing access, student success,
and equity (California Community Colleges Chancellor’s Office, 2017; Fain, 2018; Shulock et
al., 2012). In addition, the changes in statute and regulation worked to minimize the need for
developmental coursework, streamline student progression and completion, create seamless
pathways to 4-year colleges and universities, and develop a competent workforce that further
fuels social and economic mobility for California.
This chapter is divided into five sections. First, the author presents literature regarding
AB 705 and the history of remedial math courses in California’s 2-year postsecondary
institutions leading up to AB 705. Next, research, outcomes, proponents, and criticisms of AB
705 are discussed. Next, the author discusses the literature regarding how secondary schools
prepare students for college math in California. Next, the California Common Core State
Standards and programs are discussed, including dual enrollment and AP courses. The third
section details the transfer-level math approach in California Community Colleges, including
placement policies, processes, and course offerings of the most common math courses leading to
4-year university transfers. The fourth section centers on the diverse populations of California
Community Colleges, the demographics of students, the unique challenges they face, and the
mathematical learning gaps they bring. Also, literature on “what is working and not for transfers-
level students is presented. Finally, a conceptual framework is discussed, which includes
Anderson and Krathwohl’s revised Bloom’s taxonomy (2001), in conjunction with Merrill’s first
11

principles of instruction (2002) and Tomlinson’s model of instructional differentiation (2017).
This conceptual framework describes how students construct knowledge, the instructional
strategies in that process, and how instructors differentiate their lessons to meet the learning
needs of every student.
Recent California Legislation AB 705
A community college student is an individual seeking a professional certificate or an
associate degree at a 2-year public college. An associate degree in either liberal arts or science
usually takes 2 years of full-time enrollment to complete. It can be a steppingstone to earning a
bachelor’s degree at a 4-year college or university. California has the most extensive community
college system in the United States, serving nearly two million students each academic year
(California Community College Chancellor’s Office, 2022). Almost every California community
college student must complete a course (or sequence of courses) in mathematics to meet degree
and certificate requirements. The number of required math classes depends on a student’s
academic plan, declared major, and the institution to which they wish to transfer. Remedial and
college-level math courses have become an insurmountable barrier for many students, ending
their higher education opportunities (Bryk, 2010). Because of the open-door policies of
community colleges, anyone can enroll in a math class, including high school students, through
dual enrollment programs. As community college students’ diversity and learning needs expand
and state policies such as AB 705 reform the post-secondary mathematics landscape, math
educators must discover innovative instructional strategies that ensure all students develop and
master the mathematical skills needed for success in future math courses, college degrees, and
life.
12

California Assembly Bill 705 allows community college students to enroll directly in
college-level math courses such as college algebra and introduction to statistics without
matriculation or prerequisite coursework. Since AB 705’s implementation, an enormous influx
of academically underprepared students has enrolled in these transfer courses. Scholars and
practitioners argue that removing remedial math requirements and allowing greater access to
college-level math courses eliminates systemic inequity, particularly for historically
underrepresented community college students (Edley, 2017; Hern et al., 2020; Xu et el., 2018).
While this may be true, it presents significant challenges for math educators, who must now
teach and remediate a broader spectrum of learning gaps while fulfilling evolving federal and
state curriculum requirements.
Math Remediation Before AB 705
Historically, California community colleges (CCCs) had broad discretion to determine
which students could enroll directly in transferable college-level courses and which students had
to begin with remedial prerequisites. Under this arrangement, more than 75% of incoming
students took remedial math and English classes based on their performance on standardized
entrance exams and placement tests (Baily, 2009; Noel-Levitz, 2007; Rodriguez, 2017;
Schwartz, 2007). A National Center for Education Statistics (NCES) report found that nearly
three-quarters of all U.S. colleges and universities that enrolled first-year students offered at least
one developmental course (Parsad & Lewis, 2003). The same study also reported that remedial
mathematics was most likely to be provided by these schools. The average number of remedial
courses 2-year public postsecondary institutions offers is 3.4 (Bonham & Boylan, 2011). Until
recently, such programs have existed because, for policymakers, it made sense for student
retention. However, these programs have raised several concerns, including whether community
13

colleges should provide remedial programs (Levin, 2001; McCabe, 2000; Roueche & Roueche,
1999) or only in high school (Hoyt & Sorenson, 2001).
Remedial programs (also known as developmental education or learning assistance)
intend to provide the fundamental skills underprepared students need to succeed at the college
level. However, there are several pitfalls associated with placing students into remediation.
Typically, students put into remediation are much less likely to reach their educational goals than
those who are not (California Community Colleges Assessment & Placement, 2017). A 2017
report released by the Public Policy Institute of California (PPIC) asserts that 80% of entering
students took at least one developmental course in math, English, or both (Parsad & Lewis,
2003). The report also suggests that underprepared students can be placed as many as four levels
below college-level coursework (PPIC, 2017). In general, math is the more significant challenge
for entering students, with 65% of developmental education students enrolling in a
developmental math course, compared to 54% in developmental English. In addition, most
developmental math students (73%) begin the sequence of classes at least two levels below
college level (PPIC, 2017).
Over the past 2 decades, considerable attention has been devoted to the need for low-
skilled students to enroll in developmental mathematics courses (Bonham & Boylan, 2012;
Rosin, 2012). For example, in 2008, the California State University (CSU) system reported that
approximately 56% of all incoming first-year students required remediation in mathematics,
English, or both (Johnson, 2010). In 2011, more than 30% of freshmen cohorts needed
remediation, specifically in mathematics (California State University System, 2012). However,
these findings are problematic because the percentage of students completing remedial math and
English courses is underwhelmingly low (Bailey et al., 2010). Moreover, many educational
14

researchers (Attewell et al., 2006) argue that completing math remediation courses may be the
most significant barrier to increasing graduation rates.
Research has shown that community colleges are placing too many students into
remediation (Sanabria et al., 2020). Evidence suggests (Adelman 1999; Adelman 2004; Chen
2016) that significantly more students would complete transfer requirements in math and English
if enrolled directly in transfer-level English and math courses. Scholars (Xu & Dadgar, 2017)
argue that the effects of mandating supplementary courses in remedial mathematics vary in
student populations with poor math skills compared to those on the fringe of needing math
remediation. Conversely, the benefit of requiring extended and lengthy remedial math sequences
for the most underprepared students is, at best, opaque. For instance, remedial education
represents a human capital investment in which students invest time, money, and energy that
eventually enables them to realize their potential as productive members of society.
Unnecessarily extending course sequences increases schooling opportunity costs (Xu & Dadgar,
2017), resulting in a student needing to dedicate extra time and resources to developmental
education instead of to the job market, where they can gain work experience and earn wages
(Hodara & Xu, 2016).
For students with poor math skills, enrolling in longer sequences of remedial coursework
is particularly helpful in improving the necessary academic skills for subsequent college-level
success (Becker, 1994). In addition, Benken et al. (2015) believe that finding initial success in
mathematics can provide students with “early momentum” that contributes to their overall
success in college. In contrast, the lack of success can discourage students from completing their
studies (Rosin, 2012). Furthermore, unsuccessful students face a more difficult path when
15

attempting to meet their developmental math requirements and may ultimately drop out of
college before finishing the series of courses (Benken et al., 2015).
College assessment instruments and placement policies have measurable implications for
equity, as students of color and low socioeconomic strata are far more likely to be placed into
remedial courses (Kreysa, 2006). For example, Latino, African American, and low-income
students are overrepresented in developmental courses, with 87% of Latino and African
American students enrolling in developmental education, compared to 70% of Asian Americans
and 74% of white students (Walker & Plata, 2000). Moreover, 80% of African Americans
required to take more than one remedial math class do not complete their math requirements
within 6 years, compared to 67% of Hispanics and 61% of Whites (Edley, 2017, para 5).
According to an unpublished study by the Research and Planning Group for California
Community Colleges (R.P. Group, 2017), among community college students, 50 to 60% of the
racial discrepancy in degree completion is driven by decisions to place students in math
remediation. For low-income student populations, 86% enroll in developmental coursework
(PPIC, 2017).
The issues regarding remediation have a social justice component (Matz & Tunstall,
2019). Postsecondary education has had a continual problem with low enrollment, retention, and
completion rates for students of color, especially African Americans (Hussar et al., 2020). Since
remedial pass rates, retention, and completion have been lower than expected, particularly for
students of color, reform proponents have labeled the field (remediation) ineffective and have
recommended numerous ways to improve it (Bailey et al., 2015). To mitigate these issues,
California lawmakers passed Assembly Bill 705—a law that clarifies existing regulations to
ensure that students are not placed into remedial courses that may delay or deter their educational
16

progress unless evidence suggests they are doubtful to succeed. In anticipation of AB 705,
numerous community colleges throughout the state began adjusting English and math assessment
and placement policies to facilitate direct entry into and success in transfer-level courses aligned
with their degree or transfer goals (California Community Colleges Chancellor’s Office, 2017).
What Is AB 705?
Recognizing the student success deficiencies associated with developmental education
coursework, lawmakers sought to enact legislation to address these shortcomings head-on. On
October 13, 2017, the governor of California signed Assembly Bill 705, which took effect on
January 1, 2018. The bill requires a community college district or college to maximize the
probability that a student will enter and complete transfer-level English and math coursework
within 1 year of enrollment (California Community Colleges, 2020). Instead of relying on
traditional placement tests, AB 705 mandates that community colleges use other metrics such as
high school courses, grades, and GPAs as deciding factors for the placement of incoming
students.
AB 705 leaves room for colleges to exercise local control over placement in response to
research with their student body. AB 705 does not dictate specific placement rules or criteria but
sets standards colleges must use in their local decision-making. These standards ensure that
placement decisions maximize students’ likelihood of completing math and English milestones.
The bill also restricts colleges from denying students access to transferable college-level courses
and grants students the right to enroll in classes where they have the best chance of completing
the requirements for a bachelor’s degree. Unless determined to be highly unlikely to succeed, all
students will be placed in transfer-level English and math courses.
AB 705 Outcomes
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A 2019 report on the early effects of AB 705 released by the R.P. Group—a nonpartisan
organization that provides research on behalf of the California Community Colleges system—
found more students enrolling in courses that offer credits eligible for transfer to a 4-year
college. The report indicates that between Fall 2017 and Fall 2018, enrollment in math courses
eligible for transfer increased from 32% to 43%, including an increase in Black student
enrollment in math courses from 20% to 30% and an increase in Latino student enrollment from
24% to 36% (R.P. Group, 2019). According to the California Acceleration Project (2022), a
faculty-led initiative supporting California’s 116 community colleges to transform remediation,
student completion, and equity, suggest that remarkable gains have been made under AB 705. In
the first year of implementation, the law enabled tens of thousands of additional students to enter
and complete English and math milestones for university transfer (California Acceleration
Project, 2022). Furthermore, the Chancellor’s Office Transfer-Level Gateway Completion
Dashboard (2022) shows gains in enrollment and completion of transfer-level math and English
coursework for every demographic group examined, including Black and Latino students,
economically disadvantaged students, students with poor high school GPAs, disabled students,
older students, foster youth, and veterans (CCCCO, 2022). The law has also led to more students
enrolling in and completing math courses in business, science, technology, engineering, and
math (BSTEM), with noteworthy gains for Latino and Black students, who have been
historically underrepresented in BSTEM majors (PPIC, 2021).
With more students entering these courses, fewer students passed transfer-level
mathematics courses. The report (R.P. Group, 2019) acknowledges that the decreases in
completion rates and the growing number of students could mean additional help is needed, such
as tutoring or extended class times, to help students complete the courses (Smith, 2019). In
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addition, the placement policies brought forth by AB 705 and the implementation guidelines
published by the CCCCO may have unintended and undesired effects on all students, especially
underprepared students who enroll in transfer-level courses in English and mathematics (Morse,
2020). For example, when the curriculum pacing must decelerate to cover prerequisite material,
the more-prepared students are often prohibited from progressing in the same manner as they
once did. Morse (2020) asserts that even though instructors may attempt to uphold standards and
follow the course outline accurately, the content and instruction of the class change significantly.
Likewise, when underprepared students enter a transfer-level course needing remediation, how
an instructor approaches and teaches the lesson may also be impacted. Ideally, instructors work
to accommodate the needs of all students in their care. However, with such a wide range of
underprepared students, faculty must dedicate extra time and resources to issues not previously
focused on in the course curriculum (Smith, 2019). As a result, the depth to which the material
can be covered, and the students’ experience in class, may also be impacted (Morse, 2020).
The California Community College Chancellor’s Office (CCCCO) issued a guidance
memorandum in November 2021, which outlined the implementation of Assembly Bill 705 (AB
705) and presented the findings of the 2019-2020 validation of practices that support effective
implementation (CCCCO, 2021). AB 705 was passed in 2017 to improve the success rates of
community college students in transfer-level English and math courses. The guidance
memorandum reported that in the first term of full implementation (Fall 2019), access to
transfer-level math courses significantly increased from 24% to 78% compared to the 2015-2016
academic year (CCCCO, 2021). Furthermore, the 1-year completion rate for those transfer-level
courses (starting in the fall) increased from 26% to 51% in math. These findings demonstrated
that AB 705 effectively increased access to and success in transfer-level math courses.
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Despite the pandemic’s disruption, improved access to transfer-level math courses
continued during the Fall 2020 term, with 80% of students accessing transfer-level math courses
(CCCCO, 2021). Additionally, the 1-year completion rate for the Fall 2020 term stabilized at
54% in math, indicating that AB 705 continued to improve student success in transfer-level math
courses. Given the unprecedented challenges posed by the COVID-19 pandemic, these findings
were promising and suggest that implementing AB 705 has successfully increased student
success in transfer-level math courses.
Proponents and Criticisms of AB 705
Proponents of AB 705 believe that removing enrollment barriers such as placement tests
and prerequisite courses will alleviate the problems historically caused by placing students into
remedial/developmental math and English courses—particularly for marginalized and
underrepresented populations (Mejia et al., 2020). The creators of AB 705 enacted the new law
hoping that it would broaden the scope and accelerate the pace of change. Advocates assert that
this reform, which fundamentally changes placement and remedial support system-wide, has the
potential to improve long-term student trajectories (Mejia et al., 2019). Researchers Mejia et al.
(2020) suggest that broader access allows more students to complete gateway courses. College
access is now nearly universal, and most students can enroll in gateway math courses such as
calculus. This is a staggering change: compared to the fall of 2015, when access rates have more
than doubled in English and nearly quadrupled in math (Hern et al., 2020).
AB 705 has been in effect since January 1, 2018. Over the past 4 years, many community
colleges, educational advocate groups, non-profit organizations, and philanthropists have
publicly supported the bill. According to a document published by The Campaign for College
Opportunity (2019), the Alliance for Boys and Men of Color, the California Latino Leadership
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Network, the Women’s Foundation of California, the Southeast Asia Resource Action Center,
the Student Senate for California Community Colleges, and the Center for Urban Education at
the University of Southern California Rossier School of Education are some of the educational
organizations in support of AB 705. Other notable supporters include the Los Angeles Unified
School District, California Community Colleges Chancellor’s Office, the California Acceleration
Project, the Community College League of California, and the Los Angeles Area Chamber of
Commerce.
The criticisms of AB 705 raise questions and concerns about the short- and long-term
effects of student learning gaps. In 2004, 14 years before the creation and passage of AB 705, the
California Community College System began a comprehensive strategic planning process to
improve student access and success known as the Basic Skills Initiative or BSI. The Basic Skills
Initiative was designed to be a cooperative statewide effort to address the needs of academically
underprepared community college students. Many community college students need college-
level mathematics and English skill development to participate in college-level courses
successfully. Thus, BSI can be thought of as a precursor to AB 705. Similar programs such as the
Multiple Measures Assessment Project (MMAP) and the Common Assessment Initiative (CMI)
have also been working to improve placement accuracy at California’s community colleges
(Willet, 2013). However, the rapid and extreme pendulum swing from BSI to the full
implementation of AB 705 swept away advantages for many students, even as it has helped
others (Bezerra-Nader, 2020).
For example, AB 705 focuses exclusively on increasing the number of transfer
students—alienating the needs of students who need courses that prepare them for qualifying
tests like the ASVAB military test or TEAS nursing test, as well as satisfying other goals such as
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self-improvement and job advancement (Bezerra-Nader, 2020). In addition, while equity is the
goal of AB 705, some believe that the bill devalues diversity and the role community colleges
have traditionally played for returning students. For example, in an article written for the Faculty
Association of California Community Colleges, author Rosemarie Bezerra-Nader (2020)
suggests that “the needs of students across California vary dramatically, so the expectation that
all students want and can earn transferable degrees within 2 years is unrealistic.”
AB 705 rewards colleges for increasing the number of students who complete transfer
English and math classes within 1 year. Critics of the bill believe that some instructors may
succumb to subtle or direct pressure to increase passing rates in response to job-security concerns
by diluting content—leading to the eventual decline of many colleges’ reputations and perceived
prestige (Oudenhoven, 2002). In addition, the funding guidelines in AB 705 encourage
administrators to eliminate nontransferable classes (Hern, 2019). These introductory classes do
not affect GPA, encouraging students to justify not attending as the semester ends. This behavior
could potentially lead to failing grades that quickly reduce the numerical success rate and distort
the actual value of the class in the minds of administrators.
In January 2021, a report was published entitled A Qualitative Exploration of AB 705
Implementation: Report of Statewide Interview Results. Researchers Hayward et al. (2021)
interviewed 14 colleges throughout the state that were identified as scheduling either a higher
percentage (an average of 80% or more) or a lower percentage (65% or fewer) of their English
and math courses at transfer-level in Fall 2019. The report identified several challenges these
colleges face regarding implementing AB 705. While numerous interviewees cited a changing
mindset on campus as one of the positive outcomes of AB 705, this shift in perception was also
identified as a challenge. Fighting the deficit mindset on campus and transitioning to a more
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capacity-based growth mindset was reported as an ongoing difficulty for nearly 85% of the
institutions interviewed. Interviewees also observed that “the presence of those who challenge
AB 705” and those who feel “students aren’t ready for transfer-level” is prevalent on campus “so
students may experience a self-fulfilling prophecy” (Hayward et al., 2021, p. 22). Moreover,
instructors and counselors reported that this deficit mindset rubs off on students, leading them to
question whether they can succeed in transfer-level courses.
Five colleges that offered 65% or fewer and two that showed 80% or more transfer-level
English and math sections in the Fall of 2019 stated that removing the remedial sequences is an
equity issue, not a deficit mindset. From their perspective, too many students are being rushed
into transfer-level courses for which they are unprepared, setting them up for failure (Hayward et
al., 2021, p. 22). Counselors and instructors described that AB 705 had reduced the range of
options available for students. Some of them are not looking to transfer or want to move more
slowly and felt the limited pre-transfer sections were not offered at times that met the students’
needs. Some interviewees felt disabled students were negatively impacted by the pressure to
enroll directly in transfer-level courses (Hayward et al., 2021, p. 23). Five colleges that offered
65% or fewer transfer-level English and math sections in Fall 2019 described AB 705 as too
“one-size-fits-all” and expressed that colleges should have more freedom to do what is best for
their community and population. All these colleges offered one or more levels below transfer-
level English and math. Finally, some academic counselors critiqued their college for only
offering online sections of pre-transfer courses—an instructional method with its own set of
challenges for underprepared students (Hayward et al., 2021, p. 23).
The significant changes that have occurred due to the implementation of AB 705 have
indeed, in some cases, been positive. For example, many faculty would agree that the sequences
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of pre-transfer courses in English and mathematics needed to be shortened (Smith, 2019). In
addition, the new placement system has allowed faculty to consider new and innovative
approaches to their teaching. Courses in transfer-level math, such as calculus and other advanced
math courses, may benefit from a redesign influenced by AB 705 (Hodara, 2011). Yet despite
these potentially positive aspects, difficulties concerning the impact on the curriculum, faculty
workload, and fatigue are present. There has been resistance from the faculty of many colleges to
accept new policies, such as AB 705, that favor accelerated pathways. Faculty resistance to
accelerated pathways stems from several perceptions of standards, developmental student
capacity, and faculty workload (Edgecombe, 2011). Therefore, further study and potential
reformation of California’s Community College placement practices, curriculum structure, and
class sizes may be warranted to guarantee that the positive aspects of the new system are
preserved without negatively impacting the students, the content of the courses, or the faculty
who teach them.
High School Programs That Prepare Students for College Math
This section highlights how secondary schools in California prepare students for success
in college-level mathematics courses. The literature describes several ways to achieve this,
including dual enrollment programs, Advanced Placement programs (AP), and California’s
Common Core Standards.
High School to Community College to California Universities
There is increasing attention to human capital production in science, technology,
engineering, and mathematics in the United States (Darolia et al., 2020). Improved access to
STEM courses in high school has been advocated as a lever by which the STEM workforce can
be expanded and diversified. Calls for improved access to STEM coursework in high school—
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especially in schools primarily serving underrepresented minorities—have come from policy and
advocacy groups, journalists, and the highest levels of government (Tsui, 2007). Although there
are reasons to believe that the “STEM crisis” in the United States is overstated (Berliner &
Glass, 2014), the current broad policy to expand and improve STEM education in secondary and
postsecondary education institutions has increased.
Transitioning from high school to higher education is typically challenging for secondary
school students. Despite a national movement toward more-rigorous standards for high school
graduation, a pronounced skill gap has opened between secondary and postsecondary schools
(Long et al., 2009). As a result, many young people are arriving at college without the requisite
skills to succeed, putting a severe strain on college resources and prompting more marginal
students to drop out (Craig, 2000). Some observers believe better communication between K–12
educators and colleges and universities is necessary to improve students’ preparation (Rodriguez
et al., 2017).
Among California public high school students, 63% enroll in a post-secondary institution
following high school graduation, and 26% of high school students enroll in a 4-year college
(Kurlaender et al., 2018). Students unable to transition from high school to college and
eventually into the workforce may get mired in low-paying jobs. Jobs that require high levels of
education and skill pay higher wages than jobs that require few skills and little education
(Nietzel, 2021). Statistics from the Department of Labor’s Bureau of Labor Statistics (BLS)
validate this viewpoint by revealing that the unemployment rate among people who have a
professional degree is significantly lower than that of people who have a high school diploma or
an incomplete high school education (U.S. Department of Labor, 2022). In addition, earnings
increase significantly as a worker’s degree of education rises (Hout, 2012).
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Community Colleges are generally characterized as institutions that create accessible,
affordable, and expanded opportunities for individuals seeking postsecondary degrees (Cohen &
Brawer, 1982; Shaw et al., 2006; Shavit et al., 2007). Brand et al. (2014) found that enrolling at
community colleges positively affects bachelor’s degree completion for disadvantaged students
who otherwise would not have attended college. These student populations represent
the majority of community attendees (Hawley & Harris, 2005). The California Community
College system is commonly praised for remaining more affordable than other postsecondary
options offering a “second chance” at educational attainment for students who chose alternative
career paths after high school (Rouse, 1995). For many, enrolling in a community college is a
logical next step, particularly for students with low academic performance, undecided academic
ambitions, or low socioeconomic strata.
Although not every high school student plans to transition to a postsecondary institution
to earn a professional degree, college readiness today is nearly the same as career readiness since
many of the fastest-growing jobs in America require a high school diploma (Whiten et al., 2018).
In addition, there is a growing movement at the federal and state levels to prepare high school
students for college by ensuring rigorous standards for curriculum are implemented and aligned
with college readiness and career success (Conger & Tell, 2007; Paulson, 2010). Yet, despite this
effort, nearly 66% of secondary school graduates enter college academically underprepared for
the rigors of college-level work (Radford & Horn, 2012). There are policies, programs, and
strategies that California lawmakers, high school districts, and community colleges implement to
prepare better high school graduates for success in mathematics courses in college.
Dual Enrollment
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States and school districts have been searching for ways to raise the rates of college
readiness and success among students, particularly underrepresented groups in collegiate settings
(Hoffman, 2003). One promising strategy is allowing students to take college courses in high
school, known as dual enrollment (DE). Dual enrollment programs have existed as a college
acceleration opportunity for decades (Andrews & Marshall, 1991; Gerber, 1987; Mokher &
McLendon, 2009), and their popularity has grown significantly since the early 1990s, when more
emphasis was placed on college readiness, and college tuition began to increase steadily (Karp,
2012). Dual enrollment programs are partnerships between school districts and institutions of
higher education that allow high school students to enroll in college courses. Dual enrollment
provides academically challenging experiences and creates the opportunity to earn transferable
college credit before high school graduation (Greenburg, 1989; Trust, 2022). In 2016, Assembly
Bill 288 (California Education Code Section 76004) went into effect, permitting California
community colleges to offer dual enrollment college courses to high school students in a specific
pathway on high school campuses during the regular school day (Medina et al., 2016).
A study published by Karp and Hughes (2008) found that dual enrollment programs
effectively encourage student access to and persistence in postsecondary education and can be an
effective transition strategy for many college students. Participation in dual enrollment programs
helps students expand their social boundaries while learning alongside college-level students
(Peterson et al., 2001). Moreover, dual enrollment courses enable high school students to
experience the rigors of college coursework (Martin, 2013; Pretlow & Wathington, 2013),
prepare for college success, accelerate degree completion, and minimize debt (Grubb et al.,
2017; McKinney & Novak, 2013).
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For students with little “college knowledge” in their families, dual enrollment offers a
low-cost or no-cost way to earn college credit (Cowan & Goldhaber, 2013). Some notable
studies (Berger et al., 2013; Hughes et al., 2012; Karp et al., 2007; Klopfenstein, 2010; Marshall
& Andrews, 2002; Michalowski, 2007) found positive outcomes associated with dual enrollment,
such as increased high school graduation rates, college enrollment, first-year college GPA,
second-year persistence in college, and the number of colleges credits accumulated after 3 years.
Swanson (2008) found that dual enrollment participants from a National Educational
Longitudinal Study were 16 to 20% more likely than nonparticipants to earn a bachelor’s degree.
Scholars (An, 2013; Hoffman, 2003; Karp & Hughes, 2003; Struhl & Vargas, 2012) suggest that
DE in high school is a mechanism that widens college admission and completion of
economically disadvantaged student populations well as first-generation college students and
their families.
College mathematics requirements have been a significant barrier to high school
graduation, college admission, and timely degree completion (Daro & Asturias, 2019; Johnson &
Mejia, 2020). As a result, more districts are turning to dual enrollment to address this challenge
to help historically underserved students complete these requirements in their junior or senior
year of high school (Dolle et al., 2020). In 2016, the same year dual enrollment legislation
became law, California policymakers also passed the College and Career Access Pathways
(CCAP), which focuses on improving access to community college for underserved students.
This initiative also makes it easier to offer DE courses on high school campuses exclusively for
high school students (Castro & Collins, 2018). Since implementing CCAP agreements, dual
enrollment has increased, from roughly 72,000 participants in the 2015–16 graduating class to
more than 112,000 in the 2019–20 class (Wheelhouse, 2021).
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Understanding the demographics of student participation and success across DE courses
is essential. While DE programs are a helpful tool to better prepare high school students for
success in higher education, there is some indication that these programs disproportionately
serve more affluent students (Garcia et al., 2020; Museus et al., 2007). In many cases, the
students who are most likely to benefit—male students of color and students from low-income
backgrounds—are not participating at high levels (Trust, 2022). In addition, studies have shown
that white females, Asian, and high-achieving students are overrepresented in DE (Fink, 2018;
Fink et al., 2017), while Black and Latino populations are underrepresented (Gao & Rodriguez,
2021). Black and Latino students have lower dual enrollment GPAs and earn fewer units than
Asian and white students. Promoting dual enrollment participation and success among
historically underrepresented groups is critical if educational equity remains a core tenant of the
dual enrollment paradigm.
More recently, the legislators in California increased support for dual enrollment, as the
COVID-19 pandemic has fueled a surge in participation across the country, particularly from
students identifying as Hispanic or Latino. All 116 community colleges offer some form of dual
enrollment curriculum. However, a 2021 report published by the Public Policy Institute of
California (Gao & Rodriguez, 2021) indicates that in 2016–17, only 10% of students were in
high schools that offered dual enrollment courses, with that number more than tripling to 36% in
2018–19. The increase is particularly remarkable among districts that serve a high percentage of
Black and Latino students—from 7% in 2016 to 37% in 2018. Moreover, smaller subgroups of
student populations also enrolled in other formal programs such as College and Career Access
Pathways (CCAP, 11%), Early College High Schools (ECHS, 9%), and Middle College High
Schools (MCHS, 10%) (Gao & Rodriguez, 2021). Notably, about 82% (1264) of California
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public high schools have no students enrolled in community college (Burns & Leu, 2019;
Friedmann et al., 2020).
Dual enrollment programs help students prepare for college-level mathematics courses
and encourage students to pursue STEM-related degrees and certificates. For example, a 2020
study (Corin et al., 2020) found that the odds of a student choosing a STEM career were 1.3
times greater for those taking a DE course than those who did not. The study also concluded that
students who took both DE and Advanced Placement (AP) STEM courses had 2.1 times the odds
of their nonparticipating peers reporting an interest in STEM careers. Using quasi-experimental
designs, several other studies estimate the impact of dual enrollment participation on high school
students’ academic choices and postsecondary success in mathematics courses (e.g., Allen &
Dadgar, 2012; An, 2013; Giani et al., 2014; Hemelt et al., 2020; Miller et al., 2018; Speroni,
2011). Except for Speroni (2011), all found that DE program participation positively impacted
students’ postsecondary enrollment and performance in college-level math courses.
Dual Enrollment programs are challenging to implement for practitioners, including high
school or district program directors, guidance counselors, and college staff and faculty. High
school and college partnerships, articulation, funding, and student access and support are all
critical areas to address to implement these programs successfully (Cassidy et al., 2010). In
California, community colleges are encountering a lack of qualified DE instructors preventing a
more significant expansion of dual enrollment throughout the state. DE curriculum spans many
academic disciplines, with core courses in mathematics, English, and humanities making up the
largest share of offerings. College instructors teach most DE courses and are occasionally
facilitated on high school campuses. However, as of 2022, high school instructors are not
permitted to teach DE courses (Gao & Rodriguez, 2021). In addition, the low number of
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instructors with discipline-specific master’s degrees is a limiting factor for K–12 and college
schools since it greatly diminishes a college district’s ability to widen the pool of course
offerings (Castro & Collins, 2018). The lack of personnel is especially true for courses taught on
high school campuses and in rural areas, which require college instructors to commute
potentially long distances and adjust to the high school schedule. Incentivizing instructors to
acquire content-specific master’s degrees or exploring alternative qualifications, such as high
school instructors teaching DE courses, could alleviate this hurdle.
California Common Core State Standards
According to the National Governors Association’s Center for Best Practices (2010), the
California Common Core State Standards (CCSS) is a set of high-quality academic standards in
mathematics and English language arts literacy that outline what knowledge and intellectual
skills a student should possess and demonstrate at the end of each grade level. The CCSS focuses
educators’ attention on fewer, higher, and deeper standards (Kirst, 2013). The CCSS were
created to prepare high school students to succeed in entry-level careers, introductory academic
college courses, and workforce training programs, regardless of where they live (Conley, 2014).
Before CCSS, vast differences in educational expectations existed across states. A 2010 study by
the American Institute of Research (Philips, 2010) documented a huge expectations gap. Some
states expect their students to accomplish far more in school than others with much lower
standards. To better align each state’s education systems, the CCSS articulates consistent, clear
standards for student learning expectations. Forty-five states, the District of Columbia, four
territories, and the Department of Defense Education Activity have voluntarily adopted and are
moving forward with the Common Core standard (McLaughlin et al., 2014). California’s State
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Board of Education adopted the Common Core State Standards in August 2010 (Warren &
Murphy, 2014).
Are the Common Core Standards making students more college and career ready? This is
a challenging question to answer. Loveless (2014, 2016) investigated this question using state
data from The National Assessment of Educational Progress (NAEP). This organization provides
essential statistics about student achievement and learning experiences in various subjects. In the
2014 analysis, he examined the NAEP gains for states with the most and least standards, like the
CCSS, between 2009 and 2013, finding no differences in gains. However, Houang and Schmidt
(2012) found that the states with standards more “Common Core–like” saw more significant
NAEP gains before adopting the standards. Researchers Gao and Lafortune (2019) suggest that
the impact of the CCSS standards is inconclusive. They found no overall effect on graduation
rates, the students taking or passing Advanced Placement courses, the SAT exams, or completing
the “A–G” courses required by California’s 4-year public universities (Gao & Lafortune, 2019).
The adoption of the CCSS in California has been met with mixed reviews. In a 2016
WestEd survey, all educators—teachers, administrators, and support personnel—complained of a
lack of high-quality CCSS-aligned instructional materials, especially for English language arts
(Timar & Carter, 2017). Teachers also confirmed a need for more consistent and coherent job-
embedded professional development to assist their implementation efforts. Without these
supports, teachers often relied on their peers as a primary source of support for curriculum
development (Makkonen & Sheffield, 2016). Moreover, most teachers have not fully aligned
their instruction with the new standards. On average, English teachers have progressed more than
math teachers (Gao & Lafortune, 2019). Unfortunately, the full effects of instructional
implementation will likely require additional years of data to parse out fully.
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California has over six million students and is the nation’s most extensive education
system. Makkonen and Sheffield (2016) believe that the sheer number of districts (1,000) and
schools (10,000) makes the positive effects of a one-size-fits-all policy unrealistic. To date, little
is known about the total number of districts that have adopted the new standards and the extent
to which they have been implemented (Gao & Lafortune, 2019). For these reasons, even less is
known about the reforms’ effects on California’s students. Recent test score data shows
significant progress in English but stalled gains in math (Warren and Lafortune 2019), which
calls for a closer look at district-level standards implementation. In 2019, most districts aligned
their curricula/course models, instructional materials, and local assessments with the standards.
However, 30% have not begun, particularly in rural high schools.
In implementing districts, classroom instruction—the most critical factor determining
successful outcomes—lags, as most teachers have not fully adjusted their instructional practices.
Local implementation is a challenge, yet it has the potential to make or break an educational
policy (Spillane et al., 2002). The modest positive effects of CCSS are encouraging, as they are a
testament to the progress districts have made in local implementation. At the same time, they
highlight the need for continuing improvements over time to reach their full potential,
particularly in math.
In the realm of mathematics curriculum, the CCSS calls for a greater focus on fewer
topics. Rather than racing to cover topics in a “mile-wide, inch-deep curriculum,” the standards
require significant narrowing and deepening of time and energy spent in the math classroom. The
objectives move away from memorization, drills, and rote procedures and toward a focused
conceptual understanding of mathematical practices emphasizing problem-solving (Perry, 2019;
Warren & Murphy, 2014). The standards also focus on a high degree of procedural and
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conceptual skills, fluency, and the ability to apply math knowledge inside and outside the math
classroom (Conley, 2014).
Advanced Placement Programs
Originating in 1955, the Advanced Placement Program (AP) are classes developed by the
College Board—a non-profit organization in New York City—that introduces high school
students to college-level classes, which may lead to earning college credit before graduating high
school (Potter & Lena, 2000). Initially, the AP program was created as a partnership between
elite private high schools on the east coast and comparable secondary institutions (Nugent &
Karnes, 2002). Advanced Placement classes represent some of the most rigorous courses
available to high school students and are taught by secondary teachers (Thompson, 2007).
Earning college credit requires a passing grade on a summative assessment known as an “AP
exam” administered each school year nationally at the end of the spring semester. The grading
rubric for AP exams ranges from 1 to 5, with a 3 and higher designated as a passing grade
(College Board, 2006b). A mark of 5 is the highest score and means the student is exceptionally
well qualified to receive college credit for that course. Individual colleges and universities
determine a student’s score to receive college credit (College Board, 2005); thus, the policy
differs from school to school. A “passing” score on the AP exam allows students to enter a
college or university with advanced standing, as they will have supplanted the course
requirement via their exam score.
The Advanced Placement program offers 38 courses across multiple subject areas, such
as mathematics, physics, chemistry, history, and English (College Board, 2006b). Each course is
developed by a committee composed of college faculty and AP teachers and covers the breadth
of information, skills, and assignments found in the corresponding college course (California
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Department of Education, 2021). Although dual enrollment and AP programs both allow
opportunities for secondary students to earn college credit, they were historically developed at
different times, based on varying philosophies and policies (Torres, 2019). Nevertheless, the
significant advantages of AP courses are their consistent content, the same exam is administered
externally to all students, and the standard is ubiquitous. As a result, it is accepted by parents,
teachers, and college admissions officers nationwide (Robinson, 2003).
The research regarding the impact Advanced Placement courses have on students is
unsettled. For example, scholars Morris and Willingham (1986) concluded that AP enrollment
does not determine the level of success a student will achieve in college and that a student’s high
school grades and test scores are in no way a valid indicator of college achievement or readiness
whereas Scott-Clayton (2012), and Belfireld and Crosta (2012) suggests that high school
performance data is a superior predictor of course outcomes. Yet researchers (Keng & Dodd,
2006; Morgan & Ramist, 1998) present findings suggesting notable advances former AP students
make at the college level.
Regarding student equity, underserved student populations such as African American and
Latino students are underrepresented in AP programs (Wanzo, 2014). An evaluative report
published by Pachon and Zarate (2006) found a negative correlation between the number of AP
courses offered at schools with a high percentage of students eligible for free and reduced meals,
as well as in high schools with a high population of underrepresented students, throughout the
state of California. Additionally, Ornelas and Solórzano (2004) found that various school
districts in California denied students equal and adequate access to AP courses implying that the
lack of access disadvantaged these students compared to other California high school students—
weakening their competitive edge for admission to colleges and universities.
35

