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The 2003-2012 impact of Algebra When Ready on indicators of college readiness across California school districts

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The 2003-2012 impact of Algebra When Ready on indicators of college readiness across California school districts

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Content Running head: IMPACT OF ALGEBRA WHEN READY 1
THE 2003-2012 IMPACT OF ALGEBRA WHEN READY ON INDICATORS OF COLLEGE
READINESS ACROSS CALIFORNIA SCHOOL DISTRICTS

by

Nicole Lee Jacobson

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

May 2016

Copyright 2016 Nicole Lee Jacobson

IMPACT OF ALGEBRA WHEN READY 2
Dedication
To my mom and dad for loving me and guiding me through all of my decisions in life. Thank
you for prioritizing education and valuing my pursuits in life.
To my husband for his endless devotion and love. Thank you for pushing me
and always believing in me. You are a rock and I could not have done it without you.
To my beautiful children for their smiles and love for life. Thank you for being the best son
and daughter I could ever imagine and for working so hard in school.
To my brother who has always encouraged me and led me to believe that I can do anything.
Thank you for being the greatest brother and for wanting the best for me.
To my in-laws for their support. Thank you for your guidance and help during this
extraordinary journey.
To Dr. Hocevar for mentoring and advising me throughout this process. Thank you for
believing in me and trusting me to conduct a quantitative study with great implications.
To Dr. Keim for your timely support when I needed it most. Thank you for guiding me,
stepping up to the plate, and playing an important role in my doctoral accomplishments.
To my committee members, Dr. Marsh and Dr. Hausner, for being supportive and for giving
me the feedback I needed to complete my dissertation.
To Acacia and Delvin who both encouraged and inspired me to become a Trojan. Thank you
for pushing me to excel and for the countless hours we have spent together.
To my friends, old and new, thank you for understanding that writing was a priority.
To my USC cohort and professors. Thank you for making this experience meaningful.
To my former and current colleagues and administrators who have continuously encouraged
me to lead. Thank you for helping to shape my educational career.
Words cannot express how much I appreciate all of you. This is for you. Fight On!
IMPACT OF ALGEBRA WHEN READY 3
Acknowledgments
The writing of this dissertation has been a milestone in my academic career. I attribute
the completion of my dissertation to the dedicated work of many educators. In particular, I
would like to acknowledge certain individuals who guided me in the research process and
provided invaluable support.
I would first like to honor my dissertation chair, Dr. Dennis Hocevar, for his mentorship
and firm dedication throughout the dissertation process. He challenged my thinking by
imparting his statistical expertise and extensive knowledge of quantitative studies. When we
encountered obstacles, he never stopped believing in me, even if it required additional hours of
work and revision. I value his commitment and assistance in crafting a study that I am
passionate about. I thank Dr. Hocevar for his sincerity and patience in helping me to accomplish
my goal. I credit the success of this study to his unyielding desire to finish what he started and I
cannot imagine a better advisor.
Next, I would like to thank my other chair, Dr. Robert Keim, for entering the process at a
time when I needed him the most. His kindness, humor, and genuine effort to make the
transition easier was priceless. I thank him for believing in me and reminding me that “Thursday
will come”. I would also like to thank Dr. Marsh and Dr. Hausner for their professional
guidance and support throughout this journey. They were both instrumental to my success in the
doctoral program and I value their knowledge and expertise.
Finally, I thank my USC colleagues and professors for their tireless encouragement and
drive. Our countless writing and study sessions encouraged me until the end. The support we
had for each other was priceless, and I could not have done it without my Trojan family.
IMPACT OF ALGEBRA WHEN READY 4
Table of Contents
Dedication 2

Acknowledgments 3

List of Tables 6

List of Figures 7

Abstract 8

Chapter One: Overview of the Study 10

Introduction to the Problem 10

Statement of the Problem 18

Purpose of the Study 19

Research Questions 20

Significance of the Study 21

Practical Significance 22

Theoretical Significance 23

Design Summary 24

Definition of Terms 26

Organizational Overview 29

Chapter Two: Literature Review 30

The Importance of Early Algebra Access 30

Algebra as a Gatekeeper 33

Opportunity to Learn 35

Selection Processes 36

Tracking 38

Impacts of Minority/Low SES Students 39

Detracking Efforts 42

History of Algebra Curriculum 42

No Child Left Behind 42

Algebra for All Initiative (2008) 44

Common Core State Standards - New Standards 50

Traditional and Integrated Pathway Decisions 52

Accelerated Pathways 53

Selection Process 53

College Preparedness and Coursetaking Patterns 54

Summary 57

Chapter Three: Methodology 58

Design Summary 59

Variables and Path Model 61

Quantitative Research Design 63

Participants and Setting 64

Instrumentation 65

Achievement Measures 65

Data Collection 66

Limitations of the Study 67

Chapter Four: Results 71

Research Question One 72

Research Question Two 77

Impact of SES 78

IMPACT OF ALGEBRA WHEN READY 5
Short-Term Effects of Algebra When Ready 79

Long-Term Effects of Algebra When Ready 80

Chapter Five: Discussion 81

Summary of the Study 82

Research Question One Findings 82

Research Question Two Findings 87

Conclusion 90

Unintended Consequences of Algebra for All 91

Policy Implications 93

Recommendations for Future Research 96

Summary and Conclusions 98

References 100

Appendix A: Waves 1-6 Descriptive Statistics 113

Appendix B: Waves 1-6 Hypothesized Causal Model 115

Appendix C: Waves 1-6 Correlations 121

IMPACT OF ALGEBRA WHEN READY 6
List of Tables
Table 1: Structural Equations 64

Table 2: Descriptive Statistics for Grade 8 Algebra I Participation Rate 74

Table 3: Descriptive Statistics for Grade 8 Algebra I Success Rate 74

Table 4: Descriptive Statistics for Algebra II Success Rates 76

Table 5: Descriptive Statistics for Science Success Rates 76

Table 6: Effect Sizes for Eighth Grade Algebra I Participation and Subsequent
Math Success 87

Table A1: Wave 1 Descriptive Statistics 113

Table A2: Wave 2 Descriptive Statistics 113

Table A3: Wave 3 Descriptive Statistics 113

Table A4: Wave 4 Descriptive Statistics 114

Table A5: Wave 5 Descriptive Statistics 114

Table A6: Wave 6 Descriptive Statistics 114

Table C1: Wave 1 Correlations 121

Table C2: Wave 2 Correlations 122

Table C3: Wave 3 Correlations 123

Table C4: Wave 4 Correlations 124

Table C5: Wave 5 Correlations 125

Table C6: Wave 6 Correlations 126

IMPACT OF ALGEBRA WHEN READY 7
List of Figures
Figure 1: Hypothesized Causal Model 25

Figure 2: Hypothesized Causal Model 60

Figure 3: Sample Sizes for Waves 1-6 65

Figure 4: Grade 8 Algebra I Participation and Success Means Graph 74

Figure 5: Algebra II and Science Success Means Graph 76

Figure 6: Hypothesized Causal Model Correlations 78

Figure 7: Effect Sizes of College Preparation Courses 85

Figure 8: Hypothesized Causal Model Medians for Waves 1-6 89

Figure B1: Hypothesized Causal Model- Wave 1 115

Figure B2: Hypothesized Causal Model- Wave 2 116

Figure B3: Hypothesized Causal Model- Wave 3 117

Figure B4: Hypothesized Causal Model- Wave 4 118

Figure B5: Hypothesized Causal Model- Wave 5 119

Figure B6: Hypothesized Causal Model- Wave 6 120

IMPACT OF ALGEBRA WHEN READY 8
Abstract
California has been at the forefront of national efforts to increase mathematics proficiency levels
for all students. With the passage of the Public Schools Accountability Act (PSAA) in 1999, an
educational accountability system was created requiring end-of-course subject matter tests in
grades 9 through 11 in all advanced math and science courses. This accountability system was
based on the assumption that a push for universal access of algebra in eighth grade would reduce
or eliminate tracking of historically marginalized students into remedial mathematics classes. As
California attempted to enact policies such as Algebra for All to maintain equity, it increased
opportunities for students to have access to early algebra. However, Algebra for All is a
misnomer in California because a relatively small number of districts strictly followed universal
access to algebra. Most districts followed the practice of placing students in Algebra When
Ready, a term coined by the National Council of Teachers of Mathematics (NCTM, 2008).
The purpose of this quantitative study was two-fold: (a) to determine the extent to which
California students have progressed in achievement in STEM courses, specifically Algebra I,
Algebra II, and science (Chemistry and Physics scores are merged to represent science) as a
result of federal and state policies and (b) to critically examine the extent to which Algebra When
Ready had a positive impact on indicators of college readiness in terms of Algebra I success,
Algebra II success, and science success from 2003-2012. A one-way Repeated Measures (RM)
ANOVA was conducted to compare the means on the California Standards Test (CST) of the
following variables over a six-year time period: Grade 8 Algebra I participation and success
(2004-2009), Grade 10-11 Algebra II success (2007-2012), and Grade 10-11 science success
(2007-2012).
A path analysis model is widely acknowledged as a standard method for making causal
inferences from correlational data. The path model utilized in this study included a mean of 189
IMPACT OF ALGEBRA WHEN READY 9
school districts and six waves of data from 2003-2012 to determine the intended impact of Grade
8 Algebra I participation (Opportunity to Learn- OTL) and success on college preparatory
courses. The path analysis model, which included six cohorts of data, was used to test whether
or not Algebra When Ready had the intended impact on college preparedness and future success.
Specifically, the researcher utilized an ordinary least squares regression to assess the model.
Structural equations were developed to test if the inner correlations are consistent with the
correlations the model predicts.
The findings from this study are compelling evidence that California made significant
progress because tracking rates have considerably decreased. School districts have shown
immense short-term and long-term gains in OTL and proficiency in college preparation classes.
Therefore, policies such as Algebra When Ready that pursue equity by detracking remedial
mathematics, can help to create systems where all students can have greater access to advanced
courses. This study has the potential to inform future policy decisions that are intended to
increase equity. The researcher’s suggestions supported by the findings of this study are as
follows: (a) create a strong system-wide, transparent accountability system in high schools; (b)
use objective measures targeting students for accelerated mathematics pathways to combat the
inequitable tracking; (c) create system-wide accountability for holding high expectations for all
students; and (d) provide students with appropriate supports as deemed necessary to succeed in
Algebra I.
IMPACT OF ALGEBRA WHEN READY 10
CHAPTER ONE: OVERVIEW OF THE STUDY
As the United States strives to compete in a global economy and maintain its competitive
edge, it is critical that all students have access to a quality curriculum. A pressing need in the
U.S. educational system is to improve college readiness and postsecondary success. Research
suggests that one main reason students falter in college is the discrepancy between their high
school experiences and college expectations (Conley, 2007). Unless educational achievement
improves, the competitiveness of the U.S. workforce is projected to decline. By the year 2020,
the United States could face a shortage of 14 million workers with the knowledge and skills
needed to compete for middle-income jobs in the global economy (Callan, Finney, Kirst, Usdan
& Venezia, 2006). Education is often viewed as the central key to a country’s economic and
global development. Hanushek, Peterson, and Woessmann (2010) report that countries
performing at higher levels in math and science show larger increases in economic productivity
than do other countries with lower performing students.
Introduction to the Problem
There is continuous cause for concern when it comes to student performance in
mathematics in the United States. The National Assessment of Educational Progress (NAEP)
results, often referred to as “the Nation’s Report Card”, illustrate that a large number of eighth
grade students in the United States are continually failing to reach levels of proficiency in
mathematics. Results from the 2013 NAEP indicate that 36% of the nationally representative
sample of 342,000 eighth grade students assessed achieved proficiency levels, while only 8%
were advanced (National Center for Education Statistics [NCES], 2013). Between 1990 and
2013, the number of eighth graders scoring proficient increased from 15% to 36%. Although
scores have been increasing for students overall, the achievement gap remains with a decreasing,
but still large, 33-point gap between African American and White students and a 28-point gap
IMPACT OF ALGEBRA WHEN READY 11
between Hispanic and White students (NCES, 2013). Despite attempts by the federal
government to close the margins, the NAEP shows little progress in narrowing the achievement
gap. In 2013, 42% of White students scored proficient, while African Americans and Hispanics
scored 11% and 15%, respectively (NCES, 2013). Additionally, the 2011 Trends in International
Mathematics and Science Study (TIMSS) results indicate that only 7% of U.S. eighth grade
students were classified as advanced compared to Taiwan with 49% advanced, Singapore with
48% advanced, and Korea with 47% advanced (NCES, 2011). Statistically, the data present a
sense of urgency and cause for concern because many U.S. students graduate from high school
unprepared for the demands of the 21
st
century.

