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The impact of Algebra for all policies on tracking, achievement, and opportunity to learn: a longitudinal study of California middle schools
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Running head: ALGEBRA FOR ALL POLICY IMPACTS i
The Impact of Algebra for All Policies on Tracking, Achievement, and Opportunity to Learn: A
Longitudinal Study of California Middle Schools
by
Natalie A nn Raymundo
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 (LEADERSHIP)
May 2014
Copyright 2014 Natalie A nn Raymundo
ALGEBRA FOR ALL POLICY IMPACTS ii
Table of Contents
Acknowledgements ........................................................................................................................ iv
Dedication ....................................................................................................................................... v
List of Tables .................................................................................................................................. vi
List of Figure s .............................................................................................................................. viii
Abbreviations ................................................................................................................................. ix
Chapter 1: The Problem .................................................................................................................. 2
Introduction to the Problem ........................................................................................................ 2
Background of the Problem ........................................................................................................ 7
Statement of the Problem ............................................................................................................ 9
Purpose of the Study ................................................................................................................. 10
Research Questions ................................................................................................................... 12
Importance of the Study ............................................................................................................ 13
Chapter 2: Literature Review ........................................................................................................ 17
The Importance of Algebra I in Grade Eight ............................................................................ 17
Algebra as a Civil Right ............................................................................................................ 18
Opportunity to Learn and Tracking........................................................................................... 19
Benefits of Access to Algebra ................................................................................................... 24
Algebra for All Policies–The Impact ........................................................................................ 26
Policy in Practice ...................................................................................................................... 33
Common Core Standards —The End of Algebra for All? ......................................................... 37
Chapter 3: Methodology ............................................................................................................... 42
Research Design ........................................................................................................................ 44
ALGEBRA FOR ALL POLICY IMPACTS iii
Instrumentation and Procedures ................................................................................................ 47
Data Analysis ............................................................................................................................ 50
Limitations of the Study ............................................................................................................ 52
Chapter 4: Results ......................................................................................................................... 56
Tracking—Research Questions 1 and 2 .................................................................................... 57
Achievement—Research Questions 3 and 4 ............................................................................. 94
Equity in Placement —Research Question 5 ........................................................................... 136
Chapter 5: Discussion ................................................................................................................. 152
Tracking—Research Questions 1 and 2 .................................................................................. 152
Achievement—Research Questions 3 and 4 ........................................................................... 155
Equity in Placement—Research Question 5 ........................................................................... 158
Implications............................................................................................................................. 160
Limitations .............................................................................................................................. 162
Suggestions for Future Research ............................................................................................ 162
Conclusion .............................................................................................................................. 165
References ................................................................................................................................... 166
ALGEBRA FOR ALL POLICY IMPACTS iv
Acknowledgements
First, I would lik e to acknowledge and thank my committee members that gave their
time, provided support, and helped me through this process . Dr. Dennis Hocevar, my chair, was
extremely accommodating and supportive . He not only helped me to craft a study that would get
the dissertation done but also design one that engaged my passion and curiosity . His advice and
help with methodology and instrumentation was invaluable . Dr. Walton Greene, my second
committee member was flexible and helpful throughout the process . I met Dr. Greene during a
trip to China . His insights about education were intriguing and inspiring . I am lucky to have his
voice on the committee . Finally, I would like to acknowledge, Dr. Harold Vollkommer, the third
member of my committee, whom I respect and admire . Not only do I have a high regard for his
opinion and philosophy about the field of education, he is also very encouraging with regard to
personal and professional goals . I most admire his ability to speak plainly and provide needed
criticism in ways that truly are constructive.
Secondly, I would like to thank my family for their understanding and support. They
deserve kudos for putting up with a messy house , long lists of undone "to do" l ists, dinners from
Styrofoam containers, and baskets of clean but unfolded laundry with aplomb . I especially could
not have completed this endeavor without the copious am ounts of Starbucks delivered to me
every Saturday and Su nday morning by my husband Le e. I also cannot forget to mention my
youngest daughter Allison's contribution . Her meticulous editing skills were invaluable . I
cannot help but think though that she kind of enjoyed correcting her mother .
ALGEBRA FOR ALL POLICY IMPACTS v
Dedication
To my grandfather, Jean Robert Durbin,
who set the expectation that a college education is necessary;
To my mother, Cheryl Adams,
who raised me to think, read, and overcome obstacles; and
To my daughters: Marinna, Ryan and Allison,
who inspire me with their curiosity about the world and motivate me to continue finding
answers to questions.
ALGEBRA FOR ALL POLICY IMPACTS vi
List of Tables
Table 1 Number of Participating Schools by Year ....................................................................... 47
Table 2 All Students' Tracking Rates for 2003 -2013 by School Poverty Quartile ....................... 58
Table 3 Percent of Students Enrolled in Geometry or Algebra II in Grade Eight ........................ 59
Table 4 Eighth Grade Enrollment in Geometry or Algebra II by School Poverty Quartile .......... 60
Table 5 Tracking Rates by Ethnic Subgroup and School Po verty Level ..................................... 63
Table 6 Difference Between School Poverty Quartiles —Tracking Rates by Ethnic Subgroup ... 64
Table 7 Kruskal -Wallis results for significant differences between poverty quartiles ................. 66
Table 8 Tracking Rate Gaps Between Ethnic Subgroup by School Poverty Quartile ................. 70
Table 9 Kruskal -Wallis Results—Differences Between Subgroups by Poverty Quartile ............ 72
Table 10 Tracking Rates by Language Proficiency Subgroup and School Poverty Quartile ...... 75
Table 11 Kruskal -Wallis Tracking by Language Proficiency between Poverty Quartiles ........... 77
Table 12 Tracking Rate Gaps Between Language Proficiency by School Poverty Quartile ....... 82
Table 13 Kruskal -Wallis—Tracking Between Language Subgroups by Poverty Quartile ........... 83
Table 14 Tracking Rates by Socioeconomics Subgroup and School Poverty Quartile ............... 85
Table 15 Kruskal -Wallis Tracking Differences Between Poverty Quartiles by SES Subgroup .. 87
Table 16 Tracking Rate Gaps Between SES Subgroups by School Poverty Quartile .................. 91
Table 17 Kruskal -Wallis—Tracking Between SES Subgroups Within Poverty Quartile ............. 93
Table 18 Proficiency Means for All Students by School Poverty Quartile ................................... 96
Table 19 Proficiency Means by Ethnicity Subgroup and School Poverty Quartile ...................... 98
Table 20 Kruskal -Wallis Achievement Differences Between Poverty Quartiles by Ethnicity .. 101
Table 21 Proficiency Gaps Between Ethnicity Subgroups by School Poverty Quartile ............ 107
Table 22 Kruskal -Wallis—Achievement Between Ethnicity Subgroups by Poverty Quartile .. 108
ALGEBRA FOR ALL POLICY IMPACTS vii
Table 23 Proficiency Means by Language Proficiency and School Poverty Quartile .................115
Table 24 Kruskal -Wallis—Achievement by Ethnicity Subgroup Within Poverty Quartile .........117
Table 25 Achievement Gaps Across Language Proficiency by Poverty Quartile ....................... 121
Table 26 Kruskal -Wallis—Achievement Between Language Proficiency by Poverty Quartile 122
Table 27 Proficiency Means by SES Subgroup and School Poverty Quartile ............................ 126
Table 28 Proficiency Gaps Between SES Subgroups by School Poverty Quartile .................... 128
Table 29 Kruskal -Wallis—Achievement Between SES Subgroups by Poverty Quartile .......... 129
Table 30 Kruskal -Wallis—Achievement Between SES Subgroups by Poverty Quartile ........... 131
Table 31 All Subgroups Placement Means by School Poverty Quartile .................................... 138
Table 32 Placement Means by Ethnic Subgroup and School Poverty Quartile .......................... 139
Table 33 ANOVA Results Placement by Ethnicity and Poverty Level ...................................... 141
Table 34 ANOVA Results for Placement in 2011 -12 and 2012 -13 by Poverty Leve l ............... 143
Table 35 Placement Means by Language Proficiency and School Poverty Quartile ................. 144
Table 36 Main Effect of Poverty Quartile for Placement by Language Proficiency ................. 146
Table 37 Placement Means by SES Subgroup and School Poverty Quartile ............................. 148
Table 38 ANOVA Results for SES Placement ............................................................................ 150
ALGEBRA FOR ALL POLICY IMPACTS viii
List of Figures
Figure 1. Graphs of tracking means by ethnicity and school poverty quartile. ........................... 69
Figure 2. Graphs of tracking means by language proficiency and school poverty quartile. ........ 80
Figure 3. Graphs of tracking means by SES and school poverty quartile. .................................. 90
Figure 4. Proficiency mean line graphs by ethnicity subgrou p and school poverty quartile. .....112
Figure 5. Proficiency line graph by language proficiency and school poverty quartile. ........... 124
Figure 6. Line graphs of proficiency means by SES subgroup and school poverty quartile. .... 135
Figure 7. All subgroups placement by school poverty quartile. ................................................ 137
Figure 8. Placement means across language proficiency and school poverty quartile. ............. 147
Figure 9. Interaction effects of school poverty quartile and SES on placement. ....................... 151
ALGEBRA FOR ALL POLICY IMPACTS ix
Abbreviations
API Academic Performance Index
AYP Adequate Yearly Progress
CCSS Common Core State Standards
CDE California Department of Education
CST California Standards Test
EL English Learner
FRPM Free and Reduced Priced Meal
NAEP National Assessment of Educational Progress
NCTM National Council of Teachers of Mathematics
NSED Not Socioeconomically Disadvantaged
RFEP Reclassified English Proficient
SBE State Board of Education
SES Socioeconomic Status
SED Socioeconomically Disadvantaged
ALGEBRA FOR ALL POLICY IMPACTS 1
Abstract
Algebra for All policies in California were designed to open the barriers to the courses that
correlate to college achievement and wage increases. Previous findings have so far been mixed,
revealing both successes and work still to be done. It is important to determine whether these
policies had the effects intended and to consider practical implications of the policy before the
next big change in California mathematics—the implementation of Common Core State
Standards in 2014-15. This study contains data from all California middle schools between 2003
through 2013 with a focus on the differences between high and low poverty schools' outcomes
across student demographic subgroups. The focus of the study was on the impact of early
algebra policies on California eighth-graders with regard to tracking, achievement, and
placement practices. Kruskal-Wallis and two-way ANOVA were used to analyze results. The
data studied revealed that between 2003 and 2013, enrollment into Algebra I at the eighth grade
was increased for all students in all subgroups and proficiency rates in Algebra I went up for all
students across all subgroups and school poverty levels.
ALGEBRA FOR ALL POLICY IMPACTS 2
Chapter 1: The Problem
Introduction to the Problem
Mathematics skill and course taking is a gatekeeper to higher education and is associated
with better paying careers (Adelman, 1999) . Particularly, researchers have paid much attention
to the connection between early success with Algebra I and post-secondary education (Adelman,
1999; Allensworth, Nomi, Montgomery, & Lee, 2009; Bozick, Ingles, & Owings, 2008) . Yet
entry into higher level mathematics pathways is not equitably open to all students . In California,
not only is Algebra I a hig h school graduation requirement ( California Ed. Code 51224.5),
between 1997 and 2013 it has also been the suggested eighth grade level mathematics curriculum
(CDE, 1998) . Whereas most believe algebra is an important subject and recognize that students
that take Algebra I in the eighth grade have an advantage over those that do not take it until later,
some teachers, education professionals, legislators, and parents do not believe t hat it is the right
course for all eighth-graders. On one side of the debate is student mathematics readiness and on
the other are concerns over equity in placement decisions and opportunity for all students .
Researchers have clearly demonstrated that students that take Algebra I in the eighth
grade are more likely to enroll in higher -level courses in high school and are more likely to not
only go to college but also obtain bachelor's degrees (Spielhagen, 2006; Gamoran & Hannigan,
2000; Adelman, 1999; Wang & Goldschmidt, 2003) . In part , Algebra I success is important
because it is prerequisite to not only higher -level math but also science and technology . Algebra
II concepts, for example , are pre requisite to chemistry courses , and algebra concepts underlie
computer programming logic. Further evidence includes connections between students who take
higher-level mathematics and science classes in high school and increased college attendance
and completion rates , with these effects being even more significant with Latino and African
ALGEBRA FOR ALL POLICY IMPACTS 3
American students (Adelman, 1999). Beyond college going and completion rates, there is also a
positive correlation between job earnings and mathematics skill (Murnane, Willett, & Levy,
1995). In another study , Joensen and Nielson (2009) found that students that completed higher -
level mathematics in high school were more likely to complete college on t ime and were less
likely to be unemployed . The authors also noted that by taking higher -level mathematics courses
in high school, college students saved tuition money on courses .
Although the importance of mathematics education and its links to higher l earning are
clear, the path for disadvantaged students is not . Horace Mann is credited as saying, " Education
then, beyond all other devices of human origin, is the great equalizer of the conditions of men,
the balance -wheel of the social machinery" (Mann, 1848). Whereas education can open
pathways out of social class constraints, there is a divide along ethnic and socioeconomic lines
that prevents some students from attaining postsecondary education . Beginning as early as the
eighth grade , students are tracked into pathways that either lead to higher mathematics or not .
There is clear evidence that students taking advanced mathematics (pre -calculus and calculus)
are characterized by high socioeconomic status (SES), attendance at private schools, and
privileged backgrounds (Bozick, Ingles, & Owings, 2008) . It is of note that a 13 point gap exists
in grade eight NAEP mathematics performance between public and private schools , which over
time shows that private schools outscore public schools in general . The consequences of the
discrepancies in educational opportunity are materialized in higher education data . According to
2011 data from the U.S . Department of Education, white students (39%) are nearly twice as
likely as African American students (20%), and three times as likely as Latino students (13%), to
earn bachelor's degrees (Aud, et al., 2012) . Additionally, low SES students (lowest income
ALGEBRA FOR ALL POLICY IMPACTS 4
quartile) only attain bachelor's degrees at a rate of 8% by age 24 versus students from high -
income ( top quartile) families who earn bachelor's degrees at a rate of 82% (Mortenson, 2010) .
Despite the benefits of early algebra access on students' futures , students from minority
and low SES backgrounds are not given equal opportunities to learn higher-level mathematics
courses. Students with more economic and educational resources are more likely to both reach
and succeed in the most advanced mathematics courses (Bozick, Ingles, & Owings, 2008) . And
students from minority backgrounds, especially African American and Latino, are also less likely
to be given the opportu nity to study algebra beginning in the eighth grade (Wang &
Goldschmidt, 2003; EdSource, 2008; Smith, 1996) . This is not a new phenomenon .
In 1966, "The Coleman Report" was issued by the U.S . Department of Education. The
report outlined the educational outcome discrepancies between poor and minority students and
their affluent and/or white peers (Coleman, et al., 1966) . In fact, numerous studies have also
found links between student characteristics, ethnicity, and SES for example, on course taking,
opportunity to learn (OTL), and student outcomes (Gamoran & Hannigan, 2000; Spielhagen,
2006; Bozick, Ingles, & Owings, 2008 ; Liang, J.H., Heckman, & Abedi, 2012; NCES, 2010) .
This pattern, since being brought to the attention of education professionals and the media alike ,
has not changed dramatically; however, some improvements have been seen in the last decade —
especially since policies have been enacted to reform education, No Child Left Behind (NCLB)
and California's Algebra for All policies, for example.
In 1989, the National Council of Teachers of Mathematics (NCTM) produced a set of
mathematics standards to increase attention on mathematics curriculum . One of the core
components in these standards was an endorsement for early algebra, including incorporation of
algebraic concepts in elementary grades and a foundational understanding of algebra in grade
ALGEBRA FOR ALL POLICY IMPACTS 5
eight (NCTM, 2000). Following in the wake of the NCTM standards and b ecause the track to
higher-level mathematics in high school is determined by beginning Algebra I in grade eight, the
1997 California Mathematics Framework set Algebra I as the suggested course for all eighth-
graders (CDE, 1998) . The General Mathematics course was still available for eighth-graders but
was no longer considered an on grade -level course. In order to push schools to enroll students in
Algebra I versus General Math, a policy was enacted to prevent schools from inflating their test
scores by placing students in the lower General Mathematics course or placing students that
probably should be placed into Algebra I . Schools and districts that enroll ed eighth-graders in
General Mathematics were penalized through the Academic Performance Index (API) scoring
formulas. When students score d "Proficient," for example, on the CST for General Math,
schools were only given credit for a score of "Basic." This penalty , however, did not apply to the
Adequate Yearly Progress (AYP) calculations that are reported to the federal government as part
of NCLB r equirements. So, while Algebra I was not a mandated course for eighth grade,
penalties applied when the suggestion was not heeded.
To further maintain implementation of eighth grade algebra in California classrooms, o n
July 9, 2008, California's State Boa rd of Education (SBE) mandated that all eighth-graders take
the CST for Algebra I (O'Connel, 2008). This decision was in response to the U.S . Department
of Education questioning the validity of General Mathematics being used f or AYP. According to
NCLB requirements, California was out of compliance because the curriculum and course
outlined for grade eight in the mathematics framework (Algebra I) did not match the test that all
students were given . Rather than change the framework to officially make General Mathematics
(a combination of sixth and seventh grade standards) an officially sanctioned eighth grade
course, the SBE instead mandated that all students take the Algebra I test no matter which co urse
ALGEBRA FOR ALL POLICY IMPACTS 6
they were enrolled in during eighth grade . California’s decisions and evolution toward requiring
Algebra I for all eighth grade students are collectively referred to as Algebra for All.
The mandate for all eighth-graders to take the Algebra I CST, h owever, did not stand .
Shortly after the SBE decision was announced, a court case was brought by a combined group
including, the Association of California School Administrators, the California Teachers
Association, the California School Boards Association, and the Superintendent of Public
Instruction, to s top the required course (Association of California School Administrators, 2008) .
The judge in the case issued an injunction because the State Board did not provide adequate
public notice to the hearing when they voted to mandate eighth grade algebra. In spite of the
injunction, California schools still had to contend with the penalties to their API scores when
they did not enroll eighth-graders in algebra . The impact of Calif ornia’s Algebra for All policies
has included significantly increased student access to Algebra (Liang, J.H., Heckman, & Abedi,
2012); however, th e policy remains controversial due to concerns over low student achievement
and success rates (Loveless, 2008).
Most recently, the adoption of Common Core State Standards (CCSS) has brought the
debate to the forefront again . In 2010, California adopted the CCSS but used a provision that
allowed them to add back in elements of Algebra I on top of the grade eight CCSS mathematics
standards, which more resembles a pre -algebra course; however, as of early 2013, under
immense pressure, the SBE voted to adopt the CCSS for eighth grade mathematics without the
inclusion of the Algebra I standards . The SBE stated that Algebra I is still recommended for
eighth-graders that are ready (Noguchi, 2013). Marking the end of California’s Algebra for All
movement, in March 2013, the S BE removed the penalty for enrolling and testing eighth-graders
in General Mathematics . In this report, a longitudinal analysis of the impacts of California’s
ALGEBRA FOR ALL POLICY IMPACTS 7
Algebra for All movement on enrollment and success were analyzed using data from 2003 to
2013.