The access, implementation, and success of diverse college-readiness programs across
California have varied results and gaps, especially for underrepresented students. Postsecondary
math course success remains a widespread challenge for students, faculty, and community
colleges, especially for students transferring to a 4-year university.
The Transfer-level Math Approach in California Community Colleges
This section discusses the qualifications a student must comply with to transfer from a
California community college to a publicly funded 4-year university within the CSU or UC
systems. In addition, information regarding which math courses are considered transfer-level and
which are not is presented. Finally, a summary of community colleges’ historical role for
academically disadvantaged students is also discussed.
Transferring to Public Universities in California: The CSU and UC
Community colleges play an essential role in preparing students for the workforce. There
are over 1,000 community colleges in the United States, and most offer a variety of degrees and
certificates that prepare both domestic and international students for entry-level jobs. Community
colleges also serve as an access point to a traditional university for students who plan on
continuing their education towards a bachelor’s degree. The main difference between a
community college and a university is that most degrees at a community college only take 2
years to complete, while degrees at a 4-year university take 4 years.
In community college vernacular, a course in which the units earned that can be applied
towards specific bachelor’s degree requirements at 4-year institutions and universities without
taking remedial classes in those subjects first is referred to as “transfer-level” courses. This does
not imply how each course can be used to fulfill subject matter requirements at a particular
university campus but rather indicates which course can count towards degree completion.
36

Generally, “transfer” can be considered a movement between two higher educational institutions.
In the context of this study, transferring describes the advancement from a community college to
a university. In other words, transfer students are assumed to begin their bachelor’s degree at a
community college and complete it at a university.
The state of California currently has two publicly funded university systems that
California community college students can transfer into—the California State University System
(CSU) and the University of California (UC) network. Each university system determines the
specific rules, guidelines, and requirements regarding how units can be transferred from
community colleges. For example, suppose a student has at least 60 semester or 90 quarter
transferable units completed by entering a CSU. In that case, they are considered an upper-
division transfer applicant (California State University [CSU] Office of the Chancellor, 2022)
Potential CSU students must also have completed ten general education courses (30
semester units or 45 quarter units) of basic skills courses, with a grade of C- or better, and,
specifically, four courses completed in written communications, critical thinking, oral
communications, and mathematical concept and quantitative reasoning. Incoming CSU
applicants must also have an overall GPA of at least 2.00, calculated using all transferable units
attempted. In high-demand majors and campuses, a GPA of 2.00 may not be sufficient to be
admitted. If a student is applying to a high-unit major such as science, technology, engineering,
and some math-based fields, they must check with the CSU campus for their requirements in this
area.
In contrast, the UC system accepts 70 semester (105 quarter) units of credit for lower-
division coursework completed at any non-UC school. Additionally, no more than 14 semester
(21 quarter) units of the 60 semester (90 quarter) units may be taken pass/fail or credit/no credit.
37

There is a GPA requirement as well. Applicants to a UC school must earn at least a 2.4 GPA in
UC-transferable courses (2.8 for nonresident applicants), with some majors requiring a higher
GPA for admission selection. The UC system has a transferable course agreement (TCA) with all
California Community Colleges. These agreements specify the courses that will receive
baccalaureate degree credit from UC institutions. All California Community Colleges also have
articulation agreements with UC campuses that determine which transferable courses may be
used to meet various general education and major preparation requirements. These agreements
were developed to ensure continuity in students’ academic programs between different levels of
the public higher-education systems.
Community colleges play a substantial role in transferring large quantities of students to
4-year public universities in California. According to the California Community College
Chancellor’s Office, some 80,000 California community college students transfer seamlessly to a
UC or CSU campus yearly (California Community Colleges, 2022). Moreover, it is estimated
that nearly 40,000 California community college students earn an Associate Degree for transfer
that guarantees them admission as juniors to a Cal State campus and other participating
universities.
Community colleges continue to be the vehicle for increasing and democratizing access
to higher education (Baker, 2016). According to the California Education Code Section 66010.4
(a), the primary mission of California Community Colleges is to offer academic and vocational
instruction at the lower division level for both younger and older students, including those
returning to school after a prolonged hiatus. In theory, California’s Community Colleges offer
instruction through but not beyond the 2nd year of college. These institutions may grant
associate in arts (AA) and associate in science (AS) degrees but nothing higher. Moreover, CCCs
38

historically provided remedial instruction for those in need of it and, in conjunction with the
local school districts, instruction in English as a second language, adult non-credit instruction,
dual enrollment courses, and support services that help students succeed at the postsecondary
level. The mission of California Community Colleges also serves to advance California’s
economic growth and global competitiveness through education, training, and services that
contribute to continuous workforce improvement (Baker, 2016).
Education and science, technology, engineering, and mathematics skills are essential in a
global economy increasingly focused on high-growth, technology-driven occupations. Yet, many
states, including California, face a shortage of STEM-skilled students and workers (Xue &
Larson, 2015). Several states have built robust and productive STEM education and skills
strategies to address these shortages. Scholars Elizabeth Park and Fredrick Ngo (2016) found that
retaining college students in STEM fields can increase STEM degree production and bolster
competitiveness in the U.S. workforce (President’s Council of Advisors on Science and
Technology, 2012). Community colleges are uniquely positioned to grow the pipeline of STEM
professionals and produce more STEM-skilled workers to meet the demand for middle and high-
skill jobs (Darolia et al., 2019). In addition, the convenience of community colleges is a crucial
asset. According to the American Association of Community Colleges (2011), 90% of the U.S.
population lives within 25 miles of a community college, which makes these institutions highly
accessible to many people.
Transferable and Nontransferable Math Courses at California Community Colleges
There is a bifurcation between the math courses offered among California’s 116
community colleges—those below college level (remedial or developmental courses) and those
above college level (transfer-level courses). The units a student earns completing developmental
39

courses do not apply towards transferability to 4-year public universities or acquiring
baccalaureate degrees. Before AB 705, remedial classes would have been required for students to
build up their skills in math, reading, or English before they were allowed to enroll in transfer-
level courses. For some, taking a remedial class causes a delay in taking college-level courses
until they complete a developmental course sequence. Still, it also means that students pay more
for courses whose credits do not contribute to a degree.
Historically, remedial placement rates were exceptionally high among students who
enrolled at community colleges. According to the Beginning Postsecondary Students (BPS) 6-
year follow-up data from 2009, nearly 68% of students who began at a public 2-year college took
one or more remedial courses within 6 years after their initial college entry (Scott-Clayton &
Rodriguez, 2015). Despite the excessive time and costs associated with remedial education for
colleges and individuals, college completion rates remain low among students required to take
remedial coursework. For example, only 20% of students in developmental math and 37% in
developmental reading or writing pass the entry-level college-level course in the relevant subject
(Bailey et al., 2010).
In the context of mathematics curriculum, remedial math courses typically include
courses focusing on topics such as the introduction to basic arithmetic, geometry, algebra, and
statistics. In contrast, transfer-level math courses include college algebra, trigonometry,
intermediate statistics, precalculus, a three-part calculus sequence, and an introductory course in
linear algebra and differential equations. STEM degrees generally require applicants to complete
more transfer-level math coursework than non-STEM majors depending on the university and
significance. For non-STEM students seeking to transfer to a 4-year public institution in
California (CSU or UC), only one transferable math class may be required for acceptance.
40

Algebra I, also known as elementary algebra or beginning algebra, is the first-course
students take in a sequence of algebra courses. Traditionally, this class has been a high school-
level course offered as early as the seventh grade but more traditionally in the eighth or ninth
grades. Community colleges also offer the course as a fundamental skill or remedial course.
Algebra II, or intermediate algebra, has a prerequisite to Algebra I. Historically, intermediate
algebra has been a high school-level course. It is the minimum math requirement to enter a
California State University. The CSU Executive Order 1065 states, “Title 5 of the California
Code of Regulations, Section 40402.1, provides that each student admitted to the California State
University is expected to possess basic competence in the English language and mathematical
computation to the degree that may reasonably be expected of entering college students.” This
position has long been interpreted to indicate intermediate algebra for mathematical computation
competency and aligns with the California Common Core State Standards requirements.
Intermediate algebra also meets the math competency requirement for an associate degree
from a California community college. In addition, many community colleges have other courses
that meet the college math competency requirement for those students seeking an associate
degree yet not intending to transfer. Until Fall 2018, intermediate algebra was a requirement to
transfer for both UC and CSU institutions but was not recognized as a transfer-level course since
it does not count as transfer credit at the CSU or UC level. However, intermediate algebra is
considered a college-level course at community colleges since it meets the associate degree
minimum requirements.
College algebra is a transfer-level course offered at many California community colleges
and CSU campuses and generally has a prerequisite of intermediate algebra. College algebra,
statistics, and mathematical ideas are typical courses that meet baccalaureate requirements for
41

quantitative reasoning at a CSU campus. However, statistics and mathematical ideas are not
considered courses that lead to STEM degrees. The common understanding within the
mathematics community is that the role of the college algebra course is to prepare students for
calculus (Herriott & Dunbar, 2009).
Another transfer-level math course that draws large enrollments of students at community
colleges is introductory statistics courses. These courses are typically not intended for STEM of
BSTEM (business, science, technology, engineering, and mathematics) majors. Instead, statistics
is the required transfer-level math course for majors such as liberal arts, psychology, history, art,
ethnic studies, anthropology, criminal justice, political science, health education, journalism,
child development, or other non-technical fields.
College algebra and statistics are the two most significant gatekeeper mathematics
courses in California Community Colleges, but they have different challenges. Statistics is a
standalone math course where success is not reliant on foundational algebra or computational
skills. Conversely, the cumulative nature of the content in college algebra without the
opportunity for remediation as needed creates a landscape where students with significant
algebra skill gaps cannot access the college algebra content or find success.
Student Diversity in California Community Colleges
In this section, the author presents literature regarding the various student demographics
found in California’s community colleges and the diversity of this population. This section also
defines what a “nontraditional” student is. Additionally, literature is presented that outlines the
unique challenges community college students face and the mathematical skill gaps they possess.
Student Demographics
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Community colleges in America were initially created through the Morrill Act of 1862
(the Land Grant Act), which expanded access to public higher education. This expansion allowed
for the inclusion of a vast majority of individuals who had been denied access to or precluded
from higher education for various reasons (Drury, 1999). During the 1970s, community colleges
continued rapid enrollments going from 1.6 million students to more than 4.5 million in 1980
(Brint, 1989). Today, there are nearly 1,100 community colleges in America, enrolling more than
7.5 million students annually (U.S. Department of Education, National Center for Education
Statistics, 2019). Students enrolled at public 2-year institutions comprise the largest population
of undergraduate students in the United States (Staley & Trinkle, 2011). U.S. Community
colleges enroll 44% of undergraduates and 50% of incoming first-year students. In addition,
nearly 47% of minority students enroll in these colleges due primarily to their open-door policy,
accessibility, and focus on students and teaching (American Association of Community
Colleges, 2004).
Community colleges play a critical role in providing access to postsecondary education
for a wide range of student populations, including large numbers of racial/ethnic minorities, low-
income students, first-generation college students, high school graduates, dual enrollment
students, adult learners, United States veterans, and recent immigrants (Hagedorn, 2010; Levin,
2007; U.S. Department of Education, National Center for Education Statistics, 2010; Phillippe &
Gonzalez Sullivan, 2005). California has the most extensive community college system in the
United States (California Community Colleges Chancellor’s Office, 2022; United States
Department of Education, 2022). During the 2019-2020 academic year, nearly 2.1 million
students were enrolled in the California Community College system. As a result of the pandemic,
enrollment for 2021-2022 is closer to 1.8 million (Student Enrollment and Demographics |
43

California Community Colleges Chancellor’s Office, 2022). According to the Foundation for
California Community Colleges (2022), one in every four community college students
nationwide is enrolled in a California community college. Nearly 30% of Californians aged 18-
24 attend a California community college. Additionally, more than 69% of California community
college students are people of diverse ethnic backgrounds, and roughly 53% are female. Finally,
approximately 40% of California community college students are age 25 or older and are already
working adults.
Community college students enroll for a wide variety of reasons. Some students complete
required general education courses like mathematics, English, and psychology to transfer to a 4-
year university. Some may earn an associate degree or a vocational certificate, while others want
to improve their language capabilities or enhance their employability by updating their job skills.
Finally, some may wish to learn something new: a new hobby, language, Shakespeare, jazz
dance, quilting, or ceramics. There is no “typical” community college student in California—
more than half are under 24 years old, but another 11% are over 50. According to the California
Community Colleges Chancellor’s Office (2022), the demographics of enrollment consist of
24% Caucasian, 46% Hispanic, 11% Asian, 6% African American, 4% Multi-ethnic, 3%
Filipino, less than 1% American Indian and Alaskan Native, less than 1% Pacific Islander, and
6% unknown. The system uses the Perkins Economically Disadvantaged metric as a measure of
students’ income status based on their receipt of financial aid and other social benefits. Sixty-
four percent of students across the system are classified as Perkins Economically Disadvantaged,
and 36% are not Perkins Economically Disadvantaged (California Community Colleges
Chancellor’s Office, 2022).
Non-traditional Students
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A growing population on community college campuses is students who fall outside the
traditional college ages 18 to 22. These students are one of the fastest-growing demographic
groups on American campuses today (Van der Werf, 2009). Researchers identify these students
as adult learners, non-traditional students, adult students, returning adults, adult returners, and
mature learners (Deutsch & Schmertz, 2011; Hardin, 2008). Reported statistics show that the
number of students enrolled in colleges over 22 years has grown by 18% in the last 10 years and
increased by 21% between 2005 and 2016 (National Center for Education Statistics, U.S.
Department of Education, 2018). In addition, more than 14% of enrolled students in California
are over 40 (California Community Colleges Chancellor’s Office, 2022). Although the adult
student population comprises the same diverse demographics stated above, there are some
common characteristics. Adult learners are typically 25 years of age or older, have delayed
entering college for at least 1 year following high school, are usually employed full-time, often
have a family and dependents to support, started college as a traditional student but needed to
take time off to address other responsibilities, want to enhance their professional lives, may be
switching careers, may have already started a career, or served in the military (Kasworm, 2010;
MacKinnon-Slaney, 1994; Osam et al., 2017).
There are other notable student populations in California’s community colleges worth
mentioning. The California Community Colleges serve many students with unique educational
goals and needs who have been historically underrepresented and under-served in higher
education. For example, 35% of students identify as first-generation in their family to attend
college, 10% are Adult Education/English language learners, 3% are veterans, and 2% are foster
youth (California Community Colleges Chancellor’s Office, 2022). In addition, according to the
CCCCO, during the Fall 2019 term, 6% of students had a special admit status, including students
45

who were also enrolled in K–12 education (dual enrollment) and adult education students
without a high school diploma.
Student Challenges
In Fall 2017 and Fall 2018, researchers Porter and Umbach (2019) published a report
entitled Revealing Institutional Strengths and Challenges (RISC)—a survey asking students
about the challenges they faced during the current semester. The survey asked questions in five
broad areas: academic support services, campus environment, finances, financial aid, succeeding
in their courses, and work and personal issues. Porter and Umbach surveyed 50,097 students at
ten community colleges. The survey found that community college students have considerable
demands on their time and resources and reported that these present obstacles to college success
(Porter & Umbach, 2019). For example, among the students who reported work-related
challenges, 61% indicated that their work hours did not leave enough time for study. An
additional 36% said that work prevented them from using campus resources such as the library
or tutoring centers. Approximately half reported that their pay was insufficient to cover their
expenses while in school, and one-third said their work schedule conflicted with class times.
Nearly three-quarters of those who had challenges related to family and friends reported
difficulty balancing the demands of family and school. Approximately 30% struggled with the
health demands of family and friends.
The implication of these findings in a college math class is that students who must
dedicate significant amounts of personal time to their occupation or family obligations do not
have enough free time to practice and study mathematics to the level required for a successful
outcome. Math involves the use of multi-step processes to solve problems. Being able to master
the concepts can take significantly more practice time than other subjects forcing the working
46

student to choose between financially supporting themselves to cover college and living
expenses or studying math. A Higher Education Research Institute study (2003) found that the
time spent studying outside class has declined steadily with each passing year.
Offering more online math classes is one potential solution to ease college-level math
students’ time and resource demands. However, these offerings present challenges for
community college math students. For example, approximately 44% stated they were challenged
by the lack of interaction with their online faculty (Porter & Umbach, 2019).
Developmental coursework was the sixth-most cited challenge among the survey
participants. Among those students, 36% believed the developmental courses were too hard, yet
only 5% thought they were too easy. One-quarter indicated developmental courses did not
prepare them for college-level coursework. Academic under-preparedness extended beyond
developmental coursework. Approximately 15% of respondents reported they faced challenges
doing college-level work. Lack of planning and time management, poor study skills, and lack of
motivation were these students’ most frequently cited obstacles (Porter & Umbach, 2019).
For adult learners, a different set of challenges exist. Typically, adult learners have a
wider variety of cultural and educational backgrounds, abilities, responsibilities, and experiences
than their younger counterparts (Osam et al., 2017). College-bound adult learners face what
(Ekstrom, 1972) calls situational, institutional, and dispositional hurdles. Situational hurdles tend
to be external factors that come from a student’s life outside the institution, such as social
commitments, personal finances, family life, health, work conflicts, and transportation (Deutsch
& Schmertz, 2011; Elman & O’Rand, 2007; Flynn et al., 2011; Goto & Martin, 2009; Hostetler
et al., 2007). Institutional barriers are the policies and procedures ingrained in a college that
prevent adult learners from participating in educational activities. Bergman et al. (2014) found
47