Due to heightened demands of accountability and constant pressure to maintain equity,
districts are consistently striving to improve student achievement levels. In order to compete in a
globalized, 21
st
century society, all students need to be given the opportunity to learn (OTL) in
mathematics beginning with Algebra I. In the 1990s, essentially every state adopted state
content standards defining key knowledge and skills (Conley, 2013). The rationale for these
standards was to define what was needed for success in the 21
st
century society (Conley, 2013).
However, most states linked their standards to the goal of completing high school, not creating
access for all to postsecondary education. As Conley (2013) posits, failure in algebra in ninth
grade can cut in half the proportion of students aspiring to attend college, decreasing the number
of students eligible for postsecondary programs requiring a solid foundation for mathematics.
Failing algebra also inhibits student aspirations in careers in science, technology, engineering,
and mathematics (STEM). According to Conley (2013), students who are college and career
ready can “qualify for and succeed in entry-level, credit-bearing college courses leading to a
baccalaureate degree, a certificate, or career pathway-oriented training program without the need
for remedial or developmental coursework” (p. 51). Unfortunately, tracking practices limit
IMPACT OF ALGEBRA WHEN READY 12
opportunities for students to reach higher-level mathematics courses, which are indicators for
future educational and economical success.
Mathematics education is an important component of the United States’ ability to prepare
a workforce that can adapt to the challenges of the 21
st
century. As such, mathematics is
considered a “critical filter”, imparting the key for passing through the gates to higher education
(Stinson, 2004, p. 11). During the past two decades, algebra grew in significance in the U.S.
math curriculum (Loveless, 2013b). Readiness for college level mathematics and technically-
oriented jobs depends on students having a basic knowledge of algebra by the end of high school
(Loveless, 2013b). Algebra I has served as the curricular gatekeeper to higher-level math and
science courses, creating pathways for increased economic and educational opportunities
(Impecoven-Lind & Foegen, 2010; Loveless, 2013b; Matthews & Farmer, 2008; Paul, 2005;
Smith, 1996; Stein, Kaufman, Sherman, & Hillen, 2011). Ample empirical evidence
demonstrates that students completing algebra in eighth grade stay in the math pipeline longer
and have higher college attainment rates (Speilhagen, 2006). Algebra importance is reflected in
California public university admittance requirements, as it is the first of three courses needed for
college preparation (Liang & Heckman, 2013; Stotsky & Wurman, 2010). Furthermore,
mathematics courses are tied to economic access (Moses & Cobb, 2001; Rose & Betts, 2004).
Rose and Betts (2004) found that courses students take in high school are strongly correlated to
students’ earnings 10 years later. Although the benefits of early algebra access are clear, the key
is limited and the pathways do not create equal access for all students.
Despite the benefits highlighted above, access to advanced mathematics is highly
stratified along ethnic and class lines (Abedi & Herman, 2010; Domina, 2014; Walston &
McCarroll, 2010). Educational disparities in math placement practices are greatly correlated
with factors such as race, ethnicity, and social class status (Gamoran & Hannigan, 2000;
IMPACT OF ALGEBRA WHEN READY 13
Speilhagen, 2006; Walston & McCarroll, 2010). Evidence shows a dramatic underrepresentation
in advanced math courses and overrepresentation in lower-level courses among cultural and
linguistic minorities, which affects their opportunity to learn (Liang & Heckman 2013; Walston
& McCarroll, 2010). Statistically, traditionally marginalized groups are denied OTL as a result
of tracking practices, blocking the path to courses and preparation necessary for postsecondary
education. Oakes (1985) states that these grouping practices create a cycle of limited
opportunities and diminished outcomes for marginalized groups, as they are disproportionately
represented in lower tracks.
Current policies in the U.S. educational system are shaped by previous attempts of the
federal government to respond to the disparate outcomes in mathematics achievement. Several
historical events led to reform efforts attempting to shift educational ideologies to improve the
conditions of the educational system for all students. The launch of the Russian spacecraft,
Sputnik, on October 4, 1957, created concern regarding the efficacy of mathematics and science
education in the United States (Flemming, 1960). It pushed the American government to
accelerate and expand efforts to restructure the educational system and improve science and
mathematics instruction (Bybee, 2007). Sputnik probed the United States to launch efforts in
science and technology education to keep its competitive edge in the increasingly global
economy (Bybee, 2007). Essentially, Sputnik pushed the federal government to examine
disparities and increase its involvement in our educational system. The U.S. reaction to Sputnik,
coupled with criticism of the American educational system, set the stage for an unparalleled
amount of funding from the federal government to reform education (Jolly, 2009).
In effect, the launch of Sputnik led to increased public demand for a federal response to
improving American education. As a result, Congress passed the National Defense Education
Act (NDEA) in 1958, mandating schools to strengthen mathematics and science instruction
IMPACT OF ALGEBRA WHEN READY 14
(Stotts, 2011). Underlying the NDEA was the goal to create funding to stimulate American
education in order to counteract the Soviet educational system (Jolly, 2009). Providing one
billion dollars over four years in 40,000 loans, 40,000 scholarships, and 1,000 graduate
fellowships, most of the funding was intended for academically-capable students lacking the
financial means to pursue postsecondary degrees (Jolly, 2009). Additionally, this reform effort
encouraged states to strengthen initiatives to improve America’s competitiveness by matching
funds (Jolly, 2009). Ultimately, the NDEA established the federal government’s larger role and
stake in public education efforts, creating a sense of urgency to improve access to a more
rigorous curriculum for all students.
Before 1960, the federal government played a minor role in educational policy (Kantor,
1991). Due to the pressure to expand educational opportunity, the federal government pursued to
equalize education and redistribute resources to those disregarded by the system (Sunderman,
Levin, & Slee, 2010). In an effort to rectify the inequalities, Congress passed the Elementary
and Secondary Education Act (ESEA) in 1965 under the Johnson administration. The ESEA
was designed with the idea that full educational opportunity should be a top priority, indicating
the federal government’s commitment to improving education for economically disadvantaged
children. It reformed the federal role in education focusing on the educational needs of poor
students, establishing federal standards toward equitable treatment of disadvantaged students
(Kantor, 1991). The ESEA served as a stimulus for other legislation and created a new role of
the federal government in defining educational priorities and improving the educational system.
The No Child Left Behind (NCLB) Act of 2001 was a reauthorization of the ESEA, which is
discussed in further detail later in Chapter One.
Soon after the authorization of the ESEA, the Coleman Report was issued in 1966 by the
U.S. Department of Education, conveying disparities between the educational outcomes of low
IMPACT OF ALGEBRA WHEN READY 15
minorities compared to their White, middle-income counterparts (Coleman et al., 1966). This
report marked the beginning of the nation’s concern for education. The aim of the Coleman
Report was two-fold: (a) to describe aspects of the educational system and (b) to analyze the way
it was related to achievement (Cain & Watts, 1970). It presented a dismal view of the
effectiveness of our educational system in creating equal opportunities for all (Cain & Watts,
1970). Discrepancies of educational outcomes from students of different backgrounds were
outlined. This descriptive report has importance regarding the inequalities in the educational
experiences of students of different races, ethnic groups, and economic classes. The American
dream assumed these wide discrepancies can be eliminated through the public education system.
However, as the above statistics demonstrate, these discrepancies persist today.
Another report, A Nation at Risk, drew attention to the central importance of education to
our national well-being (Goldberg & Harvey, 1983). A Nation at Risk called for educational
reforms to achieve a more competitive position in relation to other nations (Heckman, 2013). It
warns of the “tides of mediocrity” threatening the nation and its people (National Commission on
Excellence in Education [NCEE], 1983, p. 112). Mathematics was singled out as a concern in
this seminal document and concerns were raised that those without skill, literacy, and training
necessary for the future will be disenfranchised (NCEE, 1983) and will not have the chance to
fully participate in society, putting the nation at risk. The risk refers to the promise that all,
regardless of race, class, or economic status, are entitled to a fair chance and to the tools needed
to develop the mind. A Nation at Risk served as a medium for a reform movement to call
attention to changing the system, by providing all students with a quality education.
Essentially, California pushed to intensify efforts to create equity in the educational
system. Response to concerns about the U.S. educational system and access to a quality
curriculum for all students have taken many different forms (Garrett, 2008). In 1989, the NCTM
IMPACT OF ALGEBRA WHEN READY 16
produced a set of math standards endorsing early algebra. Additionally, the California
Department of Education (CDE) recognized the importance of early algebra and the inequities in
access to advanced math courses across California school districts. Following the NCTM
standards, the 1997 California Mathematics Framework set algebra as the course suggested for
all eighth graders (CDE, 1998). In 1999, the California Legislature passed the Public Schools
Accountability Act (PSAA), which was designed to bring accountability measures to its public
schools and to provide incentives for improving school performance. The foundation of the
PSAA was the Academic Performance Index (API), the summary score assigned to each school
in California (Powers, 2004). The PSAA authorized the Superintendent of Public Instruction and
the California State Board of Education (SBE) to develop the API, consisting of several
indicators to measure the performance of schools. This accountability system was centered on
the assumption that a push towards universal access of algebra in eighth grade would result in
detracking.
As California attempted to enact policies to maintain equity through policies and
initiatives, it increased opportunities for students to have access to early algebra. The Bush
administration passed the reauthorization of the ESEA, the NCLB Act of 2001, focusing on
setting standards for student achievement and establishing criteria for highly qualified teachers
(Garrett, 2008). Tests mandated by NCLB were administered annually to students in grades
three through eight and at least one time in high school. Individual states determined what
constituted proficiency on state tests (Loveless, 2013b). According to NCLB requirements,
California was considered to be out of compliance because the course outlined in the California
framework for eighth grade, Algebra I, did not match the test that all students had to take. As a
result, the SBE mandated that all students take the Algebra I CST in eighth grade, despite the
course they were enrolled in. Although General Mathematics was still offered, it was not
IMPACT OF ALGEBRA WHEN READY 17
considered on grade level. In order to incentivize schools to enroll eighth grade students in
Algebra I, a policy was enacted that penalized schools and districts for placing students in the
General Mathematics course through the API. For example, when students scored “Proficient”
on the CST for General Mathematics, the API scoring formula was adjusted and schools were
only given credit for “Basic”. Although algebra was not mandated for all eighth graders, schools
and districts were penalized for placing students in the lower tracks. In California, being tracked
into pre-algebra rather than algebra in the eighth grade is often the first signal that a student will
not enter into a four-year university (Adelman, 1999; Bozick, Ingels, & Owings, 2008). Algebra
for All is a misnomer in California because a relatively small number of districts strictly followed
universal access to algebra. Most districts followed the practice of placing students in Algebra
When Ready, a practice advocated by the NCTM (2008).
In response to the inequities in access to mathematics, educational reform efforts focused
on creating universal access to accelerate middle school mathematics. Nationwide, a central
theme in educational reform is to improve access for traditionally underprivileged groups,
according to their race, socioeconomic status (SES), or English language proficiency (Harris &
Anderson, 2012). In an effort to maintain implementation and advocacy for early algebra, a
reform policy implemented in California was Algebra for All, an attempt to help level the playing
field by mandating algebra in eighth grade. Algebra for All was a mechanism used to increase
enrollment rates and expand OTL in algebra, greatly increasing the odds that disadvantaged
students gain equal access to advanced courses (Domina, 2014). Despite the success of Algebra
for All on increasing enrollment for marginalized groups, the Common Core State Standards
(CCSS) threatens to reverse the trend. The CCSS were developed to standardize expectations
across the nation and to address the fragmentation of state assessments. Currently, the
implementation of the CCSS lists Algebra I as a high school course and acceleration is needed to
IMPACT OF ALGEBRA WHEN READY 18
take at least one year of calculus in the 12
th
grade. Double acceleration is needed to enroll in
Calculus BC, the goal of students hoping to major in science or engineering at top colleges. A
range of acceleration pathways are considered by high school districts: (a) compacting three
years of mathematics into two, (b) offering double periods of math, and (c) offering a summer
bridge enhanced pathway program. Local districts are given the choice and this discretion
becomes an equity issue. Will students no matter where they go to school have the same
opportunity as those in more affluent districts? This imbalanced opportunity historically led to
differences in a student’s OTL and educational trajectories.
Statement of the Problem
With the end of Algebra for All in 2013 and the implementation of the CCSS in
California, there are concerns as to which students will receive access to the accelerated track in
mathematics. The inequitable placement of traditionally disadvantaged students in Algebra I in
eighth grade puts students on the path for lower-level mathematics, limiting their OTL and
access to advanced courses. Coursetaking in mathematics is considered to be one of the most
visible gatekeepers in the high school curriculum (Gladieux & Swail, 2000). Clearly, tracking
policies have created intractable disparities as minority groups and students in low SES have
experienced restricted access and OTL in advanced math courses.
Algebra I in isolation does not provide the necessary knowledge base needed to access
advanced courses or promote future educational success. Taking Algebra I in eighth grade gives
students the opportunity to complete Algebra II by the 10
th
grade. This allows the students more
flexibility to repeat failed classes as needed and to enroll in more advanced courses for the
remainder of high school. In other words, in order to secure the advantages of advanced
coursework in mathematics, students need to take Algebra II (Adelman, 1999). According to
Adelman (1999), Algebra II cuts the gap in half in college graduation rates between African
IMPACT OF ALGEBRA WHEN READY 19
American and Latinos and their White peers. Furthermore, completing a course after Algebra II
(Trigonometry or Pre-Calculus), more than doubles the chances that students entering college
will complete a bachelor’s degree.
With the implementation of the CCSS, the California SBE shifted its recommendations to
place algebra as the default course for ninth grade. Offering algebra in eighth grade is
considered optional, and requires acceleration in seventh grade. Limiting Algebra I to ninth
grade students may adversely affect advanced math course pathways and subsequent college
preparedness for students not accelerating. The discretion of acceleration rests in the hands of
local school districts, with the greatest potential impact affecting traditionally marginalized
students. Restricting access to Algebra I in ninth grade may be a step backwards, reversing
California’s earlier attempts to increase algebra access in eighth grade for all students. CCSS
can serve as a curricular floor guaranteeing that all students are exposed to a common body of
knowledge or it can serve as a ceiling, restricting the progress of bright students so that their
achievement looks similar to their peers (Loveless, 2015). Detracking advocates interpret the
“common” in Common Core as reason to eliminate accelerated tracks for high achievers
(Loveless, 2015, p. 3). Accelerated courses in mathematics must not be reserved for the most
fortunate students, but need to be accessible and available to all students who are ready.
Purpose of the Study
The purpose of this quantitative study was to critically examine the extent to which
California district test data (2003-2012) support the hypothesis that Algebra When Ready had a
positive impact on the following indicators of college readiness: Algebra I success, Algebra II
success, and science success across student subgroups and poverty levels in California.
Additionally, I seek to determine the extent to which California K-12 students have progressed in
achievement in STEM courses, specifically Algebra I, Algebra II, and science from 2003-2012.
IMPACT OF ALGEBRA WHEN READY 20
Importantly, this study will utilize publicly available math scores from the CST, controlling for
SES, to determine whether Algebra When Ready, as dictated by the PSAA and NCLB, led to
future success in math courses and college preparedness.
Clearly, policies influence middle school mathematics course placement practices,
increasing the odds that low-achieving students take advanced math courses (Domina, 2014).
However, there is a lack of clarity about how districts will be measured to demonstrate
compliance with these new initiatives. An analysis to assess the effect of California’s systemic
efforts to increase algebra participation and success is needed. Using historical data
downloadable from the CDE website, I will determine the effect that both state and federal
initiatives had on student participation and success in advanced mathematics courses and college
preparedness. The implementation of the CCSS recommends algebra in the ninth grade and this
may slow the trend of increased early Algebra I enrollment; however, the acceleration of middle
school mathematics remains a major force in our national educational system (Domina, 2014).
With the end to the Algebra for All initiative, some worry that the implementation of the CCSS
may reverse the detracking efforts and increased enrollment trends in advanced mathematics
courses in California. Tracking into lower-level and remedial mathematics courses serves as a
barrier restricting students’ OTL in advanced courses. These practices exasperate disparities by
isolating minority students within schools, distributing fewer educational opportunities to them
(Darling-Hammond, 2006; Oakes, 2005).
Research Questions
The study explores the following two research questions:
1. To what extent, if any, have California K-12 students progressed in grade 8 Algebra I
participation and success, and college readiness as measured by advanced math and
science success during the period of 2003-2012?
IMPACT OF ALGEBRA WHEN READY 21
2. Do California district test data (2003-2012) support the hypothesis that Algebra When
Ready had a positive impact on the following indicators of college readiness: Algebra I
success, Algebra II success, and science success.
Significance of the Study
As NCLB ended, it is important to understand the effects of policy decisions on a
student’s OTL and success in mathematics. The study examined the extent to which K-12
students in California progressed in Grade 8 Algebra I participation and success in Algebra I,
Algebra II, and science. The significance is to determine whether California district test data
(2003-2012) support the hypothesis that Algebra When Ready positively affected the following
indicators of college readiness: Algebra I success, Algebra II success, and science success.
Division along racial and SES lines is evidenced by academic achievement gaps and unequal
access to higher-level mathematics courses (Walston & McCarroll, 2010). Unequal access to
college preparatory mathematics courses unfairly denies educational success to students who
would benefit from better opportunities (Gamoran & Hannigan, 2000). Presumably, to enter the
gateway to postsecondary education, all students need to be given equal access to a rigorous
mathematics curriculum.
This study includes a critical examination of the impact that practices and policies have
on student success in mathematics. Specifically, Algebra I participation and success were
examined to determine its intended impact on access to advanced mathematics and college
readiness. The analysis will add to the research regarding the effects of educational policies and
its impact on OTL and success rates in higher-level math courses and college readiness. Before
shifting to a new paradigm of the CCSS, the successes and challenges of NCLB must be
examined to understand the intended impact on student success in advanced mathematics. This
dissertation study may equip educators with knowledge of the impact that Algebra I success has
IMPACT OF ALGEBRA WHEN READY 22
not only on subsequent courses, but also on future indicators of success. The findings may be
useful as policies at both the state and national level continue to push for mathematics reform to
maintain equity.
Practical Significance
In order to address the longstanding educational inequities, there is a national push to
improve access to mathematics for historically marginalized groups, according to their race,
SES, or English language proficiency (Harris & Anderson, 2012). California is at the forefront
of the national effort to strengthen the middle school mathematics curricula by increasing eighth
grade algebra enrollment (Domina, McEachin, Penner, & Penner, 2015). The push for most
students to complete Algebra I by the end of eighth grade was a centerpiece of state policy in
California, influenced by the Algebra for All movement (Loveless, 2015). The 2013 NAEP data
indicate that eighth grade algebra enrollment rates increased from 24% to 35% nationwide
between 2000 and 2010 (Domina et al., 2015). This increase in enrollment clearly predates the
SBE’s efforts to make algebra the course of record (Domina et al., 2015). The adoption of the
CCSS recommends pre-algebra for eighth grade students as state policy no longer mandates
accelerated algebra (Domina et al., 2015). This system-wide intervention is a policy change that
can possibly result in large effects, and can be more cost effective than smaller scale
interventions. Ultimately, this will lower eighth grade enrollment in Algebra I and eliminate
geometry as a middle school course. This may be cause for alarm as placement decisions are
now in the hands of local school districts in California. Early access to algebra may “socialize” a
student into taking more mathematics courses, regulating access to advanced pathways and
increased levels of achievement in high school (Smith, 1996, p. 141). This, in turn, opens
educational pathways to increased opportunities.
IMPACT OF ALGEBRA WHEN READY 23
Theoretical Significance
Human capital theory suggests that the pursuit of education leads to individual and
national economic growth (Sweetland, 1996). Curriculum is valuable as it “imparts” skills that
help students advance in the labor market and become more productive (Rose & Betts, 2004, p.
497). Rose and Betts note that those who enroll in a more advanced math curriculum may learn
skills that directly apply to specific jobs and may also acquire reasoning skills that indirectly
make them more productive. Algebra is identified as a serious equity and civil rights issue, as
traditionally marginalized students have been denied access to early algebra (Moses & Cobb,
2001). With increased recognition of algebra as a gatekeeper to more advanced math and
science courses, there is a push for policies mandating early algebra for all students. Early
success in Algebra I gives students more time to complete advanced courses by the time they
graduate from high school. Access and equity is at the heart of the American dream and is the
goal of education in the United States (Stein et al., 2011).
It is important to determine whether or not Algebra When Ready had its intended
consequences. Stein et al. (2011) reviewed 18 studies which collectively validate that exposure
to early algebra increases both algebra achievement outcomes and higher math coursetaking
pathways. A caution to this generalization is that the researchers purposefully separated studies
that involved explicit universal algebra policy interventions. Although the findings from studies
using nationally representative data demonstrate strong positive results for students taking early
algebra, studies conducted in settings with universal algebra policies provide mixed positive
outcomes. Stein and colleagues identify several research studies suggesting that some students,
particularly traditionally marginalized students, are barred access to early algebra despite the fact
that they have the necessary requisite skills. In response to the inequalities in access to advanced
mathematics, Algebra for All was an effort in California to improve access to early algebra for all
IMPACT OF ALGEBRA WHEN READY 24
students. Since 2003, California made substantial progress in reducing tracking of historically
marginalized students into remedial mathematics. However, with the end of Algebra for All and
the shift to CCSS in California, there may still be a serious threat to equity. This could challenge
California’s deliberate detracking attempts to make algebra and college accessible to all students.
Providing early algebra instruction to all students ensures excellence and equity, while
addressing achievement gaps among minority and low SES populations (Spielhagen, 2006).
There is a gap in the research regarding the long-term effect that algebra has on future success
indicators. Existing research fails to examine the relationship between increased participation in
Grade 8 Algebra I and achievement in future courses. Algebra I has been correlated with
subsequent course participation and success, but its impact on future indicators of college
preparedness have not been analyzed. The inferred causal model (Appendix B) has not been
assessed in a way to determine its impact on future success. Stein et al. (2011) “conclude with a
call for studies that examine the relationship among algebra policies, instruction, and student
outcomes to understand the mechanisms by which policies can lead to success for all students”
(p. 453). Research lacks in determining whether initiatives such as the PSAA and NCLB have
led to higher success rates in future mathematics courses in California.
Design Summary
This study used archival data to assess the extent to which K-12 students have progressed
in college preparation math and science courses. Additionally, the study sought to determine
whether CA district data (2003-2012) support the hypothesis that Algebra When Ready had a
positive impact on the following indicators of college readiness: Algebra I success, Algebra II
success, and science success. A quantitative approach was employed to analyze the impact of
the causal model (Figure 1) of mathematics coursetaking patterns following the passage of the
PSAA (1999) and the NCLB (2001) provision in California schools. The analysis included a
IMPACT OF ALGEBRA WHEN READY 25
mean of 189 school districts and six waves of data from 2003-2012 to determine the intended
impact of Grade 8 Algebra I participation (OTL) and success on college preparatory courses.
Specifically, this study utilized an ordinary least squares regression through a path analysis to
assess the model beginning with Grade 7 Math success to Grade 8 Algebra I participation and
success to Grade 10-11 Algebra II success to Grade 10-11 science success. College
preparedness was measured in terms of Grade 10-11 Algebra II success and Grade 10-11 science
success.
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
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2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