Background of the Problem
In 1983, the educational report, A Nation at Risk, was produced in a reaction to the
observation that America's schools were failing —putting the nation at risk economically . The
report reviewed data regarding the quality of teac hing and learning, compared the U.S . to other
nations, studied the connection between high school achievement and college admissions, and
defined problems that needed to be solved (National Commission on Excellence in Education,
1983). Further, the report included recommendations for high school courses, including three
years of mathematics . In addition, the report highlighted U.S . students' decline in mathematics
performance on College Board's Scholastic Aptitude Test (SAT), the increasing need for remedial
mathematics courses in early college, and the U.S . inferiority in science and math, as compared
with other nations in terms of performance and time spent studying the subjects . This final point
was reported often in the news media and by political leaders, namely because mathematics and
science skills are often anecdotally linked with economic growth . Some dispute the validity of
the document due to inaccurate reporting with regards to SA T data and the unproven idea that
school performance can be directly correlated to the nation's economy (Rothstein, 2008) . The
impact of this report though was to call attention to education, accountability, and reform .
Twenty-five years after A Nation at Risk, increases in student achievement have been
observed. According to the 2008 National Assessment of Educational Progress (NAEP) data,
between 1986 and 2008, 13 -year-olds taking pre -algebra and algebra increased significantly with
only 25% taking the higher courses in 1986 versus 62% in 2008 (Rampey, Dion, & Donahue,
2009). In addition to increases in eighth grade pre-algebra and algebra course taking, scores on
ALGEBRA FOR ALL POLICY IMPACTS 8
the NAEP also increased between 1986 and 2008 (Rampey, Dion, & Donahue, 2009) . Although
scores only increased by 12 points, the increase was statistically significant and indicates that
students are progressing in the higher -level courses. Steeper growth occurred between 1999 and
2004, which coincides with nationwide pushes for algebra instructi on.
In 2011, the data continue d to follow the same trends . A review of the 2011 NAEP data
for grade eight mathematics reveal ed that although there are still differences between the
performance of students along ethnic and socioeconomic lines, overall performance has
improved (NCES, 2011). Between 1990 and 2011, the numbers of eighth-graders scoring in the
proficient range grew from 15% to 35%, and the numbers scoring above basic grew from 52% to
73%.
Although mathematics scores are increasing for students overall, achievement gaps
remain with a decreasing , but still large , 31 point gap between African American and white
students and a 23 point gap between Latino and white students (NCES, 2011). In terms of
proficiency, in 2011, 41% of white California students scored in the proficient range on the
eighth grade NAEP, and African American and Latino students scored in the proficient range at
rates of 12% and 13% respectively . Compared to national data, California's white students were
more likely to be proficient, African American students matched national averages, and Latino
students scored 5% points lower .
Alongside these disparities between subgroups of our nation's youth , are positive
examples of success . Students in high poverty schools , for example, are not doomed to
underperform. Much research has been done regarding the successes some high poverty schools
and students are having . One such study found that a combinat ion of increased learning
opportunities and student behaviors (such as school attendance and student effort) helped
ALGEBRA FOR ALL POLICY IMPACTS 9
students in middle school go from below -grade level achievement to at -or-above average levels
(Balfanz & Byrnes, 200 6). Although opportunity to learn (offering a course) is rarely enough for
struggling students to succeed , it is certainly requisite .
Statement of the Problem
Inequitable placement of low SES and minority students into General Mathematics in the
eighth grade puts students on a pathway for lower level mathematics courses. The California
State University and University of California entrance requirements call for students to complete
a minimum of three years of high school mathematics, preferably four. Students who take
Algebra I in the eighth grade are set on a pathway to finish high school with Calculus or
Statistics, both Advanced Placement (AP) courses, which allow for college credit to be earned at
little student cost . Students who do not be gin Algebra I until ninth grade will not make it to the
AP mathematics courses, which make them less qualified university candidates, especially for
Science, Technology, Engineering and Mathematics fields .
Furthermore, schools that place students inequit ably into Algebra I in grade eight by
race/ethnicity are violating students' civil rights and are putting themselves at risk for legal
liability. According to Title VI of the Civil Rights Act of 1964, no agency may directly or
through policy use criteria or methods to provide opportunities for programs that have the effect
of subjecting individuals to discrimination based on race (Title VI, 28 C.F.R . § 42.104(b)(2)) .
This holds true whether there was intent or not; and the data are clear, student minorit y groups
and students of low SES have not had equal access to higher -level mathematics courses,
beginning in grade eight.
ALGEBRA FOR ALL POLICY IMPACTS 10
Purpose of the Study
The purpose of the study was to examine the access to and success in Algebra I at the
eighth grade for traditionally disadvantaged students in California and whether or not access and
achievement has been impacted by Algebra for All policies. Traditionally disadvantaged
students include students of low SES and/or minority ethnicities (in California, Latin o and
African American students are the largest subgroups) . Also included was school poverty as
measured by a school’s percentage of students participating in the Free and Reduced Price Meal
program (FRPM) , analyzed as a factor in acce ss and a chievement. In schools with low numbers
of students of poverty, the API penalties for placing students in General Mathematics may not be
a motivating factor due to the small impact of such penalties on schools that do not have high
numbers of students that would be placed in General Math . On the contrary , schools with
smaller numbers of low SES and minority students are more likely to have higher test scores in
general and thus may not be worried about a small reduction in points . In these cases, schools
may worry instead about AYP numbers and place students into General Mathematics to increase
their percentage proficient numbers . NCLB’s AYP requirements require all students to score
"Proficient" or higher by the 2014 -15 school year . If schools place their student s in General
Mathematics and the students score proficient, they lose API points (which may be of less
concern to schools already above the state’s 800 target), but their AYP scores benefit. Because of
these unknowns, this study is unique in that there is a focus on disaggregation of school -wide
poverty data when examining course enrollment and achievement data. Previous research has
shown a significant increase in the numbers of students enrolled in early algebra in California
(Waterman, 2010; EdSource, 2009) . However, research has not focused on the differences
between schools of different poverty levels .
ALGEBRA FOR ALL POLICY IMPACTS 11
In this study , enrollment and success in eighth grade algebra (and higher courses) were
examined in schools by student demographi cs (SES, language proficiency, and ethnicity) and
school level poverty (poverty level broken into quartiles) . With this information, schools can
critically examine their filters for placement in early algebra and whether or not placement
policies have been appropriate or disproportional . In addition, policymakers can analyze the
effects of policies such as penalizing API but not AYP for enrolling students in General Math .
These data are especially important for schools to examine before the California implementation
of the Common Core State Standards (CCSS) in the 2014 -15 school year . Some worry th at with
the removal of the requirement for eighth grade Algebra I , a lesser course will again become the
default rather than considered a remedial course —making Algebra I once again reserved for
honors students (Noguchi, 2013). In order to make sure that schools do not take a step backward
in their thinking about Algebra I opportunities, this study serve s as a review of the practices and
policies before the implementation of CCSS and as a benchmark for future policies . Therefore,
the purpose of this study is to explore the extent of the implementation and impact of the Algebra
for All initiative between 2003 and 2013 across student subgroups and school poverty levels and
examine the access to and success in early algebra for traditionally disadvantaged students .
Information presented include s a critical examination of early algebra placement
practices to determine whether or not traditionally disadvantaged students have been given the
same opportunities to learn as other students with similar mathematics skill and history ( previous
CST scores). Prior research has found that traditionally disadvantaged students not only start
school at lower ability levels, the achievement gap increases the longer they are in school (Lee &
Burkam, 2002; Fryer & Levitt, 2006) . But students given an opportunity to learn algebra, even
those with lower mathematic ability, are better off than those restricted to general mathematics
ALGEBRA FOR ALL POLICY IMPACTS 12
courses (Gamoran & Hannigan, 2000; Spielhagen, 2006) . Practices that keep students tracked
into lower level mathematics classes restrict a student's opportunity to learn gatekeeper subjects
in mathematics and science, such as Algebra II and Chemistry. Therefore, as well as studying
tracking (access to Algebr a I and achievement in Algebra I) , a part of the study will also include
an analysis of placement practices .
Research Questions
The author focused the study on the access to and the success in Algebra I of traditionally
disadvantaged students before and after the Algebra for All initiative in schools in California.
Data were compared to other student subgroups . The study population include d high and low
SES students who took the Algebra I CST and General Mathematics CST between 2003 and
2013 California schools. Minority and traditionally disadvantaged subgroups were also
examined where the numbers of those subgroups were significant. The research questions for
the study are intended to measure the impact of the Algebra for All policies on tracking
(questions 1 and 2), achievement (questions 3 and 4), and equity in placement (question 5) . The
research questions are:
1. To what extent, if any, have California high and low poverty schools increased enrollment
in early algebra for tr aditionally disadvantaged students between 2003 and 2013?
2. To what extent, if any, have California high and low poverty schools decreased the gap
between non -disadvantaged and traditionally disadvantaged students' access to early
algebra between 2003 and 2013?
3. To what e xtent, if any, have California high and low poverty schools increased
traditionally disadvantaged eighth grade students' success in Algebra I and above between
2003 and 2013?
ALGEBRA FOR ALL POLICY IMPACTS 13
4. To what e xtent, if any, have California high and low poverty scho ols decreased the gap
between non -disadvantaged and traditionally disadvantaged eighth grade students'
success in Algebra I and above between 2003 and 2013?
5. How are previous mathematics achievement (as measured by the seventh grade
mathematics CST), stude nt demographics (ethnicity, language proficiency,
socioeconomic status), and school poverty levels (as measured by FRPM participation
rates) related to placement in eighth grade Algebra I between 2003 and 2013?
Importance of the Study
American culture is b uilt around the philosophy of meritocracy, in direct opposition to the
entitlements of nobility . Meritocracy is at the foundation of our society . Students are accepted
into universities based on their test scores, grades, and accomplishments . People are hired for
jobs, we hope, based on the merits of the applicants . When rewards and positions are given
outside the ideals of merit, it draws concern . Teacher pay, for example, is based on years of
service, and for several years there have been calls for a merit-based pay system . Also,
affirmative action policies, meant to level the playing field for minorities, were abandoned
because affirmative action is not based strictly on merit .
Except meritocracy works only if all are given equal opportunities . If not, it is a moral
high ground that widens the divides between social, economic, and ethnic groups and serves to
deeply stratify society . The same social stratification that occurs in aristocracies, over time, are
happening in meritocracy as well . The Economic Policy Institute reported that between 1979
and 2000 the income of the bottom economic rungs grew by 6.4%, whereas that of those in the
top 20th percent grew by 70% (Meritocracy in America: Ever higher society, ever harder t o
ascend, 2004) . Furthermore, between 1981 and 2011, the lowest income families' earnings
ALGEBRA FOR ALL POLICY IMPACTS 14
(bottom 20th percent) decreased by 5%, while the highest 20% grew by 56%, and staggeringly,
the top 5% grew by 95% (The College Board, 2012). In further illustrat ion of the class
stratification that has grown over time in the U S, the United Nations' Inequality -adjusted Human
Development Index shows the U.S. as declining the most among highly developed nations in
terms of inequality indices, a change in ranking of -19 (United Nations, 2011) . This index refers
to the distributive differences in income, health and education betwe en social class groups . The
US, which is nearly at the top in terms of being a "very highly developed" nation, has one of the
highest divides between the affluent and poor . Further, U.S . economic mobility has become
increasingly inelastic with parents' incomes being highly linked to their children's earnings . For
example, African American children whose parents' earnings rank them in the bottom quartile are
almost twice as likely to remain in the bottom quartile as adults (Hertz, 2006).
Under current conditions, the division between economic and socia l classes is not only
deeply dichotomous but is increasing —evidenced by academic achievement gaps, unequal
access to algebra and higher -level mathematics, and the power of parents' social standing on their
children's future . This division is stronger than most Americans would like to think . Education
though can still break these barriers for children . In 2011, those with at least a bachelor's degree
had a median family income of $100,096, while those with only a high school diploma had a
median family in come of $48,460 (The College Board, 2012) . However, the profiles of the
students that navigate edu cational pathways successfully are divided along racial and SES lines .
In this decade, s tudents from disadvantaged minority gro ups have approximately a fifty -fifty
chance of graduating high school and graduation rates for those who attend high -poverty, high -
minority, urban school districts graduate at rates 15 -18% lower (Swanson, 2004).
ALGEBRA FOR ALL POLICY IMPACTS 15
As generations progress, those that have succeeded upon their merits, talents, and degrees
pass those benefits on to their children in the form of better resources, better schools, and better
opportunities—social capital. Even without considering the benefit s of private schools, in
education, not all children receive the same educational opportunities . Since the release of the
Coleman Report in 1966, the public has been aware of achievement gaps between white students,
minorities, and those from poverty (Coleman, et al., 1966) . These achievement gaps are about
more than just performance . Minority and poor children , for example, are more likely to have
poor quality teachers and fewer resources (Lankford, Hoeb, & Wyckoff, 2002; Darling -
Hammond L. , 2001; Almy & Theokas, 2010) . The effects of schooling and a discrepancy in
performance increases throughout primary and secondary schooling (Fryer & Levitt,
2006).Those with resources have choices; they can move to neighborhoods with better schools,
send their children to private schools, hire tutors, or drive their students to better schools using
transfer options. Those without the resources and social capita l must send their children to their
neighborhood schools, whether they are effective or not . Therefore, education reform must be
concerned with improving all schools and providing opportunities for all students.
As well as not receiving the same quality of schooling, children from backgrounds of
poverty and marginalized ethnicities do not begin school with the same sets of skills and abilities
that predict success in school . Children of low SES begin school with smaller vo cabularies and
lower cognitive skills as compared to their middle income and usually white peers (Lee &
Burkam, 2002; Hart & Risley, 2003) . As children from disadvantaged backgrounds progress
through school, th e divide increases, as substantiated by the persistent achievement gaps
evidenced by test scores, graduation rates, and college degree attainment (Lee & Burkam, 2002;
Fryer & Levitt, 2006) . Since the achievemen t gap increases as the years of schooling do, there is
ALGEBRA FOR ALL POLICY IMPACTS 16
something about the structure or process of our educational systems that cause these
discrepancies to grow rather than decrease . While California has made gains in access to
Algebra I, and therefore o pened gateways to many students, the controversy over the Algebra for
All policy and adoption of the CCSS have led to a scrapping of previous policies to require
algebra for eighth-graders. Before moving ahead to a new era of CCSS, the successes and
challenges of the policy must be examined so that educational access remains open equitably for
all students. The information in this analysis of practice and results will add to the body of
knowledge regarding the effects of education policy , as well as, provide a critical examination of
the practices and policies directly related to stud ent success in mathematics education .
ALGEBRA FOR ALL POLICY IMPACTS 17
Chapter 2: Literature Review
The Importance of Algebra I in Grade Eight
Mathematics education is progressive with successful co mpletion of one course leading
to the next , and therefore, earlier access to algebra leads students down a progressive pathway
that opens opportunities for additional mathematics courses . Prior to 1997, Algebra I taken in
eighth grade was reserved for onl y the top California mathematics students. But with the 1997
release of the California Mathematics Framework, a movement to make Algebra I the default
course for all eighth-graders began. This bold action was made to right the inequities of access
to early alge bra in California and was based, in part, on the results of correlational research
studies that showed taking Algebra I in grade eight to be key in getting students on a pathway to
taking higher level mathematics in high school , which in turn has been correlated with higher
earnings and increased college completion rates (Adelman, 1999; Bozick, Ingles, & Owings,
2008). For example, in a 1996 study using national education data, Smith found that students
taking algebra before high school , in addition to having more time in high school to take higher
level mathematics courses, were more likely to take more mathematics courses in high school
than students who did not t ake algebra until high school . Not only did they reach higher levels
of mathematics, they were more likely to take additional years of mathematics . Unfortunately,
the data from the study also revealed that those given access to algebra in eighth grade were least
likely to be from minority ethnic gr oups and were least often from socioeconomically
disadvantaged backgrounds (Smith, 1996) .
Algebra has long been considered a gatekeeper to higher education and certainly is the
prerequisite for advanced mathematics coursework . Entry requirements to California public
universities include a minimum of Algebra I, Geometry, and Algebra II, with a preference for a
ALGEBRA FOR ALL POLICY IMPACTS 18
fourth year of advanced coursework (Regents of the University of California, 2013) . The
purpose of mathematics requirement, as described in the admissions course guide, is to ensure
that students are prepared for university level coursework, but the requirement also serves as a
gatekeeper. But the completion of higher level mathematics cours es is more than just a signal of
a good applicant . Using California State University's Early Assessment Program (EAP) data
from 2009, Stotsky and Wurman (2010) cite that 88% of the students that take a course above
Algebra II in their junior year of high school are college ready according to E AP guidelines,
meaning that they are ready for college level mathematics courses without remediation .
Algebra as a Civil Right
Mathematics course taking is not only requisite to college entry but is also tied to
increased earnings. For this reason, Robert Moses, most notable for his role in the Algebra
Project, refers to algebra as a civil right due to the connections between mathematics
understanding and economic access (Moses & Cobb, 2001) . The equity in access to quality
mathematics courses is tantamount to a civil right because of its power on children’s futures . In
2004, a national study was conducted on the effects of high school mathematics c oursework on
the earnings of nearly 12,000 young people a decade after high school, and d ata from the 1991
National Center for Education Statistics’ High School and Beyond data files were analyzed . The
authors found that taking Algebra I or Geometry incre ased earnings by 8% (Rose & Betts, 2004) .
Taking Calculus in high school was correlated to increased earnings of 19.5% . In order to take
Calculus in high school, most students would have taken Algebra I in eighth grade —unless they
managed to take more than one mathematics course per year . Mathematics course taking in the
study also revealed negative correlations to earnings for courses considered “vocational math,”
which included courses lower than pre -algebra, including General Mathematics. Not only was
ALGEBRA FOR ALL POLICY IMPACTS 19
taking more than one vocational mathematics course negatively correlated with earnings, taking
any vocational mathematics course during high school (even if higher level courses were also
completed) was significantly linked t o lower earnings . Not surprisingly, the majority of students
taking vocational mathematics courses were minority students and those from socioeconomically
challenged backgrounds (Rose & Betts, 2004) .
Opportunity to Learn and Tracking
Unfortunately, it has become common knowledge, widely accepted, that achievement
gaps exist between students predicted by social class and ethnicity (Oakes, 2005; Loveless,
1999). Fortunately, cases of narrowing the achievement gaps exist, and it is clear that schools
can have positive effects (Balfanz & Byrnes, 2006) . Logically, included in the factors that
increase the likelihood that such gaps decrea se is opportunity to learn (Balfanz & Byrnes, 2006) .
Opportunity to learn refers to the access students are given to learn a particular content or to take
a particular class . For example, students placed in General Mathematics are not given an
opportunity to learn Algebra I at the same time as their peers . Opportunity to learn is constrained
by tracking policies where students are placed in courses based on test scores or perceived
ability. Tracking sorts students into abili ty groups in ways intende d to make educating them
easier but is also inequitable , as poor and ethnic minority stud ents are overrepresented in lower
tracks (Balfanz & Byrnes, 2006; Coleman, et al., 1966; Oakes, 200 5). With eighth grade
mathematics, there is little evidence that restricting student s from Algebra I by placing them in
General Mathematics provides them with a better education . Whereas, students that are
underprepared but given adequate support , through tutoring or support classes with effective
teachers, are more successful in both Algebra I and later mathematics courses (Stein, Kaufman,
Sherman, & Hillen, 2011) .