that institutional barriers affect degree completion in adult students. Hardin (2008) found that
institutional barriers such as the availability of faculty office hours and limited night, weekend,
and online class offerings greatly diminish an adult learner’s ability to participate in academic
settings.
Ekstrom (1972) describes dispositional barriers as a person’s specific characteristics,
including fear of failure, attitude toward intellectual activities, level of aspiration, and
perceptions about the ability to succeed. Dispositional barriers come from within the student and
often need to be resolved by the individual alone, usually by absolute determination and self-
reliance (Cross, 1981). For example, Crozier and Garbert-Jones (1996) found that the longer an
adult learner has been away from collegiate settings, the more challenging the adaptation to
academic activities becomes. Additionally, scholars MacAri et al. (2005) concluded that adult
learners who have been separated from academic environments for many years take longer than
traditional students to develop a sense of autonomy and self-efficacy. In light of these obstacles,
empirical evidence suggests that adult learners may perform better academically than traditional
students despite having fewer sources of support outside of their educational institutions and
more stressors (Carney-Crompton & Tan, 2002).
Mathematics Equity Gaps
High school graduation requirements should align better with postsecondary expectations
(Long et al., 2009). Wimberly and Noeth (2005) published research indicating that only two-
thirds of the sampled college students perceived that their high schools adequately prepared them
for college-level mathematics. Mickelson et al. (2013) found that gaps in math performance
begin as early as the second grade and compound over time through primary and secondary
schooling and into postsecondary education, leading to racial/ethnic disparities in measures of
48

mathematics college readiness. There are specific obstacles that underserved community college
students face that contribute to inequitable success rates in college-level math courses.
As a result of economic and racial neighborhood segregation and under-resourced K–12
schools, underserved students are more likely to be academically underprepared in math when
they arrive at a community college (Brathwaite et al., 2020). Recognition that traditional math
remediation systems do not work for most students has informed nationwide reform efforts to
address obstacles to student success, including inaccurate methods of assessment and placement,
long multi-semester course sequences, and decontextualized math instruction irrelevant to
students’ fields of study. While some of these reforms are associated with improved outcomes
for community college students in the aggregate, they fail to close gaps in postsecondary
performance between more privileged and less privileged students (Brathwaite et al., 2020).
Research by Brathwaite et al. (2020) argues that most reforms to developmental math education
seek to remedy general barriers to student progress but are not typically designed to address
equity gaps and do little to reduce them. To further eliminate gaps and create equity in student
outcomes, the next wave of reforms must focus squarely on equity and address policies and
practices that disadvantage underserved students (Brathwaite et al., 2020).
Each student’s math experience that begins in elementary school shapes their math skill,
ability, and likelihood to succeed in a transfer-level math course. Foundational math skill gaps at
a young age become larger, ongoing academic challenges for students as they persist through
high school. If not addressed, these math challenges become significant barriers that restrict
students from striving and succeeding in high school or postsecondary math. This skill gap
experience is intensified for traditionally underserved students who historically have not had
access to the same support as their high-resourced counterparts. As a new policy that removes
49

semesters of math remediation for students, the importance of high-quality teaching and
instructional planning that builds math knowledge and success should be considered.
Conceptual Framework
Effective instructors use evidenced-based learning and instructional theories in
instructional planning and classroom teaching to increase students’ knowledge and success.
Teachers who inform their practice with learning theories can help students better understand
and retain information and give them multiple ways to construct and apply content knowledge.
For the final section of the literature review, the author presents a three-component conceptual
framework. Tomlinson’s model of instructional differentiation (2014), Merrill’s first principles
of instruction (2002), and Anderson and Krathwohl’s revised Bloom’s taxonomy (2001) are
integrated into a framework to explore the instructional strategies community college math
instructors use to differentiate their lessons to meet the needs of diverse learning ability. This
framework will provide a comprehensive approach to designing instructional strategies that
address the diverse needs of learners.
The conceptual framework for this study builds upon Tomlinson’s model of instructional
differentiation, which emphasizes the importance of personalizing learning experiences to meet
the diverse needs of all learners (Tomlinson, 2014). To ensure that instructional differentiation
aligns with effective teaching principles, the author links Tomlinson’s model to Merrill’s first
principles of instruction, emphasizing the importance of clear and concise content delivery,
active learner participation, and relevant feedback (Merrill, 2002). Finally, to determine the
effectiveness of a particular instructional strategy, the author aligns it with one of the knowledge
levels as described by Anderson and Krathwohl’s revised Bloom’s taxonomy, which classifies
50

learning objectives into six categories, ranging from lower-order thinking skills to higher-order
thinking skills (Anderson & Krathwohl, 2001).
To better enhance the reader’s comprehension of the frameworks, it is important to delve
into each component framework in detail. The following section will provide an elaborate
explanation of each framework to aid in comprehending the functions of each theory. By
dissecting the frameworks into their constituent parts, one can better appreciate their
interconnectedness and how they complement one another. Figure 1 illustrates the amalgamation
of the three theories in the conceptual framework.

Figure 1
Model of the Conceptual Framework

Note. Instructors differentiate learning experiences according to Tomlinson (2014), then align
those experiences to Merrill’s (2002) five instructional principles, then determine what
knowledge level the strategy supports from Anderson and Krathwohl (2001).

Tomlinson’s Method
of Diffentiated
Instruction:
Personalized
Learning Expierences
Merrill’s Principle of
Instruction: Active
Learning, Relavent
Feeback &
Participation
Anderson &
Krathwohl’s Six
Knowledge Levels:
Lower to Higher
Order Thinking
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Tomlinson’s Model of Instructional Differentiation
Tomlinson’s model of instructional differentiation (2014) provides a framework for
designing instruction that meets the diverse needs of learners. The model includes three
components: content, process, and product. Instructional differentiation involves modifying the
content, process, or product of instruction to meet the needs of learners. This approach helps
ensure learners are challenged and engaged in the learning process (Tomlinson, 2014). In
Tomlinson’s model, teachers adjust a lesson’s content, process, and products to improve the
likelihood of students’ engagement and achievement (Figure 2). Emphasis is placed on
demonstrating, scaffolding, and lesson design, for students to understand and extend their
knowledge of the subject. Differentiated instruction is a philosophy of teaching purporting that
students learn best when their teachers effectively address the variance in students’ readiness
levels, interests, and remembering profile preferences (Tomlinson, 2005).
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Figure 2
Tomlinson’s Model of Instructional Differentiation

Note. Teachers differentiate content, process, product, and the learning environment according to
the student characteristics of readiness, interests, and learning profile.

Learners must make meaning about what teachers are teaching. The meaning-making
process is influenced by a student’s personal experiences, beliefs, interests, and prior
understandings of a subject (National Research Council, 1999). Scholars Wiggins and McTighe
(2005), Hattie (2012), and Erickson (2006) found that effective learning occurs in classrooms
where knowledge is organized and students are highly active in learning. Moreover, learning
happens best when a learning experience pushes the learner beyond their independence level
(Tomlinson, 2017). If the challenge underwhelms, little or no learning takes place. If the
challenge exceeds a student’s skill level and tasks are far beyond a student’s current point of
Teachers Can
Differentiate
Content Process Content
Learning
Environment
According to
Readiness Inerests Learning Profile
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mastery, the outcome is frustration, not learning (Sousa & Tomlinson, 2011; Vygotsky, 1986;
Willis, 2006). Additionally, learning motivation increases when the learner feels a kinship with,
interest in, or passion for the subject (Piaget, 1978; Tomlinson, 2017; Wolfe, 2010).
Merrill’s First Principles of Instruction
Merrill’s first principles of instruction (2001) are guidelines for designing effective
instruction that engages learners in meaningful and authentic learning experiences. The
principles include task-centered, activation, demonstration, application, and integration. These
principles are based on the idea that learners learn best when actively engaged in the learning
process and when instruction is tailored to their needs (Merrill, 2002). Five core principles center
on task-based learning (Figure 3). Merrill suggests compelling learning experiences are rooted in
problem-solving (Merrill, 2002). Merrill’s principles are prescriptive (design-oriented) rather
than descriptive (learning-oriented) and draw from several instructional design theories and
models.

Figure 3
Merrill’s First Principles of Instruction

Principle 1
Problem-Centered
• Learners are
engaged in
solving real-
world problems
Principle 2
Activation
• Existing
knowledge is
activated as a
foundation for
new knowledge
Principle 3
Demonstration
• New Knowledge
is demonstrated
to the learner
Principle 4
Application
• New Knowledge
is demonstrated
to the learner
Principle 5
Integration
• New knowledge
is integrated ino
the learner’s
world
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Merrill (2002) outlines that the five principles of effective instruction are engagement,
activation of new knowledge, demonstration, application, and integration. The principle of
engagement emphasizes the importance of learners’ active involvement in real-world problems,
which should be interesting, relevant, and engaging. The second principle, activation of new
knowledge, involves linking new information to pre-existing knowledge and scaffolding to build
a foundation for new understanding. The third principle is demonstration, which involves
multiple demonstrations of concepts and the consistent presentation of good and bad examples,
procedures, visualizations, and modeling of behaviors. The fourth principle focuses on
application, where practice and post-tests align with learning objectives. The learners are asked
to recall, recognize, locate, name, describe, identify new examples, and predict the correct
consequences of applying a process. Finally, the fifth principle pertains to integration, where
learners integrate new knowledge and skills into their everyday life and create personal
adaptations through reflection and exploring unique and personal ways of using new knowledge
or skill. These principles promote effective learning and improve problem-solving skills,
analytical thinking, initiative, and creativity.
Anderson and Krathwohl’s Revised Bloom’s Taxonomy
This study will analyze student learning processes through the lens of Anderson and
Krathwohl’s (2001) six stages of cognitive dimensions, also known as the revised Bloom’s
taxonomy (RBT). Anderson and Krathwohl’s revised Bloom’s taxonomy provides a framework
for organizing educational objectives and designing effective instruction. This framework
outlines six levels of learning objectives: remembering, understanding, applying, analyzing,
evaluating, and creating. In addition, the taxonomy suggests that higher-order thinking skills are
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required for effective learning and that instruction should align with these skills (Anderson &
Krathwohl, 2001). Figure 4 shows how the hierarchy of the six cognitive stages is arranged.

Figure 4
Anderson and Krathwohl’s Revised Bloom’s Taxonomy

Note. Figure 4 shows the sequence of knowledge levels a learner must ascend through according
to Anderson and Krathwohl’s six knowledge levels.

Create
Evaluate
Analyze
Apply
Understand
Remember
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The revised Bloom’s taxonomy (RBT) is a framework that classifies different cognitive
skills or learning objectives into six hierarchical levels of increasing complexity. According to
Anderson and Krathwohl (2001), the first stage of RBT is remembering, which involves
retrieving or producing previously learned information or facts from memory. This stage consists
in memorizing basic definitions, theorems, terminology, and processes required to solve specific
exercises in mathematical contexts. The second stage is understanding, which involves
constructing meaning from written or graphic messages or activities. Examples of this stage in a
mathematics context include using a definition to identify mathematical forms, determining
when various statements satisfy the conditions of theorems, and implementing specific
procedural methods. The third stage is applying, which involves using learned material through
products like models, presentations, interviews, or simulations. In mathematics, this stage
requires using more than one definition, theorem, and algorithm and using graphs and
geometrical diagrams to support calculations.
The fourth stage is analyzing, which involves breaking materials or concepts into parts
and determining how they relate to one another or how they interrelate to an overall structure or
purpose. In mathematics, this stage requires identifying appropriate theorems, algebraic forms,
graphs, and definitions and using them to generate a specific type of conclusion and
classification. The fifth stage, evaluating, involves making judgments based on criteria and
standards through checking and critiquing. In mathematics, this stage requires synthesizing
questions requiring students to judge which information should be used when solving word
problems. The final and highest cognitive stage is “create,” which involves constructing elements
to form a coherent or functional whole. In mathematics, this stage requires students to combine
parts in a new way or synthesize elements into something new and different, creating a new
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form. Examples of this stage in mathematics include developing a classification system,
abstracting findings to higher-level problems, or creating original math questions and
procedures.
Anderson and Krathwohl also described four other cognitive domains through which
learners progress. The four categories are factual knowledge, conceptual knowledge, procedural
knowledge, and metacognitive knowledge. The first three levels were identified in the original
work (Bloom, 1956) but rarely discussed initially. Metacognition was added in the 2001 revised
taxonomy. The factual knowledge dimension refers to essential facts, terminology, details, or
elements students must know or be familiar with to understand a discipline or solve a problem.
Conceptual knowledge is the interrelationships among the essential components within a larger
structure that enable them to function together.
Moreover, conceptual knowledge is knowledge of classifications, principles,
generalizations, theories, models, or systems pertinent to a particular disciplinary area.
Procedural knowledge is how to do something, methods of inquiry, and criteria for using skills,
algorithms, techniques, and procedures. Procedural knowledge also refers to information that
helps students do something specific to a discipline, subject, or area of study. Finally,
metacognitive knowledge is the awareness of one’s cognition and particular cognitive processes.
It is strategic or reflective knowledge about how to solve problems and cognitive tasks, including
contextual and conditional knowledge and knowledge of self (Anderson & Krathwohl, 2001).
Figure 5 shows the progressions of cognitive domains described by the revised Bloom’s
taxonomy (2001).
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Figure 5
The Progress of Knowledge

The universality and applicability of Anderson and Krathwohl’s revised taxonomy in vast
areas across levels of education (local, state, and national) are appealing. RBT establishes and
clarifies learning goals for both student and teacher. This type of lesson organization can benefit
instructors as it helps plan and deliver deliberate instruction, design diverse activities that address
knowledge levels, improve assessments, and ensure that all aspects of the lesson align with the
learning objectives. Instructional objectives are more effective if they include specific verbiage
indicating the learning expectations to students.
Properly designed activities and assessments challenging students to move from the most
basic skills (remembering) to more complex learning led to higher-order thinking (creating).
Further, they helped develop effective and meaningful instruction (Smith Jr., 1997). Overall, the
RBT provides a valuable framework for understanding the different levels of cognitive
complexity involved in learning and can be used to develop learning objectives, assessment
tasks, and instructional strategies to promote deeper learning.

Develop
Metacognative
Knowledge
Develop
Proceedural
Knowlege
Develope
Conceptual
Knowledge
Develope
Factual
Knowledge
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Summary of Conceptual Framework
In community colleges, math instructors teach students with varying math skills,
knowledge levels, and course readiness. Within the same classroom, the convergence of dual
enrollment students, returning adult learners, first-time college students, recent high school
graduates, English language learners, and students with no prerequisite math knowledge pose a
significant instructional challenge. Additionally, since AB 705 removed all remediation
practices, students who need to develop the fundamental algebraic skills necessary to succeed in
transfer-level math are denied access to remedial courses. Instead, they must enroll
underprepared in a transfer-level math course. Even though the law has changed, the learning
objectives, course outcomes, curriculum, semester-length, and prerequisite knowledge have not.
Differentiated math instruction refers to the collection of techniques, strategies, and
adaptations instructors can use to reach a more diverse group of learners and make mathematics
accessible to every student. This instruction is based on math exit tickets (short summative
assessments given at the end of each class), math benchmark assessments, other formative
assessments, and instructor observations during whole-group and small-group instruction. The
National Council of Teachers of Mathematics (NCTM) promotes differentiating math instruction
for learning differences, talent, interest, and confidence. NCTM advises that the need is more
significant in middle and high school, as higher-level math relies on more complex reasoning.
Differentiation math instruction suggests that teachers must provide multiple routes to
accomplishing specified goals so that each learner can progress to the most significant degree
possible.
Anderson and Krathwohl’s (2001) six stages of cognitive dimension describe the
cognitive processes students undergo while learning. Merrill’s five principles of instruction
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(2002) describe the framework of effective task-based instruction rooted in problem-solving. The
two frameworks complement one another but lack a key component. Neither theory recognizes
the differences in students’ cognitive ability, readiness, and academic skills. Furthermore,
Tomlinson’s method of instructional differentiation (2017) was included to address this
shortcoming.
Conclusion
Assembly Bill 705 changed how placement and remediation worked in California
community colleges. As a result, students and math faculty who teach transfer-level courses,
including college algebra and statistics, were impacted. Historically remedial and developmental
math courses and placement policies marginalized underrepresented student populations
functioning as an academic trap, often causing students to withdraw from pursuing a college
education. AB 705 makes it illegal for a community college or district to impose placement
policies, remedial prerequisites, or matriculation. Instead, AB 705 allows students to enroll
directly into an entry-level transfer math course regardless of their math skills. Consequently,
enrollment in these transfer-level math courses has increased substantially, especially among
students of color. However, since remediation is no longer a barrier to enrollment, droves of
mathematically underprepared students with severe math knowledge gaps fill these classes.
Community college math faculty serve diverse learners in their classes, including dual
enrollment students, adult learners returning to college after time away, English learners,
students with developmental and physical disabilities, recent high school graduates, students
seeking to transfer to a university, and students with extreme variance in math skill. These
populations coexist in the same classroom, requiring faculty to rethink and replan how they
previously taught these courses. To meet the diverse needs of math students, math faculty should
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utilize the learning and instructional theory and strategies suggested by Anderson and
Krathwohl’s six stages of cognitive dimension (2001) and David Merrill’s five principles of
instruction that build students’ knowledge and comprehension systematically. Additionally,
differentiating this instruction to meet the needs of all learners regardless of their academic skill
and preparedness is paramount. The following chapter details the methodology of this study,
including the participant population, data collection, and qualitative interview protocol.

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Chapter Three: Methodology
In the hope of repairing the harms done by more than 50 years of consigning racially
minoritized students to remedial education courses, California policymakers set aggressive
postsecondary transformational goals such as AB 705, dual enrollment, and the common core
state standards. These novel programs and laws simultaneously create new academic hurdles and
learning opportunities for community college instructors and students. This study is central to
identifying these academic hurdles and the innovative solutions instructors use to overcome
them. This study centers on the experiences and promising practices of community college math
instructors who teach transfer-level math courses such as college algebra and introductory
statistics. AB 705 makes these courses accessible without remediation to all community college
students regardless of skill level and preparedness.
This study sought to determine the following: (a) the learning strategies used to address
the diverse learning needs of all students in entry-level transfer math courses; (b) identify the
challenges community college math instructors encounter now that AB 705 has removed all
remediation and prerequisite barriers; (c) how community college math instructors differentiate
their lessons and curriculum to meet the diverse learning needs and skill gaps of their students
while covering all required course content within a semester; and (d) the deliberate planning
approaches used by community college mathematics instructors that guide their students through
the various knowledge and instructional levels as described by Anderson and Krathwohl (2001),
Tomlinson (2017), and Merrill (2002).
Research Questions
Three primary research questions guide this investigation:
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1. What challenges do community college math instructors face now that AB 705 has
removed all remediation into transfer-level math courses?
2. How do community college math instructors differentiate the curriculum to meet
students’ diverse learning needs and skill gaps in AB 705 accessible math courses?
3. What other instructional strategies are community college math instructors using with
their students that generate equitable outcomes in AB 705 accessible math courses?
Purposeful Sample and Population
This study sought postsecondary mathematics instructors that met the following criterion:
1. Participants were tenured math faculty at a community college in the Southern
California region. Tenured faculty generally have more expertise in their positions
than others and develop a broader and deeper knowledge within their fields of
expertise (Crawford et al., 2012).
2. Participants taught remedial and transfer-level mathematics courses pre-AB 705 and
currently teach AB 705 accessible courses such as college algebra and introductory
statistics.
3. Participants in the study teach transfer math courses aligned with the same C-ID
course descriptors.
Study Context
California is the third largest state in the United States and has the nation’s most
extensive community college system, with 116 colleges. Every community college offers
mathematics courses. Due to the sheer geographical size of California, surveying faculty from
each of the 116 institutions is unfeasible. Therefore, for logistics purposes, the participant pool
was limited to math faculty teaching courses at Southern California community colleges. The
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Southern California region consists of the following counties: Imperial, Inyo, Los Angeles,
Mono, Orange, Riverside, San Bernardino, San Diego, San Luis Obispo, Santa Barbara, and
Ventura. In addition, there are 19 colleges in Los Angeles County, 10 in Orange County, 12 from
the Inland Empire (San Bernardino, Riverside), ten colleges in San Diego and Imperial counties,
and eight colleges in the Central Coast region (Mono, Santa Barbara, San Luis Obispo, and Inyo
counties). In total, there are 59 eligible institutions to gather participants.
To ensure that there were commonalities in the interview system across college
campuses, instructors that participate in the study must teach courses that utilize the course
identification system known as C-ID. The C-ID, or Course Identification Numbering System, is a
faculty-driven system that assigns identifying designations (C-ID numbers) to significant transfer
courses. The C-ID places a course number to identify comparable courses. Most C-ID numbers
identify lower-division transferable courses commonly articulated between the California
Community Colleges (CCC) and universities—including the Universities of California, the
California State Universities, and many of California’s independent colleges and universities. At
the same time, C-ID focuses on transferable courses; some disciplines issue descriptors for
courses that may not transfer to UC or CSU. Any community college course with the C-ID
number is guaranteed to meet the published course content, rigor, and course objectives. The C-
ID descriptor also means that the institution will accept any other course bearing the same
number elsewhere.
Utilizing the C-ID ensures that the participants of this study, regardless of their respective
college and department, teach courses with the same name, general description, prerequisites,
course objectives, course content, unit count, and evaluation methods. In addition, the study’s C-
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ID requirement helped remove potential variability in course design between college math
departments, faculty members, colleges, and universities throughout the state.
Data Collection
A qualitative approach and methodology were used to understand better the individual
challenges and experiences of community college math instructors who teach entry-level transfer
math courses. Qualitative data related to faculty perceptions and firsthand accounts were
gathered from conversations with community college math faculty. Utilizing a qualitative
research methodology permits the data collected to be written in a way that tells a story and
allows for a rich understanding of the content to emerge more inductive and flexible (Bender &
Hill, 2016).
This study employed a non-random sampling strategy called “convenience sampling.” A
convenient sample comprises available individuals willing to complete an interview (Johnson &
Christensen, 2016, pg. 267). Ideally, this study would benefit from large numbers of participants.
However, since participation is voluntary, the number of responses was limited to ten.
Participants were notified by electronic mail regarding the objectives of the study. The
notification described the voluntary nature of participation and the confidentiality of all data
gathered throughout the research period.
The data was collected using a semi-structured interview comprised of banks of open-
ended questions. The duration of each interview was approximately 45 minutes. In addition, all
participants were interviewed via an online video conferencing application known as Zoom.
Utilizing a video conferencing application allowed both researcher and participant to gather data
with greater access since geographic restrictions and commuting challenges were minimized.
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Moreover, video conferencing applications provided audio and video recordings that were
transcribed shortly after the interview.
Recruitment
The primary recruitment method used for this study was contacting faculty directly via
email. The researcher identified 59 community colleges in the southern California region to
locate participants for the study. The names and email addresses of the math faculty members
were published online in faculty directories for each college. In addition, a list of potential
candidates was sent an email that detailed the study’s goals and invited participation.
The researcher also located participants using a snowball method. Snowball sampling is a
recruitment technique in which the research participants assist researchers in identifying other
potential subjects. In addition, employing a snowball method as a secondary recruitment strategy
allows the researcher to locate faculty that may not be detected using the primary recruitment
method.
Data Analysis
The data was gathered during the Fall 2022 and Spring 2023 semesters. Data analysis
was conducted immediately following each interview and verified for accuracy. A narrative
analysis was implemented. This analysis involves making sense of the interview respondents’
stories to highlight important aspects and critical points. Each interview recording was
transcribed into a text format. Each transcription was read thoroughly and annotated, labeling
relevant words, phrases, sentences, or sections with codes. These codes identified important
qualitative data types, patterns, activities, concepts, differences, opinions, and processes. The
data was then conceptualized by creating categories and subcategories by grouping the codes
created during the annotation process. Next, the data was segmented. The segmentation of data is
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the process of positioning and connecting categories. This allowed the establishment of cohesive
data. Next, each segment was analyzed to determine if there were hierarchies among categories.
The final step of the analysis was a presentation of the findings.
Ethical Considerations
Ethical considerations in research are principles that guide research designs and practices.
These principles include voluntary participation, informed consent, anonymity, confidentiality,
and communication. Since the nature of open-ended interview questions was potentially
sensitive, anonymity was guaranteed. In general, anonymity helps shield participants in a
qualitative study from any “unnecessary risks,” such as retaliation by faculty and staff identified
in response to an open-ended question (Glesne, 2010). Regarding anonymity, the names of the
faculty participating in this study were not recorded, and the individual’s responses or results
were not linked to their identity. Regarding confidentiality, any participant who chose to provide
personally identifying information within the interview was redacted and not made known when
disseminating the findings of this study. However, if a shared personal account of an event did
contain identifying information and that information was discussed within the research results, a
pseudonym for that participant was assigned.
Drew and Hardman (2007) enumerated three elements of informed consent: capacity,
information, and voluntariness. Capacity involves participants’ ability to understand and evaluate
the information a researcher provides. That information must be communicated in easily
understood language. Any ambiguities should be clarified so that participants clearly understand
the study’s scope and what is expected from them. Participants were informed that participation
was voluntary and had the right to withdraw from the study without repercussions. Data
collected for this study—including interview recordings, transcripts, and analyzed data—will be
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kept secured and disposed of according to the University of Southern California’s policy on the
disposal of research data. Throughout this study, respect for participants and the site was a
priority.
Recruitment and selection of participants were equitable (fair or just) within the confines
of the study. Therefore, the researcher did not exclude participants based on gender, race,
national origin, religion, creed, education, or socioeconomic status. However, the researcher
excluded participants who teach or are employed by Golden West College in Huntington
Beach—the institution where the researcher is currently employed.
Trustworthiness Measures
Trustworthiness in qualitative studies is about establishing credibility (Merriam &
Tisdell, 2016). Credibility in qualitative research is about the truthfulness of the research
findings. For this study, the researcher used detailed descriptions to show that the results apply to
the contexts of the research questions. Confirmability is the degree of neutrality in the study’s
findings based on participants’ responses and not any potential bias or personal motivations of
the researcher. Finally, for transparency purposes, the researcher provided an audit trail
highlighting every step of data analysis and a rationale for the decisions made throughout the
research process.
Personal bias is a fact of life. Everyone has different sets of morality, ethics, and ideas of
right versus wrong. Because of this, any research will be subject to a degree of bias (Locke et al.,
2009). As a math instructor at Golden West College—a California community college in Orange
County—I must be aware of any conflicts of interest between my colleagues, my institution, and
the math departments and institutions of the study’s participants. When creating data interview
protocols, I sought to avoid inherent flaws in the design process. Throughout the study, I was
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also aware of personal biases such as language usage and cultural references unknown to
members of cultures that differ from mine. Bias may occur if the language and vernacular used
in each question are over-technical or contain uncommon nomenclature that could influence the
participant’s responses. Language unfamiliarity can lead to biased responses to please the
researcher with the “right” answer or, worse, generate false positive responses where participants
mistakenly give information to questions, they don’t fully understand. These biases are subtle
and sometimes subconscious, so it’s difficult to avoid them entirely and must be considered
during the design and analysis process. Finally, because I conducted this study at various
California community colleges, I must be aware that some responses to open-ended questions
included sensitive information or contained criticisms aimed at students, coworkers, or the
institution in which the participants work. When analyzing the data collected, I had to understand
each participant’s value to this research and not become personally and emotionally sensitive to
the findings.
Role of the Researcher
I work as a full-time tenure track mathematics professor at Golden West College in
Huntington Beach, California—a midsized suburb of Orange County. I have been an educator
for nearly a decade, teaching mathematics courses in community college and university settings.
My role as a math instructor grants me the power to design, modify, and implement new
instructional practices that better align for equitable learning experiences and outcomes. I am
vested in the student’s academic success and the success of the college. Therefore, I seek to
create pathways through the curriculum that are reasonable, empathetic, thorough, hold academic
integrity, meet students’ needs, and, most importantly, are equitable. I saw firsthand how the
enterprise of teaching college mathematics transformed from a deficit model entrenched in
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systemic remediation to a more student-centered asset-based approach. The “deficit thinking”
approach refers to the notion that students (particularly those of low-income, racial/ethnic
minority background) fail in school because such students and their families have internal
defects (deficits) that thwart the learning process (Zhoa, 2016). In contrast, asset-based thinking
assumes all students have the potential to succeed (Celedón-Pattichis et al., 2018).
As the political landscape in the California community college system shifts more toward
asset-based instructional paradigms, instructors like me have the opportunity to evolve and
update instructional techniques that ensure mathematics learning is rigorous and supportive for
each student. These confounding learning issues motivate me to examine what changes are
needed in course design, curriculum refresh, academic integrity, and institutional policy to find
solutions to help bolster student success outcomes in the post-AB 705 era.
Gathering feedback directly from the faculty is necessary if educators and administrators
seek to create meaningful change in the best interest of students. I was also a member of the
faculty cohort that taught math courses during the COVID-19 pandemic when instruction shifted
from traditional “in-person” formats to completely online versions. During this time, instructors
and students had to navigate these new learning environments, revealing many unforeseen
learning obstacles.
Academic Richard Milner (2007) warns us of the dangers that can emerge during the
research process if we do not engage in methods that avoid misinterpretations, misinformation,
and misrepresentations of individuals, communities, organizations, and systemic constructs. This
sentiment reminds me that understanding how I perceive myself helps me better understand how
others may perceive me and the research findings I present. As I collect and analyze the data for
this study, I must acknowledge the privileges, power, and opportunities, both real and perceived,
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bestowed onto me by dominant societal norms that influence my pedagogical practices as a
conscience educational leader and researcher.