β
1

β
5

β
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β
8

β
10

β
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β
7

β
2

β
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β
4

Figure 1. Hypothesized Causal Model
IMPACT OF ALGEBRA WHEN READY 26
Definition of Terms
There are multiple terms that need to be operationally defined to increase clarity in this
study. These definitions are useful in the investigation to determine the extent to which
California district test data (2003-2012) support the hypothesis that Algebra When Ready had a
positive impact on the following indicators of college readiness: Algebra I success, Algebra II
success, and science success.
Academic Performance Index (API): The API is a single number ranging from
200 (low) to 1000 (high), which reflects a school’s, a Local Education Agency’s (LEA’s), or a
student group’s performance level, based on the results of statewide testing. The API was
established by the PSAA, a state law passed in 1999 that established a new accountability system
for K-12 public education in California. The purpose of an API is to measure the academic
performance and growth of schools. API is calculated by converting a student’s performance on
statewide testing across multiple content areas into points on the API scale. These points are
averaged across all students and all tests. The target API for all students to meet is 800. Schools
not reaching 800 are required to meet annual growth targets until the goal is met (CDE, 2013).
Acceleration: Students may decide at an early age that they want to take calculus or other
college level courses in high school. These students would need to take accelerating options to
begin the study of high school content in middle school, which would lead to pre-calculus or
advanced statistics as a junior and calculus, advanced statistics, or other college level choices as
a senior. Accelerated courses should cover all of the CCSS and not skip or skim over any of
them (CDE, 2015a).
Adequate Yearly Progress (AYP): The state is responsible for determining the
procedures for measuring AYP. AYP describes the amount of yearly improvements each Title I
school and district is expected to make in order to enable low-achieving students to meet the high
IMPACT OF ALGEBRA WHEN READY 27
performance levels expected of all students. AYP is a series of annual academic performance
goals established for each school, LEA, and the state as a whole (CDE, 2013).
Algebra for All: A reform policy implemented in California in 2008. In July 2008, the
California SBE voted to require all California eighth grade students to be assessed in algebra
within three years. Algebra for All was a mechanism used to increase enrollment rates and
expand OTL in algebra, greatly increasing the odds that disadvantaged students gain equal access
to advanced courses (Domina, 2014).
Algebra When Ready: The NCTM (2008) stated that all students should have access to
high quality algebra instruction when ready. Only when students exhibit demonstrable success
with prerequisite skills-not at a prescribed grade level-should they focus explicitly and
extensively on algebra, whether in a course titled Algebra I or within an integrated mathematics
curriculum. Exposing students to such coursework before they are ready often leads to
frustration, failure, and negative feelings about mathematics.
College and Career Readiness: Students who are ready for college and career can qualify
for and succeed in entry-level, credit-bearing college courses leading to a baccalaureate degree, a
certificate, or career pathway-oriented training program without the need for remedial or
developmental coursework (Conley, 2013).
Common Core State Standards-Mathematics (CCSS-Math): As of the spring of 2013, the
CCSS were adopted by 45 states and the District of Columbia. Having the same standards helps
all students get a good education, even if they change schools or move to a different state.
Teachers, parents, and education experts designed the standards to prepare students for success
in college and the workplace (CDE, 2015a).
California Standards Test (CST): The CST is the California standards-based test. It is a
criterion-referenced measure of how students are achieving the academic standards adopted by
IMPACT OF ALGEBRA WHEN READY 28
the California SBE. There are five performance levels used to describe achievement: Far Below
Basic, Below Basic, Basic, Proficient, and Advanced (CDE, 2015c).
General Mathematics: The General Mathematics CST assesses the knowledge of
California’s grades six and seven mathematics content standards. Eighth grade and ninth grade
students, who are not yet in Algebra I or who are taking the first of a two-year Algebra I course,
are required to take the General Mathematics Test. It is an arithmetic driven curriculum in
seventh and eighth grades that repeats much of what was learned in elementary school (Useem,
1992).
National Assessment of Educational Progress (NAEP): NAEP is the largest nationally
representative and continuing assessment of what America’s students know and can do in
different subjects. It provides a common measure of student achievement across the nation, and
is referred to as “the Nation’s Report Card” (NCES, 2015a).
Opportunity to Learn (OTL): OTL is access and equal opportunities to effective teachers,
curriculum, scheduling, or high-ability tracking, in order to learn standards. The notion of OTL
was introduced 40 years ago as a means to recognize curricular differences in student
achievement nationwide (Herman, Klein, & Abedi, 2000).
Pathway: A pathway comprises the typical order and timing of courses that
students follow and is intended to create smooth transitions between courses. This course
sequence, especially in mathematics, is often enforced through prerequisites. For example,
Algebra I is a prerequisite for Algebra II (Finkelstein, Fong, Tiffany-Morales, Shields, & Huang,
2012).
State Board of Education (SBE): The K-12 policy-making body for academic standards,
curriculum, instructional materials, assessments, and accountability. The SBE adopts
IMPACT OF ALGEBRA WHEN READY 29
instructional materials for K-8. The SBE has the authority to grant LEA requests for waivers of
certain provisions of the Ed Code (CDE, 2015c)
Success: Success rates in this study are defined as a score of basic or above on the CST.
The cutoff for the basic scale score is 300 (CDE, 2013).
Tracking: Tracking is a process using scholastic capabilities to group students in
differentiated classes or academic programs (Rui, 2009).
Organizational Overview
This chapter introduced the current study’s statement of the problem, purpose, research
questions, significance, and definitions of terms. Additionally, a brief overview of related
literature was provided to give an introduction to the problem. The subsequent chapters are
organized as follows: Chapter Two considers the research literature and other publications
related to this study; Chapter Three details the methodology utilized in this study and includes
the investigation’s purpose, design, instrumentation, participants, data collection procedures, and
statistical analyses; Chapter Four describes the results of the study; and Chapter Five provides a
summary, discussion of findings, conclusions, implications, and recommendations for further
research.
IMPACT OF ALGEBRA WHEN READY 30
CHAPTER TWO: LITERATURE REVIEW
The discourse on reform efforts to increase math achievement levels for students in the
United States has persisted for many decades. Schools nationwide are tasked with improving
global competitiveness in mathematics. Research substantiates math as a powerful gatekeeper
for advanced courses and postsecondary advancement (Impecoven-Lind & Foegen, 2010; Liang,
Heckman, & Abedi, 2012; Matthews & Farmer, 2008; Paul, 2005; Smith, 1996; Stein et al.,
2011). Due to its crucial role as a curricular gatekeeper, access to advanced mathematics,
beginning with algebra, can result in increased educational and economic opportunity for
students (Ladson-Billings, 1997). As a result, the national educational reform effort is predicated
on increasing math proficiency levels for all students. This can only happen when all students
are given opportunities to thrive in math. Since Algebra I is the benchmark of math literacy
(Paul, 2005), it is imperative that reform efforts focus on this domain. This chapter provides an
overview of the literature pertaining to the importance of early algebra access, algebra as a
gatekeeper, and the history of algebra. To further contextualize this study, the intended impact
of past and current algebra policies in regards to tracking and OTL are explored.
The Importance of Early Algebra Access
If eighth grade algebra is considered to be the standard for most of the world, as
evidenced from international data, then one-third of U.S. students have not had the opportunity
to learn rigorous math in eighth grade (Schmidt, 2004). Mathematics courses are organized in a
hierarchical sequence, with enrollment in progressively more advanced courses dependent upon
successful completion of prerequisite courses (Cogan, Schmidt, & Wiley, 2001; Walston &
McCarroll, 2010). In other words, skills build linearly from one course to the next, meaning that
curricula must generally be mastered before successfully advancing to the next course (Riegle-
Crumb & Grodsky, 2010). The sequential nature of math courses creates a positional advantage
IMPACT OF ALGEBRA WHEN READY 31
for students beginning high school with courses that are more advanced (Schneider, Swanson, &
Riegle-Crumb, 1998). This early entry point allows students to enter a college preparatory
pathway. Mathematics involves another problem of rigidity in that math courses in high schools
follow a tightly arranged sequence, making it hard to catch up if one starts out behind (Gamoran,
Porter, Smithson, & White, 1997). Consequently, math classes are likely to be restricted to
students who are perceived to be ready for the progression, denying access to certain groups of
students.
Research suggests that early access to algebra provides students more opportunities for
reaching higher-level mathematics courses in high school. Paul (2005) asserts that completing
three years of high school mathematics, starting with Algebra I, is the national threshold for
admission to competitive colleges. The completion of higher-level math courses is related to an
increased likelihood of entrance into a four-year college or university. In our current global
economy, few Americans can afford to be left out of advanced math courses (Ladson-Billings,
1997). Robert Moses described algebra as “the new Civil Right”, stressing the social
consequences of low-income and minority students taking remedial or general math courses in
lieu of algebra (Loveless, 2008, p. 2). As schools experience unparalleled cultural, linguistic,
and ethnic diversity, access and completion of advanced math courses can possibly help to level
the playing field.
Algebra gained momentum in the U.S. math curriculum over the past three decades in an
attempt to improve achievement levels of students (Loveless, 1998). California was at the
forefront of national efforts to universalize algebra in eighth grade (Loveless, 2008).
Traditionally, Algebra I was reserved for the most mathematically gifted eighth graders
(Loveless, 1998). In the earlier era, teachers used math as a curriculum sieve, “sifting and
winnowing” to select the top students to advance to higher mathematics courses (Ladson-
IMPACT OF ALGEBRA WHEN READY 32
Billings, 1997, p. 699). However, the revision of the 1997 California Mathematics Framework
called on middle schools to enroll all eighth graders in Algebra I, thus opening the doors of
opportunity for more students (Domina et al., 2015). Enrolling all eighth graders served to
eliminate inequities within algebra enrollment. In 1999, the PSAA was passed by the California
Senate, penalizing schools for enrolling eighth graders in pre-algebra or general math courses –
an incentive for schools to enroll students in algebra (Domina et al., 2015). This was a necessary
step in developing a system to hold schools and districts accountable for improving student
performance. With the passage of the PSAA, the Algebra I CST became the “sole test of record”
for California eighth graders to measure student achievement (Domina et al., 2015, p. 276). As a
result, between 1999 and 2008, the number of eighth graders enrolled in Algebra I tripled from
16% to 51% (Rosin, Barondess, & Leichty, 2009). The aforementioned statistics demonstrate
that California made efforts to greatly diminish tracking, and, clearly, progress was made to
increase access to advanced mathematics courses in middle school.
Research from NCES concluded that students taking Algebra I in eighth grade had a
greater chance of attending college (Liang & Heckman, 2013). Smith (1996) used transcript files
from High School and Beyond (HS & B) that included samples of 9,158 high school sophomores
in 1980, all of which stayed in the same high school until graduation in 1982. Smith compared
two groups: (a) students who took a course in algebra in high school and (b) students who took
the course before high school. Early access to algebra had a sustained positive effect on
students, leading to more advanced mathematics coursework and higher performance by the end
of high school. The group taking algebra before high school continued to take mathematics
courses and stayed in the pipeline longer than their counterparts who took algebra in high school
(Smith, 1996). Although Smith found that early access to algebra has a positive impact on
students’ math attainment, students coming from lower SES levels were disproportionately not
IMPACT OF ALGEBRA WHEN READY 33
given access to early algebra. Similar to Smith’s (1996) findings, Spielhagen (2006) reported
that students finishing algebra in eighth grade stayed in the math pipeline longer and attended
college at higher rates, suggesting access to algebra in eighth grade is a means to narrow the
achievement gap.
Other research supports the argument that early algebra keeps students in the math
pipeline longer. Loveless (2008) reported that 83% of students completing geometry in ninth
grade complete calculus or other advanced courses in high school. Evidence also suggests that
students taking algebra earlier have stronger math skills (Loveless, 2008). It is important to note
that general and remedial courses, such as pre-algebra, are described as curricular dead ends,
with no true progression in content. Paul (2005) indicates a general consensus that the capacity
to think with mathematical training in Algebra I should be the benchmark of defining
mathematical literacy. Algebra has the impact to (a) provide stronger preparation for two-year
programs in community colleges that require math backgrounds and (b) increase the pool of
students who can master high levels of math required for admission and careers in math and
science (Paul, 2005). Given these important findings related to algebra, policymakers at the
federal, state, and local level have sought to increase early access to algebra.
Algebra as a Gatekeeper
Educators and policymakers view algebra as the gatekeeper for more advanced math and
science courses, which are pathways for later success in postsecondary education and beyond
(Impecoven-Lind & Foegen, 2010; Liang & Heckman, 2013; Matthews & Farmer, 2008; Paul,
2005; Smith, 1996; Stein et al., 2011). According to Adelman (1999), students who do not
master algebra in eighth or ninth grade may have their path to advanced training and high status
careers blocked. Algebra importance is reflected in California public university admittance
requirements. Referencing the A-G requirements for admission to the University of California
IMPACT OF ALGEBRA WHEN READY 34
(UC) and California State University (CSU), algebra is the first of three courses deemed
necessary for preparation in college (Liang & Heckman, 2013; Stotsky & Wurman, 2010). Both
the UCs and CSUs require a three-year minimum of college preparatory mathematics, with a
strong recommendation of four years, including elementary algebra, advanced algebra, and two
and three-dimensional geometry. Also included are trigonometry and statistics (Regents of the
University of California, 2015). These high school math requirements prepare students for
freshman level university study. Ladson-Billings (1997) claims that admittance to universities
results in increased economic opportunities for students and for the nation as a whole. Only 25%
of students taking Algebra II in their junior year are fully prepared for non-remedial college
mathematics courses as determined by the Early Assessment Program, given in the junior year of
high school (Liang & Heckman, 2013). However, 88% of the 11
th
grade students who took
Algebra II in 10
th
grade and took another advanced mathematics course in the 11
th
grade are
considered to be college ready (Stotsky & Wurman, 2010). These percentages are evidence that
additional mathematics courses in 11
th
and 12
th
grades contribute to college readiness.
In addition to college entry requisites, mathematics courses are tied to economic access
(Moses & Cobb, 2001). Rose and Betts (2004) conducted a national study on the effects of high
school mathematics courses on the earnings of 12,000 people 10 years after high school. The
researchers revealed that courses taken in high school were strongly correlated to student
earnings 10 years later. Taking algebra or geometry increased earnings by 8%, while taking
calculus in high school was correlated to increased earnings of 19.5% (Rose & Betts, 2004). On
the contrary, a negative correlation for vocational math courses, including pre-algebra and
general math, was indicated in the study. A disproportionate number of students taking
vocational math courses were socioeconomically disadvantaged and minority students. The
IMPACT OF ALGEBRA WHEN READY 35
policy shift towards earlier access to algebra was a means to create more equitable learning
opportunities for all students, especially those who are disenfranchised.
Opportunity to Learn
The prevailing evidence in the literature is that mathematical literacy and proficiency are
integral for both individuals and the nation. Stanic (1997) contends that providing equitable
access to mathematics is not considered optional. The idea of OTL was introduced 40 years ago
as a means to recognize curricular differences in student achievement nationwide. OTL occurs
when schools provide opportunities for students to learn what is expected of them (Herman et al.,
2000). Tracking policies that place students in accelerated courses based on test scores, or
perceived ability, limit a student’s opportunity to learn.
Due to increased federal pressure and heightened accountability demands, policymakers
and educators have regained interest in OTL (Abedi & Herman, 2010). OTL has become a
policy instrument and measure of whether or not students have the opportunity to study a
particular topic (McDonnell, 1995). For example, in the early 1990s, OTL became a policy issue
in debates related to standards, accountability, and achievement. Politicians contended with a
school’s responsibility to give students an adequate OTL before being held accountable for
meeting achievement standards. Inherent in the notion of OTL is that students should not be
held accountable for knowledge that they have not had the opportunity to learn (McDonnell,
1995). In other words, students cannot be responsible for what they have not been taught.
The effort to intensify the math curriculum is predicated by the assumption that
accelerating course placements will increase a student’s OTL. Middle school mathematics has
been described as a central “nexus” of educational inequality (Domina et al., 2015, p. 1949), as
access to advanced courses is stratified along ethnic and class lines (Walston & McCarroll,
2010). In an effort to meet academic demands and prepare more students for postsecondary
IMPACT OF ALGEBRA WHEN READY 36
education, U.S. high schools intensified their curriculum to create more opportunities for
students (Domina, 2014). These increased opportunities equal more preparation for college and
career readiness by creating a path consisting of advanced math coursework.
Selection Processes
Concerns over inequitable selection processes have been the stimulus for policies
mandating algebra for all (Stein et al., 2011). Bozick et al. (2008) assert that larger percentages
of Asians, Whites, students of high SES, students living in two-parent households, students
attending Catholic/private schools, and students expecting to earn a bachelor’s degree were
enrolled in higher-level math courses. In support of these findings, Walston and McCarroll
(2010) share a similar perspective in that access to middle school math courses continue to be
stratified along ethnic and class lines. Statistically, 50% of White eighth graders and 67% of
Asian eighth graders are enrolled in algebra or a more advanced course (Walston & McCarroll,
2010). In contrast, 16% of African American students and 38% of Hispanic students are enrolled
in advanced courses. Students from non-socioeconomically disadvantaged families are twice as
likely to take algebra or more advanced courses. Walston and McCarroll’s (2010) research
highlighted inequities within algebra enrollment as they reported eighth grade algebra enrollment
patterns among students scoring in the top 40% on the Early Childhood Longitudinal Study,
Kindergarten (ECLS-K). The ECLS-K provides detailed information on the school achievement
and experiences of students followed from kindergarten to middle school. The study followed a
cohort of students longitudinally in first grade in 1999-2000 and in eighth grade in 2006-2007.
Consistent with other research, algebra enrollment varied along social and ethnic variables, even
when comparing high scoring students. For example, 35% of high scoring African Americans
were enrolled in Algebra I, compared to high scoring White students (63%), high scoring
Hispanic students (68%), and high scoring Asian students (94%). Overall, 25% of the students
IMPACT OF ALGEBRA WHEN READY 37
scoring in the highest quartile of the ECLS-K Grade 5 assessment were not enrolled in eighth
grade algebra. These findings suggest that some high scoring students at the end of elementary
school were not enrolled in algebra by the eighth grade. For the reasons stated above, universal
algebra policies were instituted to enable students to successfully complete algebra who may not
otherwise have the opportunity (Stein et al., 2011).
Research indicates that selecting certain students to enroll in algebra may exclude
students who are prepared in terms of their test scores and students from traditionally
marginalized groups (Stein et al., 2011). Stein et al. document 18 studies, which demonstrate
that exposure to early algebra increases algebra success and more advanced mathematics
coursetaking. Not all high achieving students have the opportunity to take eighth grade algebra,
despite the increased enrollment trend. Stein et al. ascertain that several studies collectively
suggest that some students, particularly STEM under-represented groups, are denied access to
early algebra despite the fact that they are ready. Further research conducted by Stone (1998)
supports the previous findings. Stone (1998) used a sample of 1,611 ninth grade students from
16 schools in a large urban district, scoring in the upper quartile on the 1993 Comprehensive
Test of Basic Skills. Stone found that students in high SES scoring in the upper quartile were
three times more likely to have access to Algebra I and Geometry compared to their low SES
counterparts scoring in the upper quartile. This data is essentially saying that SES matters – the
more money a family makes, the higher the likelihood students will have access to advanced
pathways. Statistically, it can be argued that disadvantaged subgroups are often
disproportionately placed in lower-level courses as a result of subjective selection processes.
To help mitigate these inequalities, policymakers argued for universal access to
accelerated middle school mathematics. California’s Algebra for All policy was one such
attempt to address the existing inequities. These accelerated efforts are intended to expand
IMPACT OF ALGEBRA WHEN READY 38
opportunities to learn for all students (Domina, 2014), with the assumption that accelerating
math placements can increase students’ OTL. In return, achievement levels are raised and
educational inequalities that close paths to future success are narrowed. According to Marzano
(2003), opportunity to learn has the strongest relationship to student achievement out of the
following eight identified factors: (a) opportunity to learn, (b) time, (c) monitoring, (d) pressure
to achieve, (e) parental involvement, (f) school climate, (g) leadership, and (h) cooperation.
Research on opportunity to learn demonstrates its dominance in terms of its influence on student
achievement (Marzano, 2003).
Tracking
Broadly defined, tracking is a process using scholastic capabilities to group students in
differentiated classes or academic programs (Rui, 2009). Tracking remains a universal practice
in high schools, despite extensive criticism. This creates concern as students are given access to
varied academic rigor, changing the curriculum across different subgroups. Tracking occurs in
60% of elementary schools and 80% of secondary schools in the United States (Rui, 2009). In
the United States, tracking refers to within school curriculum differentiation, which varies the
curriculum from course to course (Cogan et al., 2001). Elementary differentiation typically
occurs within classrooms as students are grouped informally according to ability for instructional
purposes, including the designation of instructional groups and programs based on test scores
and recommendations (Darling-Hammond, 2007b). Formal differentiation occurs in middle and
high schools as students are placed into different tracks, offering varying courses.
According to Oakes (1990), nowhere is tracking more persistent than in mathematics.
The structure of math courses and progressive nature of mathematical skills is one reason for
tracking. Moreover, advanced mathematics courses tend to be restricted to students who have
the perceived ability to be successful. Tracking in high school is often implemented through
IMPACT OF ALGEBRA WHEN READY 39
subtle curriculum differentiation. One example is the push for algebra for all students. Schools
create various algebra classes with different designations, such as honors algebra for high
achieving students, and regular algebra classes for low-achieving students. Tracking can result
in a given school having more than five types of eighth grade math, a practice that is unique to
the United States (Schmidt, 2004). This creates concern as students across groups are given
varied academic rigor (Harris & Anderson, 2012). Through tracking, minority and economically
disadvantaged students have less access to courses that teach the knowledge and skills necessary
to become critical thinking members of our increasingly technological workforce (Oakes, 1990).
In order to maintain leadership in our global, competitive society, the math and science capacity
of all students needs to be increased by giving all students the opportunity to learn (Flores &
Roberts, 2008). Ultimately, tracking affects student outcomes as challenging curricula is only
offered to a select group of students based on the theory that only certain students can handle the
rigor (Darling-Hammond, 2007b). The notion of tracking is inconsistent with the federal NCLB
Act of 2001, signed by President George Bush. NCLB mandated equal outcomes for all students
and was intended to raise achievement levels and close the achievement gap. Unfortunately,
NCLB failed to achieve these goals and resulted in the following unintended consequences: (a) a
narrowed curriculum, (b) focus on low-level skills, and (c) incentives to exclude low scoring
students (Darling-Hammond, 2007b).
Impacts of Minority/Low SES Students
Despite the benefits of early access to algebra, research shows an underrepresentation in
higher-level courses and an overrepresentation in lower-level courses among cultural and
linguistic minority students (Abedi & Herman, 2010; Oakes, 1990; Smith, 1996; Spielhagen,
2006). Tracking is implemented to allow teachers to gear instruction to an appropriate level and
pace for each group, but it is inequitable in practice (Gamoran et al., 1997). It leads to
IMPACT OF ALGEBRA WHEN READY 40
fundamental schooling inequities, separating students by race and class (Oakes, 1990). African
American and Hispanic students are disproportionately assigned to non-college preparatory high
school programs and low-ability classes. Jeannie Oakes’ publication Keeping Track and How
Schools Structure Inequality (1983) reported that tracking results in racial and social differences
in students’ access to learning (Rui, 2009). According to Oakes (1990), the students in different
tracks have access to different types of knowledge.
The pace, complexity, and challenge is greater in high track courses (Gamoran et al.,
1997). High track groups are more likely to study more meaningful topics, with access to high
status knowledge, while low track classes receive a lower-level curriculum, which includes
repetition of basic conceptual skills using workbooks or worksheets (Harris & Anderson, 2012).
Oakes (1990) asserts “low track classes provided students with less access to a whole range of
resources and opportunities” (p. 687). Harris and Anderson (2012) support Oakes’ research by
stating that tracking limits the opportunity for students placed in lower-level math groups.
Important to note is that students in high performing tracks are less likely to be from minority
groups (Smith, 1996; Spielhagen, 2006). Oakes (1990) expressed that low-income African
American students are more likely to be grouped in low ability math classes. As the African
American population in a school increases, the proportion of high-ability classes decreases. For
example, in schools where African Americans are the majority, there are less extensive math
programs, offering few opportunities to take gatekeeper courses which lead to more
opportunities at the postsecondary level and beyond (Darling-Hammond, 2007b; Oakes, 1990).
Darling-Hammond (2007b) also posits that high minority schools are less likely to offer
advanced and college preparatory courses than schools serving more White, affluent student
populations. A major flaw with tracking is that low ability tracking results in inequitable
opportunities (Darling-Hammond, 2007b). Enrollment and tracking trends based on ethnicity
IMPACT OF ALGEBRA WHEN READY 41
and social class negatively impact student opportunities and access by inhibiting college
prospects and achievement outcomes.
The mathematics experiences of Hispanic students parallel those of African American
students. Paul (2005) examined the course enrollment patterns and grades of students with high
proportions of low-income, minority, and predominantly Hispanic immigrant students. He
followed 3,574 students from five urban high schools, who were ninth graders in 1997-1998 and
finished four years of high school in 2000-2001. Perhaps the most important finding from the
study is the significant differences in course enrollment by race and ethnicity. Hispanic students
had the smallest percentage of students enrolled in eighth grade Algebra I, whereas Asian
students had the highest percentages, followed by White students. Without access to more
advanced mathematics courses, the doors to opportunities of four-year college enrollment are
often closed.
Race and SES play a distinct role in the differential placements of students in math
classes. Oakes (1990) reported how placement processes in two different districts were skewed
racially. Lower performing students with the same standardized test scores were tracked at
different rates by race. For example, Latino students scoring near the 60
th
percentile were less
than half as likely as White and Asian students to be placed in college preparatory courses.
Furthermore, Latino students scoring above the 90
th
percentile had only a 50% chance of being
placed in a college preparatory course, while Whites and Asians with similar scores had a 90%
chance. African American and Latino students were less likely than White or Asian students
with the same test scores to be placed in high track math courses, concluding that grouping
practices led to a cycle of restricted opportunities. As long as these practices exist, students of
color will continue to be disproportionately overrepresented in low track classes. Overall,
tracking promotes inequality and widens the achievement gap between those in high tracks and
IMPACT OF ALGEBRA WHEN READY 42
those in low tracks (Gamoran et al., 1997; Oakes, Gamoran, & Page, 1992). It is difficult to
narrow the mathematics achievement gap when students are not receiving rigorous instruction in
low-level tracks.
Detracking Efforts
The California State Superintendent of Public Instruction argues that detracking middle
schools was central to raising academic standards in high school (Domina et al., 2015). In 1987,
California officials mandated that middle schools eliminate or reduce tracking (Rui, 2009).
Schools with higher minority enrollments, fewer higher achieving students, and lower parental
influence seemed more likely to accept detracking efforts (Rui, 2009). One way California
attempted to implement detracking policies is through the SBE’s declaration in 2008 to mandate
eighth grade algebra. Detracking strategies continued to be implemented in the 1990s in an
attempt to narrow the persisting achievement gap between low track (mostly low SES, minority
students) and upper track students (Rui, 2009). Due to the increasing concern about the
inequities in educational resources, U.S. policymakers implemented a series of federal initiatives
during the Clinton and Bush administrations to establish rigorous standards, claiming that all
students should have access to a more challenging curriculum. In 1992, the State Department of
Education affirmed heterogeneous grouping and detracking as a national goal.
History of Algebra Curriculum
No Child Left Behind
The U.S. Congress approved the reauthorization of the ESEA as NCLB in December,
2001. This was a landmark federal legislation making accountability the center of the
educational agenda by considerably increasing testing requirements for schools, districts, and
states. NCLB required that 100% of students reach proficiency within 12 years by the end of the
2013-2014 school year (Horn, 2005). It set heightened accountability demands for schools with
IMPACT OF ALGEBRA WHEN READY 43
Adequate Yearly Progress (AYP) objectives for all students and subgroups (SES, race/ethnicity,
English language proficiency, and disability). States would receive federal funding through
establishing standards, annually assessing proficiency, and including accountability measures to
increase the number of proficient students. NCLB required states to develop content standards in
reading and math linked to annual testing in grades 3 through 8 and at least once in grades 10
through 12. The assessments include: grade level and end-of-course tests and the California
High School Exit Exam (CAHSEE) in Grade 10, which includes Algebra I standards. The goal
of assessment was to measure student progress and proficiency levels and to provide valid
inferences related to expectations for students and schools (Linn, Baker, & Betebenner, 2002). If
a school failed to comply in meeting the federal requirement for any subgroup of students based
on ethnicity, disability, or English Learner (EL) status for two years in a row, a school or district