ALGEBRA FOR ALL POLICY IMPACTS 20
When students’ opportunity to learn is restricted by a system of placi ng students in
differing course pathways by ability, or perceived ability, this is tracking . Pathways refer to
sequences of courses . For example, placing a student in a Spanish I class because they are
beginning Spanish speaker is no t tracking . However, placing a student in a vocational
mathematics class that does not lead to a higher level mathematics course sequence is tracking .
Most articles that reference the issue of tracking make note of Jeannie Oakes' 1985 research in
the boo k Keeping Track. Oakes researched 25 schools in her original book , and then reviewed
her own work again in her 2005 second edition . Oakes (2005) found that tracking systems,
where students are placed into coursework pathways according to test results, reinforce
inequalities between SES and minority groups . She state d, "Tracking separates students along
socioeconomic lines, separating rich from poor, whites from nonwhites . The end result is that
poor and minority chi ldren are found far more often than others in the bottom tracks" (Oakes,
2005, p. 40) .
Oakes is a strong proponent of heterogeneous grouping for all levels of schooling to
ensure equality, including the dissolution of gifted and honors programs . Oakes sees the issue as
black and white —tracking and ability grouping are inequitable . Oakes found that t eacher
expectations, time spent on content instruction, and teacher enthusiasm for the course were all
inferior in lower tracks (Oakes, 2005, pp. 80 -99). And nowhere is tracking more persistent than
it is in mathematics (p.56) . Because of the structure of courses and the beliefs of mathematics
teachers that mathematics skills build in a linear fashion from one grade level to the next,
mathematics classes are more likely to be restricted to students that are perceived as ready for the
course.
ALGEBRA FOR ALL POLICY IMPACTS 21
While it is a logical assumption that a student must be proficient in arithmetic to be able
to perform well in an algebra class , there are examples where heterogeneously grouped students
in de-tracked mathematics courses are successful not only in one course but in successive
courses as well (Burris, 2006; Rui, 2009 ). In a meta -analysis of 15 studies, Rui (2009) found
that de-tracking has resulted in higher achievement for low ability students than low ability
students in tracked courses . Additionally, contrary to anecdotal beliefs that heterogeneously
grouped courses are detrimental to high -achieving students, Rui’s (2009) meta-analyses revealed
no difference in the achievement results of high -ability students.
California has a history of increasing de-tracking policies beginning with a declaration by
the State Superintendent in 1987 that middle schools should eliminate tracking through to the
SBE’s move to mandate eighth grade algebra in 2008 . Federally, NCLB has served to provide
accountability to ensure that students are served equitably across subgroups . Loveless (1999)
reported that de-tracking policies were most prevalently implemented in urban district s with high
numbers of traditionally disadva ntaged students (low SES, minority) and least implemented in
places with large numbers of high -achieving students. While the goal of these policies was to
reduce the achievement gap, the gap remains; and while tracking is less prevalent, it still exists
(Oakes, 2005).
Most often thought of in terms of achievement are issues of race and ethnicity . In
addition to discrepancies of access and achievement between ethnic subgroups, large gaps exist
between socioeconomic groups as well. The effect of SES is sometime s even greater than the
effect of ethnicity . For example, s tudents scoring below the 25th percentile on mathematics
achievement tests are more easily predicted by SES than ethnicity (NCES, 2011). Students in the
25th percentile range were 33% white, 28% African American, 32% Latino, but 68% were
ALGEBRA FOR ALL POLICY IMPACTS 22
eligible for the Free or Reduced Pri ce Meal program , more than twice the number of any other
represented grou p. For instance, SES, more so than ethnicity, was significantly correlated to
lower performance on the eighth grade NAEP in 2011.While much of this is related to the skill
gaps that exist between subgroups before they even enter school, there is also a proble m with
providing students across subgroups equal access to the courses that would help them to be
successful on exams such as the NAE P. But Wang and Goldschmidt (2003) found that even when
they controlled for prior mathe matics achievement, their data still revealed inequitable access to
higher level mathematics courses beginning at grade eight . Some data has been presented that
shows that California's Algebra for All policy has had an impact on opportunity to learn . For
example, in an EdSource report, authors found that schools with high numbers of low income
students were more likely to place higher numbers of students into Algebra I at the eighth grade
(Williams, Haertel, Kirst, Rosin, & Perry, 2011). Although the authors also reported that many
of the students that were placed in the course were underprepared. However, this evidence is
only a part of the puzzle . In a dissertation on the impact of increased access to eighth grade
algebra on later success in high school mathematics (Algebra I in grade nine and Algebra II in
grade eleven), Levy (2012) found that participation in Algebra I at the eighth grade was
correlated with later success in Algebra I I. And also found that the non -traditional pathway of
taking Algebra I in eighth and ninth grade also was correlated with higher success in Algebra I in
high school.
Compounding the impact of SES is the issue of a whole school's poverty rate . As
suggested by the Williams et al . study (2011), there are differences in the ways schools function
related to their poverty levels . In a study of the impact o f segregation on achievement,
Rumberger and Palardy (2005) found that there were differences in both the ways schools
ALGEBRA FOR ALL POLICY IMPACTS 23
functioned and in school outcomes related to the percentages of students of poverty or wealth in
the school even controlling for student demographics . Additionally, they found that students
who attended high poverty schools were more likely to start school as much as four years behind
students entering more affluent schools . They also reported that a student's SES was related to
learning at middle and high wealth schools but did not matter much at low we alth schools ( p.
2017).
In addition to inequities between social and ethnic groups in education, English learners
(EL) present a confounding challenge . Learning a new language while attending school is
inevitably an additional challenge that presents a barrier to learning. In California, EL students
are also likely to be Latino and of low SES, which places them in three subgroups that are
associated with lower achievement levels . In 2007, California’s Legislative Analyst’s Office
reported that 25% of C alifornia’s K -12 students were English Learners with 85% of those EL
students speaking Spanish as their primary language as well as being economically
disadvantaged (California Legislative Analyst's Office, 2007) . Further, political controversy over
the education of ELs has constrained the ways in which schools can educate students speaking
another language. Moreover, many EL students do not receive the services to which they are
entitled by law . In April 2013, th e American Civil Liberties Uni on filed a suit on behalf of EL
students alleging that 251 California school districts were not providing appropriate services to 1
in 50 of California’s 1.4 million EL students (Baron, 2013). Overall, according to the most
recent data available from the CDE (2012), EL students have the highest high school dropout
rates for any subgroup in California at nearly 24%, higher than special education, migrant
students, and all ethnic groups (CDE, 2013). This population of students is of particular concern
in terms of equity of educational access and outcomes .
ALGEBRA FOR ALL POLICY IMPACTS 24
Public policies, such as No Child Left Behind (NCLB), were enacted to reform the
educational systems that allow ed these gaps and inequities to persist. California's diverse student
population has long brought attention to achievement gaps between student groups and to the
quality of an educational system that is not meeti ng the needs of students equitably . More than
an accountability issue, differences in student achievement that can be predicted by ethnicity,
economic status, and socio -cultural background are an issue of social equity . Lee and Burkham
(2002) report, "Almost half of the raci al/ethnic gaps in achievem ent are explained by taking
children's social class into account" (p . 81). Because these gaps are predictable and explained by
having a particular ethnicity or social class, there is something in the schooling system that is
preventing students from attai ning the knowledge and skills necessary to graduate from high
school and college . Without adequate education and increased social capital, the next generation
of children will also face the same challenges .
Benefits of Access to Algebra
It is important not only for individual students but also for economic and social
development to reduce achievement gaps for social equity and to build our future human capital
through education. In order for this to happen, all students must have access to high quality
courses and curriculum . Mathematics, as it turns out, is key in providing opportunity and access
for students . By creating policies, agencies seek to provide a more even playing field through
equal access for all students . Thirty-one of the fifty states currently require Algebra I for high
school graduation (Dounay, 2013b). In fact, an increasing number of states are requiring higher
level mathematics courses including Algebra II . Most universities and many employers
recommend that students take courses in high school similar to the recommendations of the
University of California’s College Board A -G requirements, which include Algebra, Algebra II,
ALGEBRA FOR ALL POLICY IMPACTS 25
and Geometry at a minimum (Dounay, 2013a). The reasons so many states are requiring at least
algebra is because of its connection to a student’s future career and college opportunities .
Sciarra and Whitson (2007) studied postsecondary education results for 866 Latino
students that attended some form of college . They found that among other variables,
mathematics knowledge was significantly and positively correlated to comp letion of a bachelor’s
degree. These findings replicate the results of other studies. Adelman (1999), for example, in a
report for the U.S. Department of Education, found similar results . Adelman’s work revealed
that high school curriculum, in particular math ematics, had a significant impact on college
degree completion, that the impact of a high qu ality high school curriculum had a stronger
impact on African American and Lati no students than white students, and that high school
academic factors (including cou rse work and test scores) have a larger impact on degree
completion than does SES . In a review of high school mathematics coursework and bachelor’s
degree completion for over 5,000 students , Trusty and Niles (2003), consistent with Adelman
(1999), found that , of all high school curriculum, mathematics courses had the strongest impact
on degree attainment . Their study also revealed several other pertinent results, including that
taking mathematics courses in high school could equalize the inequitable differences between
ethnic groups, eighth grade mathematics ability was related to course taking in high school, and
taking calculus more than doubled the chances of college completion (Trusty & Niles, 2003) .
Over and again , research supports that mathematics coursework is important for student success
in college and therefore the workforce . The pathway to these courses does not begin in high
school; students also must be prepared by taking the prerequisite courses in middle school ,
namely algebra. The entry into algebra courses is not always accessible, however, to all students
equitably. Conversely, some question the rush to have eighth-graders take algebra.
ALGEBRA FOR ALL POLICY IMPACTS 26
In a longitudinal study of a large school district (60,000 students), Spielhagen (2006)
specifically addressed opportunity to learn, tracking, and the long -term effects of eighth grade
algebra. The author fou nd that students who took algebra in eighth grade were more likely to
take mathematics longer in high school and that students who were not able to take algebra until
ninth grade were more likely to s top their mathematics pathway at Algebra II (pp. 47 -48). In
addition, in line with both the Trusty & Niles (2003) and Adeleman (1999) findings that
mathematics course work is related to college success , and extending these findings to middle
school, Spielhagen f ound that students that studied algebra in grade eight were significantly more
likely to attend college than students that took general math . These findings make sense in that
students that take algebra in middle school are more likely to take upper level mathematics
courses in high school, which is related to college success rates . Algebra then should not be
restricted at middle school to only high achieving and gifted students, but tradit ionally, this has
been the case despite policymaker efforts to equalize access .
Algebra for All Policies–The Impact
While Spielhagen’s research focused on one large school district, the results are similar to
other findings. For example, EdSource, a California non -profit agency focus ed on education
research, produced a report (2008) using California CST data from 2003 to 2007 to study the
impact of California’s Algebra for All policies. The data revealed that significantly more
students were taking Algebra I in eighth grade in 2007 than were in 2003 (49% versus 32%).
White and Asian students, however, are still more likely than other subgroups to take the course .
The data showed that while rates for all students taking algebra in eighth grade increased, they
increased at similar rates —leaving the gap between subgroups nearly constant . On a positive
ALGEBRA FOR ALL POLICY IMPACTS 27
note, students who did begin their upper mathematics coursework in eighth grade by taking
algebra had higher proficiency rates on the CST than they did in 2003 (EdSource, 2008) .
In a nother EdSource report entitled , Algebra Policy in California—Great Expectations
and Serious Challenges (2009), the organization continued their investigation of California’s
algebra policies’ effect on increasing studen t access to algebra. The report included statewide
CST data from 2003 to 2008 and concluded that the policies have had a positive effect on
opening up the opportunity for African American and Latino students to both study algebra in
grade eight and be more successful . The numbers of both groups of students taking Algebra I in
middle school nearly doubled , with an increase of 24% in 2003 to 47% in 2008 for African
Americans and from 26% to 48% for Latinos (p. 5) . The numbers of students in these ethnic
subgroups scoring proficient and advanced also increased, w ith 2.6 times more African American
students scoring proficient or higher and 3.2 times more Latino students (p. 6) . Like the
participation gaps found in EdSource’s 2008 re port, a significant achievement gap was still
apparent in the 2009 report . For example, with regard to SES, the numbers of socioeconomically
disadvantaged students scoring proficient or higher increased from 22% (11,730) in 2003 to 30%
(37,618) in 2008 while the numbers of non -socioeconomically disadvantaged students increased
from 47% (46,142) to 55% (67,387) . So, while achievement and participation have both had
positive increases for all subgroups, serious equity issues still existed as of 2008 . Furthermore,
aligned to a similar study by Wang and Goldschmidt (2003) who studied a large California
school district with 2,707 eighth-graders, not only is mathematics course taking from eighth
grade through high school inequitable at the subgroup level, it becomes increasingly more
inequitable through high school —despite the increases . Moreover, and again in agreement with
ALGEBRA FOR ALL POLICY IMPACTS 28
Wang and Goldschmidt (2003), Latino and African American students are overrepresented in
remedial tracks and courses and underrepresented in higher level mathematics courses.
The results of the EdSource reports showing continuing opportunity and achievement
gaps have been replicated at the national level as well . For example, Crosnoe and Scheinder
(2010) found that regardless of prior mathematics experiences and skill, SES was highly
correlated to high school mathematics coursework —meaning that low SES students took higher
level courses less often than their high SES peers with similar mathematics prerequisites and
abilities. The authors stated, “ Even when low and high SES students had the same starting point
in high school and the same observed skill level, the latter persisted through the mathematics
curriculum at higher rates” (Crosnoe & Schneider, 2010, p. 102) . Although one of the arguments
against Algebra for All policies is that not all students are prepared for it (Loveless, 2013); it is
clear that ethnicity and SES are significant factors in course placement even controlling for
students’ abilities to succeed in the courses .
In a 2008 position statement entitled “ Algebra: What, When, and for Whom,” the
National Council of Teachers of Mathematics (NCTM) stated that all students should have access
to high quality algebra instruction —when they are ready . The council further stated, “Exposing
students to such coursework before they are ready often leads to frustration, failure, and negative
attitudes toward mathematics and learning” (NCTM, 2008).
The move to place all students in algebra at grade eight has not been met with enthusiam
by all and has not been a n instant success . Tom Loveless (2008), in a report for the Brown
Center, analyzed NAEP data between 2000 and 2007 and found that low achievers in advanced
mathematics courses in eighth grade have brought down the average mathematics scores for
students in advanced mathematics courses by 4 points . Loveless, however, places little emphasis
ALGEBRA FOR ALL POLICY IMPACTS 29
on the data that along with an increase from 8% of low achievers being given acces s to Algebra I
in grade eight in 2000 to nearly 29% in 2005, overall mathematics achievement for eighth-
graders in that same time period went up significantly, from 273 to 281, an overall increase of 8
points.
While it makes sense that students should be well-prepared for a course before taking it,
the research is unclear about what it means to be prepared and the results about placement are
mixed. A frequently cited study of the claim that all students would b enefit from early access to
algebra was conducted by Gamoran and Hannigan (2000). The authors studied a national data
pool of 12,500 students taking algebra in the ninth grade . Their analyses revealed two
significant findings. One, all students benefited (in terms of mathematics skill improvements)
from taking Algebra I regardless of their incoming skill level . And two, students in
heterogeneous Algebra I classes with students having diverse mathematics skill levels gained no
less that homogeneous grouped classes (Gamoran & Hannigan, 2000) . This showed that despite
the reports of some (Loveless, 1999; 2013) , no wat ering down effect was observed —students in
highly diverse courses did not l earn less than when high ability students were grouped together .
Although Gamoran and Hannigan found that high achieving students did not learn less in
mixed ability classes, other studies have found that not all students do well . In 1997, Chicago
Public Schools began requiring that all ninth-graders take Algebra I (Allensworth, Nomi,
Montgomery, & Lee, 2009) . In a study of the results of this policy, the authors found that more
students completed Algebra I in ninth grade , but failure rates also increased (Allensworth et al. ,
2009). They also found no differences in achievement tests or later college going rates . In
essence, they found that de -tracking courses is necessary (more students had equitable access)
but not suff icient to have significant effects on achievement and later college success .
ALGEBRA FOR ALL POLICY IMPACTS 30
In addition to the mathematic readiness that underpins the previously referenced NCTM
position statement, the NCTM also stated that students who take algebra before they a re rea dy
will end up frustrated, with negative attitudes toward mathematics. This statement does have
some basis in research . A national six year study of self -esteem and accelerating mathematics
coursework revealed that students that demonstrated previous mat hematics achievement scores
of less than the 65
th
percentile experienced a decline in self -esteem measures (as compared to
students that did not take algebra in middle school) when placed in Algebra I in either grades
seven or eight (Ma, 2002). However, these results seem to be less weighty when paired with
Ma’s later research in 2005 using the same national, longitudinal database . In that study, Ma
(2005b) found that acceleration into Algebra I in middle sc hool had the greatest positive effects
on the achievement of average achieving students who were classified as having previous
achievement scores in the 65
th
percentile or lower . In fact, students not only had higher
mathematics achievement by grade 12 th an their non -accelerated peers, but also had nearly
caught up to the achievement of students classified as honors students —those with early middle
school achievement scores between the 66
th
and 90
th
percentiles (Ma , 2005b). These results
point to a possible need to address self -esteem issues for middle school students rather than
restricting their access to algebra because they are deemed not ready.
To muddy the waters even more, in a recent study of California’s algebra policies, Liang,
Heckman, a nd Abedi (2012) found that although California has increased the numbers of
students taking Algebra I in grade eight statewide (about 19% increase), increases in higher level
mathematics courses are less robust, with only an 8% increase in the numbers of ninth-graders
taking Geometry between 2004 and 2009 (Liang, J.H., Heckman, & Abedi, 2012, p. 333) . The
trend continues throughout the subsequent higher mathematics courses —increases in students
ALGEBRA FOR ALL POLICY IMPACTS 31
taking the course s but not as many as are taking Algebra I . The authors refer to this trend as a
leak in the pipeline, indicating that students taking Algebra I in grade eight are retaking Algebra I
again in ninth grade . Despite the leak, th e authors found that the CST data show increases in the
numbers of students scoring proficient and advanced not only on the eighth grade Algebra I CST
but also increasing proficiency rates on subsequent mathematics courses .
This loss of students between progressive mathematics courses calls into question
placement decisions for eighth grade algebra . Ma (2005b) found benef it in placing students who
were thought not ready by traditional placement benchmarks, while others suggest that their
research supports the enrollment of only proficient students . For example, Liang et al . reported
an additional twist. In their analysis, for s tudents that failed the CST in grade eight, the
likelihood of their passing the CST after ret aking the course in ninth grade is less in comparison
to students who passed the CST for General Mathematics in grade eight and took Algebra I for
the first time in ninth grade . The authors conclude d that this evidence suggests that eighth grade
students should only be enrolled in Alge bra I if they were proficient or advanced on their
previous year’s CST (Liang et al. , 2012, p. 338). While their results are significant, they are not
aligned with the other studies reported previously and their study did not address whether or not
the students that passed the General Mathematics test in grade eight were placed properly . If
those students had been proficient in grade seven, they most likely should have been placed in
Algebra I . Despite best intentions, the evidence is clear that educator s have placed minority and
low SES more often in General Math —despite their mathematic skill (Crosnoe & Schneider,
2010; EdSource, 2009; Smith, 1996; Stein, Kaufman, Sherman, & Hillen, 20 11; Wang &
Goldschmidt, 2003; Waterman, 2010) .