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Chapter Four: Findings
Chapter Four presents the findings of this study that center on the promising instructional
practices of community college math faculty after the implementation of AB 705. This chapter
aims to comprehensively analyze the data collected through semi-structured interviews with
math faculty from several community colleges in Southern California. The findings are
organized by research question and then categorized into themes that emerged from the data,
which include changes in pedagogical practices, student-centered instruction, and the impact of
the legislation on faculty and students.
This study aimed to identify what learning strategies community college math instructors
use to address the diverse learning needs of all students in transfer-level math courses. The study
also sought to understand instructors’ challenges now that AB 705 has removed all remediation
and prerequisite barriers. In addition, the researcher wished to know how community college
math instructors differentiate their lessons and curriculum to meet their students’ diverse learning
needs and skill gaps while covering the required course content within a semester. Finally, this
study sought to determine what deliberate planning approaches are used by community college
math instructors that guide their students through the various knowledge and instructional levels
described by Anderson and Krathwohl (2001) and Merrill (2002).
Three primary research questions guide this investigation:
1. What challenges do community college math instructors face now that AB 705 has
removed all remediation into transfer-level math courses?
2. How do community college math instructors differentiate the curriculum to meet
students’ diverse learning needs and skill gaps in AB 705 accessible math courses?
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3. What other instructional strategies are community college math instructors using with
their students that generate equitable outcomes in AB 705 accessible math courses?
Identified Instructional Challenges
Five major themes emerged based on the interview protocol questions related to Research
Question 1 regarding the challenges community college math instructors face now that AB 705
has removed all remediation. The five significant themes are prerequisite knowledge gaps, the
COVID-19 pandemic, meeting the needs of diverse skill levels, maintaining academic rigor and
pacing, and the lack of campus resources and funding for AB 705 support. The results discussed
in Chapter Five were influenced by these five themes, particularly regarding the crucial role of
professional development, the prevalence of prerequisite knowledge gaps, and the lack of
campus resources.
Prerequisite Knowledge Gaps in Students
Each interviewed participant communicated information related to students’ overall skills
and knowledge gaps. Dennis, a professor at Vannote City College, shared his experience with
knowledge gaps in his college algebra class. When asked about the differences between the math
skill level of his students pre- and post-AB 705, Dennis said, “in general, the students taking my
college algebra courses today are not as prepared for this class as they once were.” He admitted
that the level of math competence is more akin to students taking a developmental math course.
He said his students “do not know the basics of algebra like the order of operations or
simplifying radical expressions.” Dennis shared that he often must “water down the strength” of
the problems he selects for summative assessments to better align with his students’ collective
math skill level. “If I put the college algebra level problems on the exam, most of my students
will not pass,” said Dennis. He added, “although I believe in expanding access to education, we
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need to evaluate whether or not accelerating people who do not know the basics into more
advanced courses is a good thing for student wellbeing.”
Cynthia, who teaches at the College of the North, shared similar remarks as Dennis. She
noted a “clear difference” in her students’ skills after AB 705 took effect. This difference was
evident when she covered the textbook’s first chapter, prerequisites. Cynthia described the
content of this chapter as “the stuff they should have already learned and mastered in another
course.” These topics include solving linear equations in one variable, simplifying rational
expressions, basic arithmetic, and the properties of exponents. Before AB 705, Cynthia could
omit this content since her college offered developmental math courses. Still, she feels
compelled to include these topics since there are no other classes on her campus where students
can sharpen these skills. But, she added, “now that I include an entire chapter on prerequisite
material, I am forced to shave off the more advanced topics we typically cover towards the end
of the semester.” Cynthia feels that AB 705 puts an “insurmountable burden” of remediation
onto math instructors who must identify and close these gaps, all while still covering the material
mandated by the state.
Interviewees described student needs in terms of deficiencies. For example, Thomas at
Breezewood College commented, “most college algebra students today don’t know how to
manipulate basic symbols properly. Of course, we’ve always had this, but it’s worsened.”
Thomas’s comments about the absence of “manipulation skills” were also reported by seven of
the 10 participants. Thomas added, “my students hardly know their multiplication tables and
can’t complete simple problems involving fractions accurately.” Thomas also explained that
algebra builds upon core skills, such as simplifying expressions, factoring, and solving equations.
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He said that when students lack these skills, they fail to find success with the more complex
topics in college algebra.
AB 705 is an “unmitigated disaster,” says Jonathan, a senior faculty member at Fishman
College. He said that more students are failing entry-level classes requiring math competency. “I
don’t have time in my course to do weeks of remedial education that should have been
completed elsewhere.” Moreover, Jonathan adds, “the knowledge gaps are widening; you can’t
just throw people into these classes at the community college level and assume they’ll sink or
swim like at a university. That’s asinine.” At Fishman College, there is a push from the
administration to the academic advisers to put students into more advanced classes ignoring
prerequisites. “Now I have to do the remediation myself,” says Jonathan. “These students get
frustrated because they don’t know the basics and get marked off for it.”
Learning Disruption Caused by COVID-19
Seventy percent of the participants claimed that the COVID-19 pandemic exacerbated
knowledge gaps and academic dishonesty within their classes. Philip, a statistics professor from
Silver Coast College, shared that distance learning during the COVID-19 pandemic created more
opportunities for students to commit academic dishonesty in more significant numbers than in-
person instruction. Philip observed that the shift to remote learning forced many educational
institutions to reduce or eliminate proctoring and other forms of academic integrity monitoring.
The rapid change has made it more difficult to detect cheating, leading some students to feel that
they can “get away with it without facing the consequences.” Philip noted that “assessment
scores plummeted dramatically when in-person instruction resumed, and students could no
longer take exams unmonitored, losing access to resources like notes, textbooks, and internet
support.” Since AB 705 prohibits Philip and Silver Coast College from offering any remedial
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courses, Philip felt it was his responsibility to help close the knowledge gaps these students
encountered during the pandemic. Philip said that since AB 705 essentially let anyone enroll in
his classes, “low-skilled or no-skilled students simply used any resources necessary to assist
them during assessments,” regardless of whether those resources violated Silver Coast’s
academic integrity policies.
Jennifer, a recently tenured math faculty member from Meyers Community College, said,
“if we have just one course below transfer level math, then we could address the skill gaps
caused by the pandemic, remote learning, and AB 705 directly.” Jennifer also suggests that more
professional development is needed to help professors like she understand the impact COVID-19
combined with AB 705 has had on the students at her college. On the other hand, Lisa, a
professor with over 15 years of experience teaching transfer-level math, shared that with the shift
to remote learning, many of her students relied on online resources to learn, practice, and
develop remedial math skills. Lisa indicated that although AB 705 took effect before the
pandemic, increased access to online resources throughout the pandemic “may have helped some
students to improve their math skills without the need for remediation.” However, without a
developmental math class where students can develop prerequisite skills, access to online
materials “may have led to a dependence on these resources that hinder their ability to think
critically, independently, and authentically, especially in the post-pandemic era.” Lisa believes
AB 705 and the pandemic are two “tandem events that have together created a situation that is
working against students’ abilities to learn the course content effectively and pass her classes
successfully.”

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Widening Skill Diversity and Math Abilities
Community college math instructors must teach students with various math skills and
abilities without remedial courses. This scenario can make it difficult to create lessons and
assignments that are appropriately challenging for all students. Participants described the
extreme diversity of skills within their math classroom. A common theme that emerged
regarding this topic is covering the course content within the same timeframe (semester) as
before AB 705. Some faculty suggested that keeping course pacing is now much more complex
and, in some cases, impossible.
The existence of skill diversity within one math classroom is not new to educators;
however, the “breadth of skill is more extreme than ever,” says Cynthia. Cynthia elaborated on
her experience by saying
I recently taught a college algebra class along with its corequisite support course. It was
challenging to teach a course for such a diverse range of abilities, and it was impossible
to catch up with all their deficiencies with a two-unit support course. The number of
questions from the support course students overshadowed the class discussion, limiting
my ability to teach the course content. Instead of covering the objectives specified in the
COR, the skilled students were subjected to elementary arithmetic explanations—
damping their exposure to more rigorous problems. If we continue to remove classes our
low-skilled students need to pass college algebra, I’m concerned that we’re destroying
their math education opportunities.
Cynthia and the other research participants expressed that they work hard to meet the
needs of every student in their class. However, when confronted with such a diverse range of
student skill levels, they are “forced” to devote additional time to the fundamentals which were
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not previously a focus of the course. In addition, interviewees expressed unanimous concern
about the depth to which the material can be covered and expressed concern that the experience
of all students in their classes as well as the rigor, suffers.
Dennis from Vannote City College discussed how the rigor of his courses changed
because of AB 705. He defined rigor as the level of understanding, skill, and application of what
students have learned. Dennis argued that the law had undermined the rigor of college-level math
courses by permitting students who may not be fully prepared for college-level coursework to
enroll in these courses. He contends that AB 705 has “lowered academic standards and
diminished the quality of education” since math faculty may be required to cover more
fundamental material to accommodate students not equipped for college-level work. Dennis fears
that students not appropriately prepared for college-level math courses may have a higher risk of
dropping out and transferring at a lesser rate.
Lack of Student Support, Campus Resources, and Funding
Several faculty members cited a lack of campus resources and committed funding for AB
705 implementation and student support, such as embedded tutoring programs, extra pay for
corequisite course offerings, professional development to train faculty on AB 705, and a
dedicated math tutoring center. Many participants believe that students could complete transfer-
level math in their first year if their college provided the necessary support. Concurrent support,
corequisites, and institutional infrastructure were critical supports that should be available to
students. For example, at Breezewood College, Thomas highlighted the difficulties of ensuring
students receive comprehensive support such as a corequisite course and a well-staffed tutoring
center. “We just don’t have the manpower and are tight on funds,” says Thomas.
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Moreover, he added that “we can only offer a minimal number of support courses
compared to the number of college algebra and statistics sections we teach each semester.”
Regarding staffing, four out of five respondents indicated that locating, training, and scheduling
tutors is difficult, especially in the post-pandemic era. In addition, sixty percent of interviewees
indicated that when a support course is elective (not required), many students choose not to
enroll. For example, Philip at Silver Coast College said that students are often unaware of
corequisite support courses because these sections were not linked in the registration system
when the students enrolled in his math courses.
Robert, a full-time faculty member at Clear Mountain College, has taught college algebra
for a decade and says, “there is no remedy available. Students either enroll in a support course or
take the transfer-level course without the support and seek tutoring at Clear Mountain or hire a
private tutor.” Students with limited financial resources “lack the financial means to hire a
private tutor, so Clear Mountain is their only option,” says Robert. Jennifer at Meyers
Community College and Lisa at Hughes City College noted that their colleges have a full-service
tutoring center. Still, a staffing shortage restricts the hours of operation and thus cannot support
students needing assistance outside the 9 a.m. to 5 p.m. window or remotely.
Chloe is the mathematics department chair at Silver Coast College. She stated, “providing
the wraparound services our students need is a significant barrier. As a result, students that
require academic and non-academic support cannot receive the assistance they need to succeed.”
One issue mentioned is that Silver Coast College can only offer limited support classes due to
space constraints, staff shortages, and insufficient funds to pay faculty for the additional sections.
In addition, Chloe is concerned that “we do not have enough safety nets for students who require
additional time and support.” Another confounding issue is that “students who need support are
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not actively seeking it,” says Chloe, even though she recommends her students take advantage of
the limited resources Silver Coast does provide.
Lack of Professional Development Opportunities for Faculty
Professional development can be an effective way for college math professors to mitigate
the effects of AB 705. Still, due to funding constraints, some colleges do not train their math
faculty in pedagogical practices. Seventy percent of respondents claimed their college had done a
decent job educating various constituencies about AB 705. At the same time, all participants
stated that more professional development is needed to fully understand the law, its implications,
and its effects on student success in transfer math. For example, at Hughes City College, Lisa
states that she and her colleagues feel supported and informed about the current state of AB 705.
In addition, she said, “many of us regularly attend webinars offered through the California
Community Colleges Chancellor’s Office so we can proactively discuss up-to-date information
at our department meetings.” Jennifer at Meyers Community College stated, “since 2017, at least
one member of the faculty facilitates a seminar about AB 705 at our bi-annual faculty flex day.”
Three respondents stated their college received ample money to engage in various
professional development programs for implementing AB 705. For example, Philip at Silver
Coast College shared that every request he submitted to attend a conference, workshop, or
regional gathering was granted. He praised the leadership at his institution for recognizing that
professional development for implementers and practitioners is crucial to the success of AB 705
implementation on his campus. Most interviewees said that the conferences and workshops they
attended allowed them to learn about the policy’s objectives, restrictions, and current outcomes
of other community colleges around California. However, eighty percent of participants said
their professional development did not adequately address instructional strategies and methods
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for faculty teaching AB 705 accessible courses. Jonathan, Jennifer, and Dennis all said that more
course design and curriculum development training is needed so that professors can create or
modify classes and curricula that better align with the AB 705 standards. These topics include
learning to design course assessments that accurately measure student progress and mastery of
the course content while maintaining rigor.
Summary of the Data for Research Question 1
The research question explored the challenges that community college math instructors
face following the implementation of AB 705, which removed all remediation requirements. The
study found that instructors faced several significant challenges, including dealing with students
with significant knowledge gaps and underprepared for college-level math courses. The COVID-
19 pandemic also added another layer of difficulty, making it more challenging for instructors to
engage with students and provide the necessary support. Furthermore, instructors reported
struggling to accommodate students with diverse math abilities, often requiring them to use
differentiated instruction techniques to ensure that all students can succeed. Instructors also
reported facing challenges related to the lack of student resources and funding, which can limit
their ability to provide the support that students need to succeed. Additionally, limited
professional development opportunities were available to help instructors effectively implement
AB 705, leading to uncertainty about how best to meet the needs of their students. Finally,
instructors also reported challenges in navigating the changing prerequisites required for math
courses, as they had to adjust their curriculum to meet the new standards while ensuring that
students had the necessary foundational knowledge to succeed.
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The Presence of Differentiated Instructional Strategies
Research Question 2 sought to understand how community college math instructors
differentiate the curriculum to meet their student’s diverse learning needs and skill gaps while
covering all required course content. The five most significant themes were collaborative
learning activities, course pacing, assessment strategies, modality of course and resources, and
the unfamiliarity of instructional differentiation. The results discussed in Chapter Five were
influenced by these five themes, particularly collaborative learning, course pacing, assessment
strategies, and the unfamiliarity with differentiating instruction in planning and teaching.
Six of the ten community college math instructors interviewed indicated they
differentiate the curriculum to some degree, focusing on differentiation of the learning process to
help their students learn. For example, one common approach was using multiple teaching
strategies and materials catering to students’ diverse learning strengths, such as visual aids,
hands-on activities, and collaborative work. For example, Lisa from Hughes City College uses a
combination of direct instruction on whiteboards combined with computer-generated graphs
from Desmos, charts, and diagrams to display statistical results to help students better understand
complex mathematical concepts. “This helps my visual learners,” Lisa said. In addition, all
participants mentioned providing additional resources and support, such as office hours or extra
practice problems, to help students struggling with specific concepts or skills. Moreover, all
respondents use formative assessments in each class meeting to gauge student understanding and
adjust their teaching accordingly. Finally, some instructors prioritize topics or abilities based on
the needs of their students while still ensuring that all required course content is covered.

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Collaborative Learning and Group Work
One common practice among the interviewees was using cooperative learning models
within their classroom. For example, Cynthia described how she divides her students into small
groups and assigns each group a set of math problems to work on together. The students first
attempt the problems individually before asking for help from others. Then, her students
collaborate, comparing methods and solutions and discussing ambiguities, uncertainties, or
mathematical errors. Her skilled students are encouraged to assist those who do not understand
how to solve the exercises. Cynthia calls this “peer tutoring” and believes it “promotes social
interaction, humanizes learning, and helps students learn from one another.” She added,
“teaching someone else what you know is one of the best ways to learn, so creating peer-to-peer
learning opportunities is helpful to students.” Cynthia also stressed the importance of group work
in her classroom by saying, “my students learn best by doing the work themselves and discussing
the results with others, not by watching me demonstrate the problems on a whiteboard.”
Grouping Students by Skill Level
Although many participants have their students work in groups, only thirty percent
specifically mentioned grouping strategies that create academic discourse centered on the
concepts. Most instructors shared that they group their students randomly, by their physical
locations in the classroom, by student choice, or in online settings, using Zoom. One faculty
member, Cynthia, discussed how she groups her students based on their ability levels. Students
are grouped into teams with other students who have similar abilities. She achieves this through
classroom observations, noting which students appear knowledgeable but admits that it “takes
some time to get to know which students have high skill and comprehension.” Cynthia believes
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this strategy helps ensure that students learn from their peers with similar strengths and
weaknesses.
Lisa at Hughes City College also groups her students based on their skill level. Grouping
students by skill allows her to work with each group individually and provide targeted instruction
that meets their needs. For example, she may assign different homework assignments to each
group or provide additional practice problems for students who need more support or are ready
to advance to more challenging problems. As a result, Lisa feels like “she has significantly
improved her students’ math skills and confidence” through collaborative learning experiences.
“Students who were previously struggling have shown improvement in their grades and have
become more engaged in the learning process,” says Lisa. In addition, during the interview, Lisa
noted that her ability to differentiate her instruction “helps her students succeed in math,
regardless of their skill level or background.”
Think-Pair-Share and Peer Tutoring
Fifty percent of faculty interviewees mentioned the collaborative learning activities
“think-pair-share, jigsaw method, and peer tutoring” by name. For example, Jennifer at Meyers
Community College described the think-pair-share method as “the best way to engage my
students with the math and one another at the same time.” Jennifer added, “think-pair-share
involves students working in pairs to solve a math problem and then sharing their ideas with their
classmates.” Similarly, Chloe from Silver Coast College shared that she uses a jigsaw
instructional model. For example, she says, “for complex problems with many steps, students
form groups focusing on a subset of steps, master those steps, and share their findings with the
class.” She added, “they’re deconstructing the process into smaller bits, then reconstructing the
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solution collaboratively.” Chloe thinks the jigsaw method helps her students “see the whole
forest, not just the trees.”
The use of peer-to-peer tutoring within the classroom was mentioned frequently by nearly
all participants to engage students and promote learning. “It’s beneficial for both low and high-
skilled students,” said Philip when asked about differentiated learning strategies. He said this
strategy “helps the struggling students grasp the concepts better and improve their overall
understanding while the high-performing students reinforce their knowledge. It’s win-win.” He
thinks that when students work together in a peer-to-peer learning environment, it helps them
learn and explain complex concepts in ways that might make it easier for them to understand.
Philip described the mindset of his students when they participate in peer tutoring as “more open
to learning than direct instruction.” Philip also believes that peer-to-peer tutoring instills an “if
my colleagues can do it, so can I” culture in his classroom that can “rub off on students in a
positive way.”
Similarly, Jonathan from Fishman College also implemented group work in his classes.
He shared that “each student’s diverse backgrounds and experiences bring something unique to
the table, leading to a more well-rounded understanding of the subject matter.” Jonathan added
that “these interactions help my students develop critical thinking and problem-solving skills by
considering different viewpoints and approaches to problem-solving.” Johnathan referenced his
introduction to statistics course and mentioned that “when the students engage with diverse
viewpoints, they encounter ideas that challenge their assumptions or preconceptions.” As a
result, Jonathan asserts collaborative learning opportunities allow his students to develop a more
critical and nuanced understanding of statistics.” However, when asked about course pacing,
Jonathan said he must “balance the amount of group work with direct instruction. “Covering all
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necessary content in one semester has always been challenging.” Jonathan also discussed that
“too much collaborative learning can disrupt the course pacing.”
Course Pacing and Truncating Content
Course pacing refers to the rate at which the course content is covered over the semester.
In other words, it refers to how quickly or slowly the instructor expects students to learn the
material. The data show variability in how respondents pace their courses. For example, some
instructors, like Thomas, said they cover material quickly, assuming students have a strong
foundation in the subject matter. In contrast, Robert, Lisa, Chloe, and Philip indicated that they
cover some material slower, spending more time on the basics before moving on. “AB 705 has
made it so instructors must devote more time to the fundamentals. These extra tasks reduce the
tempo of us moving faster,” says Philip. However, as a side effect of AB 705, Philip noted that
“taking more time isn’t always a bad thing.”
While some respondents discussed AB 705 as a “great opportunity for many students,”
they also noted that they must adjust their curriculum to accommodate students who may not
have the same level of preparation as their peers. These adjustments often result in cutting out
previously covered topics to focus on the fundamentals. Some faculty participants discussed the
outright removal of specific concepts, sections, or entire chapters of the curriculum. The faculty
mentioned that since AB 705 took effect, they have not been able to successfully cover all the
topics they once did—40% of the interviews admitted to this practice. As one professor put it:
“We must make sure that we’re meeting students where they are, rather than expecting them to
come to us with a certain level of knowledge. It’s a challenge and an opportunity to be more
intentional about our teaching.” Another instructor added, “I must often take my foot off the
accelerator. If I don’t, I leave half of them behind, and ethically speaking, I can’t do that.”
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Six of the ten participants identified that they adjusted the pace of their course content to
help students succeed. “Altering the pace of the course is often required. It’s another way I
differentiate the material. However, it’s not always helpful for the highly skilled students,” said
Robert at Clear Mountain Community College. Furthermore, Robert indicated that “slowing
down the pace benefits most students, especially those with low skill and students who learn at
slower rates.” He added, “sometimes we can’t get to all the content, especially the later chapters.
But I am ok with it since most of my students are non-STEM, and this is their last math course.”
Because of AB 705, Robert said he needs to “slow things down a bit” so he does not leave
anyone behind. Robert sees this as a windfall for the underprepared students, saying, “we are
supposed to maintain the same level of rigor as before AB 705, but that’s often impossible, but
we try to make it work for everyone.”
Conversely, Dennis from Vannote City College said that he divides the objectives from
each textbook section into “essential and nonessential” to keep pace with his course calendar.
“The essential topics must be covered in depth and cannot be skipped,” said Dennis. He added
that nonessential objectives are briefly mentioned, underemphasized, and sometimes left as extra
credit. Dennis found that categorizing the material this way helps his students “stay on track”
with the course and “guarantees that we cover every section in some detail.” He added, “we can
spend more time on the most important topics needed for success in the course and future math
courses.” Dennis felt that classifying the course objectives this way is “a better option for all
students and that “my low-skilled students get more absorption time, while my high-skilled
students still get to see the advanced topics.”

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Assessment Strategies
All participants reported using formative assessments such as quizzes, knowledge checks,
or exit tickets to check for student understanding and use the outcomes of these assessments to
adjust their instruction. The interviewees also discussed using traditional summative
assessments, like unit exams, midterms, and a comprehensive final, to gauge a student’s mastery
of the material. Moreover, the faculty shared assessment strategies they implement to engage
students in mastery learning and critical thinking.
Exit Ticket Assessments
For several years, Chloe at Silver Coast College has used daily exit tickets to support
instructional differentiation in her formative assessments. She believes this strategy is crucial in
helping students succeed in college algebra, especially those struggling with the subject matter.
In each class session, students are given two short assessments to complete, one in the middle
and another towards the end of class. Furthermore, the students get unlimited attempts at the exit
ticket and can ask for help from colleagues or the instructor. Exit tickets provide Chloe with a
quick way to assess her students’ understanding and mastery of concepts. In addition, she uses
these low-stakes assessments to inform instructional decisions by identifying students who may
need additional support or increased challenge. “My students perform better on low-stakes exit
tickets than high-stakes summative exams,” says Chloe.
Moreover, Chloe believes her students are “more open to learning when they are under
less pressure to perform.” She added that “exit tickets encourage my students to reflect on their
learning and identify areas where they need additional support.” She believes “self-reflection can
help students take ownership of their learning and seek the resources and support they need to
succeed.”
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Similarly, Jennifer at Meyers Community College says daily exit tickets provide her
students with assessments that check for understanding and inform her planning for the next day
in class. At the end of each class, the exit ticket offers more information on what students have
mastered and learned and where they need more remediation. She thinks implementing exit
tickets into her courses also “supports future instructional planning and is aligned to daily warm-
up questions that my students complete each day at the start of the lecture.” Jennifer uses these
formative assessments across all math levels to drive her instructional planning, predict student
learning growth, and create an environment of continual improvement.
Multi-Attempt Assessments
Another assessment strategy mentioned by several respondents was offering students
multiple attempts at high-stakes summative assessments. Three-fifths of participants indicated
that they allow numerous tries on quizzes and exams. All participants shared that they utilize
online courseware like ALEKS, My Math Lab, or Canvas to facilitate homework assignments or
assessments. In contrast, approximately half of the interviewees said they do not use courseware
for summative and formative assessments—opting for traditional paper exams instead. For
example, Dennis and Cynthia use free online courseware called MyOpenMath for all
assignments, including homework problems and assessments. Dennis noted that “the program
allows us to determine the number of times a student can attempt a quiz or exam and choose
what to do with each score.” Dennis shared that his students could take each unit exam up to
three times, with the highest score of the three attempts recorded as their final exam score.
Cynthia said, “allowing multiple attempts on quizzes provides an opportunity for my students to
learn from their mistakes and improve their understanding of the material.” She added that
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second and third chances allow the students to review their incorrect answers and identify the
areas where they need to focus their efforts to improve their understanding.
Lisa at Hughes City College shared that multiple assessment attempts foster a classroom
culture of “making mistakes is ok so long as you learn from them.” Second chance policies
“promote a growth mindset among students, encouraging them to persevere and try again until
they achieve mastery of the material,” says Lisa. She noticed that students who struggle with
math feel discouraged after receiving a low grade on their first attempt. Using multiple attempts
as a teaching practice allows her students to demonstrate their learning and build confidence.
Lisa added, “some students may need more time to process information and understand concepts,
while others may grasp the material quickly.” By creating multiple attempts, her students can
work at their own pace and receive the support they need to succeed in the class.
Assessing Using Courseware
Some instructors do not use courseware for formative and summative assessments.
Thomas, Robert, Jennifer, Jonathan, and Philip indicated they use traditional paper examinations
for face-to-face classes. Thomas shared, “I want to see their handwritten solutions to give
targeted feedback.” Philip from Silver Coast College noted, “paper exams are better for students
since I can give partial credit for any correct steps, whereas computer programs can’t do this as
well.” When asked what strategies they implement when students perform poorly on
assessments, Thomas and Robert said they let their students submit test corrections for the
problem their students did not get correct. Thomas has his students resubmit their exams,
correcting only the question they missed and rewarding them with what he calls “redemption
points” added to the original exam score.
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On the other hand, Robert allows his students to work in groups and help one another
correct their exams, but they need to resubmit the entire exam free of errors to receive points to
increase their scores. When elaborating on differentiated assessment strategies, Robert stated,
“everyone has bad days, and when a bad day is on a test day, we must find ways to re-engage
students back into the learning process. That’s what test corrections help do.”
Modality of Course and Learning Resources
According to the data, the modality of the course, that is, face-to-face, entirely online,
hybrid, or HyFlex, determines how much-differentiated learning and instruction is provided.
Online Courses and Differentiation
Several interviewees discussed how remote learning during the COVID-19 pandemic
influenced their use and types of resources and assignments. For example, Chloe said, “I had to
rethink everything. I recorded my lectures on Zoom, made video demonstrations, assembled free
online resources, and facilitated interactive activities to support my student’s learning styles.”
She added that the pandemic transformed how she teaches college-level math, saying, “I still use
the course assets I created for remote learning for all the classes I teach today.”
Similarly, Lisa indicated remote learning was “the catalyst for a much-needed change.”
During the pandemic, she designed open-ended learning activities and assignments, allowing her
students to demonstrate their understanding in different ways, such as through written
assignments, video presentations, and creative group projects. Lisa indicated that these new
instructional supports enabled her students to “develop their strengths and interests while also
challenging them to try new methods of expressing their understanding.”