would be placed on Program Improvement status.
Federally, the NCLB heightened accountability measures to meet high demands for all
subgroups to achieve AYP targets. NCLB included several accountability provisions to
encourage student participation in testing. The API provided a summary of student achievement
for accountability purposes, and offered two incentives for advanced mathematics. The first
incentive was that schools received less API credit for scores of General Mathematics CSTs. For
example, the scores lowered one performance level in eighth grade and lowered two performance
levels in ninth grade for students taking the General Mathematics CST. Second, schools were
punished when students did not take math courses in grades 8 through 11 as students not taking
an end-of-course CST were given a score of 200 (FBB) for the purposes of API. These
incentives to take Algebra I in eighth grade were viewed as an attempt to narrow the
achievement gap and provide opportunities to create a more equitable educational system.
However, although NCLB attempted to protect equal opportunities for all students, not all
IMPACT OF ALGEBRA WHEN READY 44
students were given the same opportunities to learn (Oakes, 1992). A central goal of NCLB was
to make states, districts, schools, and teachers accountable for the learning of all students,
regardless of SES or race (Abedi & Herman, 2010). Currently, educational policies with an
emphasis on standards-based reforms assume that creating and assessing standards and holding
educators accountable will change students’ OTL. The assumption is that schools will alter their
curriculum and instruction to make sure students gain the knowledge and skills needed for
success (Abedi & Herman, 2010). Unfortunately, students were left behind and NCLB did not
achieve its desired results demanding proficiency for all in mathematics.
Algebra for All Initiative (2008)
Curriculum is central to an education system because it defines what schools should
accomplish, specifying the content students should learn at each grade level (Schmidt, 2004).
Curriculum in the United States has a tradition of local control, as school districts can have the
control to direct curriculum and establish tracking policies. Districts can create gifted programs
and can adjust standards for disadvantaged students (Schmidt, 2004). Schmidt argues that
curriculum implementation should be universal, creating an equal opportunity to learn the
material viewed critical for success. One goal of the U.S. education system is to provide
equitable opportunities for all students. The United States increased efforts in the middle school
math curricula to enroll more students in algebra over the last few decades (Domina et al., 2015).
Research consistently documents that eighth grade algebra enrollment is lower among African
American and Hispanic students, students with lower SES, and students whose parents have
fewer years of education (Smith, 1996; Stein et al., 2011; Walston & McCarroll, 2010).
National studies indicate that all students benefit from taking algebra. The students with
low prior achievement levels have somewhat smaller benefits, but algebra has a positive effect
on all students. Algebra for All was a policy aimed at creating an equal opportunity by
IMPACT OF ALGEBRA WHEN READY 45
mandating that all districts in California enroll students in Algebra I by eighth grade (Gamoran &
Hannigan, 2000). Algebra for All is one school reform effort aimed to improve achievement
levels in response to inequities and create more equitable learning environments. The policy is
supported by the NCTM, which proposes increased math literacy for all, regardless of prior
achievement or perceived ability levels.
Educators and policymakers worked to accelerate math instruction for all students by
increasing the population of middle school students enrolled in algebra (Loveless, 2008). This
trend is based on the assumption that this will increase students’ OTL and help to lessen
educational inequities, disrupting the tracking system. California is at the forefront of the
national effort to strengthen middle school mathematics by enrolling more eighth graders in
algebra. The California SBE passed a motion that regarded Algebra I as the End-of-Course
(EOC) accountability benchmark for all eighth grade students (Ed Source, 2009). California’s
accountability system penalized schools for not testing eighth and ninth grade students in
algebra. Nationally, the proportion of eighth graders enrolled in algebra more than doubled
between 1990 and 2011 (Domina, 2014). In California, the percentage of eighth graders taking
algebra increased dramatically from 32% in 2003 to 59% in 2011. The aforementioned statistics
highlight the impact that Algebra for All had on enrollment trends, giving more students access
to advanced mathematics courses and opportunity.
The EdSource Report, Algebra Policy in California- Great Expectation and Serious
Challenges (2009) indicates that California’s algebra policy increased access and opportunity for
disadvantaged minority students. According to the report, participation of eighth graders in all
racial and ethnic backgrounds taking Algebra I increased. Between 2003 and 2008, the
percentage of African Americans taking the Algebra I CST rose from 24% to 48%.
Additionally, 2.6 times more African Americans scored proficient or higher and 3.2 times more
IMPACT OF ALGEBRA WHEN READY 46
Latino students scored proficient or higher. In terms of SES, the number of disadvantaged
students scoring proficient or higher increased from 22% in 2003 to 30% in 2008, while the
number of non-socioeconomically disadvantaged student proficiency numbers increased from
47% in 2003 to 55% in 2008. These data reveal that allowing access to all students is a
mechanism to address the equity issue for minority and low-income students (Liang & Heckman,
2013).
However, studies found that many students continue to pass through the Algebra I
gateway and that participation does not automatically translate to success for all. Courses are a
means to an end, not an end to itself (Loveless, 2008). For example, Allensworth, Nomi,
Montgomery, and Lee (2009) evaluated a policy in Chicago mandating college preparatory
coursework and ending remedial classes for all students. Using an interrupted time series cohort
design, the researchers followed all ninth graders from the fall of 1994 to the fall of 2004 and
found that inequities in enrollment differences were reduced and the social distribution of
coursetaking became more equitable. Despite the rise in the number of students, grades
declined, failure rates increased, test scores stayed stagnant, and students were not any more
likely to attend college. Allensworth et al. (2009) concluded that detracking is necessary, but not
sufficient to lead to significant effects on achievement levels and postsecondary success. The
extant literature suggests that detracking may have little success if it does not address
professional development needs, instructional practices, additional support for low ability
students, and support among the community (Allensworth et al., 2009). Curricular policies need
to be paired with evident changes in the educational system, with greater attention to instruction
and efforts to improve achievement levels.
Regardless of their skills and prerequisites, educators have placed minority and low SES
students more often in general math, rather than algebra (Crosnoe & Schneider, 2010; EdSource,
IMPACT OF ALGEBRA WHEN READY 47
2009; Stein et al., 2011; Waterman, 2010). Ethnicity and SES are important factors in course
placement, even after controlling for students’ previous ability levels. Crosnoe and Schneider
(2010) found that SES was highly correlated to high school math courses. Higher SES students
took higher-level math courses more often than did their low SES counterparts with similar
mathematical abilities. The policy mandating all students to be placed in algebra in eighth grade
has been contested, as all students are not prepared for the course. Loveless (2008) concluded
that policies mandating coursetaking for all does not necessarily mean that students will learn
more. Loveless (2008) analyzed the 2007 NAEP scores and found a Pearson correlation
coefficient of -0.09 between the NAEP score and advanced course enrollment, indicating that
there is no correlation. Many states scoring high on NAEP have few students enrolled in
advanced math. North Dakota and Vermont ranked second and third in achievement
respectively, but enrolled a low percentage of eighth graders in advanced courses (21% and 26%
respectively). On the other hand, the District of Columbia (DC) is at the bottom of NAEP and is
one of the leaders in the number of students enrolled in advanced courses. Loveless (2008)
found another pattern after analyzing the national eighth grade NAEP scores. The national
eighth grade scores increased from 2000-2007 from 273 points to 281 points. However, for
eighth graders in advanced math, scores have declined from 299 in 2000 to 295 in 2007,
representing a loss of four points.
Liang et al. (2012) reported a 19% increase in the number of students taking Algebra I in
eighth grade in California, but only found an 8% increase in the number of ninth graders taking
Geometry between 2004 and 2009. The authors refer to this as a leak in the pipeline because
students taking Algebra I in eighth grade are repeating the course in the ninth grade. This
decline in the numbers of students advancing to progressive math courses calls into question the
placement decisions, as there is an evident leak in the system.
IMPACT OF ALGEBRA WHEN READY 48
Although access for all in algebra may appear to be equitable, the identification process
may result in “undetected lapses” in equity (Spielhagen, 2006, p. 29). Spielhagen ascertains that
giving all students access to eighth grade algebra opens doors of opportunity to further
mathematics for students, resulting in math achievement throughout high school. In the study,
he found that students taking early algebra enrolled in more advanced courses and stayed longer
in the math pipeline. Spielhagen (2006) examined the tracking policy in a large southeastern
suburban school district and found that SES and ethnicity predicted selection into eighth grade
algebra. For example, White students were 1.4 times as likely than their peers to get accepted
into the algebra group. African American students were only 0.84 times as likely to get into
eighth grade algebra (less than an even chance). Researchers found that affluent schools had
more students taking eighth grade algebra. On the other hand, lower SES schools had lower
numbers of students enrolled in algebra.
The pipeline leak is critical when determining eighth grade algebra placement (Liang et
al., 2012). Other research concludes that students who are successful in algebra are pushed to
take it again. For example, Waterman (2010) reveals that placements were influenced by social
class and ethnicity, without regards to their grades, diagnostic scores, or CST scores. Waterman
reports that 65% of the 1,653 students in several northern California school districts completing
Algebra I in eighth grade advanced to the next level of math in ninth grade. Two-thirds of
African Americans and Latinos were required to repeat algebra in ninth grade, even though 65%
of these students scored proficient or advanced on the CST. In addition, 44% of the students
scoring proficient on the Algebra I CST in eighth grade between 2006 and 2009 retook the
course in ninth grade. When taking the Algebra I CST for the second time, half of the students
were no more successful after repeating the course a year later. Even when given access to
Algebra I, African Americans and Latinos were more likely than their White and Asian
IMPACT OF ALGEBRA WHEN READY 49
counterparts to take the course again despite demonstrating proficiency on the CST. These
results highlight inequities within advanced math courses as a function of social class and
ethnicity. In support of this study, Smith (1996) found that students enrolled in early algebra
were less likely to be minorities, coming from families with higher SES.
As research indicates, students taking algebra in middle school are more likely to stay in
the mathematics pipeline, taking more advanced courses in high school and more likely to attend
college than students taking general math (Spielhagen, 2006). Despite efforts to equalize efforts,
early algebra has been traditionally restricted to high achieving, gifted students. Ma (2005) used
a hierarchical linear growth model to examine the effects of early algebra on growth in four
mathematical areas: basic skills, algebra, geometry, and quantitative literacy. The interaction
between early acceleration and initial math achievement was statistically significant in all math
areas. Ma concluded that low-achieving students enrolled in algebra showed performance
growth that was faster than both low-achieving students not accelerated in algebra and high
achieving students not accelerated into algebra. However, rates of growth of the accelerated
low-achieving students were comparable to rates of growth of high achieving accelerated
students. Results from this study reveal patterns that enrollment in algebra accelerates
achievement for both high and low-achieving students. This study contradicts the study by
Gamoran and Hannigan (2000), which concludes that all students benefit from taking algebra,
noting that low-achieving students enrolled in eighth grade algebra do no better or even worse
than students not taking algebra. Universal algebra policies led to increased enrollment, with
minorities and students from low SES groups increasing enrollment the most. These increases
led to more students passing algebra in all cases, but also resulted in a greater number of students
failing algebra (Stein et al., 2011). Hence, Algebra for All policies are giving some students the
opportunity to complete algebra successfully when they otherwise would not have had the
IMPACT OF ALGEBRA WHEN READY 50
opportunity (Stein et al., 2011). The progress in increased participation and achievement levels
in algebra attests to the viability of California’s accountability plan that was initially introduced
in the PSAA.
Common Core State Standards - New Standards
Efforts to mandate universal algebra have developed unevenly and results have been
mixed. Between 2003 and 2009, the percentage of students taking algebra in eighth grade
increased from 32% to 54% (Williams, Haertel, & Kirst, 2011). African American enrollment in
eighth grade algebra increased from 24% to 60%, with proficiency rates on the CST doubling to
42%. However, as research indicates, 60% of eighth grade minorities did not score proficient on
the Algebra CST. Many of these same students were required to repeat the course. A current
movement in the nation, as well as in California, is the adoption of the CCSS. The CCSS are
intended to standardize expectations across states and address the fragmented nature of state
assessments. In terms of mathematics, algebra is listed as part of the high school standards,
representing a shift from the Algebra for All policy mandating all eighth graders to take algebra
(Liang & Heckman, 2013).
Supporters of the CCSS believe that Grade 8 Common Core math will be more
challenging than the course that students not enrolled in algebra (pre-algebra) used to take. They
believe that students enrolled in Grade 8 Common Core math will be more successful in ninth
grade when they take CC Algebra I. Critics view this as a step backwards from the progress
made in giving access and opportunity to traditionally marginalized populations. They are
concerned that history will repeat itself, with minority students not being placed accordingly on
the more advanced pathways. As described in the CCSS, grade 8 standards mainly focus on
arithmetic and pre-algebra. The California Academic Content Standards Commission adopted
the CCSS in 2010, and added CA eighth grade algebra standards in alignment with California’s
IMPACT OF ALGEBRA WHEN READY 51
Algebra for All policy. Recognizing that not all eighth graders would have success in algebra,
the commission prescribed dual standards. The standards consisted of two complete sets of
standards: Grade 8 CC Math, including some algebra concepts and a full set of the old California
Algebra I standards. These two sets of standards conflicted with the federal government’s
requirement under the NCLB law, in which states can only offer one set of standards per grade
level. However, Senate Bill (SB) 1200, a bill signed in September 2012 by Governor Jerry
Brown, allowed California to approve or modify the standards in mathematics. The law
specified that one set of standards is to be adopted at each grade level.
Some critics viewed this as a step backwards in the wrong direction. However, Michael
Kirst, the President of the SBE, stated that SB 1200 was an important step in California’s efforts
to implement the CCSS and to ensure that all students have access to algebra (Fensterwald,
2012). The new law creates two course pathways, one for those ready for algebra in eighth grade
and one for those taking it a year later. It encourages algebra in eighth grade for those who are
prepared to handle the coursework, and necessitates a more gradual approach to mastering
algebra. In 2012, about two-thirds of eighth graders enrolled in algebra. However, this number
is likely to decline with the implementation of the CCSS, as selection processes across districts
may limit access to more advanced math courses (Fensterwald, 2012).
The SBE adopted a revised version of the California CCSS in January 2013, eliminating
Algebra I standards from the eighth grade math standards (Fensterwald, 2012). With this
revision, eighth grade students still take algebra if they are on the accelerated track. Currently,
the state creates math-accelerating options in middle school and high school, giving discretion to
local districts to determine which students are eligible for the options. In March 2013, the SBE
approved the elimination of the penalty of docking points for API scores for schools testing for
eighth and ninth graders in general mathematics on the CST. This move officially ended
IMPACT OF ALGEBRA WHEN READY 52
California’s controversial Algebra for All policy. The implementation of the CCSS threatens to
reverse the trend of Algebra for All, potentially decreasing gains in the number of students
enrolled in more advanced mathematics courses.
Traditional and Integrated Pathway Decisions
The California Board of Education decided that school districts should choose the
pathway that best fits their students’ needs. A questionnaire by the California Superintendent of
Educational Services Association in the fall of 2013 revealed that 34% of districts chose the
integrated pathway, while 26% chose the traditional pathway, and 40% were undecided
(Fensterwald, 2014). Local school districts need to decide whether to follow the traditional or
integrated pathway, and if students will take advanced math courses in middle school. Typically,
the traditional pathway reflects the pathway in the United States consisting of two algebra
courses and a model geometry course. In the traditional pathway, Algebra I is taught in ninth
grade followed by Geometry, Algebra II, leading to Pre-Calculus, AP Statistics, or Calculus in
12
th
grade. The integrated pathway is typically followed by high performing nations
internationally, consisting of three model courses (Mathematics I, Mathematics II, and
Mathematics III), which include algebra, geometry, and statistics/trigonometry woven together
with increasing difficulty (Fensterwald, 2014). Within the CCSS, Algebra I was moved to a high
school course, but students can enroll in Algebra I in eighth grade through acceleration. Both the
traditional and integrated pathways allow students to arrive at the same point by the end of their
third year, giving students the opportunity to complete AP Calculus with acceleration. Algebra
for All was instituted to combat inequitable tracking processes that closed pathways to advanced
mathematics. Ultimately, districts or teachers decide who is prepared for the accelerated track
using the CCSS.
IMPACT OF ALGEBRA WHEN READY 53
Accelerated Pathways
In previous years, a method of acceleration was skipping mathematics courses, usually
sixth or seventh grade math, as many standards were repeated each year in the former California
standards. The CCSS requires new paths to acceleration, as acceleration is needed to take at
least one year of calculus by 12
th
grade. Double acceleration is required to enroll in Calculus
BC, the goal of students hoping to major in science and engineering at top universities. Within
the CCSS, there are two choices for eighth grade math: Grade 8 CC Math and Integrated Math I.
The recommendation for middle school acceleration is to have a series of compacted courses,
compressing three years of math into two years. Acceleration decision points occur between
sixth and seventh grade in middle school and in high school after eighth grade. In middle school,
there is a true two pathway policy: Algebra in grade 8 for those who are ready and Grade 8 CC
for those who are not yet ready. Placement decisions are in the hands of local districts.
As acceleration is deemed necessary to advance students to calculus in 12
th
grade, high
school districts are considering a range of acceleration pathways. The range of acceleration
choices include: (a) using different compacting ratios (four years of high school math in three
years), (b) allowing students with block schedules to take math in both semesters of an academic
year, (c) offering summer courses to give equivalent experience of a full course, (d) hybrid Math
II –Pre Calculus course, and (e) offering double periods of math for districts using the traditional
sequence, enhanced pathway, or summer bridge in high school. This local district discretion
becomes an equity issue: will students no matter where they go to school have the same
opportunity as students in affluent districts?
Selection Process
Districts may turn to guidance from other education agencies when developing policy
regarding course sequences and student placement. The local decisions of whether to place
IMPACT OF ALGEBRA WHEN READY 54
students in Algebra I have been failing the majority of students, especially minority and
socioeconomically disadvantaged students. As the decision for a pathway to advanced
mathematics and a college education lies at the local level, schools have little incentive and
pressure to place eighth grade students in algebra. The increased local control in placement
decisions makes it hard to predict patterns of access to Algebra I and the impact on student
advancement and achievement levels.
With decision-making at the local level, it is important to determine which students are
being given access to the accelerated track. The wide variation in selection processes between
districts will affect access and may or may not be equitable. Accelerated pathways based on
subjective criteria could be detrimental to minority populations, and will likely impact certain
groups of students more than others. The research coalesces around an agreement that although
the push to universalize eighth grade algebra may be desirable from an equity standpoint,
problems exist in terms of placement that can compromise the effectiveness of the policy.
Districts need to have clear and objective placement criteria based on multiple measures,
including data from test scores, as well as teacher recommendations and grades to show solid
evidence of mastery of prerequisite standards. Without these criteria, there is a risk of
misplacing students and affecting pathways to postsecondary education for some.
College Preparedness and Coursetaking Patterns
One of America’s most pressing concerns is to better understand the disjuncture between
high school and college (Long, Iatarola, & Conger, 2009; Planty, Bozick, & Ingels, 2006). As
districts across California seek to improve mathematics achievement, the sequence and
acceleration of math coursework need to be considered. The importance of mathematics course
sequencing in preparing students to be college ready is reflected in a district’s recommended
sequencing and timing for math courses, called pathways (Finkelstein et al., 2012). A pathway
IMPACT OF ALGEBRA WHEN READY 55
comprises the typical order and timing of courses that students follow and is intended to create
smooth transitions between courses. This sequence, especially in mathematics, is often enforced
through prerequisites (i.e. Algebra I is a prerequisite for Algebra II). The sequence and timing of
a student’s coursework is referred to as a coursetaking pattern. Performance influences the point
in which a student can advance to a higher-level course. If a student earns a “C” or less in
Algebra I in eighth grade, he or she may have to retake the course before advancing to the next
course on the intended pathway. This may result in a different trajectory, which may or may not
lead to the student meeting university eligibility requirements.
Educational leaders have raised concerns about high school achievement patterns and
preparation for college, especially for students who have been traditionally underrepresented in
higher education. With the implementation of the CCSS in California, a central objective is to
increase math proficiency for students leaving high school. Currently, there is an emphasis on a
trajectory leading to college and career readiness for all students, resulting in a decreasing need
for remediation in postsecondary education. Courses are considered to be the complex building
blocks of the curriculum, where understanding builds cumulatively (Planty et al., 2006). A large
body of research demonstrates that coursetaking patterns in middle school and high school are
linked with attainment in postsecondary education (Adelman, 1999; Planty et al., 2006).
Adelman (1999) posits that students taking less rigorous courses are less likely to attain a college
degree than students taking more rigorous courses. Students taking a challenging curriculum
starting in middle school are better prepared for college than those taking a less rigorous
curriculum (Finkelstein & Fong, 2008).
As enrollment of first time, full time undergraduate students, in degree granting
institutions increased 32% between 2001-2011 from 15.9 million to 21 million (NCES, 2015b), it
is important to prepare them for university demands. However, the most recent data available
IMPACT OF ALGEBRA WHEN READY 56
show that the 2012 graduation rate for students pursuing a bachelor’s degree at a four-year
institution in the fall of 2006 was 59% (NCES, 2015b). University admission requirements
reflect the need for a more challenging curriculum. Applicants must take and pass with at least a
“C”, two years (three recommended) of high school science and three years (four recommended)
of high school mathematics, including Algebra I, Geometry, and Algebra II. Success in high
school math is predictive of postsecondary success and STEM careers (Adelman, 1999).
Similarly, there is a close link between student success in middle school academic experiences
and future high school performance (Oakes et al., 1992). Students who are proficient in seventh
grade math are more likely to take more advanced high school courses compared to those who
are below proficiency levels (Finkelstein et al., 2012).
In order for California students to successfully pursue postsecondary education, it is
essential to keep students on track throughout middle and high school (Finkelstein et al., 2012).
The value of having a solid math and science foundation in high school is evident in the
minimum eligibility requirements for the California public university system (Finkelstein et al.,
2012). Despite increases in the number of required courses to graduate from high school, many
graduates are still unprepared. According to Long et al. (2009) almost one-third of our country’s
college freshman are unprepared for college level mathematics. Within the CSU system in 2010,
35% of regularly admitted freshman required math remediation (Finkelstein et al., 2012).
Additionally, in the California Community College system, 85.5% of those taking the math
placement exam for the Fall of 2010 scored at a level placing them into remediation. Long et al.
(2009) used data from Florida postsecondary institutions and found that differences among
college going students in the highest courses taken in high school explains 28% to 35% of Black,
Hispanic, and poverty gaps in readiness and over 75% of the Asian advantage. Increasing the
number of courses for high school graduation seems like a straightforward policy to increase
IMPACT OF ALGEBRA WHEN READY 57
college preparedness. Finkelstein and Fong (2008) note that students completing college
preparation courses in ninth grade begin a clear trajectory that continues through high school.
Postsecondary education is a function of student readiness- the degree to which past experiences
have equipped them with the knowledge and skills needed to meet the demands and expectations
of college (Conley, 2007). Analysis reveals that the courses students take in high school
contribute significantly to college readiness, with the highest gains occurring at Algebra II. Due
to the sequential nature of math courses, courses at the secondary level are sequential so that
understanding of higher-level courses like Algebra II requires mastery of Algebra I concepts
(Smith, 1996).
Summary
Educational reform efforts have been predicated on increasing math participation (OTL)
and success rates for all students. California’s PSAA (1999) accountability system, in
conjunction with the federal NCLB Act (2001), held schools responsible for progress in college
preparedness for all students. Through API, one of the main components of the PSAA,
incentives were given to students who were enrolled in advanced courses. California’s model
required end-of-course tests in all advanced mathematics and science courses. These intentional
detracking efforts resulted in increased access and enrollment for all students, including
traditionally disadvantaged groups. These increases in OTL and success confirm the viability of
California’s accountability model. Additionally, Algebra for All served as the key to open the
gates to more advanced courses for all students. This proposed universal access to Algebra I in
eighth grade was a means to increase students’ OTL and access to a college preparatory
curriculum. However, this policy was a misnomer in California and played out as Algebra When
Ready, as very few districts were placing all students in algebra in eighth grade.
IMPACT OF ALGEBRA WHEN READY 58
CHAPTER THREE: METHODOLOGY
This research study evaluated the impact that Algebra When Ready had on the following
indicators of college readiness: Algebra I success, Algebra II success, and science success in
select California school districts. The study determined the extent to which California K-12
students have progressed in college readiness in STEM courses from 2003-2012. Figure 2 shows
the hypothesized causal model indicating the sequence of coursetaking patterns beginning with
Algebra I in eighth grade to meet federal and state accountability demands. Since 2003,
California enacted a policy through its accountability system encouraging schools and districts to
place all eighth grade students into algebra and be tested in algebra in the statewide assessment
program (Liang & Heckman, 2013). The state’s accountability system penalized schools that did
not require all of the students to take the Algebra I end-of-course examination by grade 8. The
longitudinal design tests the hypothesized causal model of mathematics coursetaking patterns to
examine future success in advanced math and science courses from 2003-2012. The study
examined trends in success in Grade 7 Math, participation and success in Grade 8 Algebra I,
success in Grade 10-11 Algebra II, and success in Grade 10-11 Science. Success rates in
Chemistry and Physics were merged to create a single science success variable. Success and
participation data were captured from CST data between 2003 and 2012 from 189 school
districts in California. In order to answer the second research question, a path analysis was
developed and analyzed.
Participating districts were selected based upon enrollment characteristics. In 2013, each
of the 189 districts reported an enrollment of at least 100 students per grade level in grades 7
through 11. Longitudinal data on participation and success rates were assessed to determine the
effect of the utilized model using the following research questions:
IMPACT OF ALGEBRA WHEN READY 59
1. To what extent, if any, have California K-12 students progressed in college readiness in
Science, Technology, Engineering, and Mathematics (STEM) subjects during the period
of 2003-2012?
2. Do California district test data (2003-2012) support the hypothesis that Algebra When
Ready had a positive impact on the following indicators of college readiness: Algebra I
success, Algebra II success, and science success.
Design Summary
A purely quantitative approach was employed to answer the research questions included
in the study. This study followed design principles of applied research to analyze the impact of
the causal model of mathematics coursetaking patterns during the NCLB provision in California
schools. To answer Research Question One, a one-way or simple Repeated Measures (RM)
analysis of variance (ANOVA) was utilized to compare the means of the following variables
over a six-year time period: Grade 8 Algebra I participation and success (2004-2009), Grade 10-
11 Algebra II success (2007-2012), and Grade 10-11 science success (2007-2012). When using
an ANOVA, each subject is measured on the same continuous scale on three or more occasions
(Pallant, 2013). These longitudinal data illustrated the change in means to show the progress
students made in California schools over the period of the study. In order to answer the second
research question, a multiple regression and path analysis model was developed and analyzed.
Figure 2 below shows the hypothesized causal model which was tested to determine the impact
that Algebra When Ready had on the following indicators of college readiness: Algebra I
success, Algebra II success, and science success. It is important to evaluate the effect of this
model in leading to college preparedness before moving on to the next set of policies. The key
variable in the model is Grade 8 Algebra I participation as California made a deliberate effort to
IMPACT OF ALGEBRA WHEN READY 60
detrack students through the Algebra for All policy. Using an ordinary least squares regression,
beta weights were computed for all paths between variables for each of the six waves.
This analysis included six cohorts of data from 2003-2012 to test whether the model
holds true and to determine whether or not the model had the intended impact on college
preparedness and future success. Specifically, this study utilized an ordinary least squares
regression. Experimental controls were not possible in the analysis of the causal model.
Therefore, it is not considered to be a true experiment. When researchers do not have control
over participants or treatment, the design is considered to be non-experimental (McEwan &
McEwan, 2003). This study examined publicly available historical data in California schools
beginning in 2003. The data for the study came from existing databases- publicly available
information from the CDE website.
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
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2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