ALGEBRA FOR ALL POLICY IMPACTS 32
Not mentioned in the Liang et al . (2012) study, which noted the leak in the pipeline of
mathematics coursetaking, is the number of students who are placed in Algebra I again in the
ninth grade even though they scored proficient or higher in the same course in grade eighth .
Placement issues in mathematics go beyon d questions of the ability cutoffs for placement in
algebra. In addition to students being placed inequitably by social class and ethnicity, sometimes
students that are successful in algebra are required to take it again . In 2010, a report funded by
the Noyce Foundation, a non -profit educational organization, provided data on several Northern
California school districts in the Bay Area . The authors found that nearly 65% of students who
took Algebra I in the eighth grade repeated it again in the ninth gra de and that the repeated
placements more heavily affected students by ethnicity without regard to their previous grades,
diagnostic scores, and California Standards Test (CST) scores (Waterman, 2010) . Approximately
two-thirds of the African American and Latino students in the study repeated Algebra I in ninth
grade while 60% of these students were proficient or advanced on their CST . Not only were
African American and Latino students less likely to be placed in Algebra I in the first place , even
if they were given access, they were more likely than their white or Asian peers to retake it
unnecessarily. Additionally, the data on the districts’ students between 2006 and 2009 revealed
that 44% of the students that scored pr oficient on the CST for Algebra I in eighth grade were
placed again in the course in ninth grade . Furthermore, of all students taking the Algebra I CST
for the second time , half were no more successful when taking it again in ninth grade (Waterman,
2010). It appear s that retaking Algebra I (even for previously proficient students) did not lead to
better performance in either the Noyce report or in the Liang et al . study.
ALGEBRA FOR ALL POLICY IMPACTS 33
Policy in Practice
Returning again to NCTM’s position that students should only take al gebra when they are
ready for it, when applying this stance , how do ed ucators determine readiness and what do they
do to prepare those that are not yet ready? The research is mixed and past practice shows that
schools and districts do not place students equitably . There have been multiple approaches to the
placement problem with varying levels of success . Some efforts to make algebra more
accessible to students have included modified courses (changing the curriculum), ability
grouping (homogeneous classes), and double -dose courses (more time) .
A modified course is one in which the traditional algebra course has been changed to
make it easier for students . Examples include stretching a course over two years instead of on e
(Algebra Ia followed by Algebra Ib) or reducing the requirements of the course to a limited
number of standards —usually those most heavily tested . A yearlong study of modified algebra
and geome try courses was conducted at a M idwestern U.S. high school t hat implemented
modified courses in 2010 . The mathematics department at the high school selected foundational
standards for both Algebra and Geometry to create the course . The author found that, despite the
educators’ good intent, these modified courses did not provide equitable access to higher level
mathematics courses and instead created a new low track (Buckley, 2010). Students that were
successful in the modified algebra and modified geometry courses were not sufficiently
preparing to take the subsequent Algebra II course, which resulted in a dead -end pathway for
students.
Also part of the study were interviews with teachers and a review of the curriculum,
which revealed that little attention was paid to peda gogical changes that may have supported
students with additional instructional needs, for example those with skill gaps . Instead the
ALGEBRA FOR ALL POLICY IMPACTS 34
course was taught in exactly the same manner with some concepts taken out , and the remaining
content taught over a longer period. Because students had already been previously unsuccessful
and their skill gaps remained , the traditional pedagogy had not helped, which meant that the
modified courses were the mathematical equivalent of speaking slower and louder . These
courses increased inequities by recreating a non -college bound track (Buckley, 2010). Even
when students were successful in the courses, they had no choice but to either s top taking
mathematics or to go back and repeat Algebra and Geometry. In her article, “ Instructional Policy
Into Practice: The Power of the Bottom Over the Top ,” Linda Darling-Hammond (1990)
discusses the ways that policies get warped by the time they reach local levels and that the local
agencies have more power over the success of implementation because they have the control to
subvert the intent of policies . Modified courses are an example of this . Students take a course
with alge bra in the title and take the Algebra I test, but in essence another track has been created
for students deemed incapable of the real algebra class .
Courses like these have been seen in school across the country but interestingly enough in
California, the Department of Education subverted their own policy by creating their own
modified course in 2005 with the adoption of Algebra Readiness. According the California
Mathematics Framework (CDE, 2005) , Algebra Readiness is an int ervention course for students
in grades eight and above that are not yet ready to take Algebra I . The course is designed to
prepare students to take Algebra I the following year . Two years after the adoption of the
standards for the course, materials and curriculum were officially adopted in 2007 . Students in
grades eight and above that take any course other than Algebra I, which includes the SBE
adopted Algebra Readiness course, take the General Mathematics CST. Intentionally or not, t his
prevents closer public analysis of the success of the Algebra Readiness course because the test
ALGEBRA FOR ALL POLICY IMPACTS 35
record databases include information about the test taken (General Mathematics) but not the
course (General Math or Algebra Readiness) .
A search of scholarly research databases and journals did not readily reveal data on the
efficacy of Algebra Readiness in California despite the course and curriculum having been
adopted in 2007. However, studies of the results of the General Mathematics test takers show
that, in gener al, students that do not take algebra at the eighth grade level are less likely to take
courses beyond Algebra II and are less likely to complete a bachelor’ s degree (Adelman, 1999;
EdSource, 2009; Spielhagen, 2006 ). Additionally, students who take Algebra I courses, in either
eighth or ninth grade , show increased rates of mathematics skill growth than do students who
take General Mathematics (Ma, 2005a) .
In addition to modified courses, a bility grouping has a lso been used to help unprepared
students to access algebra . Ability grouping is a process of grouping students into classes (same
course) by ability . It is distinguished from tracking because students are enrolled in the same
course as their peers , but they are homogeneously grouped into classes . It is a method to help
instructors provide instruction to similar groups of students that presumptively have similar
abilities, skills, and instructional needs —both high and low achieving . Gifted and honors
classes, for example, are high ability groupings in common practice .
While ability grouping makes sense for educators who have to make lesson plans to meet
the diverse needs of students, research on within school ability grouping (homogeneous whole
group) has revealed mixed results . Lleras and Rangel (2009) found that within classroom ability
grouping was detrimental to the reading achievement of African American and Latino first and
third graders. In the three year longitudinal study, they found that in classrooms with
heterogeneous reading groups, reading achievement was significantly better for students than in
ALGEBRA FOR ALL POLICY IMPACTS 36
classrooms that practiced ability grouping, even controlling for previous reading achie vement.
Similar studies have found that ability grouping had no effect at all (Betts & Shkolnik, 2000;
Hallinan & Sørensen, 1987) . While studies have found mixed results, from no benefits to
negative impacts, especial ly for traditionally disadvantaged students, a few have found small
positive effects, usually for students in high ability groups (Coleman, et al., 1966; Hoffer, 1992) .
In a study of ability grouping in middle schools , Hoffer (1992) analyzed a national
sample of 1,900 middle school students using NAEP data and measures from the Longitudi nal
Study of American Youth to measure achievement . The author found that ability grouping
during grades seven through nine in science and mathematics had a detrimental effect on
students placed in the low ability groups and only a slight positive effect for students placed in
the high groups . Overall, Hoffer concluded that the small positive effect for the students placed
in high -ability groups did not counteract the negative effects on the learning of students in the
lower-ability groups. Studies like Hoffer’s which show small gains for students in the high -
ability groups provide support for parent s of high achieving students who often demand separate
classes for their students (Loveless, 1999; Oakes, 2005) . However, are the small gains worth the
detriment to lower -ability students?
Within class a bility grouping, however, used as a short term intervention strategy, has
promise for small group instruction within heterogeneously grouped classes. For example, both
Robinson (2008) and Lleras and Rangel (2009) found that EL students in heterogeneous
kindergarten classes performed better when grouped together for small group reading instruction.
This suggests that for intervention , homogeneous small group instruction is effective . Further
supporting this idea, Sørensen and Hallinan (1986) found that small group homogeneous
grouping was better for learning gains than was whole group instruction. And data collected by
ALGEBRA FOR ALL POLICY IMPACTS 37
Adelson and Carpenter (2011) suggests again that homogeneous small groups help students
make learning gains . Although each of these studies was conducted in early elementary grades,
the key finding that homogeneous ability grouping is effective in s mall group settings has
implications for a different type of assistance for students with skill gaps in mathematics .
One way that schools have implemented small group ability interventions has been
through the use of a second period of algebra . Double-dose algebra refers to taking more than
one period of algebra or an algebra class plus a support course . There are many models of
double-dose classes, but for some students are placed in a heterogeneous class for the first period
of algebra and the n a smaller group remains or goes to another teacher for a second block of
time. In this way, students receive both the benefits of heterogeneous classes and homogeneous
small group support.
In a 2011 meta-analysis, authors reviewed 44 different studies o n the effects of eighth and
ninth grade algebra policies . Outcomes for students that were ill -prepared to take Algebra I in
either eighth or ninth grade were increased when provided support that included additional time
(such as double -dose classes). While overall results were mixed, the algebra policies under study
in the 44 research articles resulted in de-tracking Algebra I and increase d opportunities to learn
for all subgroups (Stein, Kaufman, Sherman, & Hillen, 2011) . Moreover, the authors conclude d
that because the algebra policies increased the opportunity to learn for all students, the biggest
benefit to the policies was for students that were prepared for the course and would not have
been given the opportunity to tak e it before .
Common Core Standards—The End of Algebra for All?
Common Core State Standards (CCSS) are a set of curriculum standards for English -
language arts and mathematics (science on the way) adopted by 45 states in the U.S. (National
ALGEBRA FOR ALL POLICY IMPACTS 38
Governor's Association & Council of Chief State School Officers, 2012) . The standards are
voluntary for states to adopt and not a national curriculum . They were developed in a
collaborative between the Council of Chief State School Officer s and the National Governor’s
Association for Best Practices and presented in 2010 . California adopted the CCSS for English -
language arts and mathematics in 2012 for implementation in the 2014 -15 school year (CDE,
2014).
The CCSS are designed to allow for a common language, curriculum, and assessment
system across K -12 schools the US . The design allows for up to 15% of the total standards to be
adjusted by each state (National Governor's Association & Council of Chief State School
Officers, 2012) . When California first adopted the mathematics standards, the decision at that
time was to include a vast majority of the current Algebra I standards in the eighth grade
mathematics curriculum—in alignm ent with Algebra for All policy. This middle ground did not
win advocates on either side of the algebra debate . On one side, proponents of a true eighth
grade mathematics curriculum argued that the addition of the standards would be too much to
teach in one year and that some students just are not ready for algebra in eighth grade . On the
other hand, it was not a true algebra course but more like California’s current Algebra Readiness
curriculum—still not providing a pathway to college . Under pressure f rom many, including
State Superintendent of Schools, Tom Torlakson, in January of 2013 the State Board of
Education (SBE) voted to take out the additional algebra standards they had previously elected
to add to the eighth grade CCSS mathematics course (Fensterwald, 2013). Newspapers across
California reported the decision with headlines such as, “California abandons algebra
requirement for eighth -graders.” While SBE members stated that their decision did not indicate a
ALGEBRA FOR ALL POLICY IMPACTS 39
reversal on their position for algebra in the eighth grade but rather a transfer of the decision
making to local control, the news was taken as just that —the end of Algebra for All.
With the decision point for a college pathway in mathematics clearly resting at local
levels with schools and districts, there is little pressure now for schools to place eighth-graders in
Algebra I . Some worry that this will lead to a reversal of the pro gress made in California with
the access to algebra for our traditionally disadvantaged students . Compounding this issue is that
the CCSS for mathematics through eighth grade have been adjusted to be taught through eighth
grade. With the eighth grade cou rse no longer being a repeat of grade six and seven
mathematics, skipping eighth grade mathematics is no longer an option (Stotsky & Wurman,
2010). The Common Core State Standards Initiative outlines different models for what they
term “acceleration” to get students on the A -G college pathway . The options for this are to take
a compacted curriculum in middle school . For example in grade seven taking both the seventh
grade and eighth grade mathematics courses in one year , or to accelerate in high school by taking
both Algebra I and Geometry at the same time in grade nine . The term “acceleration” alone
clearly indicates that Algebra I in eighth grade is an advanced course (not the norm) basically
creating a two track system, wh ich Algebra for All policies were enacted to combat .
Further, some have questioned the Common Core State Standards Initiative’s claim that
the CCSS are “internationally benchmarked.” Mathematics professor R. James Milgram
(Stanford University) in a testi mony about the CCSS to the Texas Legislature stated that
according to his analysis and comparisons to international standards that by the end of fifth grade
the standards are “more than a year behind the early grade expectations in most high achieving
countries,” and in those countries Algebra I and part of Geometry are completed by the middle
grades (Milgram, 2011). Milgram, was a member of the CCSS Validation Committee but
ALGEBRA FOR ALL POLICY IMPACTS 40
declined to “sign off “in support . Other researchers claim that because CCSS are aligned to the
international "A+ Standards," the CCSS are globally competitive (Schmidt & Houang, 2013) .
However, Stotsky and Wurman (2010), who compared the CCSS to international standards of
high achieving countries (rather than the A+ Standards) and against Massachusetts and
California's current mathematics standards , found that by the middle grades the CCSS will leave
students a year or tw o behind in readiness for Algebra I at the eighth grade . They report that in
high achieving countries, algebra and sometimes geometry are learned at grade eight . Stotsky
and Wurman found California's current standards better for preparing students for co llege
readiness in mathematics . They stated, "draft -writers chose to navigate an uncharted path and
subject the entire country to a large -scale experimental curriculum rather than build on the
strengths that can be documented in Massachusetts or Californi a" (p . 5). However, Stotsky and
Wurman make pertinent points —one, that the CCSS stretch over K -8 what in California's current
standards is completed by grade seven; and two, that the CCSS are indeed untried and tested —
others point out that the cognitive d emand in the CCSS is greater and therefore it is necessary to
teach the concepts at a slower pace (Porter, McMaken, Hwang, & Yang, 2011) .
There are many unknowns with the implementation of CCSS . With increased local
control and placement flexibility for students in mathematics, it is difficult to predict what will
happen with access to Algebra I in grade eight and how that will affect later course ta king in high
school. Additionally, even the SBE is unclear about the test eighth-graders will take if they are
not taking the eighth grade Common Core course. In an EdSource article on the SBE's decision
to fully adopt the eighth grade CCSS mathematics course without the addition of Algebra I
standards, the author reports that the board is unclear about the federal requirements for NCLB
and whether or not it is appropriate to have students taking different tests (Fensterwald, 2013). If
ALGEBRA FOR ALL POLICY IMPACTS 41
the SBE decides that all students, regardless of the course they are taking, must take the eighth
grade CCSS test, then that might sway more schools to place their students in that course (rather
than Algebra I) . It makes sense to want students to take a test for the course they are actually
taking. With these upcoming changes, it is even more important to evaluate past practices and
analyze the impact of the Algebra for All policies. These measures can be used as a benchmark
for future analyses of eighth grade mathematics course taking and equitable access .
ALGEBRA FOR ALL POLICY IMPACTS 42
Chapter 3: Methodology
Based on studies of successful high school and college students, the timing of when
students take Algebra I is important with research backed support that students experience better
educational outcomes by taking the course in the eighth grade (Spielhagen, 2006; Gamoran &
Hannigan, 2000; Adelman, 1999; Wang & Goldschmidt, 2003) . California’s Department of
Education not only recognized the importance of early access to algebra but also recognized that
students across California did not have equal access to the course . Starting in 19 97, California
supported this through the adoption standards that made Algebra I an eighth grade course .
However, by 2004, many students were still enrolled in General Mathematics (a combination of
both sixth and seventh grade mathematics standards) rathe r than Algebra I , and there were
concerns regarding equity of opportunity to learn for students across subgroups . As a response,
the Algebra for All initiative was introduced in 2005 , which required that schools place eighth-
graders in Algebra I or face a penalty in their API score .
The purpose of this study was to evaluate the effect the Algebra for All (2005) initiative
has had on the enrollment of traditionally disadvantaged students in eighth grade Algebra I in
California schools over time, 2003 (pre -Algebra for All) through 2013 (when the policy was
repealed) using publicly available data, including enrollment, California State Test (CST) , and
Federal Free and Reduced Price Meal (FRPM) participation data. A factorial design was utilized
to determine interactions between policy impacts (year of implementation) , student
demographics (subgroups), and school poverty levels.
Traditionally disadvantaged students in this study include Latino/ Latino students, African
American students, English Learners (EL s), and students designated as having low SES as
identified through FRPM program participation. Additionally, a comparison between the
ALGEBRA FOR ALL POLICY IMPACTS 43
policy’s effect on schools with large numbers of socioeconomically disadvantaged (SED)
students and those with smaller n umbers of SED students were conducted.
Between 1999 and 2014, the CST was the current method of accountability for reporting
school effectiveness publicly under the requirements of NCLB . According to the Standardized
Testing and Reporting Program Annual Report to the Legislature, all students in Califor nia
public schools must take a standardized test for content knowledge , with the majority of students
taking the CSTs (CDE, 2012). Students not taking CSTs include small numbe rs of special
education students who take an alternate assessment . The magnitude of the testing program
provides a plethora of data regarding student performance across the state and spanning 15 years .
The CSTs were developed to measure students' level o f achievement of the California Content
Standards and are hence a tool for measuring progress . For this study, CST data are the only
publicly available and accessible data for measuring multiple school districts' algebra enrollment
and achievement over time. While many debate the fairness of such a test based on the fact it is
given only once a year , and it is difficult to determine whether or not it is an accurate tool to
measure student achievement (some say students do not take the tests seriously, for example), it
is a reliable measure with consistent results gathered over time and across schools and districts .
In addition, the CDE employ s a process of review and analysis to ensure content validity (CDE,
2006). The data used primarily included Algebra I and General Mathematics participation rates
and Algebra I and higher course achievement (proficiency scores) on the California S tandards-
based Test (CST) under the Standardized Testing and Reporting (STAR) accountability sy stem.
Longitudinal CST data were assessed to determine whether or not California’s Algebra
for All policy has had an impact on tracking, achievement, and equity of opportunity to learn
using five research questions.
ALGEBRA FOR ALL POLICY IMPACTS 44
1. To what extent, if any, have California high and low poverty schools increased enrollment
in early algebra for traditionally disadvantaged students between 2004 and 2013?
2. To what extent, if any, have California high and low poverty schools decreased the gap
between non -disadvantaged and traditionally disadvantaged students' access to early
algebra between 2004 and 2013?
3. To what extent, if any, have California high and low poverty schools increased
traditionally disadvantaged eighth grade students' success in Algebra I and above between
2004 and 2013?
4. To what extent, if any, have California high and low poverty schools decreased the gap
between non -disadvantaged and traditionally disadvantaged eighth grade students'
success in Algebra I and above between 2004 and 2013?
5. Between 2003 a nd 2013, how are previous mathematics achievement (as measured by the
seventh grade mathematics CST), student demographics (ethnicity, language proficiency,
socioeconomic status), and school poverty levels (as measured by FRPM participation
rates) related to placement in eighth grade Algebra I?