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In-Person Face-to-Face Instruction
Jonathan at Fishman College spoke about course modality frequently throughout the
interview, indicating his ability to support his students better for in-person instruction than online
modalities. He believes it is easier to offer one-on-one consultations, peer tutoring, and study
groups to support students who need extra help since they can interact with him in person rather
than on Zoom. Jonathan shared that checking student work for online classes is difficult and
often “impossible since most students lack the technology needed to display their work
adequately over the internet.” Jonathan added that online courses make it more challenging to
assess students’ understanding of mathematical concepts and provide timely feedback than in-
person classes. He also pointed out that teaching math in person allows for more significant
interaction and engagement between him and his students. Jonathan said, “in a physical
classroom, I can easily observe and assess my student’s understanding of the concepts being
taught in real-time and provide immediate feedback, then adjust instruction accordingly.
Jonathan expressed that he isn’t opposed to online learning spaces and admits that online
instruction has advantages. Still, in-person instruction offers unique opportunities for his students
to learn and engage with mathematics more meaningfully.
HyFlex Course Modality
During the interview, Philip mentioned that his institution piloted several HyFlex courses
during the previous semester and volunteered to teach an introduction to statistics course using
the HyFlex format. Philip described HyFlex as a course that allows students to choose how they
participate, either online, in-person, or a combination of both. In addition, Philip shared that “my
students have hectic lives and have lots of non-academic responsibilities outside of class.
Choosing the learning mode that best fits their needs and schedules allows them to balance their
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coursework with these responsibilities.” He also shared that HyFlex increases accessibility since
students who might otherwise have difficulty attending in-person classes, such as those with
disabilities or transportation issues, can still participate online. Although the complexity of
simultaneously teaching multiple learning modes creates additional technological challenges,
Philip admitted that “the benefits of offering HyFlex math options to students outweigh those
difficulties.”
Faculty Are Unfamiliar With Differentiated Instruction
Fifty percent of participants either did not know what differentiated instruction was, had a
vague idea of the concept, or made interpretations of what they thought it was. For example, at
the onset of the interview, Robert commented, “I think I know what differentiated instruction is
but can’t be certain. I have my idea of what it is.” Thomas indicated, “I know what it is, but I
have to think if I am implementing those techniques in my classes.” However, Thomas did
elaborate on some instructional techniques that supported differentiated learning in his
classroom. Chloe has an EdD and is the department chair at Silver Coast College. She shared that
many of her colleagues, including the part-time faculty, are “well-versed in their specialized
content areas” but are not necessarily “equipped with effective instructional strategies.”
Jennifer said her college has an office that advocates for faculty professional
development. Still, very few programs they offer focus on differentiated learning techniques
specific to math instruction and AB 705. While many respondents provided evidence of
implementing differentiated instructional practices in their classes, they fell short of describing
what they do to address learning diversity. In addition, Cynthia provided a list of institutional
barriers she believes are the most significant regarding implementing differentiated instruction.
These barriers include lack of time, insufficient resources, restricted access to differentiated
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materials, cross-disciplinary collaboration, difficulties producing resources, and inadequate
training and professional development.
Summary of the Data for Research Question 2
The research question investigated how community college math instructors differentiate
the curriculum to meet students’ diverse learning needs and skill gaps while covering all required
course content. The study found that instructors utilized various strategies to meet their students’
needs, including collaborative learning strategies, course pacing, assessment strategies,
truncating the curriculum, course modality, second-chance learning opportunities, and
differentiated instruction. Cooperative learning strategies, such as group work and peer-to-peer
teaching, were commonly used to help students learn from and support each other. Instructors
also adjusted course pacing to accommodate students’ varying levels of preparation, ensuring
that all students could keep up with the material while still being challenged appropriately.
Furthermore, assessment strategies were also used to monitor student progress and adjust
instruction as needed, including formative assessments and regular feedback.
Truncating the curriculum was another strategy used by instructors, where less critical
content was removed to allow more time to focus on essential concepts. Course modality was
also an important consideration, with instructors using online and hybrid formats to better meet
the needs of non-traditional students. Second-chance learning opportunities, such as retakes or
additional assignments, were also provided to help struggling students catch up and succeed.
Some instructors reported unfamiliarity with differentiated instruction, suggesting a need for
more professional development and training in this area. Overall, the study found that
community college math instructors utilized a range of strategies to meet their students’ diverse
learning needs and skill gaps while still covering required course content.
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Additional Instructional Strategies
After collecting the data, it was evident that all interviewed faculty could not reasonably
discuss the alignment of their practices to any knowledge level framework or methods of
instruction like those described by Anderson and Krathwohl (2001), Merrill (2002), or
Tomlinson (2017). The participants did not discuss aligning instructional strategies with factual,
procedural, conceptual, and metacognitive knowledge, nor did they know Merrill’s five
instruction principles or Tomlinson’s methods of instructional differentiation. However, specific
strategies to increase knowledge, in general, were heard upon further questioning. The researcher
then aligned their responses to the individual knowledge levels and the five principles, but the
interviewed faculty did not do this on their own. Some general takeaways are that three-fifths of
faculty use direct lecturing at least 75% of the time for classes scheduled in two-hour blocks,
whereas the remaining two-fifths lecture 50% or less. Lecturing directly to students typically
builds factual and procedural knowledge (Anderson & Krathwohl, 2001) and aligns with
Merrill’s (2002) third principle. For the interviewees who use other learning strategies besides
direct instruction, the researcher grouped them to align with the knowledge levels described by
Anderson and Krathwohl (2001) and Merrill (2002).
Strategies That Foster Factual Knowledge
The section presents the participants’ instructional strategies that build factual
knowledge.
The Direct Instruction Approach
The data indicate that direct instruction is the most ubiquitous form of facilitating factual
knowledge in transfer-level math courses. However, some participants described their
instructional style as “traditional,” which typically involves lecturing on a particular
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mathematical concept, demonstrating how to solve a specific problem, and leading the class
through examples and exercises to reinforce learning. For instance, Philip said, “I am somewhat
of a traditionalist; I use the Socratic method, with small bursts of group work when appropriate,
but mostly I lead them through the material for the day.” Similarly, Thomas said, “I present the
relevant definitions and do a couple of examples first, then the students gather and groups and try
exercises on their own. Throughout the class, we’ll follow this pattern a few times.” Finally,
Jennifer said, “depending on the complexity of the topic, I might lecture the entire time or mix in
other forms of instruction other than direct lecturing.”
Supplemental Guided Notes and Scaffolding
The participants shared several additional instructional strategies that aligned with
accumulating factual knowledge in students. For example, some instructors provided PDF
guided notes ahead of class that organized the content with definitions, theorems, axioms, and
some worked examples but did not necessarily copy the content from the class lecture. These
notes function more as supplementary resources that students can bring to class, like a “cheat
sheet” or “formula sheet.” Utilizing these supplemental notes decreases students’ time copying
notes, creating additional class time for practicing problems.
Another strategy used to augment direct lectures was providing guided notes for
scaffolding. The respondents described guided lecture notes as a type of note-taking system that
provides a structured outline of the lecture material, which students can add more detail to during
the class. The outline typically includes key concepts, definitions, and important theorems or
formulas. For example, Chloe said, “I upload guided notes to Canvas in advance of class, then as
we cover the material in class, my students interactively write in the notes. As a result, they can
look ahead and prepare questions.” Additionally, Lisa discussed that her guided lecture notes
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often included questions such as “what is the main idea of this section?” or “what is an example
of how this formula is used?” Lisa believes these questions help her students stay engaged and
focused during the lecture and provide a helpful framework for later studying and reviewing the
material.
Building Mathematical Vocabulary
Some interviewees expressed their use and emphases of deliberate language and
vocabulary to get their students more accustomed to the vernacular of mathematics. For example,
Robert indicates that he gives his students short, low-stakes quizzes that test their ability to recall
definitions and phrases. In addition, he provides his students with a formula sheet containing all
the definitions needed for success in a particular chapter or section. Robert shared that Clear
Mountain College has a large student population whose native language is not English and
believes that “offering definition quizzes help English language learners become more familiar
with math’s expansive lexicon.”
Some participants indicated that when lecturing, they often take periodic breaks to check
for understanding throughout a lesson using the Socratic dialogue method. Philip described the
Socratic dialogue method as “a questioning technique that encourages critical thinking and deep
understanding of a subject.” Philip uses this method to ask students to explain their reasoning
behind a particular solution and then asks follow-up questions to challenge assumptions and
encourage deeper thinking. Additionally, he presents a problem and asks his students to identify
the concepts and steps needed to solve it. He indicated that engaging the students this way helps
them “clarify and refine their understanding.”

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The Accessibility of Course Materials
Finally, some additional instructional strategies the faculty mentioned were color coding
notes, lecture slides, and Canvas communications according to accessibility standards. The
faculty shared that highlighting essential concepts, relevant definitions, and results of theorems
with bold, colorful fonts supports visual learners and increases accessibility for students with
visual impairments.
Strategies That Foster Conceptual Knowledge
In a math class, conceptual knowledge refers to understanding the underlying concepts
and principles that govern mathematical operations and relationships. Conceptual knowledge
often is the logical next step once factual knowledge is established. For our participants, the
formation of conceptual understanding generally took place after the direct lecturing phases of
instruction. Some examples of how faculty cultivate conceptual knowledge were collaborative
learning exercises such as “think, pair, share,” faculty-led math workshops, and facilitating
discussions focused on linking previous, current, and future content. “I start every class meeting
with the phrases ‘where we were, where we are, and where we are going,’” said Chloe. She
thinks holding discussions at the start of each class meeting helps her students “recalibrate our
tasks and link old and new concepts.” This section presents the instructional strategies the
participants utilize to foster conceptual knowledge in their students.
Engaging Students in Dialogue
Conversations with students, group discussions, looking at student work, and analyzing
solutions to problems in group settings are more ways participants curate conceptual knowledge
with their students. For example, Jonathan shared that after a solution is demonstrated, he will
facilitate a discussion with his students, asking them to identify alternative methods and
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processes to find the answer. “Sometimes we forget that there are numerous ways to solve,
understand, and conceptualize math problems. It’s important to let students express their ideas
even if they are inaccurate,” says Jonathan. Likewise, Dennis stated, “one of the best ways to
measure a student’s ability to conceptualize and understand an idea is to discuss it with them,”
adding that “if they can explain it clearly, they can usually compute it.” Cynthia also shared
similar remarks to Dennis, saying, “when they can’t explain it using words, they probably don’t
have the concept yet.”
When interviewing Thomas, he shared that “when students understand the concept
underlying the material, that’s when critical thinking occurs.” He believes that students with a
solid conceptual understanding can solve more complex math problems—even if presented in
unfamiliar ways. Thomas said, “I try to have my students reason through problems instead of just
applying memorized rules.”
Some study participants shared that when they demonstrate solutions to the class, they
ask their students to call the “play-by-play.” For example, Cynthia shared that at the onset of
solving an exercise, she asks her students, “what is a good first step?” She revealed how
surprised she is with the variety of responses she gets. This variation of ideas allows her to
“debunk inaccurate suggestions” and “try-out” alternative methods and see where they lead. She
then gives real-time feedback so students can “explore options” promptly. Cynthia believes this
method “brings student ideas into the fold,” not just “hear and see the way I want them to
understand the problem.”
Solving Real-World Applications
Another theme that emerged during the interview process regarding conceptual
knowledge is linking abstract mathematical concepts to applications found in the “real world.”
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Some participants, particularly those that teach statistics, stressed the importance of “making
connections to real life phenomenon” and “interpreting results into meaningful inferences.”
Jennifer, Philip, Dennis, Lisa, and Chloe all teach or have taught an introductory statistics course
in the AB 705 era. Although they expressed their thoughts differently, a common notion was that
a student’s ability to calculate statistical findings correctly is less important than their ability to
interpret those numbers reasonably and accurately. For instance, Dennis said, “if my students can
understand what the outcome of the computation means, I’ve done my job.” Lisa said, “using
formulas properly is important, but understanding what they communicate could be more
important. So, I focus on that.”
Each of the following quotes are centered on the development of conceptual knowledge.
For example, Jennifer said the following
By connecting my course content to the [real world], I hope my students can better
understand the practical implications of the mathematical concepts they learn. Showing
my students how to calculate their taxes, understand compound interest, or interpret
statistical data might help them make better financial decisions in the future.
Moreover, Philip said
I always try to connect theory to practice so the students can learn how to apply concepts
and develop problem-solving skills. If I can help build an appreciation for the importance
of math in various fields, perhaps they’ll be inspired to pursue careers in STEM. We need
more STEM students.
The Implementation of Technology
The use of technology in the classroom is another procedural instructional strategy that
was mentioned by half of the interviewees, especially those who teach college algebra,
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trigonometry, and introduction to statistics. For instance, Dennis said he relies heavily on a free
online graphing utility, desmos. “Connecting a function and its graph has never been easier,”
says Dennis. He added that in his experience, students often don’t connect the shape of a graph
to the form of an equation. Dennis praised desmos for minimizing the “absorption time” needed
to learn, adding that “intuitive to use, and my students quickly become very proficient.” He also
shared that desmos has prompted him to rethink how he teaches algebra. Dennis also commented
on Desmos’ ability to animate transformations of graphs by tweaking parameters. “Students can
see with their eyes the effect of altering the various parameters of an equation. They can play
around and see the outcome instantly,” says Dennis. He stressed the importance of incorporating
desmos by noting, “I sketched every graph by hand in the past. This wasted way too much class
time. With desmos, I can allocate more time to other important issues.”
The Cross-Curricular Linkage
Two participants mentioned linking problems in their classes to other subjects within the
institution. Jonathan calls this linkage “cross-curricular.” He said, “students would benefit if
instructors could integrate more cross-curricular concepts that appear in other disciplines and
future classes—but it doesn’t really happen.” For example, Jonathan teaches college algebra,
trigonometry, and calculus 1. He said, “the knowledge in these courses builds up in sequence.
The skills you learn in college algebra are used daily in calculus.” When planning his course, he
emphasizes the most important topics for success in calculus. But, he added, “even if some
students don’t plan to take calculus, I assume they will one day, and consider this when
organizing my course content.” Jonathan explained that applying abstract algebra concepts to a
real-world application is an important skill to develop in students, but linking the course content
to calculus is his focus.
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Strategies That Foster Procedural Knowledge
When the faculty supplied responses to the interview protocol questions, they alluded to
procedural knowledge but did not directly use that language. When asked about what
instructional strategies they utilize in their classroom to assist the students in need of support,
several themes came to light, including the instructional methods known as “chunk and chew,” “I
do, we do, you do,” and “a gradual release of responsibility.” Several respondents described how
they interlace direct instruction with frequent breaks, allowing the students to “digest the
concept” or “try a similar example to the one just demonstrated.” One participant, Chloe,
referred to this method as “chunk and chew.” She said, “my math teachers did this when I
learned algebra, so I use it with my students.” Chloe believes the chunk-and-chew method allows
her students to see a demonstration, then immediately try it themselves. “Students just need
practice, and the more they practice a procedure, the more they understand the concept,” says
Chloe.
The Gradual Release of Responsibility
Another instructional technique that facilitates procedural knowledge described during
the interview process is “I do, we do, you do,” also known as the “gradual release of
responsibility” method. The gradual release of responsibility is a teaching strategy that gradually
shifts the responsibility for learning from the teacher to the students. This strategy is commonly
used in higher education to help students become more independent and self-directed learners.
The study participants describe this technique as “turning over the reins” and “putting the pen in
the hands of the learner.” Lisa described the gradual release of responsibility technique as “a
progressive transition from direct instruction to students doing the work themselves.”
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Moreover, the faculty shared that these methods allow students to “take control of their
learning” and not just be “told what to do.” Philip said, “sometimes students have the concept but
can’t algebraically manipulate the symbols. The rubber meets the road when the students do the
work themselves.” Philip also shared some insights into the links between conceptual knowledge
and procedural knowledge, saying that
It is important to note that procedure alone is insufficient to completely understand an
idea in math. Students must also develop an understanding of the concept, which involves
a deeper understanding of mathematical ideas and relationships. For success in math, our
students need a firm grasp of processes and concepts.
Showing Knowledge With Personalized Whiteboards
Most participants made inferences about students’ ability to manipulate algebraic
expressions and equations in response to the protocol. Jonathan said, “having a solid foundation
in the order of operations is vital for success in my classes.” He revealed that he dedicates extra
time during his lecture to helping students improve their ability to apply arithmetic operations in
the correct sequence. Jonathan said, “I have a classroom set of small personal whiteboards. Each
student has a pen. They do the work, they show me, and I give instant feedback when there is an
operational misunderstanding.” This technique has transformed how Jonathan teaches his
courses, saying, “you’d be surprised how fast I can correct long-standing PEMDAS errors and
get my students back into the game.”
Collaborative Learning Activities
Other faculty shared that having their students work in groups is a very effective way to
increase procedural knowledge, primarily when the task engages students in process-orientated
objectives where they work on a procedure and get real-time feedback. Jennifer shared, “in a
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class of sixty students, the skill level varies from student to student. The highly skilled students
can help the low-skilled ones.” In addition, she thinks that students sometimes learn better from
their peers than from an instructor since the power dynamic between student and instructor isn’t
present. She added that “each student has a unique way of approaching problems. When they
collaborate, the students get exposed to different strategies. This is helpful.”
Jennifer described a group activity she often does in her class. She provides her students
with problems that have already been solved. Each problem carefully lays out the exact steps
taken to find a solution. Some of the exercises have correct answers, while many are inaccurate.
But, she noted, “to the untrained eye, the math looks sound.” She then asks her students to
analyze each step of the solution carefully, determine if there is a misstep, and then identify what
went wrong. She said, “sometimes the errors are very subtle, sometimes I make them egregious,
but I try to infuse common mistakes students often make.” Jennifer believes that having her
students analyze a worked solution in groups not only builds camaraderie within the students but
also allows them to identify “common procedural errors” to avoid when they go to solve
problems independently on homework, quizzes, and exams.
Computational Technology Assistance
In Robert’s statistics course, he allows his students to use graphing calculators to help
compute various statistical quantities. He talked about how he shows his students the formulas
that guide the theory but doesn’t focus on their computational abilities; instead, he has his
students use technology to make the numerical findings as “accurate as possible.” In addition,
Robert uses a statistical software called SAS. This software helps students analyze data faster by
creating graphs, charts, and tables. Similarly, when discussing her statistics class, Jennifer said,
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“calculators and computers reduce the computational burden, allowing my students more time
for the exploration of statistical concepts while accelerating lengthy procedural steps.”
Strategies That Foster Metacognitive Knowledge
In a math class, metacognitive knowledge involves reflecting on one’s mathematical
problem-solving processes, monitoring one’s progress in understanding mathematical concepts,
and evaluating mastery of mathematical skills. The participants did not use metacognitive
knowledge terminology during their interviews; however, some responses did align with
instructional strategies that foster metacognitive knowledge. Several themes became apparent as
the data were analyzed and presented below. The major themes were assessment retakes, error
tracking and analysis, personal reflection, goal setting, synthesizing, increasing student
awareness, and mastery learning. The most discussed instructional strategy was allowing multi-
attempt assessments to strengthen students’ understanding and metacognitive knowledge.
Second Chance Learning Opportunities
The interviewees described a multi-attempt assessment as “a tool to get students re-
engaged with the material, especially if they received a bad grade.” Lisa, from Hughes City
College, described how she uses multiple-attempt exams to foster mastery learning. A setting in
the courseware allows her to determine the number of times a student can take an assignment,
quiz, or exam. She shared that her students get three tries for lower-stakes formative quizzes and
two attempts for higher-stakes summative assessments. “Allowing multiple attempts helps my
students see the value of incremental improvements. Most do not achieve a perfect score on the
first attempt, but by continuing to work and progress, they can eventually achieve mastery of the
material.” She admits that sometimes convincing her struggling students to participate in extra
attempts can be challenging but provide a benefit. Lisa indicated that her students must retake the
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entire assessment, not just the questions they missed. She explained that these policies create an
opportunity for mastery learning since her students can take the feedback from their first attempt,
research the questions they got incorrect, practice similar examples to prepare for another
attempt, and try the assessments again.
Exam Corrections and Error Analysis
Allowing students to submit test corrections to earn additional exam credit is another
strategy the interviewees discussed. For example, Dennis at Vannote Community College creates
optional test correction assignments. “I want to ensure that my students learn from their
mistakes,” says Dennis. Moreover, Dennis believes that test corrections “invite students back
into the learning process.” He added that he returns the exams to his students after an exam is
initially graded. Then, while working in groups or with a campus tutor, his students go back and
correctly solve every problem on the exam, not just the incorrect ones. One week later, Dennis
collects the “updated exam” and issues “redemption points.” Dennis shared the following quote
regarding why he offers class text corrections.
As an instructor, I aim to create as many pathways to success as possible. One path is
allowing students to correct the problems they missed on their exams to increase their
grades. Doing test corrections by revisiting the problems set is an excellent way of seeing
the error in their understanding. From there, they can make the necessary adjustments to
complete the problem correctly.
Dennis also said that he had his students write complete sentences about what was needed
to solve the problem correctly. He believes having his students describe their errors by writing
their thoughts in words helps connect the symbolic forms of mathematics to English words, a
skill Dennis asserts is “lacking in most math courses.” Several participants used a form of
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assessment correction, but Dennis was the most transparent about implementing this strategy in
his classes.
Reflection Assignments and Online Discussions
Another prominent theme that emerged from the protocol questions is using reflection
practices in discussions or essays to foster cognitive knowledge in students. For instructors who
teach purely online classes, that is, classes that do not have officially meet, the use of discussion
board assignments was present. The participants said they use discussion board assignments to
get “students to stop, think, and reply to others using words and sometimes math symbols.”
Many respondents said that discussions “allow students to discuss and reflect” on math-related
topics but not necessarily solve math problems. Jennifer, Chloe, Philip, Jonathan, Robert, and
Lisa all use discussion boards to increase a student’s cognitive knowledge by providing a prompt
to reply to. For example, Robert stated that “I never ask them to solve problems. Instead, I’ll
include a video for them to watch and make comments on.” Robert said that the topics of his
discussion videos include “how to increase students’ self-efficacy, overcoming math anxiety,
deepening the analysis of a concept, or linking mathematics with art and music.” Robert added
that using discussions “breaks the pattern of learning and assessing knowledge. Allowing
students to describe math using words can help develop critical thinking skills.”
On the other hand, Philip and Chloe from Silver Coast College use their discussion
boards to have students analyze the solutions to problems and provide commentary with error
analysis. Chloe indicated that having her students describe inaccurate steps and identifying errors
using words helps to “better socialize my students in the language of mathematics.” Since Chloe
and Philip work at the same institution, some of their content and strategies tend to align. Chloe
stated, “since COVID, our department has aligned many of our course resources, including
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discussion assignments on Canvas. It’s a nice change of pace from solving problems using
algebra.” Philip shared that reading his student’s thoughts and opinions provides another
opportunity for him to get to know his students more personally and respond to their needs
quickly and accurately.
During a regular 16-week semester, Philip assigns eight discussions—one every 2
weeks. Four of the eight discussions center around a self-reflection assignment. He asks his
students to rate their performance, identify what he can do better as an instructor, and what his
students can do better to improve their performance. Philip also asks his students to set short-
term goals that can be accomplished before the following reflection prompt. “When I read their
replies, I can adjust the course pacing, content, and assignments much faster,” says Philip. He
added that students take greater responsibility when they reflect on their progress and articulate
their needs. Philip also indicated, “although some students complain about discussion
assignments, most of my students appreciate the chance to offer their opinions about the class.”
Creating and Synthesizing Mathematics
According to Anderson and Krathwohl’s revised taxonomy of learning (2001), the
highest level of knowledge is “Creating,” which involves using existing knowledge to generate
new ideas, products, or ways of viewing things. Creating (or synthesizing) was an instructional
strategy that two-fifths of the faculty said they used. For example, Cynthia described a group
exercise that involves “the creation of problems that generate specific outcomes.” For example,
when her class is learning how to solve quadratic equations, the students are shown several ways
to achieve this, such as factoring, using the square roots method, completing the square, and
using the quadratic formula. During the interview, she noted that the solutions to quadratic
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equations come in several forms; “either as two unique real numbers, repeated real numbers or
complex conjugates.”
Cynthia said, “From afar, it’s difficult to determine which solution any given equation
will have without doing the work.” So, while her students were in small groups, she asked them
to create equations that generated one of the specified outcomes. She has her students “work
backward, from the end to the beginning.” She added that she uses some problems her students
generate on future quizzes and exams. “They have more skin in the game if they know they are
creating the exam problems,” said Cynthia. Cynthia believes that asking her students to create
problems that output a specified result “closes the loop—the students are now creating the
problems they’ll eventually solve.” Cynthia also indicated that generating questions requires her
students to reflect on their learning process and consider how to evaluate their knowledge. She
said, “this skill can help my students become more self-aware learners, which can improve their
performance over time.”
Robert also asks his students to generate math problems from scratch to cultivate
metacognitive knowledge. For example, before a big exam, Robert asks his students to compile a
bank of exercises from each section covered in the upcoming assessment. He then uses the
student-generated list to create study guides and exam problems. “When students create their test
questions, they need to think about the underlying concepts in greater depth. This process can
help them solidify their understanding of the material and identify areas where they may need
more practice,” says Robert. In addition, he added, “I feel it’s important for students to have
more ownership of their learning.” Robert believes this sense of ownership can lead to increased
motivation and a willingness to put in more effort to understand the material.