β
1

β
5

β
6

β
8

β
10

β
9
β
7

β
2

β
3

β
4

Figure 2. Hypothesized Causal Model
IMPACT OF ALGEBRA WHEN READY 61
Variables and Path Model
A single stage path model (Figure 2) refers to a model in which a dependent variable is
affected by a set of inter-correlated independent variables (Pedhazur & Schmelkin, 1991). In the
model, the independent variable (X) is treated as an exogenous variable, a variable whose
variability is assumed to be determined by causes outside the model. Hence, no attempt was
made to explain the variability of an exogenous variable or relations with other exogenous
variables. In contrast, an endogenous variable is one whose variation is explained by exogenous
or other endogenous variables in the model (Pedhazur & Schmelkin, 1991). The exogenous
variable (X) has only direct effects on the dependent variable, as indicated by the arrows
emanating from them. In this causal model, the effect of a given variable may be indirect
through the mediation of other variables.
Exogenous variables. SES is the one exogenous measurable variable (X
1
) that was
included in the study. The PSAA (1999) required that school rankings based on API include
how growth rates compared in schools with similar characteristics. SES was measured utilizing
the School Characteristics Index (SCI). SES was measured two times in all of the school
districts included in the study in 2003 and again in 2006, as the average SES across school
districts remained relatively stable over time. It cannot be measured yearly because of both
power and multicollinearity issues, as there are not enough school districts utilized in the study.
SES 2003 and SES 2006 were highly correlated (.96), so SES 2006 was eliminated from the
study.
The SCI was created in April 2000 by the CDE and is used with the California PSAA as a
way of measuring similarities among schools in terms of various demographic characteristics
(CDE, 2015d). The SCI is a three-digit composite variable derived through a multiple regression
analysis used to measure school’s demographic information. The SCI includes the following list
IMPACT OF ALGEBRA WHEN READY 62
of 16 demographic characteristics to measure similarities in demographic characteristics among
schools: percent of students eligible for Free and Reduced Meals (FRM), parent education level,
student mobility, student race and ethnicity, student SES, percent of teachers who are fully
credentialed, percent of teachers who hold emergency credentials, percent of students who are
ELs, average class size per grade, whether or not the school operates in a multi-track year round
educational program, percent of span enrollments, percent of students in the Gifted & Talented
Education, percent of students with disabilities, percent of reclassified fluent English proficient
students, and the percent of migrant education students.
For the purposes of this study, three variables were selected to measure SES: parent
education level, percent of students with FRM, and the SCI mean. In order to standardize the
means for a variance for each of the three variables, Z scores were created to give each item the
same weight. The inter-item correlations of the three Z scores were highly correlated (.929).
This SES composite variable was used as a measure of a district’s relative socioeconomic
advantage compared to other districts. For the purposes of this study, the SES variable was
computed by combining the Z-score averages across all schools in the districts. These three
items were coded to standardize the means so that high numbers meant high SES. Thus, the
scale of FRM was flipped to become the percentage of school not having FRM. This was
accomplished by subtracting FRM from 1.0.
Endogenous variables. There are multiple endogenous variables included in the
hypothesized causal model (Figure 2): enrollment variables and achievement variables. The
endogenous variables (Y) that were utilized in the study are as follows: enrollment
(participation) in Grade 8 Algebra I and achievement (success) variables in Grade 7
Mathematics, Grade 8 Algebra I, Grade 10-11 Algebra II, and Grade 10-11 Science. Grade 8
Algebra I participation was computed between 2003-2012 by adding the number of students
IMPACT OF ALGEBRA WHEN READY 63
enrolled in Algebra I in Grade 8 divided by the total number of students in the eighth grade
cohort, as measured by the number of students with scores on the English Language Arts (ELA)
CST. The ELA CST was used as a benchmark to determine the total number of students in each
grade level. Success was determined through the CST and is defined as scoring “Basic” or
above on specified grades or subjects. There are two ways to determine student success of
California’s policy decisions in regards to algebra: (a) student participation in higher math (OTL)
and (b) student success in those specified courses (Rosin et al., 2009). The model includes these
two indicators as a means to determine future success in mathematics.
Quantitative Research Design
The following quantitative research design utilized CST data from the 2003-2012
administration of the CST and files were imported and analyzed through the Statistical Package
for the Social Sciences (SPSS) Version 20 to calculate the OTL (participation) and SS scores
(Figure 2). As shown in Table 1, structural equations were utilized in the study to determine the
success rates for each of the five endogenous variables. The table illustrates how OTL and
success were calculated for each grade level and course identified in the hypothesized causal
model: Algebra I, Algebra II, and science are taken in grades 8, 10-11, and 10-11 respectively.
In the model, students participating in eighth grade algebra are on track for high school
graduation and have started their eligibility to enter a four-year postsecondary program.
Structural equations (Table 1) were created to test if the inner correlations are consistent with the
inner correlations that the model predicts. When writing structural equations, the rule is to
regress the dependent variable on the variables that point to it.
IMPACT OF ALGEBRA WHEN READY 64
Table 1
Structural Equations
Structural Equations
Y
1=
β1X1
Y
2=
β7Y1 + β2X1
Y
3=
β8Y2 + β3X1 + β6Y1
Y
4=
β4X1 + β9Y3
Y
5=
β10Y3 + β5X1

Participants and Setting
Schools were identified through the use of the CDE downloadable student and school
data files. School success data was downloaded from the Standardized Testing and Reporting
Results (STAR) website. The CDE data files were then sorted to include schools that service
seventh graders through twelfth graders including all unified models for middle and high school
age students- middle schools, K-8 schools, high schools, and K-12 schools. Schools with less
than 50 students per grade level as measured by the number of students taking the ELA CST,
were excluded from the study, as these schools are limited in the reports of STAR data needed.
Additionally, a minimum of 20 students was needed to take each assessment in order for the
variable to be included in the study. Districts needed to have scores for all variables in the study,
otherwise the district was not considered. In order for this to occur, the option to exclude cases
listwise was employed. Figure 3 shows the numbers of participating school districts for each of
the six waves of the study. The mean number of districts included in the study was 189.
IMPACT OF ALGEBRA WHEN READY 65