Research Design
This quantitative study followed design principles of applied research with a goal to
analyze the impact of the Algebra for All policy. With the sunsetting of California's 1997
standards and adoption of the Common Core State Standards (CCSS), the requirement that
California schools place eighth-graders in Algebra I has also ceased . It is important to evaluate
the effect of California's push for algebra has had on school placement policies, student ac cess,
and equity before moving on to the next set of standards and policies . The purpose of the
Algebra for All policies was to bring equity of access for all students regardless of ethnicity, SES,
ALGEBRA FOR ALL POLICY IMPACTS 45
or language proficiency . It is imperative to determine whether or not these policies had the
intended effect before moving to a new set of expectations . Because this was an evaluation of a
policy in practice, experimental controls were not possible and therefore is not a true experiment .
Specifically, this was a study of policy impact to determine the extent to which the Algebra for
All initiative increased (or not) students' opportunity to learn algebra and increased (or not)
algebra proficiency rates in schools since its inception (Research Questions 1 -4). Means of the
dependent variables were compared across subgroups, school poverty levels, and years of policy
implementation. Each student subgroup type (language proficiency, ethnicity, and SES) was
analyzed separately . According to McEwan and McEwan (2003), a research design where the
researchers do not have control over participants or treatments are considered non -experimental
(p.64). This study involves looking at historical data about the schools in California b efore and
during the implementation of Algebra for All policies and no experimental controls were possible
and is therefore non -experimental and descriptive in nature . Although descriptive trends,
correlations, and interactions are presented, the data pre sented are not causal in nature .
Research Questions 1 -4 utilize the same factorial design for each subgroup type where
the Language Proficiency subgroups were analyzed using 3 x 4 x 11 factorial design with three
language proficiency levels, English Only (EO), Reclassified Fluent English Proficiency (RFEP),
and English Learner (EL); school poverty level was represented in quartiles and analy zed over
11 years (2003 -2013). Practical (versus statistical) differences in mean tracking and proficiency
between subgroups were analyzed using a 5 x 4 x 11 factorial design where there are five ethnic
subgroups included in the study —African American, Asian, Filipino, Latino/ Latino, and white.
These five ethnic subgroups were chosen as they represent the largest ethn ic subgroups in
California. Finally, the practical differences in means of SES subgroups were analyzed using a 2
ALGEBRA FOR ALL POLICY IMPACTS 46
x 4 x 11 factorial design, where there are two subgroups for SES, not socioeconomically
disadvantaged (NSED) or socioeconomically disadvantaged (SED). Using a factorial design
allows for both main effects of student subgroup, school poverty quartile, and year of the
Algebra for All policy implementation to be analyzed as well as interactions . The statistical
significance of the dif ferences between means could not be measured; however, the practical
significance of the differences could be analyzed .
Further, relationships between achievement results and enrollment in algebra were
examined (Research Question 5) . The purpose of Rese arch Question 5 was to examine whether
or not students have been equitably placed in algebra at rates similar to the previous seventh
grade mathematics CST proficiency rates . In addition to using this measure to determine equity,
data provided placement benchmarks across schools . Flexor (1984), in a study of the factors that
influence algebra achievement, states that “ performance in seventh grade -mathematics as the
most influential predictor of algebra grades .” Moreover, use of previous mathematics scores is a
common practice for placement in Algebra I . Therefore, it is logical to assume that schools place
proficient students into Algebra I in eighth grade rather than the General Mathematics course,
which, by policy, is considered a remedial pathway . Data were evaluated to determine whether
students were placed equitably into courses according to their previous mathematics success and
whether or not there were differences in treatment by subgroup or within different sch ool poverty
levels.
Participants. The data for the study is from extant databases —publicly available
information from the California Department of Education, available via the Internet . Schools
were identified for this study through use of the California Department of Education (CDE)
downloadable student and school data files . All schools' data were initially downloaded from the
ALGEBRA FOR ALL POLICY IMPACTS 47
Standardized Testing and Reporting Results website at http://www.star.cde.ca.gov . In order to
identify schools, the CDE data files were sorted to include schools that service eighth-graders,
including all school models for middle grades students —middle schools, K -8 schools, and
intermediate schools. All types of schools were included in the data set, including charter
schools. Schools serving fewer than 50 eighth-graders were excluded, as these schools are too
small to have reports on all types of STAR and FRPM data . The number of schools included in
each year's data sets varied and are listed below in Table 1.
Table 1
Number of Participating Schools by Year
Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
n 1946 2000 2013 1999 2026 2101 2116 2105 2110 2249 2275
Instrumentation and Procedures
Data Collection. All data were collected from the CDE website (CDE, 2013) . CST data
are publicly available through the Standardized Testing and Assessment Reporting (STAR)
Results site. FRPM data for schools between the years 200 3-2013 were downloaded in an Excel
spreadsheet format from the CDE website's "Student Poverty – FRPM Data" page located at
http://www.cde.ca.gov/ds/sd/sd/filessp.asp. FRPM data from 2003 were available from the
"CalWORKS Data Files " page in a self -executing compressed file, which had to be extracted
before use .
STAR data research files were downloaded also for the years 2003 through 2013 . These
data were downloaded from the STAR database available on the CDE website in a comma
ALGEBRA FOR ALL POLICY IMPACTS 48
separated values format (.csv) and imported into IBM’s Statistical Package for the Social
Sciences (SPSS). Data were filtered to exclude unnecessary data including data for grades and
subjects not being evaluated (for example, primary grades and tests for langu age arts) . Further
filtering limited the data to schools with a minimum of 10 eighth-graders. In addition to eighth
grade mathematics CST data, the seventh grade proficiency data (question 5) was also filtered
into data files by year in SPSS .
The FRPM data files were merged with the STAR data by matching school codes and
years. For each year a quartile rank was applied using each school's FRPM participation rate . A
rank of one indicates that a school has the fewest numbers of participating FRPM studen ts,
whereas a rank of four indicates that a school has the highest numbers of FRPM participating
students.
Variables. The focus of this study was eighth grade Algebra I enrollment and success
(proficiency) for students in high and low income California schools (broken into quartiles)
disaggregated by the subgroups ethnicity, SES and language fluency . Therefore for research
questions 1 and 2 the dependent variable was tracking rates, or the percentage of students taking
the General Mathematics CST instea d of Algebra I . In schools across the years of study students
taking the General Mathematics CST included many different courses including pre-algebra and
Algebra Readiness curriculums . Tracking rates were calculated for each school by subgroup to
determine the placement rates into courses considered lower than Algebra I. Because some
schools did not have any students taking General Mathematics, the data from these schools had
to be merged to get accurate tracking rates for all schools . Further, for the years 2003 -2006, the
STAR data are inconsistent with the coding for students taking the General Mathematics CST;
some are coded with a test identification number of 8 and others with the code 28 . Therefore, for
ALGEBRA FOR ALL POLICY IMPACTS 49
the years 2003 -2006, some schools had dupli cate records with students taking both test 8 and 28 .
These records were merged into one by calculating the total numbers of students taking test 8
and 28.
Since all eighth-graders (including English Learners in a U.S . school more than one
year) are re quired to take the English Language Arts (ELA) exam, the total numbers of eighth
grade test takers at each school, by subgroup, was determined by the number of eighth grade
students taking the ELA test . The calculation for tracking is as follows:
∑(
)
∑(N)
.
In illustration, a tracking rate of 0 indicates a school that places all of its eighth-graders into
Algebra I, whereas a tracking rate of 1.0 indicates a school that places none of its eighth-graders
into Algebra I.
For research questions 3 and 4 the dependent variable was Algebra I achievement —the
percentage of proficient students on the Algebra I CST . A score of proficient was used to
measure achievement, as opposed to a score of basic, as used by Levy (2012) beca use proficient
is the accepted level of mastery for the CST under California API growth measures and NCLB's
AYP requirement. The CDE STAR data includes a variable for "Proficient and Above," which is
inclusive of the students scoring both proficient and a dvanced for all subgroups . However, when
analyzing the "all students" subgroup, the variable is empty . The variable was computed in
SPSS by adding the proficient and advanced variables for the "all students" grou p.
Research question 5 required a calculation utilizing a previous year mathematics
proficiency rate and a subsequent year Algebra I enrollment rate . The dependent variable of
"placement" was operationalized as the number of students taking the eighth grade Algebra I
CST subtracted by the number of seventh graders that scored proficient on the previous year's
CST. In order to calculate students taking Algebra I (or higher), records had to be merged for
ALGEBRA FOR ALL POLICY IMPACTS 50
students taking Algebra I, Integrated Math I -III, Geometry, and Algebra II in eighth gr ade.
Placement was calculated as follow:
𝑃𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = % 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑡𝑎𝑘𝑖𝑛𝑔 𝐴𝑙𝑔𝑒𝑏𝑟𝑎 𝐼
− % 𝑝𝑟𝑜𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
For example, if a school had 50% of their students taking the CST for Algebra I (or higher) and
70% were proficient on the seventh grade CST (-20% placement rate), the school is under-
placing 20% of their eighth-graders into Algebra I. A positive placement rate indicates over-
placement of students, whereas a negative placement rate indicates under-placement. Placement
rates were compared over time (2003-2013), by subgroup (SES, Language Proficiency, and
Ethnicity), and by school poverty level.
The independent variables for the study include time in years (as indicating
implementation of the 2005 Algebra for All initiative—before and during the implementation),
student background or demographic data including ethnicity ( white, Asian, African American,
Filipino and Latino), SES (eligibility for the FRPM program or not), and la nguage fluency
(English Learner, reclassified previous English Learner, or an English Only student ), and a
school poverty quartile ranking where a rank of one indicates a school has the least poverty rates
(as measured by FRPM) and a rank of four indicates a school has the greatest poverty rates.
Data Analysis
The research questions were designed to reveal trends in school data with regard to the
impact of the Algebra for All (2005) initiative. Additionally, interactions of time, subgroup, and
school pover ty level are important to reveal whether or not the policy has had the effects
intended. While the non-experimental design of this study cannot produce causal results,
analysis should reveal whether or not the initiative is associated with changes in outc omes,
namely increased opportunity for students to take Algebra I in the eighth grade and students'
ALGEBRA FOR ALL POLICY IMPACTS 51
success rates on the Algebra I CST across subgroups and across school poverty rates . The study
is centered around a comparison of means . Because of the no n-normality of the dependent
variables of tracking and achievement , despite usual transformations, parametric statistics
designed for factorial analyses were not appropriate for use . Therefore, a practical and
descriptive analysis was analyzed first and t hen followed by nonparametric tests where
differences appeared practical for questions 1 -4.
Where practical differences were noted, Kruskal -Wallis tests were run to determine
statistical significance. Kruskal-Wallis tests are used for non -parametric data analyses and are
similar to one -way analysis of variance ( ANOVA) (Leech & Onwuegbuzie, 2002) . Therefore,
only one factor could be compared at a time . The assumptions for running Kruskal -Wallis tests
are that the distribution s are similar and that there is homogeneity of variance . Although the data
sets used in the study were non -normal, the distributions of each set by factor are similar, and
thus the assumptions for the test are met (data sets are all similarly skewed and distributed) . In
addition, a non -parametric equivalent of Levine's test was performed on each data set to
determine homoscedasticity. This was conducted by running an analysis of variance on the
absolute difference (between the each case calculated rank and the overall mean for a dataset
split by factor) . Assumptions for the Kruskal -Wallis test were met .
Because the Kruskal-Wallis test cannot run multiple comparisons at one time, as can be
done with a factorial ANOVA, the test must be run multiple times, which results in a multiple
testing problem (Lund Research, Ltd., 2013) . This presents the possibility of incorrectly
rejecting the null hypothesis that there are no differences between groups . To control for the
problem of multiple comparisons post-hoc Bonferroni corrections were applied to all Kruskal -
Wallis results . Test statistics were adjusted automatically in SPSS for ties . A significance level
ALGEBRA FOR ALL POLICY IMPACTS 52
of p < .05 was used consistently throughout the stu dy. Effect sizes were calculated using
Cohen's f measure of effect size . SPSS does not provide a calculation for Cohen's f and
therefore, data tables were imported into Excel to calculate this statistic using the equation:
𝑓 = √
( )
This calculation results in a measure that is an extension of Cohen's d statistic and
allows for its use with ANOVA and nonparametric statistics . The effect size statistic (f) is a
measure of the average effect of a dependent measure (tracking, achievement, or placement)
across levels of independent variables (subgroup or school poverty level) . Cohen's
recommendations for measuring the strength of an effect size using f are 0.10 for a small effect
size, 0.25 for a moderate effect size, and 0.40 for a large ef fect size (Parke, 2010). To obtain the
partial eta -squared ( ) calculation from the Kruskal -Wallis results the following formula was
used: = √
( )
.
The data set for the placement variable (question 5) approximated normality and met
most of the assumptions for generalized linear models (Parke, 2010). Therefore, for analysis of
placement one and two -way ANOVA was used to determine statistical significance along with
Cohen's f to measure ef fect size.
Limitations of the Study
When using a non -experimental quantitative design, determining causality is not possible .
The goal of this study was to analyze the impact of Algebra for All policies on tracking,
achievement, and placement; however, the true causes of the results may or may not be related to
the policy under study . Many factors go into education including funding, teacher effectiveness,
and environmental factors . Therefore, only correlational comparisons could be made .
ALGEBRA FOR ALL POLICY IMPACTS 53
Comparing means across subgroups and looking for interactions to infer correlations also
has its difficulties, as it is possible that any noted differences are purely coincidental ; however,
the inclusion of all California middle schools with 10 or more eighth graders makes for an
extremely large sample size, which limits the likelihood of mere coincidence in the results .
Additionally, a direct influence of the Algebra for All policies on the results is not g uaranteed.
Any observed differences in the data could be due to other factors such as political climate or
changes in local policies ; however, again, the inclusion of all California middle schools in the
sample size helps to control for this possibility . Ultimately, educational research includes many
limitations including the dynamic and unique systems in which each school operates —local
school boards for example . The methods used to analyze results come with their own difficulties
including the fact that with such a large data set, even small differences can be statistically
significant. Therefore, effect sizes were also reported to provide another layer of scrutiny .
As with any study of a real world implementation, random assignment of participants is
either difficult or impossible . This study is no exception . Random assignment helps protect
external validity of results and so in this case, the results of the study are onl y generalizable to
the schools in the sample (Creswell, 2009). To control for this threat, analysis and claims are
restricted to the schools studied. However, this study includes nearly every school in California
with eighth grade students . Very few schools were excluded due to low numbers of students .
Therefore, the sample is very nearly equivalent to the population .
An instrumentation threat to internal validity also may exist, in that the CST changes over
time and the tests given in 2003 are not the same as the tests given in 2013 . However, accord ing
to the CDE the tests (same subject and level) are considered equivalent (CDE, 2012) . Creswell
(2009) suggests using the same test for both pre and posttest measures to reduce this threat;
ALGEBRA FOR ALL POLICY IMPACTS 54
however, in the case of historical data, such as the CSTs, this is not possible . Additionally, using
the CST as the main construct to measure proficiency or success in a course may not be the best
method; however, it is the only method available for all schools across the time p eriod of study .
Using one measure to quantify student success in Algebra I (proficiency on the CST), is not
likely sufficient to measure something as complicated as student learning, which represents a
construct validity issue . Further, because the CST i s a high -stakes test for schools but not for
students, the test takers may not take the test seriously or try their best . Every teacher has
examples of their star pupil who scored abysmally on the CST . While it is impossible to control
for this type of c onstruct problem, due to the unavailability of other measures, it is assumed that
the test is generally reliable for most schools and most students . Because multiple years were
studied, eleven in all, this reduces the problem of using one measure .
Another issue of concern is the threat of extraneous variables that may contribute to the
changes in the dependent variables under study . While there are several demographic data being
used as independent measures, there may be other factors not considered tha t may affect results .
For example, while this study analyzes the effect of school poverty rates, it does not include
other factors such as the quality of the teaching, which logically would contribute to student
achievement results. To control for the po ssibility of extraneous and confounding variables, the
analysis only include d associations between the variables under study . For example, if school
poverty rates show ed a difference in mean tracking, analysis only reveals an association between
school poverty rate and tracking . No conclusion can be made that school poverty levels cause a
difference in tracking .
A more significant threat to internal validity is that of history . It is possible that events
outside the Algebra for All initiative have affected the results . Especially in education, changing
ALGEBRA FOR ALL POLICY IMPACTS 55
policies and the implementation of various programs in schools can have effects on the progress
of students. Even parent involvement and community agendas can influence how individu al
schools and districts implement policy . In addition, as educator opinion with regard to the
initiative has changed over time, this may also be a factor . For example, as the adop tion process
of the CCSS continues, the focus on the 1997 Mathematics Fram ework and the mandates of the
Algebra for All policy has moved away from center stage . It is suggested that the effects of
history can be mitigated by all participants experiencing the same events over time (Creswell,
2009). Since all data are collected through the STAR system simultaneously, this procedure
should minimize the effects of history or at least distribute the effects equally across groups . As
results are analyzed an analysis of changing policies were also conducted. For example, the
direction of the State Board of Education with regard to CCSS over time were compared to the
results.
Additionally, school population attrition (or change) between years may also confound
results, especially with regard to question 5 . Comparing non -matched scores over two years
does pose a threat to the validity of the results; however, in experimental procedures participant
mortality can be controlled for through sample size (Creswell, 2009) . Because the sample size is
large (n approximately 2000 over each of 11 years), the small differences in population size from
one year to the next should not interfere with the results .
ALGEBRA FOR ALL POLICY IMPACTS 56
Chapter 4: Results
The purpose of this analysis was to evaluate the effects of the Algebra for All initiative in
California middle schools on opportunity to learn and achievement for traditionally
disadvantaged students between 2003 and 2013 . In analyses, missing data were left out of the
analyses for that year only . For example, a school that was in existence between 2003 and 2006
but not in subsequent years, was included in the years 2003 -2006. Schools that were missing
school poverty data (FRPM) were excluded from analysis only for the years the data were
missing. Schools with no reported CST data were excluded from analyses .
In rare cases, in the tracking data, the calculations resulted in some schools having a
tracking rate over 100% . Each case was investigated for accuracy and then recoded to be 100%
to avoid outliers . All cases of tracking rates being calculated over 100% were due to the school
testing more students than their reported enrollment . This occurred with no more than 20
schools per year (<1% of the schools) . During the investigation of these schools, many were
small county run programs, such as juvenile detention schools with a high mobility rate .
With most factorial designs, a n analysis of variance (ANOVA) is conducted to determine
whether or not the differences betw een groups is statistically significant as well as whether or not
there are any interaction effects present . In this study ANOVA measures were not appropriate for
questions 1 -4 due to the data not meeting the necessary assumptions for ANOVA , namely
normality. Mathematical transformations including, bootstrapping, random sampling,
logarithms, and even the complex Box -Cox lambda calculations were unsu ccessful in
normalizing the data . Therefore, Kruskal -Wallis nonparametric tests were used with research
questions 1 -4 and a bootstrapped ANOVA was used with research question 5 . The results of the
data analyses are presented by research question .