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Strategies Aligned to Merrill’s First Principles
This section presents the data that aligns with Merrill’s first principles of instruction
(2002). Many of the techniques and instructional strategies presented above are also included in
this alignment. It is important to note that Merrill’s first principles, like Anderson and
Krathwohl’s revised Bloom’s taxonomy, are hierarchical structures one progresses through from
fundamental levels upward to higher levels of knowledge and instruction.
Principle 1: Problem Centered
Principle one is the engagement and application of knowledge to real-world phenomena.
Merrill (2002) argues that learning is promoted when learners are engaged in solving real-world
problems. The data suggest that some instructors implement principal one in their classes,
particularly those teaching statistics. The statistics instructors indicated that drawing connections
to the real world is of top priority, more so than procedural and factual rigor. Understanding how
to interpret statistical results into meaningful inferences is a highly desired learning outcome for
their students. Some instructors use computer technology to assist students with tedious
computations so that more focus can be placed on the application of the concept rather than the
accuracy of their arithmetic.
Jonassen (1999) suggests that learners will assume ownership only if the problems to be
solved are interesting, relevant, and engaging. For example, some faculty shared that they
continuously update their problem sets to include personally relevant and meaningful topics for
their students. Some respondents disclosed that they assign group projects where their students
choose a topic appealing to them, conduct an experiment, calculate relevant statistical data, and
present their findings to the class. Other instructors use online discussion boards to gather
personal information from their students like their hobbies, interests, and academic aspirations to
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form a deeper connection. These instructors use this information to better link students’ interests
to the topics found in the problem sets. This linkage is not as emphasized for the faculty
participants that teach college algebra. Some respondents shared that they focus more on the
conceptual and procedural skills needed to succeed in sequential courses like calculus than apply
the concepts to the outside world.
Principle 2: Activation
Merrill’s second principle is described as activating new knowledge. Acquiring the
information isn’t enough to promote learning. Learners must also be able to link it to pre-existing
knowledge and mental schemata (Merrill, 2002). For study participants who teach college
algebra, achieving this can be difficult because of the inclusion of underprepared students in their
classes. However, these faculty do utilize some strategies that develop activation. For example,
many participants shared that they changed their course pacing to accommodate students with
low skills. While some faculty admit that slowing the course may stifle the learning of their
advanced students, they also recognize that slowing the pace creates extra time they spend
reinforcing fundamental conceptual and procedural knowledge needed for success in future
topics.
In addition, some college algebra instructors include a comprehensive review section at
the start of the semester called “prerequisite topics.’ These prerequisite topics include basic
arithmetic, the order of operations, fractions, properties of exponents, factoring principles, and
solving equations. It is assumed that most students are somewhat familiar with these topics. The
prerequisite problems for highly skilled students reactivate prior knowledge already acquired,
while lower-skilled students activate this knowledge for the first time. Jonathan shared that
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“assigning prerequisite material guarantees that all students in the class have studied this material
and are better suited for the chapters ahead.”
Finally, some faculty use classroom discussions to activate and link previous knowledge
to new knowledge. For example, at the start of each class session, Chloe uses the phrase “where
we were, where are, and where we’re going?” This strategy aligns with activating new
knowledge from existing knowledge. Chloe achieves this by facilitating a conversation that
explicitly addresses some of the past concepts students should know, discusses what knowledge
will be learned that day, and foreshadows how that knowledge will be applied to future lessons.
Principle 3: Demonstration
The third principle is often characterized as the “show me” principle and addresses the
role of proper demonstration in learning. According to Merrill (2002), when delivering content,
instructors should incorporate multiple demonstrations of the concepts to provide context and
deepen learners’ understanding of its application.
According to the data, the third principle is the most ubiquitous instructional strategy
among the study’s participants. Direct instruction in the form of demonstrative lecturing is used
by all respondents to some degree. The interviewees use this instructional methodology to
introduce new definitions, explain concepts and demonstrate how to solve problems. Some
faculty use a “chunk and chew” method where longer chunks of direct instruction are woven
together with small breaks where students can (chew) practice similar problems to the
demonstration. Students may also be encouraged to reflect on newly acquired knowledge. Other
faculty utilize an “I do, we do, you do” methodology. This methodology involves an instructor
demonstrating a procedure. The student then attempts the process with support, and finally, the
student tries to solve the problem independently without the aid of others.
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The use of technology such as Desmos also aligns with the demonstration principle.
Many participants use applications like desmos to create graphs and model data. One faculty
claimed that desmos had transformed the way he teaches. For example, Dennis said, “this
technology allows students to “bring life to lifeless equations,” and “see the cause and effect of
varying quantities in real-time.” The participants also shared that integrating desmos into their
lectures saves valuable class time. Some interviewees believe using technology in class can also
help create an engaging and dynamic learning environment, allow students to interact with
mathematical concepts hands-on, and help spark interest and enthusiasm for math.
Principle 4: Application
The fourth principle of instruction centers on knowledge application and comes in the
form of interactive problem-solving and task performance. Merrill (2002) believes learning is
promoted when the practice and the posttest are consistent with the learning objectives.
Typically, this principle is implemented using formative and summative assessments where
students must recall or recognize, locate, name, describe, identify new examples, and predict a
consequence of applying a process correctly. How instructors assess their students and the
policies that govern those assessments were discussed frequently throughout the data collection
process.
Most transfer-level faculty utilize online courseware to summatively and formatively
assess their students. Some faculty shared that they select exam problems directly from the
homework questions. Jennifer said, “if my students practice using the homework, they typically
do fine on the exams.” Lisa added, “using similar problems in exams ensures that my students
are being assessed on the skills they have been practicing.” In addition, Chloe admits that she
aligns her homework problems with exam questions. She believes that students who have “put in
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the effort” to master the homework problems should be rewarded for their hard work on the
exam and vice versa.
Fifty percent of participants shared that they use multi-attempt assessments and second-
chance opportunities to reinforce learning and promote mastery. Using a multi-attempt
instructional strategy for assessments aligns with principle four because it allows students more
opportunities to demonstrate, apply, and strengthen the knowledge they have learned. Settings
located within the various courseware allow faculty to determine the number of times their
students can access quizzes and exams. The idea is that students get feedback on their initial
attempt, identify areas for improvement, practice, and try the assessment again. Some
respondents indicated that they do not use the courseware to assess their students but allow
second-chance opportunities. Instead, they use traditional examinations where students are asked
to write their solutions on paper. Once the assessment is graded, the instructors encourage
students to submit test corrections, which involves redoing any incorrect problems to increase
their original exam scores.
Principle 5: Integration of New Knowledge
The fifth and final principle, integration, pertains to personal meaning and context.
Merrill (2002) believes learning is promoted when learners are encouraged to integrate new
knowledge or skill into everyday life. An analysis of the data indicates that principle five
instructional strategies are the most underrepresented by the faculty. As mentioned above, some
faculty, particularly statistics professors, prioritize linking theory to practice. They value the
application of knowledge and its relevance to the real world. Others create group projects where
students select a topic of interest, apply their knowledge, conduct an experiment, and explain the
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results. Finally, some faculty use discussion boards to gain insight into their students and
integrate that information into their curriculum.
Creating, revising, editing, synthesizing, and refocusing are critical final phases of a
learning experience (Merrill, 2002). The data shows that the interviewees implement several
strategies that align with these characteristics. For example, regarding the skill of creating, some
professors ask their students to create equations that generate a specific outcome when solved.
For example, the student could be asked to create a rational equation that has one solution, two
solutions, or no solution. In addition, some instructors allow their students to develop formula
sheets to assist them on high-stakes exams, promoting information synthesis. In contrast, others
revise knowledge by allowing second-chance opportunities and exam correction to improve
student scores.
Synthesizing information is another way students can integrate their knowledge to higher
levels. Many interviewees utilize group work to improve students’ ability to synthesize
information. These faculty encourage their students to work in small groups to share their
knowledge and perspectives on a topic. They believe that collaboration helps the student learn
from each other and build on each other’s ideas leading to the synthesis of new and innovative
ideas that may not have been possible if individuals worked alone. One faculty member shared
that he uses case studies to help his students synthesize knowledge from different disciplines,
such as math and science or math and business.
Conclusion
The summary of data gathered from faculty interviews revealed valuable insights into the
implementation and impact of AB 705 and promising instructional strategies. The discussions
highlighted several key themes, including concerns about the implementation process, perceived
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benefits and drawbacks of AB 705, and suggestions for improvement. The data also indicated
several faculty instructional strategies to differentiate their lessons, learning, and outcomes.
Many faculty members expressed concerns about the lack of resources and support provided for
implementing the changes required by AB 705, such as developing a new curriculum and
providing additional student support services. However, most faculty members agreed that the
legislation had positive effects, including improved student outcomes and increased equity,
particularly for non-STEM/Business majors. The findings from these interviews provide
valuable insights into the implementation and impact of AB 705 and offer suggestions for
improvement to benefit both faculty and students, which will be discussed in Chapter Five.
The researcher also identified several other themes worth mentioning at this time that
encapsulate the findings from the research. All faculty agreed that most students in their classes
are underprepared and could use some form of remediation. Other participants noticed that their
students lacked the basic study skills needed for success at the college level. In addition, math
faculty generally teach how they were taught, relying heavily on direct instruction. While some
faculty shared that they try to incorporate other forms of instruction than direct instruction, many
interviewees still rely on that technique. The data also suggests a general lack of deliberate
strategies aligned with different knowledge levels. Only two participants shared that they
knowingly create learning experiences that promote metacognitive knowledge. Only one
participant mentioned Bloom’s taxonomy—the predecessor to Anderson and Krathwohl’s
theory. This lack of knowledge meant that the data had to be categorized on behalf of the
participants since they were not aware of the theories of Anderson and Krathwohl (2001), Merrill
(2002), or Tomlinson (2017).

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Chapter Five: Discussion and Recommendations
Chapter Five presents an analysis of the study’s findings. This chapter aims to
comprehensively discuss the results and draw meaningful conclusions about the data. The
chapter begins by revisiting the research questions and outlining the research design and
methodology employed in the study. Then the researcher summarizes the most significant
findings, highlighting key themes from the data. Next, the discussion focuses on how these
findings contribute to the literature on instructional practices for teaching transfer-level math at a
California community college. Chapter Five also addresses the implications of the results for
policy and practice. Additionally, the researcher considers how the instructional practices
identified in the study can be scaled up and applied in other contexts to improve student success
in math courses. Overall, this chapter provides a rich discussion of the promising instructional
practices of California community college math instructors and their implications for improving
student success in transfer-level math courses in the post-AB 705 era.
Discussion
The implications of this study have significant potential to inform policy and practice in
community college math education, particularly in California. By examining the instructional
practices of community college math instructors who teach transfer-level math courses after the
implementation of AB 705, this study sheds light on the challenges and opportunities facing
math education in California. This study’s findings provide insight into how instructors diversify
their instructional practices to meet the needs of their students. This study also highlights the
importance of providing professional development opportunities for math instructors to enhance
their pedagogical knowledge and teaching skill of evidence-based instructional strategies in
transfer-level math courses affected by AB 705. Finally, the implications of this study can inform
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the development of policies and programs aimed at improving math education in community
colleges and promoting equitable outcomes for all students.
AB 705 has been a significant reform that has changed how math courses are taught at
community colleges in California. A critical challenge that AB 705 brings is the need for
instructors to adapt their instructional practices to accommodate the diverse preparedness levels
of students (Hodges, 2018). This diversity in preparedness levels has created difficulties for math
instructors who must adjust their instructional approaches to address the varying needs of their
students (Nardi & Steward, 2019). Additionally, AB 705 has led to changes in course content
and learning outcomes, requiring math instructors to develop new instructional strategies and
assessment methods (Beach, 2020). These changes may require math instructors to undergo
additional training and professional development to adjust their practices and ensure that their
teaching meets the new standards set by AB 705. However, some community colleges either lack
funding for such training or appropriate funds elsewhere (Lynch, 2018). The data gathered for
this study supports the literature regarding the instructional challenges brought about by AB 705
and is summarized below.
One of the impacts of AB 705 has been the increased access to transfer-level math
courses for underprepared students. As a result, more underprepared students can now take
transfer-level math classes. This change has improved student success rates and decreased time
to degree, which is particularly beneficial for low-income, first-generation, and historically
underrepresented students. However, despite the positive effects of AB 705, the research
participants cite under-preparedness and lack of fundamental math skills as the number one issue
they must contend with in the post-AB 705 era. Some professors see a perceivable difference
between students’ math skills pre- and post-AB 705. Many faculty members shared that these
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“knowledge gaps” have forced them to change their instructional strategies, including altering
the curriculum, adjusting the pace of the course, or in some cases, removing topics because of
insufficient class time. The participants shared that slowing the pace and removing topics to
address knowledge deficiencies is required now but concurrently disenfranchises students with
adequate or advanced math skills. Additionally, some faculty remarked that AB 705 put the
burden of remediating students onto the faculty and thus has notably increased their workload.
The difficulty of teaching students with a broad knowledge base is another major issue
from the data. The faculty said that designing a curriculum that challenges the more advanced
students while providing ample support for those with weaker skills is a considerable
instructional obstacle. Mitigating this “push and pull” can be particularly challenging when the
course covers a broad range of mathematical topics.
Providing appropriate support for students who require it was also identified in the study
as a concern. The data suggest that while some instructors feel their institutions’ academic
support programs provide adequate math support for their students, other faculty claim that their
college does not support their students to the level of AB 705. Several participants claim that
students who should be using academic support do not get it. Moreover, many students
underutilize academic assistance even when their institution offers robust support programs.
Professional development can also help California community college math instructors
mitigate the adverse effects of AB 705 by providing them with the necessary skills, knowledge,
and resources to implement the law effectively. In addition, the findings align with the literature,
which states that effective professional development can help instructors implement new policies
and initiatives, such as AB 705 (Chval et al., 2015). Therefore, investing in professional
development for math instructors can be a viable way to mitigate the potential adverse effects of
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AB 705. More professional development opportunities centered on instructional practices that
assist with implementing AB 705. Finally, most respondents indicated that more funding is
required to train better and staff educational support programs, but a shortage of qualified labor
makes staffing difficult even when funding is available.
The Need for Differentiated Instruction
The data from the interview revealed that only a small proportion of the study
participants have formal training in techniques of instructional differentiation. However, many
faculty use varying degrees of instructional practices that support differentiated learning
regardless of whether they are aware of it. Differentiated instruction is an integral approach to
teaching that aims to help students in diverse learning environments, particularly in the post-AB
705 era, where there is a growing need to remediate students with different levels of
preparedness (Beach, 2020; Hodges, 2018). By using differentiated instructional strategies,
instructors personalize the learning experiences and cater to each student’s unique needs and
abilities—leading to improved learning outcomes and engagement (Tomlinson, 2017).
Additionally, differentiated instruction can help address equity gaps by providing targeted
support for students who have been historically marginalized, such as low-income students, first-
generation college students, and underrepresented minority students (National Center for
Education Statistics, 2019). The data gathered on the study participants indicate the use of
various differentiated instruction strategies, such as flexible grouping, varied assessments, and
tiered assignments, to meet the needs of their diverse students.
The importance of differentiated instruction in mathematics education has been well
documented in the literature. For example, one study found that differentiated instruction
improved students’ attitudes toward mathematics, reduced math anxiety, and increased their
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engagement in the learning process (Nietfeld et al., 2017). Another study demonstrated that
differentiated instruction positively impacted students’ problem-solving abilities and increased
their self-efficacy in mathematics (Perrone et al., 2017). Thus, incorporating differentiated
instruction strategies in post-AB 705 mathematics classrooms may help improve students’
achievement, reduce equity gaps, and promote positive attitudes toward mathematics.
Other Instructional Strategies Discussed
The importance of diversifying instructional practices in postsecondary math education
has been shown to improve students’ attitudes, motivation, and performance in math
(Linnenbrink-Garcia & Patall, 2016). In addition, instructors who use various instructional
methods, such as active learning, peer instruction, and flipped classrooms, can create a more
inclusive learning environment that engages students from diverse backgrounds and fosters their
math learning (Freeman et al., 2014). Therefore, diversifying instructional practices can be an
effective strategy to simultaneously address the challenges brought by AB 705 while supporting
the success of their students.
Unfamiliar With Evidenced-Based Instructional Strategies
California community college math instructors play a critical role in helping students
develop mathematical proficiency and preparing them for success in future academic and
professional pursuits. To effectively do this, instructors need to be knowledgeable about theories
of learning and theories of effective classroom instruction. This knowledge can inform
instructional practices and help instructors create a learning environment that supports student
success. Incorporating learning theories and effective classroom instruction into teaching
practices can improve student outcomes. A study by Willett and Cullen (2019) found that
community college math instructors who used evidence-based teaching practices, such as those
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informed by learning theory and classroom instruction theory, had higher student success rates
than those who did not. The authors suggest incorporating these practices can improve student
engagement and deeper learning and increase student success.
Although the interviewees discussed several instructional strategies, the data indicates
that many community college math faculty do not have a working knowledge of evidence-based
instructional practices or theories of learning, such as those described by Anderson and
Krathwohl (2001), Merrill (2002), or Tomlinson (2014, 2017). Instead, the respondents provided
several examples of teaching practices that could align with some evidence-based practices but
were not specified by name during the discussion. Despite the effectiveness of active and
student-centered approaches to teaching, many of the community college math instructors
interviewed continue to rely on traditional lecture-based methods. Although there may be a
shortage of community college math instructors who implement evidence-based practices (Sato
& Adler, 2017), some professional development programs have successfully improved teaching
effectiveness and student engagement (Prather et al., 2017). Providing more support, resources,
and training for community college math instructors who wish to implement evidence-based
practices may be necessary to address this shortage.
A Strong Need for Increased Professional Development
The study’s findings reveal a need by the faculty for more professional development
aligned with the guidelines of AB 705 that focus explicitly on instructional practices that support
both students and faculty. Moreover, the findings indicate the need for targeted funding for
professional development opportunities. Additionally, the evidence suggests that all essential
stakeholders tasked with implementing AB 705—and similar reforms such as AB 1705—must
have increased access to relevant training, not just professors who teach AB 705-accessible
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courses. Furthermore, college budgets must allocate compensation for faculty to teach more co-
requisite support courses, develop new curricula, and attend statewide seminars. Community
college instructors are generally experts in their content area and may lack the instructional
expertise needed to realign their course content to adjust to the AB 705 mandate (Cavanagh et
al., 2016). The data also underscores the need for educational leaders to create a statewide
professional development effort that better aligns the instructional practices of all 116 California
community colleges to the intended goals of AB 705.
Professional development opportunities can play a crucial role in helping math instructors
in California mitigate the instructional challenges caused by AB 705. One way in which
professional development can help math instructors is by providing them with training in active
learning strategies. Active learning strategies, such as group work and problem-based learning,
have improved student engagement, retention, and success in college math courses (Freeman et
al., 2014). Professional development can also train math instructors to use technology, such as
online learning platforms and digital tools, to enhance student learning, differentiate course
materials, and facilitate effective student communication (Kumar et al., 2021). Finally, the data
suggest additional training on instructional strategies that engage learning styles and skill
diversity will benefit student outcomes in AB 705 accessible math courses.
COVID-19 Influenced Levels of Differentiated Instruction
This study shows that the COVID-19 pandemic and the simultaneous implementation of
AB 705 changed how instructors taught their transfer-level math courses. The COVID-19
pandemic has emphasized the importance of differentiated instruction in community college
mathematics courses, particularly in remote and hybrid settings. With remote instruction,
instructors have had to find creative ways to deliver content and engage students.
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In community college math courses, differentiated instruction can take many forms,
including the use of technology to provide personalized feedback and instruction (Larsen &
Watson, 2019), the incorporation of real-world applications to make the material more relevant
and engaging (Barrera & Ainley, 2019), and the use of small-group activities to provide targeted
support and practice (Lawson & Crooks, 2019). These strategies have improved student
outcomes in mathematics courses (Tomlinson, 2014). The COVID-19 pandemic has only
highlighted their importance in promoting student success in remote and hybrid learning
environments.
The COVID-19 pandemic and AB 705 have both had significant impacts on the
education system in California. AB 705 took effect at the start of the Fall 2019 semester. One
semester later, COVID-19 disrupted the education system with school closures, a shift to remote
learning, and rapid changes in instruction delivery. COVID-19 and AB 705 are distinct
phenomena with unique societal impacts, but their effects are interrelated. One way these events
influence each other is their impact on student enrollment and completion rates. The pandemic
has forced many community colleges to shift to remote learning, making it difficult for some
students to adapt to the new format. This abrupt transition resulted in lower enrollment rates in
some colleges, which could have affected the implementation of AB 705.
The disruptions in education caused by the pandemic led to a decline in the quality of
education students received (Stolzenberg et al., 2021). This decline in education quality may
have adversely affected students’ ability to complete transfer-level courses within 1 year as
mandated by AB 705. Furthermore, the pandemic created challenges in collecting data on
student performance and measuring the effectiveness of AB 705’s implementation (McDowell et
al., 2021). In contrast, AB 705 may have also influenced the response of community colleges to
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the COVID-19 pandemic. By emphasizing the importance of transfer-level courses in English
and math, the law may have encouraged colleges to prioritize the delivery of these courses
during the pandemic. This prioritization may have helped to mitigate some of the adverse effects
of COVID-19 on students’ academic progress.
However, it is difficult to determine the effectiveness of AB 705 on student success since
the data collected on AB 705’s impact was taken from semesters during the pandemic, where
most instruction and learning occurred remotely. Additionally, the confluence of these two
events on one another can make the data unreliable to justify its successes or failures attributed to
AB 705. Therefore, to date, there hasn’t been an explicit connection between the effectiveness of
the state’s policy changes on remediation and the instructional practices inside the classroom.
Centering Faculty Voices
California Assembly Bill 705 aims to improve student success rates in community
colleges by changing how students are placed into transfer-level courses. While the law’s intent
is laudable, the way it was implemented without proper faculty consultation and collaboration
could lead to negative consequences. The primary focus of this research was to center the voices
of math faculty who teach AB 705 accessible math courses and discover what challenges the law
created for them and how they are overcoming those challenges with their instructional practices.
Moreover, the faculty perceptions regarding the effects of AB 705 on instruction related to
student performance are underrepresented in the literature. California Lawmakers have neglected
to recognize that faculty members are the primary stakeholders in college-level instruction and
are well-positioned to provide valuable insight into student readiness for college-level
coursework. Faculty have years of experience teaching and assessing student performance and
should have the opportunity to offer their perspectives on the most appropriate measures for
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predicting course success. Excluding faculty from decision-making could lead to suboptimal
placement decisions that negatively impact student success rates.
Research has shown that involving faculty in decision-making leads to better outcomes.
For example, a study by El-Mekkawy et al. (2018) found that faculty involvement in developing
placement policies resulted in more accurate placement decisions and improved student success
rates. The authors suggest that faculty are best suited to decide on course placement because they
have the most knowledge about the content and skills required for success in their courses.
Furthermore, excluding faculty from the decision-making process can lead to a lack of faculty
buy-in, negatively impacting implementation. Faculty who feel their perspectives were not
considered may be less likely to support the new policies, which could lead to resistance and lack
of compliance. This information is particularly relevant for AB 705, which requires significant
changes in how community colleges place students into courses.
Recommendations
Based on the findings of this study, several recommendations can be made for policy and
practice regarding the instructional practices of community college math instructors in California
who teach AB 705 accessible courses. These recommendations include improving professional
development opportunities for instructors, providing more support for students, and increasing
collaboration among stakeholders.
Faculty Need More Training
Firstly, it is essential to provide ongoing professional development opportunities for math
instructors to improve their pedagogical practices. The professional development should focus on
evidence-based practices for teaching math and include strategies for addressing the needs of
students from diverse backgrounds. Additionally, the professional development should be
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tailored to meet the specific needs of the instructors and the courses they teach and keep them up
to date with the latest research in math education. As noted by Handelsman et al. (2007),
professional development programs must be “sustained, content-focused, and practice-based” (p.
1059) to be effective.
Secondly, colleges should invest in developing and implementing student-centered
instructional strategies that promote active learning and student engagement. One such strategy
is inquiry-based learning, which has improved student achievement and retention in math
courses (Sadeh, 2013). Instructors should also incorporate technology, such as online simulations
and interactive whiteboards, to enhance student learning experiences (Clark & Mayer, 2011). By
implementing these strategies, instructors can create a more supportive learning environment that
promotes student success.
Colleges Must Academically Support Students
Ensuring students have access to appropriate support services to enhance their success in
transfer-level math courses is critical. These services may include tutoring, co-requisite classes,
academic coaching, and counseling. In addition, colleges should also offer workshops and non-
credit courses to help students develop their study skills, time management, and metacognitive
strategies, which are crucial for success in math courses (Hernandez-Martinez et al., 2020).
Colleges can create a more equitable learning environment and promote student success by
providing students with these support services.
A Better Alignment of Policies to AB 705
Colleges should consider revising their assessment policies to align with the goals of AB
705. For example, assessments should be designed to measure students’ skills accurately and
placed into courses appropriate for their skill level. Furthermore, instructors should provide
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students with regular feedback on their progress to help them identify areas for improvement and
promote their success (Cavanagh et al.,2016).
Fostering a Culture of Collaboration
Fostering a culture of collaboration among math instructors, administrators, and staff is
essential. Collaboration can help instructors share best practices, learn from one another, and
provide opportunities for joint professional development. Additionally, a strong partnership
between math instructors and support services staff can help ensure students receive the support
they need to succeed in transfer-level math courses. Colleges can create a more supportive and
successful learning environment by creating a collaborative culture.
Better Preparatory Alignment for Secondary and Post-Secondary Schools
California high schools and community colleges have faced a significant challenge in
preparing students for college-level math courses. The lack of alignment between the
instructional practices and curriculum of high schools and community colleges often leads to
students arriving unprepared for the rigor of college-level math courses. To better address this
challenge, there is a need to develop a more comprehensive approach to aligning instructional
practices and curricula to better prepare students for college-level math courses.
One approach is to develop partnerships between high schools and community colleges to
identify the essential skills and knowledge needed for college-level math courses. These
partnerships could help create a seamless transition between high school and college-level math
courses by aligning both institutions’ curricula and instructional practices. This approach has
been successful in other states, such as Texas, where the University of Texas at Austin
collaborated with high schools to develop a standardized curriculum for high school math
courses that align with college-level math courses (Lee, 2018).
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Another approach is to provide professional development opportunities for high school
and community college math teachers to enhance their instructional practices. Professional
development can help teachers improve their understanding of the expectations and demands of
college-level math courses and gain expertise in teaching the relevant content and skills.
Additionally, it can facilitate communication between high school and community college math
teachers, allowing for the sharing of best practices and the alignment of curriculum and
instructional practices.
Finally, it is essential to ensure that high school students have access to rigorous math
courses that adequately prepare them for college-level math courses. High schools can support
students struggling with math by offering tutoring, peer mentoring, or additional coursework.
Additionally, community colleges can offer developmental math courses that provide
remediation for students who need it while still preparing them for college-level math courses.
Low-Skilled Students Still Need Remediation
Math remediation has long been a contentious issue in community colleges, with some
arguing that it wastes time and resources. In contrast, others say that it is essential for
underprepared students to succeed in college-level math courses. However, in the post-AB 705
eras, the need for math remediation has become more critical than ever. Despite what lawmakers
say, math remediation can help underprepared students develop the foundational skills and
knowledge necessary for college-level math courses. Without these foundational skills, students
will likely struggle in college-level classes, leading to frustration and lower retention rates
(Boylan et al., 2019). Math remediation can allow students to develop the skills and knowledge
they need to succeed in college-level courses, setting them up for success in their academic
careers.
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Furthermore, math remediation can help close the equity gap in community colleges.
Underprepared students are often from underrepresented groups and may lack the educational
resources and support to succeed in college-level courses (Jaggars, 2014). Community colleges
can help level the playing field by providing math remediation, allowing underprepared students
to succeed in college-level courses and achieve their educational goals.
In addition, math remediation can be designed in a way that is contextualized and
relevant to the students’ academic and career goals, which can help increase student motivation
and engagement (Martinez & Klopott, 2016). By contextualizing math instruction to student’s
interests and goals, community colleges can help students see math’s relevance in their lives,
increasing their motivation to learn and succeed.
Summary of Recommendations
In summary, the recommendations outlined above can help improve policy and practice
related to instructional practices of community college math instructors in California in the wake
of AB 705. By providing ongoing professional development, implementing student-centered
instructional strategies, providing support services, revising assessment policies, and fostering a
culture of collaboration, colleges can promote student success in math courses and contribute to
a more equitable and prosperous society.
Future Research
It is important to note that this study has limitations that must be considered when
interpreting the findings. One limitation is that the study only focuses on community college
math instructors in California who are full-time employees and are tenured at their institution.
Moreover, the study only considers the experiences of faculty who teach transfer-level math
courses that AB 705 now grants access to. Another limitation is that only ten faculty participated
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in the interview process. Many participants, including adjunct faculty, could yield more
informative results. Although qualitative research is often not intended to produce generalizable
results, having a large and diverse sample can better understand this population’s range of
experiences and perspectives. Additionally, this study only explores the perceptions and
experiences of instructors and does not consider the perspectives of students or other
stakeholders. Future research should aim to address these limitations and explore the impact of
different instructional practices on student success and outcomes in AB 705 math courses.
The findings of this study suggest that there is a need for further research to explore the
effectiveness of instructional practices in helping students and institutions meet the goals of AB
705. The study found that instructors used various instructional methods, including active
learning strategies, collaborative learning, and technology-enhanced instruction. However, it is
unclear which instructional practices are most effective in helping students meet the goals of AB
705. Future research could explore the effectiveness of different instructional approaches in
improving student success in transfer-level math courses.
Effectiveness of Technology in AB 705 Classes
One potential area for future research is to investigate the impact of technology-enhanced
instruction on student success in transfer-level math courses. The study found that instructors
used technology in various ways, including online homework systems, online resources, and
classroom technology. However, the study did not explore the impact of technology on student
success. Future research could examine the effectiveness of technology-enhanced instruction in
helping students meet the goals of AB 705. For example, the study could compare the efficacy of
traditional lecture-based instruction to technology-enhanced instruction in improving student
success in transfer-level math courses.
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What Instructional Strategies Best Fulfill AB 705 Outcomes
Another area for future research is to explore the impact of active learning strategies on
student success in transfer-level math courses. The study found that instructors used active
learning strategies like group work and problem-based learning. However, the study did not
explore the effectiveness of these strategies on student success. Future research could examine
the effectiveness of active learning strategies in helping students meet the goals of AB 705. For
example, research could compare the effectiveness of traditional lecture-based instruction to
active learning strategies in improving student success in transfer-level math courses.
How Can Professional Development Aid With AB 705 Implementation
In addition, future research could explore the impact of professional development on
instructional practices aligned with the goals of AB 705. The study found that instructors who
had received professional development on AB 705 reported using more student-centered
instructional practices. However, the study did not explore the impact of professional
development on student success. Future research could examine the effectiveness of professional
development in helping instructors align their instructional practices with the goals of AB 705
and improve student success in transfer-level math courses.
The Impact of Class Size on AB 705 Outcomes
Future research could explore the impact of contextual factors on instructional practices
aligned with the goals of AB 705. For example, the study found that instructors who taught high-
enrollment math courses and those with a higher percentage of underrepresented students
reported using more student-centered instructional practices. In addition, future research could
investigate the impact of contextual factors, such as course size and student demographics, on
instructional practices aligned with the goals of AB 705. For example, research could explore
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whether instructors in courses with a high percentage of underrepresented students are more
likely to use student-centered instructional practices and whether these practices are more
effective in improving student success in transfer-level math courses.
Longitudinal Effectiveness of AB 705 on Student Success
A study examining the long-term impact of AB 705 on students’ academic outcomes
could shed light on whether this legislation is achieving its intended goals. For example, the
study could investigate the impact of AB 705 on students’ persistence, retention, and graduation
rates in community colleges, as well as transfer rates to 4-year institutions. By evaluating these
outcomes over a more extended period, researchers can assess whether the initial positive effects
of AB 705 are sustained and whether the reforms have contributed to long-term improvements in
student success. Additionally, the study could explore how the AB 705 reforms have impacted
equity gaps in terms of race, ethnicity, and socioeconomic status. AB 705 was designed to reduce
equity gaps by ensuring all students can access transfer-level math courses. However, it is not yet
clear whether the legislation has achieved this goal. By examining the impact of AB 705 on
different student groups, researchers can assess whether the reforms have reduced equity gaps or
whether additional measures are needed to address disparities in access to transfer-level math
courses.
Conclusion
In conclusion, this study aimed to explore the instructional practices of community
college math instructors in California who teach transfer-level math courses after the passage of
AB 705. The study also wished to identify the challenges these faculty encounters and the
instructional strategies they use to overcome them. This study’s findings suggest a need for a
more student-centered approach to teaching math in community colleges in California. This
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includes providing more opportunities for student-centered instruction, such as inquiry-based
learning and personalized learning experiences that accommodate individual student needs.
Additionally, instructors need to focus on developing math study skills in students to increase
their success in math courses.
Furthermore, the study indicates that instructors should use evidence-based instructional
strategies such as Merrill’s first principles of instruction (2002) and Tomlinson’s model of
institutional differentiation (2017) to promote student learning and success. Additionally, as
remediation laws evolve, professional development opportunities must be adequately funded and
accessible so instructors can improve their instructional practices.
Overall, the findings of this study have significant implications for policy and practice for
California community colleges. Therefore, it is recommended that community college leaders
and policymakers consider the results of this study when making decisions about instructional
practices and professional development opportunities for math instructors. By adopting a more
student-centered approach to teaching math and providing instructors with evidence-based
instructional strategies, community colleges in California can help increase student success and
improve educational outcomes for all students.
Reflecting on the journey that has led me to this point, I am filled with a deep sense of
gratitude and accomplishment. Writing this dissertation has been a challenging yet rewarding
experience—allowing me to delve deeper into my passion for education and mathematics.
Through countless hours of research, writing, and revision, I have gained a greater understanding
of the intricacies of teaching and learning. This dissertation has also been a journey of personal
and professional growth. It has forced me to confront my assumptions and biases and examine
how my experiences as a student and a teacher have shaped my perspective. It has challenged me
135