Figure 3. Sample Sizes for Waves 1-6
Instrumentation
Achievement Measures
The CST, a criterion-referenced exam, was deemed as one of the official measures of
school performance designated by the PSAA. The CST was developed in conjunction with the
California academic content standards based on what students were expected to learn and
teachers were expected to teach. The CST was developed to measure students’ progress and
includes publicly accessible data for measuring multiple school districts’ participation and
achievement over time. While some debate as to whether or not a test given once a year is an
accurate measure of success, it is considered a reliable measure over time and across schools and
districts. CST mathematics and science data was utilized from the CDE to measure proficiency
in Algebra I, Algebra II, and science. Scale scores range from 150 (low) to 600 (high) for each
grade level and specific test. These scores were used to determine performance levels and to
equate test scores from year to year.
As some of the CST questions are different each year, scale scores help to adjust for any
differences in difficulty levels resulting from question replacement. Due to the fact that scale
IMPACT OF ALGEBRA WHEN READY 66
scores are not scaled vertically across grade levels or subjects, scale scores cannot be used to
measure success in this study. The average number of questions correct cannot be compared
from year to year. However, a student’s scale score and the percent of students scoring at each
performance level can be compared within grade levels and subject areas. For example, a scale
score of 350 on an Algebra I test might not represent the same level of competency as a scale
score of 350 in Algebra II. Scale scores are categorized into five established performance levels:
Advanced (A), Proficient (P), Basic (B), Below Basic (BB), and Far Below Basic (FBB). For
the purpose of this study, students scoring Basic or above are considered to be successful. The
minimum scale score required to score in the basic range is 300 for every subject and every
grade level (CDE, 2015b). This makes the Basic cutoff point appropriate for use in the study.
The students scoring below the Basic range are unlikely to advance to the subsequent course in
the suggested path.
Data Collection
Data were collected by means of the CDE website (www.cde.ca.gov). From 1999-2013,
the CST was the method of accountability for reporting school effectiveness under the NCLB
requirements. All students in California public schools were required to take a standardized test
for content knowledge. Special education students took an alternate assessment, the California
Modified Assessment. For the purposes of this study, CST data were the available and
accessible data that were utilized to measure multiple school districts’ math participation and
achievement over time in California. Publicly accessible STAR data was downloaded from the
STAR database available on the CDE website in the form of research files in .dbf format. These
files were imported and analyzed through the SPSS. The data were filtered to exclude
unnecessary data for grades and subjects not being examined. Grades 7, 8, 10, and 11
achievement data were filtered into data files by year in SPSS. Individual database files were
IMPACT OF ALGEBRA WHEN READY 67
created for each of the six waves and were merged with the SES files. Each wave contained data
for each test aggregated by district and disaggregated by grade level. Additional enrollment
variables were added to the files to compute means of success and participation.
Limitations of the Study
According to Creswell (2014), validity in quantitative research refers to whether or not
one can draw meaningful inferences from scores on the instruments being utilized in a study.
Researchers need to be able to identify potential threats to the internal validity and design their
study so that the threats will be minimized (Creswell, 2014). There are three types of limitations
to the validity of a quantitative study: Statistical Conclusion Validity, Internal Validity, and
External Validity. First, threats to statistical validity occur when researchers draw inaccurate
inferences from the data due to inadequate statistical power or when statistical assumptions are
violated (Creswell, 2014). In this study, the main threat to statistical conclusion validity was
diminished power due to a relatively low sample size (N = 189). The method utilized in the
study to increase the power of the study include was controlling for demographic variables by
utilizing the SES index and combining the six cohorts into a single data analysis for summative
purposes.
Second, threats to internal validity were acknowledged. Creswell (2014) notes that
threats to internal validity are experimental procedures, treatments, or experiences of the
participants that threaten the researcher’s ability to draw correct causal inferences from the data
about the population. Internal validity refers to “the validity of assertions regarding the effects of
the independent variable(s) on the dependent variable(s)” (Pedhazur & Schmelkin, 1991, p.
224). Generally, the more powerful the controls one uses, the more internally valid the study
(Pedhazur & Schmelkin, 1991). Non-experimental quantitative designs are characterized by
weak to moderate causal inferences as it is very difficult to tell whether the observed differences
IMPACT OF ALGEBRA WHEN READY 68
among groups on the dependent variables are due to the treatment, prior differences, or a
combination of the two (Pedhazur & Schmelkin, 1991). Random assignment is often difficult or
impossible when using a study of real world implementation. A true experiment (also known as
a randomized trial) is the only design that justifies a strong causal inference. The following list
includes the threats to internal validity in this study: instrumentation, history, selection, and
mortality. Internal validity may be compromised when differences in outcomes may be
attributed to aspects of the instruments being utilized (Pedhazur & Schmelkin, 1991). An
instrumentation threat to internal validity may be that the CST changed from year to year. The
test given in the year 2003 may have been different from the test given in 2012. However, the
tests are considered to be equivalent. One suggestion to reduce the threat to internal validity is to
use the same pre-test and post-test (Creswell, 2014). When using historical data, this is not
possible as the CST is the assessment used to measure student progress towards achieving
California’s adopted state standards, describing what students are able to do in each subject
assessed. This may be considered a construct validity issue because using one construct, the
CST, to quantify success may not be sufficient to measure student learning. However, using data
from multiple cohorts from 2003-2012 reduces the potential threat of using one measure.
Additionally, history may be a threat to internal validity as factors outside the model may
have affected the outcomes. History refers to events that took place during the study that might
have affected its outcome (Pedhazur & Schmelkin, 1991). Creswell (2014) states that the effects
of history may be mitigated when all participants experience the same events over time. For the
purpose of this study, data were collected through STAR at the same time, so this minimized the
threat or spread the effect equally across the groups. The implementation of new programs and
policies, such as Algebra for All, can affect achievement and enrollment results. Selection may
also be a threat to internal validity, as participants can be selected who have certain
IMPACT OF ALGEBRA WHEN READY 69
characteristics that predispose them to have certain outcomes (Creswell, 2014). Random
assignment is not a viable option for this study, as the researcher cannot select participants
randomly so that characteristics have the probability of being equally distributed. Mortality is
the final threat to internal validity, as differential dropout rates may affect the results of the
study. Dropout rates vary greatly across districts and are not measured in the study. Participants
may drop out of classes or school due to several possible reasons (Creswell, 2014).
There is also a threat of extraneous variables contributing to changes in the endogenous
variables. There may be factors outside of the study, such as quality of the school or teacher,
which may affect the achievement results. External validity refers to generalizing findings to
and across target populations, settings, and times (Pedhazur & Schmelkin, 1991). Threats to
external validity occur when researchers draw incorrect inferences from the sample to other
people, settings, and past or future situations (Creswell, 2014). In order to control for
confounding variables, the analysis included associations between variables, not causal
connections.
There are other threats to external validity in this study: (a) the interaction of selection
and treatment and (b) the interaction of setting and treatment, and (c) the interaction of history
and treatment. Due to the narrow characteristics of the participants in the study, the researcher
cannot generalize to other individuals who do not have the characteristics of the participants
(Creswell, 2014). Additionally, due to the interaction of the setting in California, a researcher
cannot generalize to individuals in other settings. External validity threats may occur when the
researcher generalizes beyond the groups in the experiment to other groups not under study, to
different settings, or to past or future situations. As demographics and the political climate
change from year to year and across states, it is impossible to generalize to new populations or
settings. In this case, the results of the study are generalizable only to the districts included in
IMPACT OF ALGEBRA WHEN READY 70
the sample. However, the results are not generalizable to states outside of California because
other states constitute substantially different students, settings, testing, and implementation of
Algebra When Ready. The nature of Algebra When Ready as implemented in California can
never be replicated. To control for generalizability, the analysis of results was restricted to the
districts being studied. This study utilized practically every middle school and high school in
California, resulting in a sample that is nearly equivalent to the population.
IMPACT OF ALGEBRA WHEN READY 71
CHAPTER FOUR: RESULTS
The purpose of this study was to evaluate the effects of California’s systemic attempts to
increase algebra participation and access to advanced mathematics and science courses for all
student groups. Research suggests that early access to algebra beginning in the eighth grade
provides students with more opportunities for later success in postsecondary education.
Educators and policymakers view algebra as the gatekeeper for reaching higher-level
mathematics and science courses in high school, which are pathways for college entrance. The
study was designed to critically examine the extent to which California K-12 students progressed
in eighth grade Algebra I participation and consequent success in advanced math and science
courses. Additionally, this study utilized a path analysis model to determine the extent to which
Algebra When Ready positively affected participation and success rates in college readiness
mathematics and science courses across California school districts between 2003 and 2012. For
the purposes of this study, success was considered to be a score of Basic and above on the CST
in grade 7 mathematics, grade 8 Algebra I, grades 10 through 11 Algebra II, and grades 10
through 11 science. Grade 8 Algebra I participation was determined by taking the total number
of students enrolled in Algebra I in eighth grade divided by the number of students taking the
ELA CST in eighth grade.
In order to examine the relationship between Grade 8 Algebra I participation and future
measures of college readiness, specifically Algebra II and science success as determined by
Chemistry and Physics success, a path analysis model was developed. The path diagram (Figure
2) includes six waves of data, allowing for six different replications of the analysis. Each wave
provided a different test of the effects of grade 8 Algebra I participation, grade 8 Algebra I
success, grades 10 through 11 Algebra II success, and grades 10 through 11 science success.
The results of the data analyses are presented by research question.
IMPACT OF ALGEBRA WHEN READY 72
Research Question One
1. To what extent, if any, have California K-12 students progressed in Grade 8 Algebra I
participation and success, and college readiness as measured by advanced Math and science
success during the period of 2003-2012?
To answer this research question, a RM-ANOVA was employed using four variables:
grade 8 Algebra I participation, grade 8 Algebra I success, grades 10-11 Algebra II success, and
grades 10-11 science success. Tables 2 through 5 below present a summary of key descriptive
statistics for the means of participation and/or success for Algebra I participation, Algebra I
success, Algebra II success, and science success, respectively. The descriptive statistics,
including the means and standard deviations of the CST scores for all six waves are reported in
Appendix A.
The most frequently followed guidelines for effect size are those recommended by Cohen
(1988), proposing criteria for small, medium, and large effects. Thus, Cohen proposed an effect
size of .2 of a standard deviation is deemed as small, .5 as medium, and .8 as large. Cohen’s d
was computed for the change in participation and success in the six waves of data. Cohen’s d is
the ratio of the difference between the means of two independent groups divided by the standard
deviation of the pretest (Cohen, 1988). In addition to Cohen, Hattie (2012) averaged the effects
across 337 meta-analyses to set a benchmark of the typical effect of .40 of a standard deviation
(with a se=.05) to describe most innovations in schools that improve student achievement. An
effect size of .40 is referred to as the hinge point for identifying what is and what is not effective
in schools (Hattie, 2012).
Results for the change in means for Grade 8 Algebra I participation from 2004 to 2009
are shown in Table 2. Results indicate a change in means from .44 to .62 in terms of the
percentage of participation rates in Grade 8 Algebra I. The linear effect of the change was highly
IMPACT OF ALGEBRA WHEN READY 73
significant, F(1,668)=199.36, p=.001. As noted in Figure 4, the trend shows a linear increase of
.18 percentage points in means from 2004 to 2009. An effect size ascertains the strength of the
conclusions about group differences or the relationships among variables, showing the practical
significance of the results (Creswell, 2014). In this study, the effect size was computed by
dividing the raw change (.18) by the 2004 standard deviation as noted in Table 2 (.252). Using
the means and standard deviations reports (Table 2), Cohen’s d for the change in Grade 8
Algebra I participation from 2004 to 2009 was .710, nearly double the size of the standard effect
size of schooling as reported by Hattie (2012). The change in Grade 8 Algebra I participation
rates approaches effect sizes reported by Cohen as large.
Results for the change in means for Grade 8 Algebra I success from 2004 to 2009 are
shown in Table 3. Results indicate a change in means from .28 to .43 in terms of success rates in
Grade 8 Algebra I. The linear effect of the change was highly significant, F(1, 678)=3505.36,
p=.001. As noted in Figure 4, the trend shows a linear increase of .15 percentage points in means
from 2004 to 2009. The effect size was computed by dividing the raw change (.15) by the 2004
standard deviation as noted in Table 3 (.167). Using the means and standard deviations reports
(Table 3), Cohen’s d for the change in Grade 8 Algebra I success from 2004 to 2009 was .898,
more than double the size of the standard effect size (.40) of schooling as reported by Hattie
(2012). The effect size of Grade 8 Algebra I success rates surpasses effect sizes reported by
Cohen as large. In Figure 4 below, the means for the Grade 8 Algebra I participation and success
scores from 2004 to 2009 are represented linearly.
IMPACT OF ALGEBRA WHEN READY 74
Table 2
Descriptive Statistics for Grade 8 Algebra I Participation Rate
Variable Mean Standard Deviation N
Grade 8 Algebra I Participation Rate 2004 .4433 .25177 669
Grade 8 Algebra I Participation Rate 2005 .4815 .25739 669
Grade 8 Algebra I Participation Rate 2006 .5263 .26360 669
Grade 8 Algebra I Participation Rate 2007 .5529 .25934 669
Grade 8 Algebra I Participation Rate 2008 .5724 .25712 669
Grade 8 Algebra I Participation Rate 2009 .6216 .26036 669

Table 3
Descriptive Statistics for Grade 8 Algebra I Success Rate

Figure 4. Grade 8 Algebra I Participation and Success Means Graph
Variable Mean Standard Deviation N
Grade 8 Algebra I Success Rate 2004 .2801 .16711 679
Grade 8 Algebra I Success Rate 2005 .3265 .17827 679
Grade 8 Algebra I Success Rate 2006 .3541 .18695 679
Grade 8 Algebra I Success Rate 2007 .3683 .18572 679
Grade 8 Algebra I Success Rate 2008 .3976 .18773 679
Grade 8 Algebra I Success Rate 2009 .4277 .20145 679
IMPACT OF ALGEBRA WHEN READY 75
In order to analyze the trends in student success in grades 10 through 11 Algebra II and
Science from 2007 to 2012, means were computed utilized a RM-ANOVA. The descriptive
statistics showing the change in means for Algebra II success from 2007 to 2012 are shown in
Table 4. Results indicate a change in means from .27 to .37 in terms of success rates in Grade
10-11 Algebra II. The success rates were computed by adding the number of students scoring
Basic or above on the specific CST and dividing by the district’s grade 11 enrollment as
measured by the number of students taking the grade 11 ELA CST. Using the means and
standard deviations reported in Table 4 and Table 5, Cohen’s d was computed for both Algebra
II and science success. To compute Algebra II success means, the effect size was computed by
dividing the raw change (.10) by the 2007 standard deviation as noted in Table 4 (.140). Using
the means and standard deviations reports (Table 4), Cohen’s d for the change in Grade 10-11
Algebra II from 2007 to 2012 was .714, which approaches the criteria of .80 reported by Cohen
as large. The effect size of .71 is nearly double the standard effect size (.40) of school
achievement as reported by Hattie (2012). The linear effect of the change was highly significant,
F(1, 338)=760.99, p=.001.
The change in means for science success as noted in Table 5 is .067 from 2007 to 2012.
To compute science success means, the effect size was computed by dividing the raw change
(.067) by the 2007 standard deviation as noted in Table 5 (.121). Using the means and standard
deviations reports (Table 5), Cohen’s d for the change in Grade 10-11 Science from 2007 to
2012 was .554, which is above the criteria of .50 reported by Cohen as medium. The effect size
of .554 is above the standard effect size (.40) of most innovations that are introduced in schools
as reported by Hattie (2012). The linear effect of the change was highly significant,
F(1, 196)=387.48, p=.001. As shown in the graph in Figure 5, the mean success rates increased
consistently over time for both Algebra II and science success from 2007-2012.
IMPACT OF ALGEBRA WHEN READY 76
Table 4
Descriptive Statistics for Algebra II Success Rates
Variable Mean Standard Deviation N
Grade 10-11 Algebra II Success Rate 2007 .2673 .13971 339
Grade 10-11 Algebra II Success Rate 2008 .2824 .14194 339
Grade 10-11 Algebra II Success Rate 2009 .2953 .14036 339
Grade 10-11 Algebra II Success Rate 2010 .3192 .14500 339
Grade 10-11 Algebra II Success Rate 2011 .3441 .15344 339
Grade 10-11 Algebra II Success Rate 2012 .3670 .15304 339

Table 5
Descriptive Statistics for Science Success Rates
Variable Mean Standard Deviation N
Grade 10-11 Science Success Rate 2007 .2778 .12060 197
Grade 10-11 Science Success Rate 2008 .2808 .12266 197
Grade 10-11 Science Success Rate 2009 .2932 .12435 197
Grade 10-11 Science Success Rate 2010 .3158 .12338 197
Grade 10-11 Science Success Rate 2011 .3351 .12869 197
Grade 10-11 Science Success Rate 2012 .3471 .12914 197
Note: Chemisty and Physics scores are merged to represent Science

Figure 5. Algebra II and Science Success Means Graph
IMPACT OF ALGEBRA WHEN READY 77
While it is tempting to conclude that the changes in math and science success were
caused by increases in Grade 8 Algebra I participation rates, these data are correlational.
Correlation does not prove causality. However, causality does imply a specific pattern of
correlation among the measured variables. It is commonly acknowledged that path analysis is a
standard method for making causal inferences from correlational data. Thus, a path analysis is
the focus of Research Question Two below.
Research Question Two
Research Question Two was developed to critically examine the effects of California’s
systemic efforts to increase Algebra I participation in the eighth grade. Presumably, to enter the
gateway to college, all students need to be given the OTL and access to a rigorous mathematics
curriculum. In this study, both the short-term and long-term effects of Algebra When Ready in
terms of OTL and success were analyzed. To study the impact of this policy on California K-12
students, the following research question was examined through the use of a path analysis: Do
California district test data (2003-2012) support the hypothesis that Algebra When Ready had a
positive impact on the following indicators of college readiness: Algebra I success, Algebra II
success, and science success. To determine what impact if any, the Algebra When Ready policy
had on Grade 8 Algebra I participation and success, Algebra II success, and science success, a
path analysis was developed. The path analysis utilized six replications of the analysis to test the
hypothesis and the results were combined into one dataset. The success means for Algebra I
participation, Algebra I success, Algebra II success, and science success are reported and the
values for each wave are listed in Appendix A. Each wave provided a different test of the effects
of Grade 8 Algebra I participation. The results are discussed using three headings: Impact of
SES, short-term effects of Algebra When Ready, and long-term effects of Algebra When Ready
on future success on college preparedness courses.
IMPACT OF ALGEBRA WHEN READY 78
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model- Medians for Waves 1-6
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
$
2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