ALGEBRA FOR ALL POLICY IMPACTS 57
Tracking—Research Questions 1 and 2
Research questions 1 and 2 deal with the issues of placement . In grade eight , placement
into General Mathematics rather than Algebra I tracks students into a course sequence that does
not align with the correlates of those that attend college (Adelman, 1999). The first two research
questions were:
1. To what extent, if any, have California high and low poverty schools increased
enrollment in early algebra for traditionally disadvantaged students between 2004
and 2013?
2. To what extent, if any, have California high and low poverty schools decreased
the gap between non -disadvantaged and traditionally disadvantaged students'
access to early algebra between 2004 and 2013?
All students analyses by school poverty level. Between 2003 and 2013, the mean
tracking rate of students into General Mathematics decreased over time , meaning the fewer
students were placed in General Mathematics and more students were placed in Algebra I or
higher courses. Table 2 shows the mean (M) tracking rates and standard deviation ( SD) for each
year by school poverty quartile, where a rate of one indicates a California school in the bottom
quartile in terms of FRPM participation (most affluent) and a rate of four is a school with the
highest rates of FRPM participation (most poverty).
For all school poverty levels, tracking rates gradually went down over time . By 2012, all
poverty quartiles reduced tracking nearly by half, from .6 in quartile 1 to .33 (a decrease of 45%)
and from .72 in quartile 4 schools to .38 (a decrease of 47%) . However, in 2013, poverty level 4
schools increased tracking rates by 5% ; the decrease of 47% became a decrease of 40% in 2013 .
Additionally, the gap in tracking rates across school poverty levels decreased over time, until
ALGEBRA FOR ALL POLICY IMPACTS 58
2011, where the gap between high a nd low poverty schools and tracking was only 0.05 ( M = 0.33
for quartile 1 and M = 0.38 for quartile 4) . But in 2012, the gap began increasing again to 0.1 in
2013 (M = 0.33 for quartile 1 and M = 0.43 for quartile 4) , only 0.02 shy of the 2003 difference
of 0.12 ( M = 0.6 for quartile 1 and M = 0.72 for quartile 4) . This difference in the tracking rates
for quartile 4 schools is statistically significant ( x
2
(1) =5.29, p = .02, f = 0.0 7) but the effect size
was not large.
Table 2
All Students' Tracking Rates for 2003-2013 by School Poverty Quartile
School Poverty Quartile
Year
1 Low 2 3 4 High
M SD M SD M SD M SD
2003 0.6 0.25
0.61 0.23
0.66 0.24
0.72 0.27
2004 0.57 0.25
0.57 0.26
0.61 0.28
0.63 0.29
2005 0.52 0.26
0.56 0.26
0.55 0.31
0.59 0.33
2006 0.48 0.27
0.52 0.27
0.54 0.30
0.56 0.32
2007 0.44 0.26
0.48 0.28
0.47 0.32
0.53 0.32
2008 0.42 0.26
0.47 0.29
0.45 0.30
0.47 0.33
2009 0.39 0.26
0.44 0.30
0.43 0.32
0.45 0.33
2010 0.37 0.26
0.41 0.29
0.43 0.32
0.42 0.33
2011 0.36 0.26
0.39 0.29
0.4 0.31
0.38 0.32
2012 0.33 0.25
0.39 0.30
0.4 0.32
0.38 0.35
2013 0.33 0.26
0.41 0.28
0.41 0.32
0.43 0.33
% Change -45% -33% -38% -40%
In addition to opening up Algebra I for eighth grade students, between 2003 and 2013,
California witnessed an increase of eighth-graders placed in Geometry and Algebra II . Table 3
shows the percentages of eight h grade students in California enrolled in Geometry or Algebra II .
ALGEBRA FOR ALL POLICY IMPACTS 59
The numbers for Integrated Math II and III are not shown because the numbers were extremely
small (<.1%). Between 2003 and 2013, the numbers of eighth-graders taking Geometry tripled .
Table 3
Percent of Students Enrolled in Geometry or Algebra II in Grade Eight
Year
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Geometry 2% 2.5% 2.7% 3% 3.2% 3.6% 4% 4.8% 5.4% 6.2% 6.7%
Algebra II 0% .1% .1% .1% .1% .1% .2% .1% .2% .2% .2%
Although the numbers of students taking courses above Algebra I in eighth grade are too
small to examine by student subgroup, the numbers are high enough to compare across school
poverty quartiles. Table 4 contains the total number of students enrolled in Geometry and
Algebra II between 2003 and 2013 by school poverty quartile . Clearly the majority of students
taking these courses increase over time, but the majority of students taking the courses attend the
more affluent schools (quartile 1 and 2 schools) . The smallest numbers of students taking the
courses come from California's poorest schools (quartile 4) . Although, in 2013, quartile 4
schools began to enroll additional students in Geometry —increasing from an average of 9.5% in
previous years to 17% in 2013 . However, even with this increase the majority of students taking
these high school courses in middle school attend the most affl uent schools. For all years in the
sample 64% to 74% of students taking Geometry and Algebra II attend quartile 1 and 2 schools .
ALGEBRA FOR ALL POLICY IMPACTS 60
Table 4
Eighth Grade Enrollment in Geometry or Algebra II by School Poverty Quartile
Geometry Algebra II Total
Year
School
Poverty Level
Total Ss
Tested
% of Total
Tested
Total Ss
Tested
% of Total
Tested
Total Ss
Tested
% of Total
Tested
2003
1 Low 3814 38% 110 32% 3924 38%
2 3026 30%
116 34%
3142 30%
3 2202 22%
97 28%
2299 22%
4 High 986 10% 19 6% 1005 10%
2004
1 Low 5344 43% 108 24% 5452 42%
2 3684 30%
222 49%
3906 30%
3 2262 18%
98 22%
2360 18%
4 High 1148 9% 25 6% 1173 9%
2005
1 Low 5872 43% 142 29% 6014 43%
2 3720 27%
225 46%
3945 28%
3 2710 20%
104 21%
2814 20%
4 High 1357 10% 19 4% 1376 10%
2006
1 Low 6229 42% 150 26% 6379 41%
2 4439 30%
238 42%
4677 30%
3 2919 20%
149 26%
3068 20%
4 High 1282 9% 35 6% 1317 9%
2007
1 Low 6849 43%
286 48%
7135 44%
2 4667 30%
193 32%
4860 30%
3 2760 18%
87 15%
2847 17%
4 High 1474 9%
28 5%
1502 9%
2008
1 Low 7788 44% 175 26% 7963 43%
2 4498 25%
280 42%
4778 26%
3 3532 20%
132 20%
3664 20%
4 High 1878 11% 79 12% 1957 11%
2009
1 Low 9138 47% 274 39% 9412 47%
2 5247 27%
326 46%
5573 28%
3 3262 17%
88 12%
3350 17%
4 High 1814 9% 22 3% 1836 9%
2010
1 Low 9910 43%
258 39%
10168 43%
2 6999 31%
304 46%
7303 31%
3 3847 17%
71 11%
3918 17%
4 High 2084 9%
34 5%
2118 9%
2011
1 Low 11083 44% 270 35% 11353 44%
2 7233 29%
338 44%
7571 29%
3 4453 18%
148 19%
4601 18%
4 High 2313 9% 13 2% 2326 9%
2012
1 Low 12316 42%
245 33%
12561 42%
2 8605 30%
372 50%
8977 30%
3 5351 18%
88 12%
5439 18%
4 High 2810 10%
37 5%
2847 10%
2013
1 Low 12028 39% 276 28% 12304 39%
2 7493 24%
527 53%
8020 25%
3 6149 20%
84 8%
6233 20%
4 High 5268 17% 116 12% 5384 17%
Note. The abbreviation Ss is used for Sum of Students.
ALGEBRA FOR ALL POLICY IMPACTS 61
Ethnicity subgroup analyses by school poverty level. While looking all students
across school poverty rates does reveal a picture about the differences in tracking rates among
schools just by their FRPM participation rates, this does not control for other factors such as
student demographics. When adding the element of ethnicity into the analysis, there was a clear
reduction in tracking between 2003 and 2013 for all ethnic subgrou ps under study —African
American (AfAm), Asian, Fi lipino (Fil), Latino (Lat), and white (Wh). Table 5 shows the mean
(M) and standard deviation (SD) for tracking for each year by subgroup and school poverty level .
The "% Change" column contains a calculation of the percentage difference in mean tracking
rates between 2003 and 2013 over time by subgroup and for each school poverty level .
For all school poverty quartiles, mean tracking rates (percentages of students placed in
General Mathematics) were reduced each year for all subgroups and all school poverty quartiles
until 2012. In 2012 and 2013, there was a slight increase in tracking in quartile 4 schools . In
quartile 4 schools, the tracking rates increased for all subgroups except the Asian subgroup,
which remained the same . Quartile 4 schools showed the largest increase in 2013, after 10 years
of decreasing tracking rates, with increases of 6% in the African American subgroup and 7% for
the Filipino subgroup. Small differences were seen in some of the poverty quartiles 1 -3 schools
but increased no more than 3% in any subgroup.
In 2003, the schools with the lowest poverty levels (quartile 1 schools) had the highest
levels of tracking for African American students —75%. Though by 2013, quart ile 4 schools
(those with the highest levels of poverty) had the highest tracking rates for African American
students at 49% . Not significantly different from the African American tracking rates in 2003,
Latino students also had very high rates of trackin g in 2003 ranging from 72% -74%. However,
by 2013, these rates were reduced to between 41% and 44% . As indicated in the range column
ALGEBRA FOR ALL POLICY IMPACTS 62
of Table 5, the largest reductions in tracking by subgroup were Filipino students in all schools (a
percentage decrease between 63% and 71%) between 2003 and 2013 .
In looking at differences in tracking means by school poverty quartiles, the practical
differences were minor for most subgroups –differences of less than 10% and in most case s even
smaller. However for the Asian subgroup, school poverty level made a larger difference . In
2003, quartile 1 (low poverty) schools tracked 33% of their Asian students into General
Mathematics classes, while quartile 4 (high poverty) schools tracked 50%. Across the quartiles ,
this number increased by school poverty level . By 2013, quartile 4 schools continued to track
more Asian students into General Mathematics (20%) than did quartile 1 schools (10%) . Asian
students though had the lowest rates of tracking across subgroups and school poverty rates .
ALGEBRA FOR ALL POLICY IMPACTS 63
Table 5
Tracking Rates by Ethnic Subgroup and School Poverty Level
School
Poverty
Quartile
Subgroup
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
%
Change
M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD
1 Low AfAm .75 .25 .69 .23 .69 .24 .66 .26 .61 .28 .59 .27 .54 .29 .49 .30 .44 .31 .44 .29 .41 .28 -45%
Asian .33 .18 .31 .19 .27 .18 .24 .17 .22 .18 .19 .16 .17 .16 .14 .14 .13 .13 .12 .13 .10 .11 -70%
Fil .53 .23 .51 .23 .46 .25 .42 .25 .40 .27 .34 .25 .29 .23 .25 .23 .23 .19 .21 .20 .19 .18 -64%
Lat .74 .23 .70 .22 .66 .25 .62 .26 .58 .29 .56 .29 .53 .30 .49 .30 .48 .30 .45 .29 .44 .29 -41%
Wh .59 .27 .55 .24 .49 .24 .44 .25 .41 .25 .39 .25 .36 .25 .34 .24 .32 .24 .29 .23 .30 .23 -49%
2 AfAm .72 .26 .65 .27 .64 .28 .57 .31 .53 .33 .54 .32 .52 .33 .47 .33 .44 .32 .42 .32 .43 .31 -40%
Asian .40 .22 .37 .23 .33 .23 .29 .22 .24 .22 .25 .22 .22 .21 .19 .19 .16 .17 .16 .18 .14 .15 -65%
Fil .54 .23 .47 .25 .44 .26 .37 .26 .31 .26 .31 .25 .28 .23 .22 .21 .22 .21 .20 .21 .16 .15 -70%
Lat .72 .27 .66 .26 .64 .27 .60 .30 .55 .32 .52 .31 .50 .32 .48 .31 .46 .32 .44 .32 .46 .31 -36%
Wh .57 .25 .52 .26 .50 .26 .45 .27 .41 .28 .40 .28 .37 .27 .35 .26 .32 .26 .32 .27 .34 .26 -40%
3 AfAm .71 .28 .63 .31 .58 .34 .58 .32 .49 .34 .50 .32 .45 .33 .41 .34 .41 .34 .39 .33 .39 .34 -45%
Asian .48 .25 .43 .26 .36 .27 .30 .25 .26 .23 .22 .20 .19 .20 .17 .19 .14 .17 .13 .17 .14 .17 -71%
Fil .49 .24 .45 .26 .39 .29 .34 .27 .25 .25 .26 .25 .22 .22 .18 .19 .15 .15 .17 .18 .14 .17 -71%
Lat .73 .27 .64 .30 .59 .33 .56 .32 .50 .32 .48 .32 .46 .33 .43 .32 .41 .32 .40 .32 .41 .31 -44%
Wh .59 .26 .54 .27 .47 .31 .44 .29 .40 .27 .38 .28 .37 .28 .36 .28 .33 .28 .36 .28 .35 .28 -41%
4 High AfAm .72 .30 .64 .30 .61 .34 .56 .32 .57 .31 .50 .34 .54 .34 .50 .34 .43 .33 .43 .35 .49 .33 -32%
Asian .50 .25 .44 .26 .39 .26 .35 .27 .35 .25 .26 .24 .31 .25 .22 .20 .22 .21 .20 .21 .20 .20 -60%
Fil .48 .22 .40 .28 .40 .25 .35 .26 .41 .24 .30 .24 .35 .19 .23 .24 .15 .17 .11 .14 .18 .16 -63%
Lat .72 .30 .63 .30 .58 .34 .55 .33 .53 .33 .47 .34 .46 .32 .41 .32 .38 .32 .36 .34 .41 .32 -43%
Wh .67 .28 .55 .30 .55 .29 .51 .27 .50 .28 .44 .29 .45 .31 .36 .30 .35 .29 .40 .32 .41 .30 -39%
Note. "School Poverty Level" is broken into quartiles with 1 having the least students participating in FRPM and 4 indicating the
highest levels of participation in FRPM .
ALGEBRA FOR ALL POLICY IMPACTS 64
To illustrate the direction of difference in tracking subgroups at each school poverty
quartile, Table 6 contains the differences in mean tracking for each ethnic subgroup across school
poverty quartiles. These data indicate that there is a practical and observable interaction between
tracking and school poverty level with differences across the quartile s and subgroups from 7% to
11% —meaning that belonging to a particular ethnic group was related to differences in tracking
rates, but the school's poverty rate was also related to tracking rates at the same time . For
example, in 2007 , Filipino students had a 17% difference in tracking rate depending on their
school poverty level . On average, there was a 7 to 11 percent difference in the treatment of
students in particular subgroups by ethnic subgrou p.
Table 6
Difference between School Poverty Quartiles—Tracking Rates by Ethnic Subgroup
Ethnicity 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Avg.
AfAm .03 .05 .11 .09 .12* .10* .09* .09 .03 .06 .10* .08
Asian .17* .13* .11* .11* .13* .08 .14* .09* .09* .08 .09* .11
Fil .06 .11 .07 .08 .17* .08 .13* .07 .08* .10 .05 .09
Lat .03 .07 .08 .07 .08* .09* .08* .08* .11* .10* .05* .08
Wh .10* .03 .08* .07* .10* .06 .08 .02 .03 .11* .12* .07
Note. The asterisk (*) indicates differences that are statistically significant (p <.05).
In Table 6, the differences marked with asterisks were found to be statistically significant
using a Kruskal -Wallis test. Although the identification of a significant difference in the
treatment of a subgroup by poverty level is important, this analysis does not provide the pairwise
comparisons by poverty quartile . Pairwise comparisons were performed with an additional
Bonferroni correction to adjust for multiple comparisons . The following table summ arizes the
ALGEBRA FOR ALL POLICY IMPACTS 65
analysis by significant poverty quartile comparison. The table contains the overall significance
value for the subgroup comparison by year in the "result" colu mn. The adjusted significance
(Adj. p) column contains the Bonferroni corrected sign ificance level.
For instance, in 2003, the Asian subgroup's tracking rates were significantly different by
poverty quartile, x
2
(3) =54.835, p <.001. Post-hoc analysis showed that q uartile 1 (low poverty)
tracking rates for Asian students were significantly different tha n quartiles 2 ( p=.014), 3 ( p
<.001), and 4 ( p <.001). Additionally, quartile 2 tracking rates for Asian students were
significantly different than quartile 3 ( p=.003) and 4 ( p=.001) schools. The effect sizes (f)
ranged from small to medium. For example, for the Asian subgroup in 2003, there was a
moderate effect ( f = 0.29) on tracking across poverty levels .
Non-significant results were not provided in the table . Notice that in the years 2003 to
2006, minority subgroups were not in cluded. This means that for Latino and African American
subgroups in the years 2003 through 2006, poverty quartile was not significantly related to
tracking rates. But beginning in 2007 poverty quartile did make a difference for Latino students
with a sm all effect size of f = 0.1. In that year, data from the Poverty Quartile Comparison
column indicates that the differences that were significant were between quartile 1 and 3 ( p
< .001) and quartile 2 and 3 schools ( p = .04).
ALGEBRA FOR ALL POLICY IMPACTS 66
Table 7
Kruskal-Wallis results for significant differences between poverty quartiles
Year Subgroup Result
Poverty Quartile
Comparison
1 = Low; 4 = High
Adj. p f*
2003 Asian x
2
(3)=54.835, p <.001 1 - 2 .014 0.29
1 - 3 <.001
1 - 4 <.001
2 - 3 .003
2 - 4 .001
Wh x
2
(3)=27.820, p <.001 1 - 4 <.001 0.14
2 - 4 <.001
3 - 4 .001
2004 Asian x
2
(3)=31.241, p <.001 1 - 2 .048 0.21
1 - 3 <.001
1 - 4 <.001
2005 Asian x
2
(3)=17.317, p=.001 1 - 3 .010 0.16
1 - 4 .002
Wh x
2
(3)=9.281, p=.026 1 - 4 .041 0.08
3 - 4 .022
2006 Asian x
2
(3)=11.765, p=.008 1 - 4 .005 0.12
Wh x
2
(3)=9.437, p=.024 1 - 4 .016 0.08
2 - 4 .047
2007 AfAm x
2
(3)=12.288, p=.006 3 - 4 .004 0.12
Asian x
2
(3)=18.532, p <.001 1 - 4 <.001 0.16
2 - 4 .001
3 - 4 .017
Fil x
2
(3)=22.320, p <.001 1 - 3 <.001 0.25
3 - 4 .005
Lat x
2
(3)=15.470, p=.001 1 - 3 .001 0.10
2 - 3 .036
Wh x
2
(3)=16.640, p=.001 1 - 4 .004 0.11
2 - 4 .001
3 - 4 .001
2008 AfAm x2(3)=8.318, p=.04 1 - 3 .049 0.10
Lat x2(3)=22.258, p <.001 1 - 3 .001 0.11
1 - 4 <.001
2 - 4 .050
ALGEBRA FOR ALL POLICY IMPACTS 67
Table 7 Continued
Year Subgroup Result
Poverty Quartile
Comparison
1 = Low; 4 = High
Adj. p f*
2009 AfAm x
2
(3)=11.839, p=.008 1 - 3 .044 0.12
3 - 4 .017
Asian x
2
(3)=23.144, p <.001 1 - 4 <.001 0.18
2 - 4 .038
3 - 4 <.001
Fil x
2
(3)=10.631, p=.014 3 - 4 .021 0.17
Lat x
2
(3)=19.733, p <.001 1 - 3 .001 0.11
1 - 4 .002
2010 Asian x
2
(3)=9.613, p=.022 1 - 4 .042 0.11
Lat x
2
(3)=20.928, p <.001 1 - 3 .022 0.11
1 - 4 .001
2 - 3 .044
2 - 4 .003
2011 Asian x
2
(3)=8.578, p=.035 1 - 4 .045 0.11
3 - 4 .041
Fil x
2
(3)=10.187, p=.017 1 - 3 .020 0.17
Lat x
2
(3)=29.415, p <.001 1 - 3 .004 0.13
1 - 4 .002
2 - 4 .004
2012 Lat x
2
(3)=27.684, p <.001 1 - 3 .004 0.12
1 - 4 .002
2 - 4 .001
Wh x
2
(3)=16.916, p=.001 1 - 3 .006 0.11
1 - 4 .006
2013 AfAm x
2
(3)=10.712, p=.013 3 - 4 .008 0.13
Asian x
2
(3)=12.54, p=.006 1 - 4 .007 0.14
3 - 4 .034
Lat x
2
(3)=10.290, p=.016 2 - 4 .035 0.08
Wh x
2
(3)=20.43, p <.001 1 - 4 <.001 0.11
2 - 4 .047 0.12
Note. *Effect size of f ≥ 0.10 is considered small, f ≥ 0.25 is considered medium, and f ≥ 0.40 is
considered large.