to step outside my comfort zone, embrace new ideas and approaches, and continually strive for
improvement and innovation.
As I move forward in my career as an educator, I will carry with me the lessons and
insights gained through this study. I am committed to lifelong learning and will continue seeking
new knowledge and experiences to enrich my teaching practice. I am also excited to share the
findings of this study with my colleagues and to contribute to the ongoing dialogue regarding
post-secondary mathematics instruction. In closing, I am proud of the work that I have
accomplished and grateful for the support and guidance of my advisors, colleagues, and loved
ones. This dissertation represents the culmination of my academic journey and a steppingstone
toward a fulfilling and meaningful career in education.

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References
About AB 705. (n.d.). California Community Colleges Assessment and Placement.
https://assessment.cccco.edu/AB 705-implementation
Adelman, C. (1999). Answers in the toolbox: Academic intensity, attendance patterns, and
bachelor’s degree attainment. Office of Educational Research and Improvement, U.S.
Department of Education.
Adelman, C. (2004). Principle Indicators of Student Academic Histories in Post-Secondary
Education, 1972–2000. U.S. Department of Education, Institute of Education Sciences.
Advanced Placement - Postsecondary (CA Dept of Education). (2021). Incentives for Public
High Schools to Provide Access to Rigorous, College-Level Courses.
https://www.cde.ca.gov/ci/gs/ps/apgen.asp
Allen, D., & Dadgar, M. (2012). Does dual enrollment increase students’ success in college?
Evidence from a quasi-experimental analysis of dual enrollment in New York City. New
Directions for Higher Education, 2012(158), 11–19. https://doi.org/10.1002/he.20010
American Association of Community Colleges. (2004). 2004 demographics: Community college
presidents [Electronic fact sheet].
http://www.ccleadership.org/resource_center/demo_snapshots.htm
American Association of Community Colleges (2011). Community Colleges Can’t Deliver for
Us Unless We Deliver for Them, Fact Sheet. American Association of Community
Colleges. http://www.aacc.nche.edu/Advocacy/toolkit/Documents/factsheet.pdf
An, B. P. (2013). The Impact of Dual Enrollment on College Degree Attainment: Do Low-SES
Students Benefit? Educational Evaluation and Policy Analysis, 35(1), 57–75.
https://doi.org/10.3102/0162373712461933
137

Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich,
P. R., Raths, J., & Wittrock, M. C. (2001). A taxonomy for learning, teaching, and
assessing: A Revision of Bloom’s Taxonomy of Educational Objectives. Longman.
Andrews, H. A., & Marshall, R. P. (1991). Challenging high school honor students with
community college courses. Community College Review, 19(1), 47–51.
https:// doi.org/10.1177/009155219101900109
Attewell, P.A., Lavin, D.E., Domina, T., & Levey, T. (2006). New Evidence on College
Remediation. The Journal of Higher Education, 77(5), 886-924.
https://doi.org/10.1353/jhe.2006.0037.
Baker, R. (2016). The effects of structured transfer pathways in community colleges.
Educational Evaluation and Policy Analysis, 38(4), 626–646.
https://doi.org/10.3102/0162373716651491
Baker, L. (2021). Bill Would Require Support Services for Community College Students.
EdSource. https://edsource.org/2021/bill-would-require-support-services-for-community-
college-students/651516.
Bailey, T. (2009). Rethinking developmental education in community college (Issue Brief No.
40). Community College Research Center Publications.
Bailey, T., Jeong, D. W., & Cho, S.-W. (2010). Referral, enrollment, and completion in
developmental education sequences in community colleges. Economics of Education
Review, 29, 255–270. https://doi.org/10.1016/j.econedurev.2009.09.002
Bailey, T. R., Jaggars, S. S., & Jenkins, D. (2015). Redesigning America’s community colleges:
A clearer path to student success. Harvard Press.
138

Barrera, M. E., & Ainley, J. (2019). Differential mathematics instruction through the lens of
equity. Journal of Mathematics Education, 12(2), 1–21.
Beach, K. (2020). AB 705 implementation: A case study. Community College Journal of
Research and Practice, 44(10), 718–723.
Becker, G. (1994). Human Capital: A Theoretical and Empirical Analysis with Special
Reference to education (3rd ed.). The University of Chicago Press.
Belfield, C. R., & Crosta, P. M. (2012). Predicting success in college: The importance of
placement tests and high school transcripts (CCRC Working Paper No. 42). Community
College Research Center, Columbia University.
Bender, S. B., & Hill, K. (2016). Pedagogical considerations for effectively teaching qualitative
research to students in an online environment. Journal Of Effective Teaching, 16(2), 93–
103.
Benken, B. M., Ramirez, J., Li, X., & Wetendorf, S. (2015). Developmental mathematics
success: Impact of students’ knowledge and attitudes. Journal of Developmental
Education, 38(2), 14–31. http://www.jstor.org/stable/24614042
Bensimon, E. M. (2004). The diversity scorecard: A learning approach to institutional change.
Change: The magazine of higher learning, 36(1), 44–52.
Berger, A., Turk-Bicakci, L., Garet, M., Song, M., Knudson, J., Haxton, C., Zeiser, K., Hoshen,
G., Ford, J., Stephan, J. (2013). Early college, early success: 80 Early College High
School Initiative impact study. American Institutes for Research.
Bergman, M., Gross, J. P., Berry, M., & Shuck, B. (2014). If life happened but a degree didn’t:
Examining factors that impact adult student persistence. The Journal of Continuing
Higher Education, 62, 90–101.
139

Berliner, D. C., & Glass, G. V. (2014). 50 myths & lies that threaten America’s public schools.
Teachers College Press.
Bezerra-Nader, R. (2020). AB 705 and its unintended consequences.
https://www.faccc.org/index.php?option=com_dailyplanetblog&view=entry&year=2019
&month=12&day=18&id=6:AB 705-and-its-unintended-
consequences#:%7E:text=While%20equity%20is%20the%20goal,students%20across%2
0California%20varies%20dramatically.
Bloom, B. S. (1956). Taxonomy of Educational Objectives, Handbook I: The Cognitive Domain.
David McKay Co Inc.
Bonham, B. S., & Boylan, H. R. (2011). Developmental mathematics: challenges, promising
practices, and recent initiatives. Journal of Developmental Education, 34(3), 2–10.
http://www.jstor.org/stable/42775378
Boylan, H. R., Bliss, L. B., & Bonham, B. S. (2019). Defining developmental education: A
systematic review of the literature. Journal of Developmental Education, 42(3), 4–18.
Brand, J. E., Pfeffer, F. T., & Goldrick-Rab, S. (2014). The community college effect revisited:
The importance of attending to heterogeneity and complex counterfactuals. Sociological
Science, 1, 448–465. https://doi.org/10.15195/v1.a25
Brathwaite, J., Fay, F., & Moussa, A. (2020). Improving developmental and college-level
mathematics: Prominent reforms and the need to address equity. Community College
Research Center. Teachers College, Columbia University.
Brint, Steven and Jerome Karabel (1989). The diverted dream: community colleges and the
promise of educational opportunity. Oxford University Press.
140

Bryk, A. S., & Treisman, U. (2010). Make math a gateway, not a gatekeeper. Chronicle of
Higher Education, 56(32), B19–B20.
Burns, L., & Leu, K. (2019). Advanced Placement, International Baccalaureate, and dual-
enrollment courses: Availability, participation, and related outcomes for 2009 Ninth
Graders: 2013 (NCES 2019–430) [Report]. National Center for Education Statistics.
California Community Colleges Chancellor’s Office. (2022) Key Facts.
https://www.cccco.edu/About-Us/Key-Facts
California Community Colleges Chancellor’s Office. (2022). Transfer.
https://www.cccco.edu/Students/Transfer#:~:text=Some%2080%2C000%20California%
20community%20colleges,State%20University%20campus%20every%20year.
California Community Colleges Chancellor’s Office, 2022, Student Enrollment &
Demographics: Frequently Asked Questions. https://www.cccco.edu/
California Community Colleges Chancellor’s Office. (2017). AB 705 Implementation and
Timeline. https://www.cccco.edu/-/media/CCCCO-Website/About-
Us/Divisions/Educational-Services-and-Support/Academic-Affairs/Whats-
New/Files/AA17_63_AB%20705ImplementationandTimeline_Memo_pdf.pdf
California Community Colleges Chancellor’s Office. (2017). Vision for success: Strengthening
the California community colleges to meet California’s needs.
http://californiacommunitycolleges.cccco.edu/Portals/0 /Reports/vision-for-success.pdf
California Community College Chancellor’s Office. (2021). Guidance memorandum regarding
AB 705 English math improvement plans.
https://cccco.box.com/shared/static/5dqqfh8gnoz4t2s4s4if21t1m8cq4swm.pdf
141

California State University System. (2012). Fall 2011 final regularly admitted first-time
freshmen remediation system-wide.
http://www.asd.calstate.edu/remediation/11/Rem_Sys_fall2011.htm
California State University Office of the Chancellor | CSU. (2022). The California State
University. https://www.calstate.edu/
Carney-Crompton, S., & Tan, J. (2002). Support systems, psychological functioning, and
academic performance of nontraditional female students. Adult Education Quarterly, 52,
140-154. https://doi.org/10.1177/0741713602052002005
Cassidy, L., Keating, K., & Young, V. (2010). Dual enrollment: Lessons learned on school-level
implementation. SRI International.
Castro, N., & Collins, L. (2018). The dual enrollment landscape in California: A CLP working
paper. Career Ladders Project. https://www.careerladdersproject.org/wp-
content/uploads/2019/06/DualEnrollmentWorkingPaper_Oct2018_Final.pdf
Cavanagh, R. F., Chen, J., & Koedinger, K. R. (2016). Towards reliable assessment of skill
knowledge in cognitive tutors. International Journal of Artificial Intelligence in
Education, 26(1), 368–395.
Celedón-Pattichis, S., Borden, L. L., Pape, S. J., Clements, D. H., Peters, S. A., Males, J. R., &
Leonard, J. (2018). Asset-based approaches to equitable mathematics education research
and practice. Journal for Research in Mathematics Education, 49(4), 373–389.
Chen, X. (2016). Remedial coursetaking at U.S. public 2- and 4-year institutions: Scope,
experiences, and outcomes (NCES 2016–405). U.S. Department of Education. National
Center for Education Statistics.
142

Chval, K. B., et al. (2015). Professional development in higher education: A model for
meaningful institutional engagement. Innovative Higher Education, 40(4), 327–341.
Clark, R. C., & Mayer, R. E. (2011). E-learning and the science of instruction: Proven
guidelines for consumers and designers of multimedia learning (3rd ed.). Wiley.
Coast Community College District (2022). About Coast Colleges.
https://www.cccd.edu/aboutus/index.html
Cohen, A. M., & Brawer, F. B. (1982). The American Community College. Jossey-Bass
Publishers.
College Board. (2005). AP program guide: 2005–2006.
College Board. (2006). Advanced Placement report to the nation: 2006.
Conger, S. B., & Tell, C. (2007). Curriculum and assessment systems. In more student success:
A systemic solution (pp. 37–52). State Higher Education Executive Officers.
Conley, D. T. (2014). The common core state standards: Insight into their development. Council
of Chief State School Officers.
Corin EN, Sonnert G, Sadler PM. The role of dual enrollment stem coursework in increasing
stem career interest among American high school students. Teachers College record
(1970). 2020;122(2), 1–26. https://doi.org/10.1177/016146812012200210
Cowan, J., Goldhaber, D., & Walch, J. (2013). Is a good elementary teacher always good?
Assessing teacher performance estimates across subjects. Economics of Education
Review, 36, 216–228.
Crawford, C., Burns, R., & McNamara, R. H. (2012). Promotion to full professor: Moving
beyond tenure and associate professorship. Journal of Criminal Justice Education, 23(1),
41–64.
143

Cross, K. P. (1981). Adults as learners: Increasing participation and facilitating learning.
Jossey-Bass Publishers
Cuellar, M., Rodriguez, O., & Johnson, H. (2019). What happens when colleges broaden access
to transfer-level courses? Public Policy Institute of California.
Cuellar, M., Rodriguez, O., & Johnson, H. (2020). A new era of student success at California’s
community colleges. Public Policy Institute of California.
Daro, P., & Asturias, H. (2019). Branching out: Designing high school math pathways for
equity. Just Equations. https://justequations.org/wp-content/uploads/Just-Equations-2019-
Report-Branching-Out-Digital.pdf
Darolia, R., Koedel, C., Main, J. B., Ndashimye, J. F., & Yan, J. (2020). High school course
access and postsecondary stem enrollment and attainment. Educational Evaluation and
Policy Analysis, 42(1), 22–45. https://doi.org/10.3102/0162373719876923
Deutsch, N. L., & Schmertz, B. (2011). “Starting from ground zero”: Constraints and
experiences of adult women returning to college. The Review of Higher Education, 34,
477-504. https://doi.org/10.1353/rhe.2011.0002
Dolle, J. R., Bowman, A., Hirschboeck, K., & Miles, K. (2020). Equity-focused dual enrollment
mathematics: Lessons for improving the outcomes of historically underserved students.
WestEd. https://www.wested.org/resources/equity-focused-dual-enrollment-mathematics
Drew, C. J., & Hardman, M.L. (2007). Intellectual disabilities across the lifespan (9th ed.).
Merrill.
Drury, R. L. (1999). Entrepreneurship education in the Virginia community college system.
ERIC Documentation Reproduction Service No. JC 010515.
Edgecombe, N. (2011). Accelerating the academic achievement of students referred to
144

developmental Education (CCRC Working Paper No. 30). Community
College Research Center.
Edley, C., Jr. (2017, June 5). At Cal State, algebra is a civil rights issue. EdSource.
https://edsource.org/2017/at-cal-state-algebra-is-a-civil-rights-
issue/582950#:~:text=The%20next%20civil%20rights%20court,rates%20and%20address
%20equity%20gaps.
Educational Level and Pay | U.S. Department of Labor. (2022). Educational Level and Pay.
https://www.dol.gov/general/topic/wages/educational
Ekstrom, R. B. (1972). Barriers to women’s participation in postsecondary education. A review
of the literature. National Center for Educational Statistics.
Elman, C., & O’Rand, A. O. (2007). The effects of social origins, life events, and institutional
sorting on adults’ school transitions. Social Science Research, 36, 1276–1299.
El-Mekkawy, T., Desjardins, S., & McCallum, C. M. (2018). Faculty involvement in the
development of placement policies: Impact on placement accuracy and student outcomes.
Community College Review, 46(1), 31–50.
Executive Office of the President, President’s Council of Advisors on Science and Technology.
(2012). Engage to excel: Producing one million additional college graduates with degrees
in science technology engineering and mathematics.
www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-engage-to-excel-
final_feb.pdf.
Fain, P. (2018, June 12). As California goes? Inside Higher Ed. https://www.insidehighered
.com/news/2018/06/12/calif-finalizes-performance-funding-formula-itscommunity-
colleges
145

Fink, J. (2018, November 5). How does access to dual enrollment and advanced placement vary
by race and gender across states? [Blog post]. Community College Research Center.
Retrieved from https://ccrc.tc.columbia.edu/easyblog/access-dualenrollment-advanced-
placement-race-gender.html
Fink, J., Jenkins, D., & Yanagiura, T. (2017). What happens to students who take community
college ‘‘dual enrollment’’ courses in high school? Community College Research
Center, Teachers College, Columbia University.
Flynn, S., Brown, J., Johnson, A., & Rodger, S. (2011). Barriers to education for the
marginalized adult learner. Alberta Journal of Educational Research, 57, 43–58.
Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., &
Wenderoth, M. P. (2014). Active learning increases student performance in science,
engineering, and mathematics. Proceedings of the National Academy of Sciences,
111(23), 8410–8415.
Foundation for California Community Colleges (2022). Facts and Figures.
https://foundationccc.org/about-us/about-the-colleges/facts-and-figures
Friedmann, E., Kurlaender, M., Li, A., & Rumberger, R., (2020). A leg up on college: The scale
and distribution of community college participation among California high school
students. Wheelhouse: The Center for Community College Leadership and Research.
Gao, N., & Lafortune, J. (2019). Common Core State Standards in California: Evaluating Local
Implementation and Student Outcomes. Public Policy Institute of California.
Gao, N. Rodriguez, O., (2021). Dual enrollment in California. promoting equitable student
access and success. Public Policy Institution of California.
146

https://www.ppic.org/publication/dual-enrollment-in-california/#dual-enrollment-has-
been-growing-in-california
Garcia, H. A., Eicke, D., McNaughtan, J., & Harwood, Y. (2020). Understanding dual credit
programs: Perspectives from faculty, staff, and administrators. Community College
Journal of Research and Practice, 44(8), 584–594. https://doi.org/10.10
80/10668926.2019.1626301
Garcia, M. (202). Do you know AB 1705? A new law that could water down transfer-level
courses. https://laschoolreport.com/do-you-know-ab-1705-a-new-law-that-could-water-
down-transfer-level-courses/.
Gerber, C. (1987). High school/college brief (Supplement to AACJC Letter, No. 242). American
Association of Community and Junior Colleges.
Giani, M., Alexander, C., & Reyes, P. (2014). Exploring variation in the impact of dual credit
coursework on postsecondary outcomes: A quasi-experimental analysis of Texas
students. High School Journal, 97(4), 200–218. https://doi.org/10.1353/ hsj.2014.0007
Glesne, C. (2010). Becoming Qualitative Researchers: An Introduction (4th Edition). Pearson.
Goto, S. T., & Martin, C. (2009). Psychology of success: Overcoming barriers to pursuing
further education. The Journal of Continuing Higher Education, 57, 10–21.
https://doi.org/10.1080/07377360902810744
Greenburg, A. R. (1989). Concurrent enrollment programs: College credit for high school
students. Phi Delta Kappa Educational Foundation.
Grubb, J. M., Scott, P. H., & Good, D. W. (2017). The answer is yes: Dual enrollment
benefits students at the community college. Community College Review, 45(2),
79–98.
147

Hagedorn, L. S. (2010). The pursuit of student success: The directions and challenges facing
community colleges. In J. C. Smart (Ed.), Higher education: Handbook of theory and
research (Vol. XXV, pp. 181–218). Agathon Press.
Hardin, C. J. (2008). Adult students in higher education: A portrait of transitions. New Directions
for Higher Education, 2008 (144), 49–57. https://doi.org/10.1002/he.325
Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. Routledge.
Hayward, C., Morris, T., Newell, M., White, M. (2021). A Qualitative exploration of AB 705
implementation: Report of statewide interview results. R.P. Group.
https://files.eric.ed.gov/fulltext/ED611916.pdf
Hawley, T. H., & Harris, T. A. (2005). Student characteristics related to persistence for first-year
community college students. Journal of College Student Retention: Research, Theory &
Practice, 7(1), 117–142.
Hemelt, S. W., Schwartz, N. L., & Dynarski, S. M. (2020). Dual-credit courses and the road to
college: Experimental evidence from Tennessee. Journal of Policy Analysis and
Management, 39(3), 686–719. https://doi.org/10.1002/pam.22180
Hern, K., Snell, M., and Henson, L. (2020). Still Getting There: How California’s AB 705 is
(and is not) transforming remediation and what needs to come next. Public Advocates.
Hernandez-Martinez, P., Contreras, L. R., de la Fuente, J., Fernández-Cabezas, M., & González-
Torres, M. C. (2020). Effects of a metacognitive intervention program on mathematical
problem-solving skills and self-regulation strategies in university students. Frontiers in
Psychology, 11, 582615. https://doi.org/10.3389/fpsyg.2020.582615
Herriott, S. R., & Dunbar, S. R. (2009). Who takes college algebra? PRIMUS, 19(1), 74–87.
https://doi.org/10.1080/10511970701573441
148

Higher Education Research Institute. (2003). The official press release for the American
freshmen 2002. University of California Press.
Hodara, M. (2011). Reforming mathematics classroom pedagogy: Evidence-based findings and
recommendations for the developmental math classroom (CCRC Working Paper No. 27).
Community College Research Center.
Hodara, M., & Xu, D. (2016). Does developmental education improve labor market outcomes?
Evidence from two states. American Educational Research Journal, 53, 781–813.
https://doi.org/10.3102/0002831216647790
Hodges, L. C. (2018). AB 705: The journey toward student-centered math classrooms in
community colleges. American Mathematical Association of Two-Year Colleges, 42(4),
244–248.
Hoffman, N. (2003). College credit in high school: Increasing postsecondary credential rates of
underrepresented students. Jobs for the Future.
Hostetler, A. J., Sweet, S., & Moen, P. (2007). Gendered career paths: A life course perspective
on returning to school. Sex Roles, 56, 85–103.
https://doi.org/10.1016/j.ssresearch.2006.11.001
Hout, M. (2012). Social and economic returns to college education in the United States. Annual
review of sociology, 38, 379–400.
Hoyt, J. E. & Sorenson, C. (2001). High school preparation, placement testing, and college
remediation. Journal of Developmental Education, 25(2), 23.
Hussar, B., Zhang, J., Hein, S., Wang, K., Roberts, A., Cui, J., Smith, M., Bullock Mann, F.,
Barmer, A., & Dilig, R. (2020). The condition of education 2020 (NCES 2020–144). U.S.
149

Department of Education, Institute of Education Statistics, National Center for Education
Statistics.
Hughes, K. L., Rodriguez, O., Edwards, L., & Belfield, C. (2012). Broadening the benefits of
dual enrollment: Reaching underachieving and underrepresented students with career-
focused programs. Community College Research Center for the James Irvine Foundation.
Jaggars, S. S. (2014). Choosing between traditional and alternative developmental education: A
descriptive analysis of student enrollment patterns in the wake of California’s AB 705.
Community College Review, 42(1), 57–74.
Johnson, H. (2010). Higher Education in California: New goals for the master plan (Research
report). Public Policy Institute of California.
Johnson, R. B., & Christensen, L. B. (2016). Educational Research: Quantitative, Qualitative,
and Mixed Approaches (6th ed.). SAGE Publications, Inc.
Johnson, H., & Mejia, M. C., (2020b). Increasing Community College Transfers: Progress and
Barriers. Public Policy Institute of California.
Karp, M. M., Calcagno, J. C., Hughes, K. L., Jeong, D. W., & Bailey, T. R. (2007). The
postsecondary achievement of participants in dual enrollment: An analysis of student
outcomes in two states. Community College Research Center, Teachers College,
Columbia University.
Karp, M. M., & Hughes, K. L. (2008). Study: Dual Enrollment Can Benefit a Broad Range of
Students. Techniques: Connecting Education and Careers (J1), 83(7), 14–17.
Karp, M. (2012). “I don’t know, I’ve never been to college!” Dual enrollment as a college
readiness strategy. New Directions for Higher Education, 2012(158), 21–28.
https://doi.org/10.1002/he.20011
150