.824 -.117

.
.480
.239
.620
.294
.448
.476
.403

.117

Figure 6. Hypothesized Causal Model Correlations
Impact of SES
SES was controlled for in both 2003 and 2006. To illustrate the stability of SES, the
Pearson correlations between SES 2003 and SES 2006 were as follows: .969, .968, .967, .963,
.972, and .963 respectively in Waves one through six. The range in SES 2003 and 2006
correlations was .963 to .972 (mean= .967). Due to the different samples in each wave, there is
slight variance in the SES correlations each wave of the study. The high correlations make the
argument that SES is extremely stable, so SES 2006 was not included in the study due to
multicollinearity issues. Multicollinearity refers to correlations among independent variables,
IMPACT OF ALGEBRA WHEN READY 79
resulting in adverse effects on the stability of regression coefficients. Multicollinearity causes
unstable beta weights due to large standard errors, resulting in insignificant path coefficients
(Pedhazur & Schmelkin, 1991).
As shown in Figure 6, the 2003 effects of SES had a strong impact on Grade 7 Math
success (β = .824), but had no impact on Grade 8 Algebra I participation (β = -.117) and Grade
8 Algebra I success (β = .117). The critical significance was set at p=.05. Hence, the effect of
SES on Grade 8 Algebra I participation and success was mostly through the effect of Grade 7
Math success. SES had a significant, positive impact on both science (β = .403) and Algebra II
success (β =. 448). These significant path coefficients are evidence that SES exerts a unique
effect on advanced mathematics and science success. Although the effect of SES on science is
significant, it is .045 less than the effect on Algebra II success. The correlations for waves one
through six are reported in Appendix B.
Short-Term Effects of Algebra When Ready
The path analysis was utilized to determine the effect of Grade 8 Algebra I participation
on future outcomes of success. As noted in Figure 6, arrows in the path diagram are used to
represent relationships hypothesized to be causal. Correlations were then computed to determine
the statistical significance and strength of each relationship represented in Figure 6 above. There
is a lower than expected direct path between Grade 7 Math success and Grade 8 Algebra I
participation (β = .239). On the other hand, there is a strong indirect effect of Grade 7 Math
success on Grade 8 Algebra I success (β = .480). Student success in Algebra I was mediated by
participation of Algebra I in Grade 8. As noted in Figure 6, this yielded a high path coefficient
(.480). There is a significant, positive effect of Grade 8 Algebra I participation on Grade 8
Algebra I success (β = .620), supporting the hypothesis that Algebra When Ready had a positive
impact on indicators of Algebra I success.
IMPACT OF ALGEBRA WHEN READY 80
Long-Term Effects of Algebra When Ready
Students’ tendency to be successful in advanced mathematics and science courses in
grades 10 and 11 was mediated by Grade 8 Algebra I participation and success. To determine
the correlations among variables, simple correlations were computed among four variables:
Grade 8 Algebra I participation, Grade 8 Algebra I success, Grade 10-11 Algebra II success, and
Grade 10-11 science success. The correlation matrix for each wave is reported in Appendix C.
The path analysis results indicate the causal effect of Algebra When Ready on college
preparedness. Algebra I success in the eighth grade has a positive, significant impact on both
Algebra II and science success. Algebra I success in grade 8 had a small positive, but significant
impact on science success (.294). However, the impact of Grade 8 Algebra I success on Algebra
II success was higher (.476).
IMPACT OF ALGEBRA WHEN READY 81
CHAPTER FIVE: DISCUSSION
In pursuit of equity, a push to have most students take algebra by the end of the eighth
grade has been a focus of California state policy since the passage of the PSAA in 1999
(Loveless, 2015). One focus of this study was to determine whether or not the PSAA and NCLB
Act of 2001 increased student participation and achievement in advanced mathematics and
science courses across California school districts. A second focus was to examine the effects of
Algebra When Ready in California on future indicators of college readiness between 2003 and
2012, specifically Algebra II and Science. Algebra for All is a misnomer in California because a
relatively small number of districts strictly followed universal access to algebra. The NCTM
coined the term Algebra When Ready, stating that all students should have access to high quality
algebra instruction when ready. Only when students exhibit demonstrable success with
prerequisite skills-not at a prescribed grade level-should they focus explicitly and extensively on
algebra, whether in a course titled Algebra I or within an integrated mathematics curriculum
(NCTM, 2008). Exposing students to such coursework before they are ready often leads to
frustration, failure, and negative attitudes toward mathematics and learning (NCTM, 2008).
California has been more aligned to what NCTM recommended in the first place, that students
should take Algebra I when ready.
The next section of this dissertation provides a brief summary of the study, a review of
the findings, unintended consequences of Algebra When Ready, policy implications, and
recommendations for future research. A discussion of the conclusions and their connections to
the literature presented in Chapter Two was used to support the findings. Conclusions are based
on the two overarching research questions used to guide the study.
IMPACT OF ALGEBRA WHEN READY 82
Summary of the Study
This study tracked California students’ progress in advanced mathematics and science
from 2003 to 2012, the point in which the Common Core State Standards (CCSS) began
implementation in schools across the nation. The purpose of this quantitative study was two-
fold: (a) to determine the extent to which California students have progressed in achievement in
STEM courses, specifically Algebra I, Algebra II, and science as a result of federal and state
policies; and (b) to critically examine the extent to which Algebra When Ready had a positive
impact on indicators of college readiness in terms of Algebra I success, Algebra II success, and
science success. The study added to the literature pertaining to the effects of Grade 8 Algebra I
on college preparedness courses, including science success.
The two research questions were as follows:
1. To what extent, if any, have California K-12 students progressed in Grade 8 Algebra I
participation and success, and college readiness as measured by advanced mathematics
and science success during the period of 2003-2012?
2. Do California district test data (2003-2012) support the hypothesis that Algebra When
Ready had a positive impact on the following indicators of college readiness: Algebra I
success, Algebra II success, and science success.
A brief summary of the results by research question is presented below.
Research Question One Findings
In order to create a more equitable learning environment, all students need to be given the
OTL with increased access to college preparation courses. Research Question One, on the
degree of participation and success, was used to determine whether or not California students
have made progress in terms of participation rates in Grade 8 Algebra I and success in advanced
mathematics and science courses. Achievement rates in advanced courses significantly
IMPACT OF ALGEBRA WHEN READY 83
improved in this study, according to the analysis of results of the standards-based CST scores.
Substantial progress was made on Algebra I participation, Algebra I success, Algebra II success,
and science success during the period of 2003 to 2012.
Algebra I Participation and Success. School districts across California have shown
immense gains in access and proficiency in Grade 8 Algebra I. Grade 8 Algebra I participation
(M= .443 in 2004 and M= .622 in 2009) means have shown remarkable gains over the course of
the study (Table 2). In terms of participation, there was a linear increase of .18 percentage points
in means from 2004 to 2009. As shown in Figure 7, the effect size for the change in Grade 8
Algebra I participation from 2004 to 2009 was .710, nearly double the size of the standard effect
size typically reported in education (average effect size = .40, Hattie, 2012). The change in
Grade 8 Algebra I participation rates approach effect sizes (.80) reported by Cohen as large.
Results for the change in means for Grade 8 Algebra I success from 2004 to 2009 (Table
3) indicate a positive change in means (M=.280 in 2004 and M=.428 in 2009). The trend shows
a linear increase of .15 percentage points in means from 2004 to 2009. As noted in Figure 7,
Cohen’s d for the change in Grade 8 Algebra I success from 2004 to 2009 was .898, more than
double the size of the standard effect size typically reported in education (average effect size =
.40, Hattie, 2012). The effect size of Grade 8 Algebra I success rates surpass effect sizes (.80)
reported by Cohen as large.
The results of this study are consistent with the results of previous studies illustrating
positive longitudinal growth for all student subgroups using standardized test scores to measure
success (EdSource, 2009; Raymundo, 2014; Veith, 2013). Results from the EdSource (2009)
report indicated that statewide testing data revealed that traditionally marginalized student
subgroups that might not have previously had access to eighth grade Algebra I are participating
and rising to the challenge. EdSource (2009) reports substantial gains in the percentage of
IMPACT OF ALGEBRA WHEN READY 84
socioeconomically disadvantaged (SED), African Americans students, and Latino students in
terms of proficiency rates. SED eighth grade students scoring proficient or advanced on the
Algebra I CST improved by eight percentage points between 2003 and 2008. This means that
3.2 times as many SED eighth graders increased their scores in 2008. Additionally, EdSource
revealed that 2.6 times as many African American students scored proficient or advanced on the
Algebra I CST in 2008 as in 2003, with the percentage of students scoring in the Below Basic
(BB) and Far Below Basic (FBB) range decreasing. There were also 3.2 times as many Latino
eighth grade students scoring proficient or advanced on the Algebra I CST in 2008 as in 2003,
with the percentage scoring BB and FBB decreasing. These data show that larger numbers of
traditionally disadvantaged subgroups are succeeding when provided access.
In support of EdSource (2009), Raymundo (2014) noted substantial gains in access and
proficiency in eighth grade Algebra I for all subgroups from 2003 to 2013. As noted in Table 6,
Raymundo (2014) reported that access increased drastically for African Americans (ES= .77)
and Hispanics (ES= 1.33). Raymundo demonstrated that African American (ES=1.54) and
Latino students (ES=.95) had substantial gains in Algebra I proficiency rates with the effect size
for African Americans being particularly significant. These remarkable gains are far larger than
the effect sizes typically reported in education (average effect size = .40, Hattie, 2012).
Similarly, Veith (2013) found that increasing access to eighth grade Algebra I opened
doors for English Language Learners (ELLs) when she studied 18 of California’s largest school
districts. Veith reported that the mean percent change in ESL OTL in the 18 large California
urban school districts increased for Algebra I by grade 9 by an average of 38%. Additionally,
since the inception of Algebra for All, the median success rate change for all the 18 districts
studied was 32%. Table 6 lists the effect sizes from previous research, showing that ELL access
(ES= 2.50) and success (ES= 2.65) in Grade 8 Algebra I proved to be large (Veith, 2013). The
IMPACT OF ALGEBRA WHEN READY 85
effect sizes reported from prior research (Table 6) exceed the effect sizes reported in this study
(Figure 7) because the aforementioned studies were conducted over longer periods of the time.
Algebra II and Science Success. A unique contribution of this study deals with Algebra
II and science success. Results for the change in means for Grade 10-11 Algebra II success
(Table 4) from 2007 to 2012 indicate a .10 positive change in means (M=.267 in 2007 and
M=.367 in 2012). Cohen’s d for the change in Grade 10-11 Algebra II from 2007 to 2012 was
.714, which approaches the criteria of .80 reported by Cohen as large. The effect size of .71 is
nearly double the standard effect size typically reported in education (average effect size = .40,
Hattie, 2012).
Results for the change in means for Grade 10-11 science success (Table 5) from 2007 to
2012 indicate a positive change in means (M=.278 in 2007 and M=.347 in 2012). The change in
means for science success is .067 from 2007 to 2012. Cohen’s d for the change in Grade 10-11
Science from 2007 to 2012 was .554, which is above the criteria of .50 reported by Cohen as
medium. The effect size of .554 is above the standard effect size typically reported in education
(average effect size = .40, Hattie, 2012). The mean success rates increased consistently over
time for both Algebra II and science success from 2007-2012 (Figure 5).

Figure 7. Effect Sizes of College Preparation Courses
IMPACT OF ALGEBRA WHEN READY 86
Recent studies support that increases in OTL in Algebra I correlate with success in future
indicators of college readiness (Gavrilovic, 2013). Gavrilovic (2013) reported a 17% increase in
ninth grade Algebra I OTL and an 11% increase in Algebra II OTL between 2004 and 2012. As
Table 6 shows, Gavrilovic reported an effect size of .85 for 11
th
grade Algebra II success. These
gains are double the standard effect size typically reported in education (average effect size =
.40, Hattie, 2012), exceeding effect sizes (.80) reported by Cohen as large. Gavrilovic reported
that the percent increase in OTL means for Algebra II were close to the percent increase in
success means. These results support the conclusion that the more students are given the OTL in
higher-level math, the higher the likelihood of them being successful (Oakes, 1985).
IMPACT OF ALGEBRA WHEN READY 87
Table 6
Effect Sizes for Eighth Grade Algebra I Participation and Subsequent Math Success
Study Grouping Level of Analysis Outcome Effect Size
of 2003-2012
Change
Raymundo
2014
Hispanic CA Middle Schools 8
th
Grade Tracking 1.33
Raymundo
2014
Hispanic CA Middle Schools 8
th
Grade Algebra I
Proficiency
.95
Raymundo
2014
African American CA Middle Schools 8
th
Grade Tracking .77
Raymundo
2014
African American CA Middle Schools 8
th
Grade Algebra I
Proficiency
1.54
Gavrilovic
2013
All Students CA High Schools 9
th
Grade Algebra I
Participation
1.10
Gavrilovic
2013
All Students CA High Schools 11
th
Grade Alg. II
Participation
.64
Gavrilovic
2013
All Students CA High Schools 9
th
Grade Algebra I
Success
1.23
Gavrilovic
2013
All Students CA High Schools 11
th
Grade Alg. II
Success
.85
Veith 2013 English Language
Learners
18 Largest CA
School Districts
8
th
Grade Algebra I
Participation
2.50
Veith 2013 English Language
Learners
18 Largest CA
School Districts
9
th
Grade Algebra I
Success
2.65
Levy 2011 All students 152 CA Districts 8
th
Grade Algebra I
Participation
1.77
Levy 2011 All students 152 CA Districts 9
th
Grade Algebra I
Success
1.66
Levy 2011 All students 152 CA Districts Algebra II Success 1.20

Research Question Two Findings
The findings from Research Question One suggest that grade eight Algebra I
participation does have its intended effects in terms of both short-term and long-term (Algebra II,
science) implications. However, the descriptive data reported to this point is correlational and
correlation does not prove causation. Path analysis is recognized as the most powerful approach
to causation when the data are correlational. Causality does imply a specific pattern of
correlations among the measured variables. Hence, a path analysis is utilized which includes six
IMPACT OF ALGEBRA WHEN READY 88
replications of the analysis to test the hypothesis. Using medians, the results from the six waves
were combined into one summary diagram (Figure 8). Each replication provided a different test
of the effects of Grade 8 Algebra I participation. Research Question Two was used to determine
if California district test data (2003-2012) support the hypothesis that Algebra When Ready had a
positive impact on the following indicators of college readiness: Algebra I success, Algebra II
success, and science success. The path diagram and corresponding regression weights for each
wave are reported in Appendix B.
Short-Term Effects on Algebra I Success. The first key finding was the direct effect
that Grade 8 Algebra I participation had on subsequent Grade 8 Algebra I success (Figure 8).
The key variable in this path diagram is Grade 8 Algebra I participation, as California made a
deliberate attempt to increase access by encouraging all eighth grade students to enroll in
Algebra I. There is a significant, positive effect of Grade 8 Algebra I participation on Grade 8
Algebra I success (β = .620), supporting the hypothesis that Algebra When Ready had a positive
impact on indicators of Algebra I success. This strong effect between Grade 8 Algebra I
participation and success is evidence that achievement follows from opportunities. Tracking
denies these opportunities. Therefore, policies such as Algebra When Ready that pursue equity
by detracking remedial mathematics, can help close the achievement gap by creating systems
where all students can have an OTL with access to advanced courses.
IMPACT OF ALGEBRA WHEN READY 89
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model- Medians for Waves 1-6
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
$
2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