A visual representation of the differences in the treatment of subgroups across school
poverty levels are presented in Figure 3 . Although the Kruskal -Wallis analysis provides a test
ALGEBRA FOR ALL POLICY IMPACTS 68
for significance in the differences in tracking, the direction of the difference is not provided .
Therefore, the figure is provided for additional information about the direction . Additionally, the
Kruskal-Wallis analysis uses ranked data, which is not meaningful in application . Therefore,
mean tracking data in the figure can provide applicable detail (tracking rates). In the figure, the
tracking data by ethnicity subgroup (different color lines) is presented by school poverty level (x
axis) for the years 2003, 2006, 2009, 2012 and 2013 . Data were presented for each three years
but the final year (201 3) was also included as previous data already discussed showed that there
was a slight increase in tracking in 2013 .
The line graphs in Figure 1 reveal that there was a gap between student subgroups across
all years, with the highest rates of tracking with African American and Latino students. In 2003,
there was a 42 point difference in the percentages of African American versus Asian students
tracked in quartile 1 (low poverty) schools. Although there were still differences between the
tracking rates of African American and Asian students across school quartiles, in the years 2003
to 2009, the less affluent the school, the smaller the gap. For example, in 2003, the gaps between
African American and Asian subgroup tracking rates for quartile 2, 3, and 4 schools is 32, 23, 22
percentage points respectively, which means that as school poverty levels increased the gap
decreased. However, in 2012 and 2013, a widening of the gap in quartile 4 (high poverty)
schools was seen.
ALGEBRA FOR ALL POLICY IMPACTS 69
Figure 1. Graphs of tracking means by ethnicity and school poverty quartile .
ALGEBRA FOR ALL POLICY IMPACTS 70
Table 8 contains a summary of the differences between subgroups across poverty levels
from 2003 -2013. The gaps were calculated by taking the highest tracked subgroup rate and
subtracting the lowest tracked subgroup rate. In all years and school quartile level the
differences calculated are between African American and Asian subgroups with the exception of
2012 and 2013 for quartile 4 (high poverty) groups where the Fi lipino subgroup was the lowest
tracked subgroup. For quartile 1 (low poverty) schools, the tracking rate gap decreased over time
by 19% . Quartile 4 schools though, which had a lower gap to begin with, remained fairly
constant from 2003 -2009 but began to i ncrease the gap in tracking between 2010 and 2013 and
rather than decreasing the gap in tracking between subgroups increased it by 33% . This increase
resulted in a smaller difference overall in 2013 between school poverty levels but increased the
tracking gap at the subgroup level.
Table 8
Tracking Rate Gaps between Ethnic Subgroup by School Poverty Quartile
School
Poverty
Quartile
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
%
Change
1 Low 0.42 0.39 0.41 0.42 0.39 0.41 0.37 0.36 0.35 0.33 0.34 -19%
2 0.33 0.29 0.31 0.31 0.31 0.29 0.29 0.29 0.30 0.28 0.32 -3%
3 0.25 0.22 0.23 0.28 0.25 0.28 0.26 0.26 0.27 0.27 0.27 9%
4 High 0.24 0.25 0.22 0.21 0.22 0.24 0.23 0.27 0.28 0.32 0.31 33%
Note. Calculated differences are based on the raw data, not rounded data displayed . All
differences are significant at the p < .01 level .
In addition to a gap between the highest and lowest tracked subgroups there are also
significant differences between subgroups across poverty quartiles. Although interactions could
not be analyzed with the Kruskal -Wallis tests, the data file was split by year and school poverty
quartile so tha t the analysis could be run to compare tracking between subgroups. Table 9
ALGEBRA FOR ALL POLICY IMPACTS 71
contains the Kruskal -Wallis results by year and poverty quartile . Post-hoc pairwise comparisons
were made between subgroups and adjusted significance levels are provided in the columns .
Effect sizes (f) were calculated and indicate that there is a stronger effect size for differences
between subgroups as poverty increases . For example, in quartile 1 (low poverty) schools there
are large effect sizes for subgroup across all years (0.65≥ f ≥ 0.5). This effect decreases as
school poverty increases, and decreases for all quartiles ov er time until 2011 when values begin
to slowly increase , which means that the gap in tracking between subgroups is larger at schools
with less poverty as was also apparent in the descriptive data and on the graphs in Figure 1 .
Also of note and in alignment with analyses made on descriptive data so far, tracking
rates between the African American and Latino subgroup are not significantly different for all
years and all school poverty quartiles . Additionally, there is no significant difference b etween
the tracking rates for Filipino and Asian students at poverty quartile 3 and 4 (high poverty)
schools, yet there was a significant difference in the tracking rates between the subgroups at
quartile 1 (low poverty) schools over all years studied .
ALGEBRA FOR ALL POLICY IMPACTS 72
Table 9
Kruskal-Wallis Results—Differences between Subgroups by Poverty Quartile
Year
Poverty
Quartile
Result f *
Highest
- Lowest
Asian-
Fil
Asian-
Wh
Asian-
Lat
Asian-
AfAm
Fil-
Wh
Fil-
AfAm
Fil-
Lat
Wh-
AfAm
Wh-
Lat
AfAm-
Lat
2003 1 x
2
(4)=266.306, p <.001 0.65 <.001 .001 <.001 <.001 <.001
<.001 <.001 <.001 <.001
2 x
2
(4)=339.962, p <.001 0.53 <.001 <.001 <.001 <.001 <.001
<.001 <.001 <.001 <.001
3 x
2
(4)=255.008, p <.001 0.44 <.001
<.001 <.001 <.001 .001 <.001 <.001 <.001 <.001
4 x
2
(4)=97.665, p <.001 0.36 <.001
<.001 <.001 <.001 <.001 <.001 <.001 .158 .024
2004 1 x
2
(4)=330.597, p <.001 0.64 <.001 <.001 <.001 <.001 <.001
<.001 <.001 <.001 <.001
2 x
2
(4)=249.690, p <.001 0.44 <.001 .02 <.001 <.001 <.001
<.001 <.001 <.001 <.001
3 x
2
(4)=157.987, p <.001 0.35 <.001
<.001 <.001 <.001 .04 <.001 <.001 <.001 <.001
4 x
2
(4)=64.541, p <.001 0.30 <.001
.018 <.001 <.001
<.001 <.001 .010 .008
2005 1 x
2
(4)=347.510, p <.001 0.63 <.001 <.001 <.001 <.001 <.001
<.001 <.001 <.001 <.001
2 x
2
(4)=254.415, p <.001 0.45 <.001 .009 <.001 <.001 <.001
<.001 <.001 <.001 <.001
3 x
2
(4)=121.216, p <.001 0.30 <.001
<.001 <.001 <.001
<.001 <.001 <.001 <.001
4 x
2
(4)=50.446, p <.001 0.27 <.001
.002 <.001 <.001
.001 .003
2006 1 x
2
(4)=320.077, p <.001 0.60 <.001 <.001 <.001 <.001 <.001
<.001 <.001 <.001 <.001
2 x
2
(4)=240.776, p <.001 0.42 <.001
<.001 <.001 <.001
<.001 <.001 <.001 <.001
3 x
2
(4)=151.324, p <.001 0.36 <.001
<.001 <.001 <.001 .02 <.001 <.001 <.001 <.001
4 x
2
(4)=52.125, p <.001 0.26 <.001
<.001 <.001 <.001
.001 .001
2007 1 x
2
(4)=290.275, p <.001 0.53 <.001 <.001 <.001 <.001 <.001
<.001 <.001 <.001 <.001
2 x
2
(4)=199.933, p <.001 0.38 <.001
<.001 <.001 <.001 .02 <.001 <.001 <.001 <.001
3 x
2
(4)=116.130, p <.001 0.31 <.001
<.001 <.001 <.001 <.001 <.001 <.001 .002 <.001
4 x
2
(4)=44.883, p <.001 0.24 <.001
.002 <.001 <.001
.024
Note. Only significant p-values are reported. Blanks represent non-significant differences between subgroups. *Effect size of f ≥
0.10 is considered small, f ≥ 0.25 is considered medium, and f ≥ 0.40 is considered large.
ALGEBRA FOR ALL POLICY IMPACTS 73
Table 9 Continued
Year
Poverty
Quartile
Result f *
Highest
- Lowest
Asian-
Fil
Asian-
Wh
Asian-
Lat
Asian-
AfAm
Fil-
Wh
Fil-
AfAm
Fil-
Lat
Wh-
AfAm
Wh-
Lat
AfAm-
Lat
2008 1 Low x
2
(4)=308.650, p <.001 0.56 <.001 <.001 <.001 <.001 <.001
<.001 <.001 <.001 <.001
2 x
2
(4)=157.229, p <.001 0.36 <.001
<.001 <.001 <.001
<.001 <.001 <.001 <.001
3 x
2
(4)=128.207, p <.001 0.33 <.001
<.001 <.001 <.001 .007 <.001 <.001 <.001 <.001
4 High x
2
(4)=62.784, p <.001 0.23 <.001
<.001 <.001 <.001 .045 .001 .005
2009 1 Low x
2
(4)=306.738, p <.001 0.52 <.001 .001 <.001 <.001 <.001 .045 <.001 <.001 <.001 <.001
2 x
2
(4)=171.359, p <.001 0.35 <.001
<.001 <.001 <.001 .014 <.001 <.001 <.001 <.001
3 x
2
(4)=115.389, p <.001 0.30 <.001
<.001 <.001 <.001 <.001 <.001 <.001
.004
4 High x
2
(4)=31.298, p <.001 0.20 <.001
.022 .002 <.001
.04
2010 1 Low x
2
(4)=269.013, p <.001 0.51 <.001 .005 <.001 <.001 <.001 .004 <.001 <.001 <.001 <.001
2 x2(4)=195.758, p <.001 0.38 <.001
<.001 <.001 <.001 <.001 <.001 <.001 <.001 <.001
3 x2(4)=113.211, p <.001 0.31 <.001
<.001 <.001 <.001 <.001 <.001 <.001
.029
4 High x2(4)=48.437, p <.001 0.25 <.001
.029 <.001 <.001 .582 .001 .039 .005
2011 1 Low x2(4)=272.822, p <.001 0.51 <.001 .002 <.001 <.001 <.001 .008 <.001 <.001 .006 <.001
2 x2(4)=180.875, p <.001 0.37 <.001 .757 <.001 <.001 <.001 .002 <.001 <.001 .001 <.001
3 x2(4)=123.588, p <.001 0.32 <.001
<.001 <.001 <.001 <.001 <.001 <.001
.007
4 High x2(4)=33.755, p <.001 0.21 <.001
.025 .001 <.001 .037 .001 .010
2012 1 Low x2(4)=287.080, p <.001 0.50 <.001 .004 <.001 <.001 <.001 .010 <.001 <.001 <.001 <.001
2 x2(4)=162.415, p <.001 0.34 <.001
<.001 <.001 <.001 <.001 <.001 <.001 .02 <.001
3 x2(4)=121.308, p <.001 0.32 <.001
<.001 <.001 <.001 <.001 <.001 <.001
4 High x2(4)=39.677, p <.001 0.22 <.001
<.001 .006 <.001 <.001 <.001 .003
2013 1 Low x2(4)=282.507, p <.001 0.52 <.001 .004 <.001 <.001 <.001 .001 <.001 <.001 .004 <.001
2 x2(4)=199.290, p <.001 0.43 <.001
<.001 <.001 <.001 <.001 <.001 <.001
<.001
3 x2(4)=151.359, p <.001 0.36 <.001
<.001 <.001 <.001 <.001 <.001 <.001
4 High x2(4)=74.658, p <.001 0.26 <.001
<.001 <.001 <.001 <.001 <.001 <.001
ALGEBRA FOR ALL POLICY IMPACTS 74
Language subgroup analyses by school poverty level. Between 2003 and 2013, tracking was
reduced for all students in all language proficiency subgroups in the sample —Reclassified
English Proficient (RFEP), Eng lish Learner (EL), and English Only ( Eng. Only). Table 8
contains the mean tracking rates by school poverty quartile . Most unexpected in these data are
that the RFEP subgroup has the lowest levels of tracking in every year evaluated, quite
significantly lower than both ELs and English only students . In 2003, RFEP tracking rates
ranged from 45% to 56%, while English Only student tracking means ranged from 60% to 71% .
Of the language proficiency subgroups, ELs had the highest tracking rates in 2003, with a low of
70% at quartile 1 low poverty schools and 81% at the two middle quartiles . In 2013, similar to
the results by ethnicity analyses, a pattern of increasing trac king is observed in quartile 4 high
poverty schools with an increase of 10 percentage points in tracking mean for the EL subgroup
and much smaller increases for the RFEP and English Only groups (3 percentage points each) .
Looking at the percentage change over time (percent change column) of Table 10, the
RFEP subgroup experienced the greatest percentage change from 2003 to 2013 . The rate of
change increased across school poverty levels with a 42% decrease of RFEP students placed in
General Mathematics in quartile 1 low poverty schools to a 59% decrease in the tracking rates
for quartile 4 high poverty schools. This decrease was higher than the decreases for both the
English Only and EL subgroups . The least change was observed in the EL subgroup with only a
9% decrease at quartile 1 schools increasing again over quartile levels with a 23% and 22%
decrease in tracked students for quartile 3 and 4 schools respectively . EL students continued to
have the highest tracking rates . The 2013 trend of increased tracking is quite large at the quartile
4 schools (mean difference of 0.10); howeve r the differences in means were not statistically
significant.
ALGEBRA FOR ALL POLICY IMPACTS 75
Table 10
Tracking Rates by Language Proficiency Subgroup and School Poverty Quartile
School
Poverty
Quartile
Subgroup
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
%
Change
M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD
1 Low RFEP .45 .25 .44 .25 .42 .25 .43 .26 .40 .27 .35 .25 .34 .26 .28 .25 .27 .25 .27 .25 .26 .24 -42%
EL .70 .24 .74 .24 .74 .23 .71 .26 .69 .31 .64 .32 .68 .34 .65 .35 .64 .35 .66 .36 .64 .33 -9%
Eng.
Only
.62 .27 .57 .25 .51 .25 .47 .26 .43 .26 .42 .26 .38 .26 .36 .26 .35 .26 .32 .25 .32 .25 -48%
2 RFEP .56 .27 .49 .28 .48 .28 .43 .29 .40 .30 .39 .29 .33 .27 .30 .27 .28 .26 .27 .27 .30 .28 -46%
EL .81 .26 .77 .26 .76 .27 .73 .30 .68 .34 .66 .35 .68 .37 .66 .36 .67 .38 .69 .36 .72 .34 -11%
Eng.
Only
.60 .25 .55 .25 .55 .26 .50 .27 .45 .28 .44 .29 .42 .30 .40 .28 .36 .28 .37 .29 .38 .27 -37%
3 RFEP .51 .28 .47 .29 .40 .30 .35 .29 .31 .27 .30 .27 .27 .25 .22 .24 .21 .23 .23 .25 .22 .25 -57%
EL .81 .26 .72 .31 .66 .35 .64 .35 .60 .36 .61 .36 .60 .39 .58 .38 .60 .39 .62 .40 .62 .39 -23%
Eng.
Only
.66 .26 .59 .28 .52 .32 .51 .30 .44 .31 .44 .30 .42 .32 .42 .31 .39 .30 .39 .32 .40 .31 -39%
4 High RFEP .51 .29 .42 .30 .38 .30 .33 .27 .31 .26 .27 .27 .24 .23 .19 .22 .17 .21 .18 .24 .21 .24 -59%
EL .78 .30 .68 .32 .65 .37 .63 .35 .63 .34 .57 .37 .60 .38 .56 .39 .53 .40 .51 .41 .61 .40 -22%
Eng.
Only
.71 .29 .62 .29 .60 .33 .54 .32 .52 .32 .46 .33 .46 .32 .44 .32 .39 .32 .39 .33 .42 .32 -41%
ALGEBRA FOR ALL POLICY IMPACTS 76
Table 11 contains the results of a Kruskal -Wallis test of significance on the tracking
differences between school poverty quartiles by language proficiency subgrou p. Only significant
differences are s hown. Again, Bonferroni corrections were used to adjust for multiple
comparisons. The table contains the overall significance value for the subgroup comparison by
year in the " Result" column. The adjusted significance ( Adj. p) column contains the Bonfer roni
corrected significance level s. The final column is the effect size (f).
In illustration, in 2003, the RFEP subgroup's tracking rates were significantly different by
poverty quartile, x
2
(3) =14.438, p=.002, f = 0.12 (small effect size) . Post-hoc analysis with
Bonferroni corrections showed that quartile 1 (low poverty) tracking rates for RFEP students
were significantly different than quartile 2 (p=.001) schools only . The differences between the
other quartile groups were not significant . However, for the English Only subgroup, there were
significant differences between quartile 1 and 3 (p=.013), 1 and 4 ( p <.001), 2 and 3 ( p <.001), 2
and 4 ( p <.001), and also between 3 and 4 ( p <.001), with a small (approaching moderate) effect
size of 0.22. This is the largest effect size in the language proficiency differences by poverty
level data set.