Kasworm, C. E. (2010). Adult learners in a research university: Negotiating undergraduate
student identity. Adult Education Quarterly, 60, 143–160
https://doi.org/10.1177/0741713609336110
Keng, L., & Dodd, B. G. (2006). An investigation of college performance of AP and non-AP
student groups. Paper presented at the AP Annual Conference. Lake Buena Vista, FL.
Kirst, M. W. (2013). The common core meets state policy: This changes almost everything.
policy memorandum. Stanford University Graduate School of Education. Policy Analysis
for California Education.
Klopfenstein, K. (2010). Does the advanced placement program save taxpayers money? The
effect of ap participation on time to college graduation. Promise and impact of the
advanced placement program. Harvard Education Press.
Kreysa, P. G. (2006). The impact of remediation on persistence of under-prepared college
students. Journal of College Student Retention: Research, Theory & Practice, 8(2), 251–
270.
Kurlaender, M., Reed, S., Cohen, K., Naven, M., Martorell, F., & Carrell, S. (2018). Where
California high school students attend college [Report]. Policy Analysis for California
Education. https://edpolicyinca.org/publications/where-california-high-school-students-
attend-college
Kurlaender, M. (2021). New law promises to address concerns over community college
placement but falls short. The Campaign for College Opportunity.
https://collegecampaign.org/new-law-promises-to-address-concerns-over-community-
college-placement-but-falls-short/.
151

Kumar, R., Upadhyaya, A., & Yadav, N. (2021). Use of technology in teaching mathematics for
distance education. In Handbook of Research on Emerging Trends and Technologies in
Distance Education (pp. 52–67). IGI Global.
Larsen, M. A., & Watson, J. M. (2019). Personalizing mathematics instruction in a college
remedial math classroom. International Journal of Educational Technology in Higher
Education, 16(1), 1–14.
Lawson, J. H., & Crooks, T. J. (2019). Small-group activities in mathematics instruction. The
Mathematics Teacher, 112(3), 200–206.
Lee, J. (2018). Seamless Transition to College Mathematics: Development of a standardized
curriculum for high school mathematics. Journal of Mathematics Education at Teachers
College, 9(1), 28–36.
Levin, J. (2001). Globalizing the community college: Strategies for change in the 21st century.
Palgrave.
Levin, J. S. (2007). Non-traditional students and community colleges: The conflict of justice and
neoliberalism. Palgrave Macmillan.
Linnenbrink-Garcia, L., Patall, E. A., & Pekrun, R. (2016). Adaptive motivation and emotion in
education: Research and principles for instructional design. Policy Insights from the
Behavioral and Brain Sciences, 3(2), 228–236.
Locke, L. F., Silverman, S., & Spirduso, W. W. (2009). Reading and Understanding Research
(Third ed.). SAGE Publications, Inc.
Long, M. C., Iatarola, P., & Conger, D. (2009). Explaining gaps in readiness for college-level
math: The role of high school courses. Education Finance and Policy, 4(1), 1–33.
https://doi.org/10.1162/edfp.2009.4.1.1
152

Loveless, T. (2014). The 2014 Brown Center report on American education. Brookings
Institution.
Loveless, T. (2016). The 2016 Brown Center report on American education. Brookings
Institution.
Lynch, M. F. (2018). The impact of reduced funding for professional development on
community college mathematics instructors. Community College Journal of Research
and Practice, 42(5), 319–327. https://doi.org/10.1080/10668926.2016.1255286
MacKinnon-Slaney, F. (1994). The adult persistence in learning model: A road map to
counseling services for adult learners. Journal of Counseling & Development, 72, 268–
275. https://doi.org/10.1002/j.1556-6676.1994.tb00933.x
Makkonen, R., & Sheffield, R., (2016). California standards implementation presentation to the
California state board of education. WestEd.
Marshall, R. P., & Andrews, H. A. (2002). Dual-credit outcomes: A second visit. Community
College Journal of Research & Practice, 26(3), 237–242.
Martin, T. C. (2013). Cognitive and noncognitive college readiness of participants in
three concurrent-enrollment programs. Community College Journal of Research
and Practice, 37(9), 704–718.
Martinez, M. E., & Klopott, K. A. (2016). Reimagining remediation: Contextualized math
pathways at scale. Journal of Developmental Education, 39(1), 16–25.
Matz, R., & Tunstall, S. (2019). Embedded remediation is not necessarily a pathway for
equitable access to quantitative literacy and college algebra: Results from a pilot study.
Numeracy, 11(1). https://doi.org/10.5038/1936-4660.12.2.3
McCabe, R. (2000). No one to waste. Community College Press.
153

McDowell, T., Daiute, C., Rios-Aguilar, C., & Melguizo, T. (2021). AB 705 implementation in
the time of covid-19: Impacts on placement, enrollment, and success in California’s
community colleges. Journal of Applied Research in the Community College, 28(2), 40–
53.
McKinney, L., & Novak, H. (2013). The relationship between FAFSA filing and
persistence among first-year community college students. Community College
Review, 41(1), 63–85.
McLaughlin, M., Glaab, L., & Carrasco, I. H. (2014). Implementing common core state
standards in California: A report from the field. Policy Analysis for California
Education, PACE.
Medina, J., Baker, C. B., Bloom, R., Chavez, R. J., Harper, M., Irwin, J., Williams, D. (2016).
2015-2016 Mid-Session Legislative Update.
https://ahed.assembly.ca.gov/sites/ahed.assembly.ca.gov/files/reports/AHED%20
2015-16%20Mid-Session%20Report%20webpage%20double-sided.pdf
Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: A guide to design and
implementation (4th ed.). Jossey-Bass.
Merrill, M. D. (2002). First principles of instruction. Educational technology research and
development, 50(3), 43–59.
Michalowski, S. (2007). Positive effects associated with college now participation. Collaborative
Programs Research & Evaluation, The City University of New York.
Mickelson, R. A., Bottia, M. C., & Lambert, R. (2013). Effects of school racial composition on
K–12 mathematics outcomes: A meta regression analysis. Review of Educational
Research, 83(1), 121–158.
154

Miller, T., Kosiewicz, H., Tanenbaum, C., Atchison, D., Knight, D., Ratway, B., Delhommer, S.,
& Levin, J. (2018). Dual-credit education programs in Texas: Phase II. American
Institutes for Research.
Mokher, C. G., & McLendon, M. K. (2009). Uniting secondary and postsecondary education: An
event history analysis of state adoption of dual enrollment policies. American Journal of
Education, 115(2), 249–277. https://doi.org/10.1086/595668
Morgan, R., & Ramist, L. (1998). Advanced Placement students in college: An
investigation of course grades at 21 colleges (No. SR–98–13). Educational Testing
Service.
Museus, S. D., Lutovsky, B. R., & Colbeck, C. L. (2007). Access and equity in dual enrollment
programs: Implications for policy formation. Higher Education in Review, 4, 1–19.
Nardi, A. H., & Steward, M. K. (2019). The impact of AB 705 on student course success and
equity: Early evidence from the California community colleges. Public Policy Institute of
California.
National Center for Education Statistics, U.S. Department of Education. (2010). Digest of
education statistics, 2010. https://nces.ed.gov/pubs2011/2011015.pdf
National Center for Education Statistics, U.S. Department of Education. (2018). Postsecondary
education. Digest of education statistics 2017. http://nces.ed.gov/programs/digest/
National Center for Education Statistics, U.S. Department of Education, Integrated
Postsecondary Education Data System (IPEDS), “12-month Enrollment component 2019-
20 provisional data.” https://nces.ed.gov/ipeds/TrendGenerator/app/build-table/2/2?cid=1
National Center for Education Statistics. (2019). Status and trends in the education of racial and
ethnic groups. US Department of Education.
155

National Center for Education Statistics, U.S. Department of Education (2022). Integrated
Postsecondary Education Data System (IPEDS, “Institutional Characteristics, 2000–01”
survey.
National Governors Association. (2010). Common core state standards.
National Research Council. (1999). How people learn: Brain, mind, experience, and school.
National Academies Press.
Nietfeld, J. L., Enders, C. K., & Welsh, M. E. (2017). The effects of differentiated instruction on
student mathematics achievement in primary classrooms. Journal of Educational
Psychology, 109(3), 326–340.
Nietzel, M. T. (2021). New Study: College degree carries big earnings premium, but other
factors matter too. Forbes.
https://www.forbes.com/sites/michaeltnietzel/2021/10/11/new-study-college-degree-
carries-big-earnings-premium-but-other-factors-matter-too/?sh=55052d3e35cd
Noel-Levitz, Inc. (2006). Student success in developmental math: Strategies to overcome barriers
in retention. Noel-Levitz. https://www.noelevitz.com/NR/rdonlyres/B4148B72-C135-
4AD4-A04C-2F66821C872C/0/ENABLEMATH_paper_0706indd.pdf
Nugent, S. A., & Karnes, F. A. (2002). The Advanced placement program and the
international baccalaureate program: A history and update. Gifted Child
Today, 25(1), 30–39.
Osam, E. K., Bergman, M., & Cumberland, D. M. (2017). an integrative literature review on the
barriers impacting adult learners’ return to college. Adult Learning, 28(2), 54–60.
https://doi.org/10.1177/1045159516658013
156

Oudenhoven, B. (2002). Remediation at the community college: Pressing issues, uncertain
solutions. New directions for community colleges, 2002(117), 35–44.
Piaget, J. (1978). Success and understanding. Harvard University Press.
Park, E. S., & Ngo, F. (2021). The effect of developmental math on stem participation in
community college: Variation by race, gender, achievement, and aspiration. Educational
Evaluation and Policy Analysis, 43(1), 108–133.
https://doi.org/10.3102/0162373720973727
Parsad, B., & Lewis, L. (2003). Remedial education at degree-granting postsecondary
institutions in fall, 2000 (NCES 2004-010). U.S. Department of Education, National
Center for Education Statistics. http://nces.ed.gov/pubs2004/2004010.pdf
Paulson, A. (2010, March 23). No Child Left Behind embraces ‘college and career readiness.’
The Christian Science Monitor. http://www.csmonitor.com/USA/Society/2010/0323/No-
Child-Left-Behind-embraces-college-and-career-readiness
Perrone, K. M., Clark, S. G., & Shure, L. (2017). Differentiated instruction and the mathematical
practices: A case study of a middle school classroom. Mathematics Education Research
Journal, 29(1), 35–56.
Peterson, M. K., Anjewierden, J., & Corser, C. (2001). Designing an effective concurrent
enrollment program. In P. F. Robertson, B. G. Chapman, & F. Gaskin (Eds.), Systems for
offering concurrent enrollment at high schools and community colleges. New Directions
for Community Colleges, No. 113 (pp. 23–32). Jossey Bass.
Phillippe, K. A., & Gonzalez Sullivan, L. (2005). National profile of community colleges: Trends
and statistics (4th ed.). Community College Press.
157

Phillips, G. W. (2010). International benchmarking: State education performance standards.
American Institutes of Research.
Porter, Stephen R. and Umbach, Paul D. (2019). What challenges to success do community
college students face? Percontor, LLC.
Potter, G., & Lena, P. (2000). Improve your advanced placement program: What one high school
did. American Secondary Education, 29(2), 2–8.
Prather, E. E., Rudolph, A. L., Brissenden, G., & Schlingman, W. M. (2017). A national study of
STEM readiness at community colleges. CBE-Life Sciences Education, 16(1), ar6.
https://doi.org/10.1187/cbe.16-07-0240
President’s Council of Advisors on Science and Technology. (2012). Engage to excel: Producing
one million additional college graduates with degrees in science, technology,
engineering, and mathematics.
Pretlow, J., & Wathington, H. (2013). Access to dual enrollment courses and school-level
characteristics. Community College Journal of Research and Practice, 37(3),
196–204. https://doi.org/10.1080/10668926.2013.739513
Radford, A. W., & Horn, L. (2012). An overview of classes taken and credits earned by
beginning postsecondary students. WEB table (NCES 2013–151rev). National Center for
Education Statistics
Rutschow, E. Z., Cormier, M. S., Dukes, D., & Cruz Zamora, D. E. (2019). The changing
landscape of developmental education practices: Findings from a national survey
and interviews with postsecondary institutions. Center for the Analysis of Postsecondary
Readiness
158

Remedial Courses in Community Colleges Are a Major Hurdle to Success. (2017, June 12).
Public Policy Institute of California. https://www.ppic.org/press-release/remedial-
courses-in-community-colleges-are-major-hurdle-to-success/
Robinson, M. (2003). Student Enrollment in High School AP Sciences and Calculus: How does
it Correlate with STEM Careers? Bulletin of Science, Technology & Society, 23(4), 265–
273. https://doi.org/10.1177/0270467603256090
Rodriquez, N. N., DiSanto, J., Varelas, A., Brennan, S., Wolfe, K., & Ialongo, E. (2017).
Building understanding of high school students’ transition to college. International
Journal of Teaching and Learning in Higher Education, 29(2), 402–411.
Rodriguez, O., Jackson, J., & Mejia, M.C. (2017). Remedial Education in California’s Colleges
and Universities [Blog post]. Just the FACTS. Public Policy Institute of California.
https://www.ppic.org/publication/remedial-education-in-californias-colleges-and
universities/s://nces.ed.ov/pubsearch/pubsinfo.asp?pubid=2020144
Rosin, M. (2012, February). Passing when it counts: Math courses present barriers to student
success in California community colleges (Issue Brief). EdSource.
https://edsource.org/wp-content/publications/pub12-Math2012Final.pdf
Roueche, J., & Roueche, S. (1999). High stakes, high performance: Making remedial education
work. Community College Press.
Rouse, C. E. (1995). Democratization or diversion—The effect of community colleges on
educational attainment. Journal of Business and Economic Statistics, 13(2), 217–224.
Sanabria, T., Penner, A., & Domina, T. (2020). Failing at remediation? College remedial
coursetaking, failure and long-term student outcomes. Research in higher education,
61(4), 459–484. https://doi.org/10.1007/s11162-020-09590-z
159

Sato, B. K., & Adler, J. (2017). Supporting the use of evidence-based teaching practices among
adjunct faculty: An institutional case study. Journal of Research in Mathematics
Education, 48(2), 127–154. https://doi.org/10.5951/jresematheduc.48.2.0127
Savoye, C. (2000) Making the college leap from High school to college-level work in a single
bound? For many students, that transition is difficult. The Christian Science Monitor
https://ezproxy.gwclib.nocccd.edu/login?url=https://www.proquest.com/newspapers/mak
ing-college-leap-high-school-level-work-single/docview/405653666/se-
2?accountid=40389
Schmidt, W. H., Houang, R. T. (2012). Curricular coherence and the common core state
standards for mathematics. Educational Researcher, 41, 294–308.
Schwartz, A. E. (2007). New standards for improving two-year mathematics instruction.
Education Digest, 73(2), 39–42.
Scott-Clayton, J. (2012). Do high-stakes placement exams predict college success? (CCRC
Working Paper No. 41). Community College Research Center.
Scott-Clayton, J., & Rodriguez, O. (2015). Development, discouragement, or diversion? New
evidence on the effects of college remediation policy. Education Finance and Policy, 10,
4–45. doi:10.1162/EDFP_a_00150
Shavit, Y., Arum, R. & Gamoran A. (2007). Stratification in higher education: A comparative
study. Stanford University Press.
Shaw, K., Goldrick-Rab, S., Mazzeo, C. & Jacobs, J. (2006). Putting poor people to work: How
the work-first idea eroded college access for the poor. Russell Sage.
160

Shulock, N., Moore, C., Jez, S. J., & Chisholm, E. (2012). Career opportunities: Career technical
education and the college completion agenda.
https://files.eric.ed.gov/fulltext/ED534075.pdf
Smith, A. (2019). More California community college students entering, passing transfer-level
math and English as result of landmark law. EdSource. https://edsource.org/2019/more-
california-community-college-students-entering-passing-transfer-level-math-and-english-
as-result-of-landmark-law/
Solorzano, D. G., & Ornelas, A. (2004). A critical race analysis of Latina/o and African
American Advanced Placement enrollment in public high schools. The High School
Journal, 87(3), 15–26.
Sousa, D., & Tomlinson, C. (2011). Differentiation & the brain: How neuroscience supports the
learner-friendly classroom. Solution Tree.
Spillane, J. P., Reiser B. J., & Reimer, T., (2002). Policy implementation and cognition:
Reframing and refocusing implementation research. Review of Educational Research, 72
(3), 387–431.
Speroni, C. (2011). High school dual enrollment programs: Are we fast-tracking students too
fast? (NCPR Working Paper). National Center for Postsecondary Research.
https://ccrc.tc.columbia.edu/media/k2/attachments/dual-enrollmentfast-tracking-students-
too-fast.pdf
Staley, D. J., & Trinkle, D. A. (2011). The changing landscape of higher education. EDUCAUSE
Review, 46(1), 16–32.
161

Stolzenberg, E. B., Sanders, J., & Frank, V. M. (2021). The COVID-19 pandemic and
community college students: Impacts on equity in coursework and academic support.
Community College Review, 49(1), 23–44.
Struhl, B., Vargas, J. (2012). Taking college courses in high school: a strategy for college
readiness and the college outcomes of dual enrollment in Texas. Jobs for the Future.
https://www.jff.org/documents/1988/TakingCollegeCourses_101712.pdf
Swanson, J. L. (2008). An analysis of the impact of high school dual enrollment course
participation on post-secondary academic success, persistence, and degree completion.
Graduate College of The University of Iowa.
Thompson, K. S. (2007). The open enrollment of advanced placement classes as a means for
increasing student achievement at the high school level. University of Southern
California.
Timar, T., & Carter, A. (2017). Surprising strengths and substantial needs: Rural district
implementation of common core state standards. Policy Analysis for California
Education. PACE.
Tomlinson. (2005). Grading and differentiation: Paradox or good practice? Theory into Practice,
44(3), 262–269. https://doi.org/10.1207/s15430421tip4403_11
Tomlinson, C. A. (2014). The differentiated classroom: Responding to the needs of all learners.
ASCD.
Tomlinson, C. A. (2017). How to Differentiate Instruction in Academically Diverse Classrooms
(3rd ed.). ASCD.
162

Torres, O. (2019). Determining the Degree to Which Participation in Dual Credit and Advanced
Placement Programs During High School Affects Completion and Success Rates of
Community College Graduates (Doctoral dissertation, University of La Verne).
Transfer Level Gateway Completion Dashboard | California Community Colleges Chancellor’s
Office. (2022). Transfer level gateway completion dashboard.
https://www.cccco.edu/About-Us/Chancellors-Office/Divisions/Educational-Services-
and-Support/transfer-level-dashboard
Trust, E. (2022). Dual enrollment. The Education Trust. https://edtrust.org/issue/dual-enrollment/
Tsui, L. (2007). Effective strategies to increase diversity in stem fields: A review of the research
literature. The Journal of Negro Education, 76(4), 555–581.
http://www.jstor.org/stable/40037228
Van der Werf, M. (2009). The college of 2020: The students. Chronicle Research Services.
Vygotsky, L. (1986). Thought and language (A. Kozulin, Ed. & Trans.). MIT
Press.
Walker, W., & Plata, M. (2000). Race/gender/age differences in college mathematics students.
Journal of Developmental Education, 23(3), 24.
Wanzo, T. (2014). The underrepresentation of black students in advanced placement classes: a
local response to a national issue (doctoral dissertation, Duquesne University).
https://dsc.duq.edu/etd/1336
Warren, P., & Murphy, P. (2014). Implementing the common core state standards in California.
Public Policy Institute of California.
Warren, P., Lafortune, J, (2019). Achievement in California’s public schools: What do test scores
tell us. Public Policy Institute of California.
163

Wheelhouse. (2021). A Foot in the door: growth in participation and equity in dual enrollment in
California.
https://education.ucdavis.edu/sites/main/files/wheelhouse_research_brief_vol_6_no_7_fi
nal.pdf
Whiten, J., Rethinam, V., & Preuss, M. D. (2018). High school factors predicting enrollment in
developmental courses. Journal of Developmental Education, 42(1), 9–14.
Wiggins, G., & McTighe, J. (2005). Understanding by design (Expanded 2nd ed.). ASCD.
Willett, R. L., & Cullen, T. A. (2019). Effects of an evidence-based teaching professional
development program on student success in developmental mathematics. Journal of
Developmental Education, 42(2), 2–14.
Willis, J. (2006). Research-based strategies to ignite student learning: Insights from a
neurologist and classroom teacher. ASCD.
Wimberly, G. L., & Noeth, R. J. (2005). College readiness begins in middle school.
http://www.act.org/research/policymakers/pdf/CollegeReadiness.pdf
Willingham, W., & Morris, M. (1986). Four years later: A longitudinal study of Advanced
Placement students in college (No. 86–2). College Board.
Wolfe, P. (2010). Brain matters: Translating research into classroom practice (2nd ed.). ASCD.
Xue, Y., & Larson, R. C. (2015). STEM crisis or STEM surplus? Yes and yes. Monthly labor
review. https://doi.org/10.21916/mlr.2015.14
Xu, D., & Dadgar, M. (2018). How effective are community college remedial math courses for
students with the lowest math skills? Community College Review, 46(1), 62–81.
https://doi.org/10.1177/0091552117743789
164

Zarate, M. E., & Pachon, H. P. (2006). Equity in offering advanced placement courses in
California high schools 1997–2003: Gaining or losing ground? Tomas Rivera Policy
Institute, University of Southern California.

165

Appendix A: Protocols
The following interview protocol serves as a structured guide that outlines the questions
and prompts utilized during the interviews conducted for the research study. It provides a
detailed framework for the interviewer to follow, ensuring consistency and reliability in data
collection.
Research Questions
The following research question guide this study:
1. What challenges do community college math instructors face now that AB 705 has
removed all remediation into transfer-level math courses?
2. How do community college math instructors differentiate the curriculum to meet
students’ diverse learning needs and skill gaps in AB 705 accessible math courses?
3. What other instructional strategies are community college math instructors using with
their students that generate equitable outcomes in AB 705 accessible math courses?
Introduction
Hello and welcome [insert participant name]. Thank you very much for your generous
time. My name is Shawn Taylor, and I am a researcher at the University of Southern California’s
Rossier School of Education. I am gathering research for a dissertation study that centers on the
challenges community college math faculty face now that AB 705 has removed the need for
remediation. I also wish to discover what instructional strategies math faculty implement to
overcome these challenges. You have been selected to speak with me today because you have
been identified as someone with a great deal to share about teaching transfer-level math courses
at a California community college post-AB 705 era.
166

To facilitate notetaking, I would like to record the audio and video of our conversation on
Zoom today. May I have your permission to record our conversation? Please sign the release
form. For your information, only researchers on the project will be privy to the recordings, which
will eventually be destroyed after they are transcribed. In addition, you must sign a form devised
to meet the university’s human subject requirements. Essentially, this document states that: (a)
all information will be held confidential, (b) your participation is voluntary, and you may stop at
any time if you feel uncomfortable, and (c) we do not intend to inflict any harm with the findings
of the research.
It is estimated that the interview will require approximately 35 minutes to complete.
During this time, I will ask several questions covering a wide range of topics related to the math
courses you teach and the classes you have taught pre-AB 705. If time begins to run short, it may
be necessary to interrupt you to push ahead and complete our line of questioning. Please provide
as much information and in-depth detail as possible during the interview. It is important that you
answer each question carefully so that the information provided reflects your experience
accurately.
Before we begin, do you have any questions you’d like to ask me regarding the context of
this study, the confidentiality of your responses, or how the data obtained today will be used?
Please do not hesitate to request an explanation if clarification is needed for a particular question
during the interview. I plan to use some of what is said today as direct quotes. However, none of
the data you provide will be directly credited to you. I will use a pseudonym to protect your
identity and de-identify any information I gather from you. Your cooperation in completing this
interview is greatly appreciated. Thank you again for agreeing to participate.
167

Interview Questions
Ok, let’s begin by gathering some personal information. I will also ask you for some
basic background information about the math classes you teach and have previously taught.
1. For the record, can you please state your first name and the first letter of your last
name?
2. How long have you been teaching remedial and transfer-level math courses?
3. What remedial and transfer-level math courses did you teach before AB 705?
4. What remedial and transfer-level math courses do you currently teach?
Thank you, [participant’s name]. For the next group of questions, I would like to talk
about AB 705, your perceptions of its impact, and how that looks in your classroom.
1. Describe, in general, the challenges you encounter daily teaching AB 705 accessible
math courses.
2. Describe the challenges your students face in AB 705 accessible math courses.
3. What are the long- and short-term implications of the student challenges you
described?
4. Describe how you address these challenges with your planning, instruction, and
assessment.
5. How have your instructional strategies changed since remediation is no longer a
prerequisite?
6. Describe the differences between the math skill level of your student pre- and post-
AB 705.
Thank you for sharing your responses [participant’s name]. Next, I’d like to ask you
some questions regarding your instructional style and strategies.
168

1. How would you describe a typical day in your AB 705 math classroom?
2. How do you determine a student’s skill level starting each semester?
3. Describe the strategies you utilize to meet your student’s learning needs while
covering all course content described in the COR.
4. What learning strategies do you implement to address significant skill gaps in
students?
Thank you for your responses. Let’s move on to our final round of questions. This group
of questions is about differentiated instruction.
1. What does the term differentiated instruction look like in your classroom?
2. How do you plan your lessons to differentiate the content for all learning levels?
3. Describe any learning theories and strategies you use to support mastery learning for
all.
4. In what ways do you differentiate assessments in your class?
5. What strategies do you implement when students perform poorly on assessments and
assignments, like exams and quizzes?
Thank you for your responses.
Closing Statements
Our interview has come to an end. I have no further questions for you. I would like to
personally thank you on behalf of the University of Southern California for your time, patience,
and detailed responses to my questions. [Participant’s name], may I contact you again in the
future if any clarification or ambiguities arise in this interview? We will also send you a copy of
the interview transcript to review and confirm the transcribed information. Finally, do you have
any follow-up questions for me now that we have concluded our interview? Have a pleasant day.

Abstract (if available)

Abstract Historically, California Community Colleges (CCCs) had broad discretion to determine which students could enroll directly in transferable college-level courses and which students had to begin with remedial prerequisites. These policies have disproportionately affected students of color and low socioeconomic status by placing them into remedial classes. Remediation may also impede graduation rates, particularly in math courses. AB 705 was passed to address this issue, which aimed to improve student success by using multiple measures to determine course placement. Since its passage, there has been an influx of academically underprepared students, creating new challenges for instructors. However, little research has focused on the experiences of math faculty in AB 705-affected courses. This study aimed to identify instructional practices that address learning gaps while meeting the needs of a diverse student population. Qualitative data were collected through conversations with community college math faculty. Findings suggest the need for a more student-centered approach to teaching math, including inquiry-based and personalized learning experiences. Additionally, professional development opportunities must be funded and accessible for instructors to stay current with the latest research and best practices. This study contributes to the development of effective strategies for closing learning gaps while promoting equity in community college math education.

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Asset Metadata

Creator Taylor, Shawn Michael (author)

Core Title Promising practices of California community college mathematics instructors teaching AB 705 accessible courses

School Rossier School of Education

Degree Doctor of Education

Degree Program Educational Leadership

Degree Conferral Date 2023-05

Publication Date 06/12/2023

Defense Date 04/13/2023

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

Tag AB 705,California Community Colleges,instructional strategies,math remediation,OAI-PMH Harvest

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Filback, Robert (committee chair), Hasan, Angela (committee member), Miranda, Alex (committee member)

Creator Email hughesdrive@gmail.com,shawntay@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113170482

Unique identifier UC113170482

Identifier etd-TaylorShaw-11951.pdf (filename)

Legacy Identifier etd-TaylorShaw-11951

Document Type Dissertation

Format theses (aat)

Rights Taylor, Shawn Michael

Internet Media Type application/pdf

Type texts

Source 20230613-usctheses-batch-1055 (batch), 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 author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

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

Repository Email cisadmin@lib.usc.edu