.824 -.117

.
.480
.239
.620
.294
.448
.476
.403

.117

Figure 8. Hypothesized Causal Model Medians for Waves 1-6
Long-Term Effects for College Readiness. A second key finding is that Grade 8
Algebra I participation and success has long-term effects on future indicators of college
readiness. Algebra I students’ tendency to be successful in advanced mathematics (Algebra II)
and science (Chemistry/Physics) courses in Grades 10 and 11 was precipitated by Grade 8
Algebra I participation and success. The path analysis results shown in Figure 8 above indicate
the causal effect of Algebra When Ready on subsequent courses that are indicative of college
readiness.
As shown in Figure 8, there is a strong, positive effect of Grade 8 Algebra I success on
Algebra II success (β = .476), supporting the hypothesis that Algebra When Ready had a positive
IMPACT OF ALGEBRA WHEN READY 90
impact on future indicators of college readiness. There is a smaller, but significant, positive
effect of SES 2003 on Grade 10-11 Algebra II success (β =.448). Algebra I success is more
highly correlated with Algebra II success (β =.476), as the two courses share common
mathematical content. There is also a positive, direct effect of Grade 8 Algebra I success on
science success (β =.294). This effect is smaller, but significant due to the integration of
mathematics in Chemistry and Physics courses.
In support of this study, Levy (2012) used a path analysis to examine the relationship
between SES and success in Algebra I and Algebra II. Using a sample of 152 school districts,
the primary finding was that increasing participation in Grade 8 Algebra I is effective in
increasing students’ OTL and success in both Algebra I and Algebra II. Levy found that Grade 8
Algebra I participation roughly doubled from 31.75% in 2003 to 62.25% in 2011 (ES=1.77).
Additionally, Algebra I success by grade 9 increased from 41.70% in 2003 to 68.49% in 2011 to
33.23% in 2011 (ES=1.60). Algebra II success nearly doubled, improving from 17.74% in 2003
to 33.32% in 2011 (ES=1.20). The effect sizes (Table 6) all were all at least three times the
standard effect size typically reported in education (average effect size = .40, Hattie, 2012),
surpassing effect sizes reported by Cohen as large (.80). These effect sizes are much larger than
the effect sizes reported in this study due to the longer time period that was examined. These
data support the results of this study in that increasing participation in eighth grade algebra
expands students’ OTL and success in both Algebra I and Algebra II.
Conclusion
Regression weights were computed using ordinary least square regressions to determine
the statistical significance and strength of each relationship represented in the path diagram in
Figure 6. These findings suggest that Grade 8 Algebra I participation has a higher direct effect
on Algebra II success (β = .476) than SES has on Algebra II success (β = .448). The strength of
IMPACT OF ALGEBRA WHEN READY 91
this effect demonstrates that the state’s efforts to increase students’ OTL in Grade 8 Algebra I by
dismantling tracking in remedial math had a significant effect on future indicators of college
readiness. Grade 8 Algebra I participation had an effect on long-term outcomes through Grade 8
Algebra I success. The size of this effect is bigger than the SES effect, revealing that effective
interventions such as Algebra When Ready, can lead to positive changes in student performance,
despite immense SES differences.
There is an assumption supported by research from the Coleman Report concluding that
schools have limited impact on narrowing the achievement gap (Coleman et al., 1966).
However, results from Research Question Two refute this argument, demonstrating that
increasing access and OTL to advanced mathematics courses can serve to weaken the effect to
which factors such as income and race relate to course placement and success.
Unintended Consequences of Algebra for All
Universalizing Algebra I in the eighth grade is grounded on the notion that students learn
more in rigorous educational environments; a theory referred to OTL (Domina et al., 2015).
Algebra for All was one such policy intended to expand OTL and improve proficiency for those
students who would not otherwise take Algebra I in the eighth grade (Nomi, 2012). However,
several studies outlined the unintended consequences of mandating Algebra for All: (a) a
“watering down effect” (Loveless, 2013a, p. 28), (b) negative effects on student achievement
(Domina et al., 2015; Liang et al., 2012), and (c) high failure rates (Allensworth et al., 2009;
Nomi, 2012; Williams et al., 2011).
Increases in success rates resulting from Algebra for All are contrary to Loveless (2013a),
who indicated that increasing participation rates in advanced courses resulted in a “watering
down effect”, creating a mismatch between students’ skills and content (p. 28). Loveless was
widely cited stating that scores declined, but this is not counter to the results reported herein.
IMPACT OF ALGEBRA WHEN READY 92
Loveless’ research was widely misinterpreted for two reasons. First, it is obvious that scores
may decrease because there is no longer “creaming of the crop”, as advanced courses become
more accessible to those who did not have access previously. Second, the trends reported by
Loveless were analyzed in terms of NAEP assessment data, rather than standards-based
assessment results.
This “watering down effect” described by Loveless (2013a) supports the notion that the
policy is likely to have negative unintended consequences in terms of achievement (Allensworth
et al., 2009; Domina et al., 2015; Gamoran & Hannigan, 2000; Liang et al., 2012). Nomi’s
(2012) analysis of the 1997 Chicago policy requiring all ninth grade students to take Algebra I,
indicated that there were unintended negative effects for high achieving students. Nomi (2012)
reveals that when eliminating remedial courses, schools created more mixed level classes. These
mixed classrooms resulted in a decline in peer skill levels and test scores for high achieving
students. Declines in peer ability levels could have resulted in less rigorous content, slower
paced teaching, lower expectations, and greater disruption. Domina and colleagues (2015)
analyzed district level panel data to provide a view of the consequences of changing course
placement practices, highlighting a serious unintended consequence. He refers to “spillover”
effects for teaching and learning as not just whether a student receives access to Algebra I, but
the change also effects the teachers and students that all individuals are likely to encounter in
these classes (p. 639). Domina et al. (2015) reported that enrolling more students in advanced
courses corresponded with declines in average 10
th
grade performance on the mathematics
section of the California High School Exit Exam (CAHSEE). In conclusion, although there have
been increases in Grade 8 Algebra I enrollments for traditionally marginalized students, it is less
clear if student achievement improved (Domina et al., 2015).
IMPACT OF ALGEBRA WHEN READY 93
Liang, Heckman, and Abedi (2012) posit that the Algebra for All policy increased the
number of students taking algebra in eighth grade, but 60% of these students failed to score
proficient on the end-of-course CST. Further, Liang et al. (2012) describe the “significant
deterioration between the number of eighth graders taking the CST for Algebra I and the number
of ninth graders taking the CST for Geometry leads us to suggesting this idea of a leak in the
pipeline” (pp. 337-38). While progress was made, it is not seen as evidence that Algebra for All
worked. The best criticism of Algebra for All is the low success and participation rates in
Algebra II.
While it is true that success rates are low, the fact that they are much higher over the last
decade cannot be ignored. This indicates that more may need to be done to lay the foundation
for success in mathematics in prior years. As a result of these aforementioned unintended
consequences, there have been large increases in algebra failure rates. These large failure rates
among STEM underrepresented group have caused scholars to rethink early algebra.
Policy Implications
The current study was designed to critically examine the extent to which California
district test data (2003-2012) support the hypothesis that Algebra When Ready had a positive
impact on future indicators of college readiness across student subgroups and poverty levels in
California. Additionally, the study determined the extent to which California K-12 students have
progressed in achievement in STEM courses, specifically Algebra I, Algebra II, and science from
2003-2012. Results suggest that Grade 8 Algebra I OTL and success does have its intended
effects on future outcomes. However, because of the unintended consequences and other
concerns of Algebra for All, there is almost universal agreement among scholars that the policy
did not work. However, the findings from this study are compelling evidence that California
made substantial progress because tracking rates have significantly decreased. This study may
IMPACT OF ALGEBRA WHEN READY 94
have the potential to influence and inform future policy decisions that are intended to increase
equity and access across California school districts. The researcher’s suggestions supported by
the findings of this study are as follows: (1) create a strong system-wide, transparent
accountability system in high schools that emphasizes detracking, (2) use uniform, objective
measures targeting students for accelerated mathematics pathways, (3) hold high expectations for
all students recognizing that Algebra When Ready is needed, and (4) provide students with
appropriate supports as deemed necessary to succeed in Algebra I.
1. In order to create equity in access to college preparation courses, it is imperative to have
a strong accountability system that assesses student progress in end-of-year math and
science courses. Prior to 2013, California had an accountability system in which all
students in grades 3-11 were required to take end-of-course assessments. This study
comes at an important time in education as we are in the midst of the transition into the
CCSS, and students are currently only assessed in grades 3 through 8 and 11. This is
worrisome as students in grades 9 and 10 will not be assessed, and without an
accountability system to track student progress, we will not know how students are
progressing.
2. Policies need to rely on objective measures targeting students for acceleration. Current
selection processes may place inequitable barriers on future opportunities, denying access
to those unprepared for the course. Stein et al. (2011) argue that schools should select
students to take algebra based on evidence of their readiness. However, some students
who are prepared based on achievement scores are being excluded on other grounds
(Stein et al., 2011). Leaving placement decisions in the hands of local school districts is
troublesome because it may restrict access for certain groups of students, denying them
access to a rigorous, college preparation curriculum. Dougherty, Goodman, Hill, Litke,
IMPACT OF ALGEBRA WHEN READY 95
and Page (2015) described one such measure, which involved a predicted probability of
success on the North Carolina End-of-Course (EOC) Algebra I assessment. This process
was a means to help standardize the process of assigning students to mathematics courses
in order to identify students who might be overlooked for recommendation due to
variations in course grading practices and the subjective beliefs about the capabilities of
students. Additionally, district tracking practices and rates need to be transparent by
making it known to all stakeholders that tracking is occurring. One method to have
increased visibility is to report tracking by ethnicity and SES on a school report card to
show which students are gaining access to college preparation courses. Schools that are
excessively tracking need to be held accountable to the school board and superintendent.
3. In order to minimize biased recommendations, it is important to have high expectations
for all students. Subjective beliefs and practices come from teachers or counselors who
may otherwise make placement recommendations based on student characteristics, such
as ethnicity and SES. Changing the beliefs of counselors and teachers can help increase
participation and success rates for underrepresented students. High expectations
(ES=1.44) for students is viewed by Hattie (2012) as having the largest effect on student
learning. These expectations of success may become a barrier for some as they may only
perform to the expectations they previously have of their ability.
4. The educational system will be forced to adjust to address the challenges associated with
teaching algebra to a heterogeneous prepared group of students (Stein et al., 2011).
Adjustments include supports needed to help underprepared students “catch up” and the
design of approaches to counteract the tendency of universal policies that include new
forms of tracking with “hidden differentiation” (Smith, 1996, p. 151). Clearly, providing
appropriate supports and structures for underprepared students is a critical component of
IMPACT OF ALGEBRA WHEN READY 96
a universal acceleration policy. As an example, Allensworth and Easton (2007)
demonstrate that Chicago Public Schools enrolled half of their students in double dose
Algebra I to ensure success in Algebra for All by grade nine (Allensworth & Easton,
2007). Dougherty et al. (2015) stated that “simply mandating that all students take
algebra without giving attention to their preparation, what an algebra course entails, or
how it is taught may be damaging to the very students the policy was intended to help”
(p. 83S).
Policies such as Algebra for All can serve to reduce the extent to which factors such as income
and race relate to course assignment. Policies based solely on ability may not be sufficient to
improve the longstanding disparities to access to college preparation courses.
Recommendations for Future Research
As Algebra I is recognized as the gateway to college, it is important that all students who
are ready, are given the OTL and access to this course. Contingent on future research,
accelerated mathematics pathways in the CCSS may be considered a viable practice to open
barriers to college preparation courses for students who would otherwise not have access. Close
scrutiny and investigation regarding policies and practices is necessary. Suggestions for future
research to identify effective approaches for implementing district or school level policies to
maintain equity are as follows:
1. Disaggregated subgroup data: Future research disaggregated along ethnic/racial, special
education, SES, and language proficiency lines would be valuable data to enhance equity.
Disaggregated data on participation and success rates of various subgroups would help to
make tracking more transparent and visible to all stakeholders. Transparency would
make policymakers, parents, educators, and the community aware of placement strategies
which have limited opportunities and access to a rigorous curriculum for different
IMPACT OF ALGEBRA WHEN READY 97
subgroups. Transparency is necessary to maintain continuous pressure to sustain equity
and the OTL for all students.
2. Case studies: Future research can include case studies highlighting districts or states that
have policies and systems that maintain equity. To the extent possible, participation and
success rates can be measured to determine the impact on subsequent achievement and
coursetaking outcomes. When looking at improving student outcomes, there are several
unintended consequences and tradeoffs, which need to be considered. Unfortunately,
low-achieving students assigned to low-level classes fall further behind rather than
attaining higher-level knowledge and skills (Burris, Heubert, & Levin, 2004).
Presumably, as you raise the ceiling and increase student expectations, the middle and
bottom seem to follow. Without access and opportunity to take advanced classes,
students may lose the motivation to excel. Essentially, further research is needed on
promising practices that can help students to progress by supporting learning for
underprepared students. This could include the study of supports including bridge
courses or summer school programs.
3. Tracking and achievement rates since implementation of CCSS: Since 2003, California
made substantial progress in making Algebra I and college preparation course available
to all students, including traditionally marginalized subgroups. However, with the
implementation of the CCSS in California, Algebra I is now considered to be a ninth
grade course. Detracking advocates interpret the “common” in Common Core as reason
to eliminate accelerated tracks for high achievers (Loveless, 2015). As such, accelerated
courses in mathematics must not be reserved for the most fortunate students, but need to
be accessible and available to all students who are ready. With local district discretion, it
is important to carefully examine the equity of these placement decisions being made.
IMPACT OF ALGEBRA WHEN READY 98
Inequitable placement decisions could undermine the great progress California made in
reducing the tracking into remedial math.
4. College readiness measure: California’s accountability system intentionally reduced
tracking as superintendents and principals were held accountable for annual progress.
Toward this end, California required end-of-course subject matter tests in grades 9-11 in
all advanced math and science courses. The current ESEA model only requires a single
test in high school. Hence, research needs to continue to determine which students are
getting access to the accelerated pathway and to measure how the 11
th
grade California
Assessment of Student Performance and Progress predicts college readiness.
5. Expectations: Future research is needed to determine what schools are doing to create a
theory of high expectations. Hattie (2012) reported that the single most effective
intervention, with the highest effect size (ES= 1.44) is student expectations. However,
expectations of success might become a barrier for certain students as they may only
perform to whatever expectations they already have of their ability (Hattie, 2012). At this
point in time we have local control accountability, as individual districts have discretion
on decisions regarding course placement. How is it that states under the CCSS can keep
high expectations at the system level?
Summary and Conclusions
Equity for all students lies at the heart of the American dream and is considered to be a
centerpiece of the U.S. educational system (Stein et al., 2011). California’s accountability
system set out to reduce tracking of traditionally disadvantaged students into remedial
mathematics and to make a quality education available to all students. In fact, Algebra for All
can be viewed as a detracking methodology. There is almost universal agreement in the extant
research that Algebra for All was a failure. However, there is an erroneous line of inquiry in
IMPACT OF ALGEBRA WHEN READY 99
these prior studies that international and national assessments, such as the TIMSS and NAEP,
reflect what is occurring in California. The use of CST data in this study is much more aligned
with the courses included in the path analysis model. The CST is a standards-based, more valid
measure of what students are learning in California schools. As noted, findings from this study
challenge prior research and provide compelling evidence that California has made significant
progress in improving access and proficiency levels, especially for students who have previously
been denied access to college preparation courses. School districts across the state have shown
immense short-term and long-term gains in OTL and achievement levels in advanced
mathematics and science courses, after controlling for SES. This research suggests that policies,
such as Algebra When Ready, can help close the achievement gap by creating systems where all
students can have greater access to advanced mathematics pathways.
Inevitably, with the end of Algebra for All and the implementation of the CCSS in
California, attention needs to be given to maintain a commitment to access, equity, and a quality
education. California could serve as a model for the rest of the country to follow. In turn, school
districts across the state need to continue to strive to further advance their policies and
procedures to maximize the potential of all students so that they can become productive members
of an ever-changing society.
IMPACT OF ALGEBRA WHEN READY 100
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IMPACT OF ALGEBRA WHEN READY 113
Appendix A
Waves 1-6 Descriptive Statistics
Table A1
Wave 1 Descriptive Statistics
Variable Mean Std. Deviation N
SES 2003 .0575 .89424 197
SES 2006 .0551 .86735 197
Grade 7 Math Success 2003 .6596 .14653 197
Grade 8 Algebra I Participation 2004 .3879 .19854 197
Grade 8 Algebra I Success 2004 .2802 .13452 197
Grade 10-11 Algebra II Success 2007 .5858 .29642 197
Grade 10-11 Science Success 2007 .5424 .26565 197

Table A2
Wave 2 Descriptive Statistics
Variable Mean Std. Deviation N
SES 2003 -.0064 .96348 188
SES 2006 -.0112 .94324 188
Grade 7 Math Success 2004 .6576 .14467 188
Grade 8 Algebra I Participation 2005 .4543 .23466 188
Grade 8 Algebra I Success 2005 .3319 .14328 188
Grade 10-11 Algebra II Success 2008 .6173 .29617 188
Grade 10-11 Science Success 2008 .5398 .24821 188

Table A3
Wave 3 Descriptive Statistics
Variable Mean Std. Deviation N
SES 2003 -.0020 .96569 196
SES 2006 -.0040 .94807 196
Grade 7 Math Success 2005 .6811 .13651 196
Grade 8 Algebra I Participation 2006 .5137 .24338 196
Grade 8 Algebra I Success 2006 .3694 .14974 196
Grade 10-11 Algebra II Success 2009 .6506 .30118 196
Grade 10-11 Science Success 2009 .5653 .25214 196

IMPACT OF ALGEBRA WHEN READY 114
Table A4
Wave 4 Descriptive Statistics
Variable Mean Std. Deviation N
SES 2003 .1113 .85294 197
SES 2006 .1144 .84332 197
Grade 7 Math Success 2006 .7166 .12362 197
Grade 8 Algebra I Participation 2007 .5389 .23256 197
Grade 8 Algebra I Success 2007 .3958 .15007 197
Grade 10-11 Algebra II Success 2010 .7062 .30981 197
Grade 10-11 Science Success 2010 .6188 .25454 197

Table A5
Wave 5 Descriptive Statistics
Variable Mean Std. Deviation N
SES 2003 -.0018 .96866 169
SES 2006 -.0034 .94615 169
Grade 7 Math Success 2007 .7344 .11469 169
Grade 8 Algebra I Success 2008 .5729 .22148 169
Grade 8 Algebra I Success 2008 .4310 .15472 169
Grade 10-11 Algebra II Success 2011 .7845 .31951 169
Grade 10-11 Science Success 2011 .6524 .24061 169

Table A6
Wave 6 Descriptive Statistics
Variable Mean Std. Deviation N
SES 2003 -.0055 .96115 181
SES 2006 -.0062 .94907 181
Grade 7 Math Success 2008 .7435 .11444 181
Grade 8 Algebra I Participation 2009 .6133 .21748 181
Grade 8 Algebra I Success 2009 .4633 .14788 181
Grade 10-11 Algebra II Success 2012 .8294 .31561 181
Grade 10-11 Science Success 2012 .6697 .25021 181

IMPACT OF ALGEBRA WHEN READY 115
Appendix B
Waves 1-6 Hypothesized Causal Model
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model- Wave 1, N=198
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
$
2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

.807
.166
.410
.461
,275
.557
.532
.361
-.124
(p=..077)
.256

Figure B1. Hypothesized Causal Model- Wave 1

IMPACT OF ALGEBRA WHEN READY 116
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model- Wave 2, N=189
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
$
2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

.847
.154
.464
.459
,204
(p=.138)
.644
.501
.293
-.120
(p=.382)
.389

Figure B2. Hypothesized Causal Model- Wave 2

IMPACT OF ALGEBRA WHEN READY 117
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model- Wave 3, N=197
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
$
2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

.841
-.242
(p=.064)
.417
.352
.461
.295
.525
.596
.107
(p=.052)
.446

Figure B3. Hypothesized Causal Model- Wave 3

IMPACT OF ALGEBRA WHEN READY 118
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model- Wave 4, N=198
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
$
2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

.737
.127
.467
.250
.490
.305
-.066
(p=.275)
.589
.439
.335

Figure B4. Hypothesized Causal Model- Wave 4

IMPACT OF ALGEBRA WHEN READY 119
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model- Wave 5, N=170
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
$
2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

.872
.088
(p=.136)
.532
.514
.228
(p=.147) .646
.264
.428
.537
-.114
(p=.468)

Figure B5. Hypothesized Causal Model- Wave 5

IMPACT OF ALGEBRA WHEN READY 120
Grade 8
Algebra I
Success
Grade
10-11
Chemistry/
Physics
Success
Y
1
Y
2
Y
3
Y
4

Hypothesized Causal Model- Wave 6, N=182
2003$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2004$
$
2005$
$
2006$
$
2007$
$
2008$
$
2009$
$
$
2007$
$
2008$
$
2009$
$
2010$
$
2011$
$
2012$
$
$
SES
2003
X
1

Grade 8
Algebra I
Partici-
pation
Grade 7
Math
Success
Grade
10-11
Algebra
II Success

Y
5

.737 -0.59
(p=.588)
.
.493
.192
(p=.080)
.648
.252
.449
.453
.059
(p=.329) .105

Figure B6. Hypothesized Causal Model- Wave 6
IMPACT OF ALGEBRA WHEN READY 121
Appendix C
Waves 1-6 Correlations
Table C1
Wave 1 Correlations

IMPACT OF ALGEBRA WHEN READY 122
Table C2
Wave 2 Correlations

IMPACT OF ALGEBRA WHEN READY 123
Table C3
Wave 3 Correlations

IMPACT OF ALGEBRA WHEN READY 124
Table C4
Wave 4 Correlations

IMPACT OF ALGEBRA WHEN READY 125
Table C5
Wave 5 Correlations

IMPACT OF ALGEBRA WHEN READY 126
Table C6
Wave 6 Correlations

Abstract (if available)

Abstract California has been at the forefront of national efforts to increase mathematics proficiency levels for all students. With the passage of the Public Schools Accountability Act (PSAA) in 1999, an educational accountability system was created requiring end-of-course subject matter tests in grades 9 through 11 in all advanced math and science courses. This accountability system was based on the assumption that a push for universal access of algebra in eighth grade would reduce or eliminate tracking of historically marginalized students into remedial mathematics classes. As California attempted to enact policies such as Algebra for All to maintain equity, it increased opportunities for students to have access to early algebra. However, Algebra for All is a misnomer in California because a relatively small number of districts strictly followed universal access to algebra. Most districts followed the practice of placing students in Algebra When Ready, a term coined by the National Council of Teachers of Mathematics (NCTM, 2008). ❧ The purpose of this quantitative study was two-fold: (a) to determine the extent to which California students have progressed in achievement in STEM courses, specifically Algebra I, Algebra II, and science (Chemistry and Physics scores are merged to represent science) as a result of federal and state policies and (b) to critically examine the extent to which Algebra When Ready had a positive impact on indicators of college readiness in terms of Algebra I success, Algebra II success, and science success from 2003-2012. A one-way Repeated Measures (RM) ANOVA was conducted to compare the means on the California Standards Test (CST) of the following variables over a six-year time period: Grade 8 Algebra I participation and success (2004-2009), Grade 10-11 Algebra II success (2007-2012), and Grade 10-11 science success (2007-2012). ❧ A path analysis model is widely acknowledged as a standard method for making causal inferences from correlational data. The path model utilized in this study included a mean of 189 school districts and six waves of data from 2003-2012 to determine the intended impact of Grade 8 Algebra I participation (Opportunity to Learn-OTL) and success on college preparatory courses. The path analysis model, which included six cohorts of data, was used to test whether or not Algebra When Ready had the intended impact on college preparedness and future success. Specifically, the researcher utilized an ordinary least squares regression to assess the model. Structural equations were developed to test if the inner correlations are consistent with the correlations the model predicts. ❧ The findings from this study are compelling evidence that California made significant progress because tracking rates have considerably decreased. School districts have shown immense short-term and long-term gains in OTL and proficiency in college preparation classes. Therefore, policies such as Algebra When Ready that pursue equity by detracking remedial mathematics, can help to create systems where all students can have greater access to advanced courses. This study has the potential to inform future policy decisions that are intended to increase equity. The researcher’s suggestions supported by the findings of this study are as follows: (a) create a strong system-wide, transparent accountability system in high schools

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Asset Metadata

Creator Jacobson, Nicole Lee (author)

Core Title The 2003-2012 impact of Algebra When Ready on indicators of college readiness across California school districts

School Rossier School of Education

Degree Doctor of Education

Degree Program Education (Leadership)

Publication Date 02/24/2016

Defense Date 02/02/2016

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

Tag 8th grade,access,accountability,algebra,algebra for all,Algebra When Ready,California,equity,OAI-PMH Harvest,opportunity to learn,path analysis

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Keim, Robert (committee chair), Hausner, Larry (committee member), Marsh, Julie (committee member)

Creator Email nbucciarelli@hotmail.com,nljacobs@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-215282

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