ALGEBRA FOR ALL POLICY IMPACTS 77
Table 11
Kruskal-Wallis Tracking by Language Proficiency between Poverty Quartiles
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2003 RFEP x
2
(3)=14.438, p=.002 1 - 2 .001 0.12
EL x
2
(3)=38.280, p <.001 1 - 2 <.001 0.18
1 - 3 <.001
1 - 4 <.001
Eng. Only x
2
(3)=89.791, p <.001 1 - 3 .01 0.22
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 <.001
2004 RFEP x
2
(3)=11.650, p=.009 2 - 4 .008 0.11
EL x
2
(3)=12.703, p=.005 2 - 4 .005 0.11
Eng. Only x
2
(3)=29.557, p <.001 1 - 3 .02 0.12
1 - 4 <.001
2 - 3 .002
2 - 4 <.001
2005 RFEP x
2
(3)=20.606, p <.001 2 - 3 <.001 0.14
2 - 4 .003
EL x
2
(3)=14.753, p=.002 2 - 3 .007 0.11
2 - 4 .005
Eng. Only x
2
(3)=31.755, p <.001 1 - 4 <.001 0.13
2 - 4 .001
3 - 4 .001
2006 RFEP x
2
(3)=31.449, p <.001 1 - 3 .006 0.17
1 - 4 <.001
2 - 3 .001
2 - 4 <.001
EL x
2
(3)=17.280, p=.001 2 - 3 .002 0.12
2 - 4 .002
Eng. Only x
2
(3)=21.569, p <.001 1 - 3 .021 0.11
1 - 4 <.001
2 - 4 .02
2007 RFEP x
2
(3)=27.259, p <.001 1 - 3 .001 0.15
1 - 4 .003
2 - 3 .001
2 - 4 .003
EL x
2
(3)=13.321, p=.004 2 - 3 .007 0.11
Eng. Only x
2
(3)=29.622, p <.001 1 - 4 <.001 0.12
2 - 3 <.001
2 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 78
Table 11 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2008 RFEP x
2
(3)=36.751, p <.001 1 - 4 <.001 0.17
2 - 3 .001
2 - 4 <.001
EL x
2
(3)=15.259, p=.002 2 - 4 .001 0.11
2009 RFEP x
2
(3)=32.486, p <.001 1 - 3 <.001 0.16
1 - 4 <.001
2 - 3 .01
2 - 4 <.001
EL x
2
(3)=19.470, p <.001 1 - 4 .02 0.13
2 - 3 .01
2 - 4 .002
Eng. Only x
2
(3)=12.036, p=.007 1 - 4 .003 0.03
2010 RFEP x
2
(3)=42.302, p <.001 1 - 3 .006 0.18
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
EL x
2
(3)=24.653, p <.001 1 - 4 .007 0.14
2 - 3 .007
2 - 4 <.001
Eng. Only x
2
(3)=13.198, p=.004 1 - 4 .003 0.08
2011 RFEP x
2
(3)=45.599, p <.001 1 - 3 .006 0.18
1 - 4 <.001
2 - 3 .003
2 - 4 <.001
EL x
2
(3)=28.374, p <.001 1 - 4 .02 0.16
2 - 4 <.001
3 - 4 .0364
2012 RFEP x
2
(3)=36.813, p <.001 1 - 3 .034 0.16
1 - 4 <.001
2 - 4 <.001
3 - 4 .02
EL x
2
(3)=41.095, p <.001 1 - 4 <.001 0.19
2 - 4 <.001
3 - 4 <.001
Eng. Only x
2
(3)=10.142, p=.017 1 - 3 .02 0.07
2013 RFEP x
2
(3)=29.443, p <.001 1 - 4 .01 0.14
2 - 3 <.001
2 - 4 <.001
EL x
2
(3)=14.186, p=.003 2 - 3 .03 0.11
2 - 4 .001
Eng. Only x
2
(3)=24.659, p <.001 1 - 2 .008 0.11
1 - 3 .003
1 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 79
Figure 2 is a display of line graphs of the tracking rate means for placing students into General
Mathematics by the language proficiency subgroups across school poverty levels . Data are
displayed for each third year from 2003 -2012. Additionally, 2013 is included because it is the
last year of data in the sample and there was an observed increase in tracking for some data sets
in 2013. On first analysis, in 2003 , all school poverty quartiles had similar gaps between their
highest and lowest tracked subgroups (EL and RFEP), but by 2006 and persisting through to
2013, quartile 1 low poverty schools had a much smaller gap between their Englis h Only
subgroup and EL subgroup than did quartile 4 high poverty schools. And similarly between
2003 and 2012, quartile 4 schools had smaller gaps between their EL and English Only
subgroups. By 2013, however, quartile 4 schools widened the gap between their language
proficiency subgroups, with 20 percentage points separating each subgrou p.
Looking at the line graph for 2003, the EL subgroup was the group highest tracked by all
school quartile groups . Although quartile 1 low poverty schools in 2003 trac ked fewer students
than did the other 3 quartile groups, all quartile groups tracked the EL subgroup of students at the
highest rates, between 70 and 81 percent . In 2006, a decrease in the tracking rates for the EL
subgroup was observable. While quartile 1 schools did not change much (71% up from 70%)
quartile 3 and 4 high poverty schools decreased the tracking of the EL populations from 81% and
78% respectively to 64% and 63% . The levels of tracking for the EL subgroups remains fairly
constant until 201 2 where quartile 4 schools decreased tracking to 51% , a quite significant
decrease from 2003 when quartile 4 schools were tracking 78% of their EL students . Although,
in 2013, tracking for quartile 4 schools increased 10 percentage points back to 61% simi lar to the
rates of quartile 1 -3 schools that tracked EL students at rates between 62 -72%.
ALGEBRA FOR ALL POLICY IMPACTS 80
Figure 2. Graphs of tracking means by language proficiency and school poverty quartile .
ALGEBRA FOR ALL POLICY IMPACTS 81
The least tracked language proficiency group was not English Only students but instead
reclassified EL or RFEP students. Across school quartile levels and across the years from 2003
to 2013, there is a small difference in the treatment of the RFEP students with no more than a 10
percentage point difference in the tracking rates between the quartile ranges in any year . With
the exception of 2003, quartile 1 (low poverty) schools had the least gap with a range between
four and six percentage points between the treatment of RFEP and English Only student
subgroups while quartile 4 (high poverty) schools had the greatest gap with a range of 20 to 22
percentage points.
In further analysis of the gaps between the tracking into General Mathematics for the
language proficiency subgroups between 2003 and 2013, Table 12 contains the tracking rate gaps
between the highest and lowest tracked subgroups (EL and English Only) for each school
poverty quartile. Although tracking means decreased to varying degrees over tim e for all
subgroups, there was an increasing gap between subgroups between 2003 and 2013 . Across
school poverty levels, RFEP students experienced a gradual decrease in tracking between 2003
and 2013, while the tracking rates for EL students remained fairly stable. This increased
difference between the treatment of subgroups was greatest for quartile 2 -4 schools, with
increases between 47 -56%, and least for quartile 1 low poverty schools with an increase of 27% .
ALGEBRA FOR ALL POLICY IMPACTS 82
Table 12
Tracking Rate Gaps Between Language Proficiency by School Poverty Quartile
School
Poverty
Quartile
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
%
Change
1 Low .25 .30 .32 .28 .28 .29 .33 .37 .37 .39 .39 27%
2 .26 .28 .29 .30 .28 .27 .35 .36 .39 .42 .42 49%
3 .30 .26 .26 .29 .29 .31 .33 .36 .39 .39 .40 56%
4 High .27 .27 .27 .31 .32 .29 .36 .36 .35 .32 .39 47%
Note. Calculated differences are based on the raw data, not rounded data displayed. All
differences are significant at the p < .01 level (see Table 13).
Table 13 contains the Kruskal-Wallis analysis of the differences between language
proficiency subgroups for each poverty quartile . Differences between subgroups at each poverty
quartile were all statistically significant at the p <.001 level . The adjusted p-values for
differences between each subgroup are located in the table along with the effect size ( f). With
the exception of 2003, the effect size of the overall differences in tracking between language
proficiency groups is fairly stable over time and not significantly dif ferent between subgroups
(see Table 11). In the table, only significant p-values are reported . Blanks in the table indicate
there was no statistically significant difference . Overall, even though tracking was reduced for
all language proficiency subgroups the gap between subgroups remained fairly stable over time
(little change in f).
ALGEBRA FOR ALL POLICY IMPACTS 83
Table 13
Kruskal-Wallis—Tracking Between Language Subgroups by Poverty Quartile
Year
Poverty
Quartile
Result f
Significant p-values Between Groups
RFEP - EO RFEP - EL EL- EO
2003 1 Low x
2
(2)=266.306, p <.001 0.31 <.001 <.001 .008
2 x2(2)=244.578, p <.001 0.52
<.001 <.001
3 x2(2)=283.182, p <.001 0.52 <.001 <.001 <.001
4 High x2(2)=152.478, p <.001 0.44 <.001 <.001 <.001
2004 1 Low x2(2)=118.521, p <.001 0.42 <.001 <.001 <.001
2 x2(2)=230.561, p <.001 0.50
<.001 <.001
3 x2(2)=185.606, p <.001 0.41 <.001 <.001 <.001
4 High x2(2)=109.900, p <.001 0.38 <.001 <.001 .001
2005 1 Low x2(2)=137.338, p <.001 0.44 <.001 <.001 <.001
2 x2(2)=216.592, p <.001 0.47 .007 <.001 <.001
3 x2(2)=147.411, p <.001 0.37 <.001 <.001 <.001
4 High x2(2)=112.404, p <.001 0.38 <.001 <.001 .012
2006 1 Low x2(2)=111.968, p <.001 0.39
<.001 <.001
2 x2(2)=218.029, p <.001 0.46 .014 <.001 <.001
3 x2(2)=160.846, p <.001 0.39 <.001 <.001 <.001
4 High x2(2)=139.798, p <.001 0.42 <.001 <.001 <.001
2007 1 Low x2(2)=124.266, p <.001 0.40
<.001 <.001
2 x2(2)=165.738, p <.001 0.39
<.001 <.001
3 x2(2)=142.041, p <.001 0.36 <.001 <.001 <.001
4 High x2(2)=147.253, p <.001 0.43 <.001 <.001 <.001
2008 1 Low x2(2)=106.762, p <.001 0.37 .007 <.001 <.001
2 x2(2)=119.366, p <.001 0.36 .047 <.001 <.001
3 x2(2)=156.234, p <.001 0.39 <.001 <.001 <.001
4 High x2(2)=148.206, p <.001 0.35 <.001 <.001 <.001
2009 1 Low x2(2)=131.376, p <.001 0.39
<.001 <.001
2 x2(2)=182.560, p <.001 0.42 <.001 <.001 <.001
3 x2(2)=168.010, p <.001 0.37 <.001 <.001 <.001
4 High x2(2)=156.411, p <.001 0.43 <.001 <.001 <.001
2010 1 Low x2(2)=128.583, p <.001 0.40 <.001 <.001 <.001
2 x2(2)=189.052, p <.001 0.42 <.001 <.001 <.001
3 x2(2)=187.917, p <.001 0.41 <.001 <.001 <.001
4 High x2(2)=169.535, p <.001 0.43 <.001 <.001 .001
2011 1 Low x2(2)=122.351, p <.001 0.40 <.001 <.001 <.001
2 x2(2)=197.822, p <.001 0.43 <.001 <.001 <.001
3 x2(2)=198.999, p <.001 0.43 <.001 <.001 <.001
4 High x2(2)=143.418, p <.001 0.39 <.001 <.001 <.001
2012 1 Low x2(2)=132.384, p <.001 0.39 .017 <.001 <.001
2 x2(2)=227.952, p <.001 0.46 <.001 <.001 <.001
3 x2(2)=200.133, p <.001 0.42 <.001 <.001 <.001
4 High x2(2)=114.493, p <.001 0.34 <.001 <.001 .003
2013 1 Low x2(2)=127.032, p <.001 0.41 .002 <.001 <.001
2 x2(2)=201.908, p <.001 0.49 <.001 <.001 <.001
3 x2(2)=204.644, p <.001 0.44 <.001 <.001 <.001
4 High x2(2)=249.387, p <.001 0.43 <.001 <.001 <.001
ALGEBRA FOR ALL POLICY IMPACTS 84
Socioeconomic status subgroup analyses by school poverty level. For school
socioeconomic subgroups, all school poverty quartiles reduced tracking by large amounts. The
mean (M) and standard deviations ( SD) of tracking rates for schools by poverty quartile and SES
are found in Table 14. In 2003, quartile 1 schools (least poverty) tracked most of their
socioeconomically disadvantaged (SED) students at a rate of 75% . By 2013, quartile 1 schools
reduced this number to 49%, meaning just over half of their SED students were taking Algebra I
in eighth grade . Quartile 4 schools though (highest poverty) had an even greater reduction in
tracking. In 2003, quartile 1 schools started at a tracking rate of 72% but reduced that rate to
38% by 2011 and 2012 . Unfortunately, there was a small increase of 4% in 2013 —a small
percentage which represents an additional 2,040 students in General Mathematics rather than
Algebra I . In addition, 2013 was the only year where increases in tracking were observable in
the data . Tracking increased for SED students in every school poverty quartile, except in quartile
1 schools, which remained the same . The differences between 2012 and 2013 are not statistically
significant for quartile 1, 2, or 3 schools, but is statistically significant for the SED subgroup at
quartile 4 schools (x
2
= 4.22, p = .04, f = .06), but the effect size does not meet the standard for a
small effect. For not -socioeconomically disadvantaged students (NSED), tracking also
decreased over time . Not only did the NSED subgroup begin at a lower tracking rate than those
in the SED subgroup, they decreased at greater rates . Looking at the percent change (% Change)
column of Table 14, in quartile (low poverty) 1 and 4 (high poverty) schools there was a 53%
decrease in the tracking rates for placement into General Math, versus the SED subgroups that
decreased by no more than a 42% ( quartile 4 schools) . Again, quartile 1 schools had the highest
tracking rates for the SED subgroup at 75% and had the least decrease in tracking with a 35%
decrease resulting in an ending tracking rate of 49% in 2013 .
ALGEBRA FOR ALL POLICY IMPACTS 85
Table 14
Tracking Rates by Socioeconomics Subgroup and School Poverty Quartile
School
Poverty
Quartile
SES
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
%
change
M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD
1 Low SED .75 .25 .72 .25 .69 .25 .65 .27 .61 .30 .60 .29 .57 .32 .54 .31 .52 .30 .49 .32 .49 .30 -35%
NSED .58 .26 .54 .24 .49 .25 .44 .26 .40 .25 .38 .25 .35 .24 .32 .24 .30 .24 .27 .23 .28 .23 -53%
2 SED .73 .26 .68 .26 .66 .26 .61 .29 .56 .31 .53 .32 .51 .33 .49 .31 .46 .32 .45 .32 .49 .31 -33%
NSED .56 .25 .51 .26 .48 .25 .44 .27 .40 .27 .39 .27 .35 .26 .32 .25 .29 .25 .29 .26 .30 .25 -46%
3 SED .72 .27 .65 .28 .58 .32 .56 .31 .50 .32 .47 .31 .46 .33 .44 .32 .42 .32 .41 .33 .43 .33 -41%
NSED .60 .27 .53 .28 .46 .30 .42 .28 .38 .28 .36 .27 .33 .27 .31 .26 .28 .25 .27 .25 .28 .25 -54%
4 High SED .72 .29 .63 .29 .59 .34 .56 .33 .54 .32 .48 .34 .46 .32 .42 .33 .38 .32 .38 .35 .42 .33 -42%
NSED .67 .28 .56 .30 .51 .31 .48 .28 .46 .27 .38 .29 .38 .28 .32 .27 .30 .27 .30 .28 .31 .27 -53%
ALGEBRA FOR ALL POLICY IMPACTS 86
The results for the Kruskal -Wallis analysis, where significant, are found in Table 15. The
results show that while differences between the tracking rates of an SES subgroup across school
poverty quartiles are often statistically significant, the effect sizes (f) are generally small (greater
than 0.1 but less than 0.25) . While in 2005 ( Table 14), for example, the tracking rate difference
for SED students between quartile 1 (M =0. 69) and quartile 4 ( M =0. 59) schools was 0.1 ( a
statistically significant difference, p < .001), the effect size of this difference was only 0.12 —a
small effect.
ALGEBRA FOR ALL POLICY IMPACTS 87
Table 15
Kruskal-Wallis Tracking Differences Between Poverty Quartiles by SES Subgroup
Year Subgroup Result
Poverty Quartile
Comparison
1 = low; 4 = high
Adj. p f
2003 NSED x
2
(3)=46.539, p <.001 1 - 4 <.001 0.17
2 - 3 .0334
2 - 4 <.001
3- 4 <.001
2004 SED x
2
(3)=18.447, p <.001 1 - 3 .002 0.11
1 - 4 .001
NSED x
2
(3)=9.696, p=.021 2 - 4 .014 0.08
2005 SED x
2
(3)=25.415, p <.001 1 - 3 <.001 0.12
1 - 4 .009
2 - 3 .002
2006 SED x
2
(3)=22.664, p <.001 1 - 3 <.001 0.12
1 - 4 .001
2 - 3 .048
2007 SED x
2
(3)=30.422, p <.001 1 - 3 <.001 0.14
1 - 4 .004
2 - 3 .007
NSED x
2
(3)=14.44, p=.002 1 - 4 .02 0.10
2 - 4 .015
3- 4 .001
2008 SED x
2
(3)=40.19, p <.001 1 - 3 <.001 0.15
1 - 4 <.001
2 - 3 .003
2 - 4 .029
2009 SED x
2
(3)=36.637, p <.001 1 - 2 .012 0.14
1 - 3 <.001
1 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 88
Table 15 Continued
Year Subgroup Result
Poverty Quartile
Comparison
1 = low; 4 = high
Adj. Sig. Effect Size
2010 SED x
2
(3)=36.111, p <.001 1 - 3 <.001 0.14
1 - 4 <.001
2 - 3 .022
2 - 4 .002
2011 SED x
2
(3)=45.42, p <.001 1 - 2 0.011 0.16
1 - 3 <.001
1 - 4 <.001
2 - 4 <.001
2012 SED x
2
(3)=30.917, p <.001 1 - 3 .001 0.13
1 - 4 <.001
2 - 4 .001
2013 SED x
2
(3)=20.188, p <.001 1 - 3 .041 0.10
1 - 4 .007
2 - 3 .020
2 - 4 .002
Figure 3 illustrates the tracking data patterns across school poverty levels over time .
Data are displayed for each three year period (2003, 2006, 2009, and 2012) . Plus the data for
2013 are included to show the change that occurred in 2013 with some schools increasing
tracking in 2013 . Worth mentioning in the figure is the difference in tracking between the SED
and NSED subgroups was higher for low poverty schools than high poverty schools and that
between 2003 and 2013 the gap in tracking between SED and NSED students increases over
time. While tracking rates went down for all subgroups and all school poverty quartile levels,
the gap between SES groups increased . For example, in 2003, in quartile 1low poverty schools
the gap between NSED and SED General Mathematics placement rates was .17 . In 2006, the
ALGEBRA FOR ALL POLICY IMPACTS 89
gap increased for quartile 1 schools to .21 . This gap increased over the next three years to .22
where it remained constant until 2013 with a slight decrease back to .21 . For quartile 4 high
poverty schools, the gap was smallest in 2003 at .05 . This number increased in 2006 to .08,
where it remained constant until 2013 when it increased to .11 . Overall, the largest decrease in
tracking displayed in Figure 3 is the decrease in General Mathematics placement for NSED
students in Quartile 4 schools . In 2003, this subgroup was tracked into General Mathematics at a
rate of 67% . In 2006, there was a large decrease in this percentage to a tracking rate of 48% .
This number continued to decrease until 2012, where NSED students were tracked at a rate of
30% in quartile 4 schools , a large difference of 55% .
ALGEBRA FOR ALL POLICY IMPACTS 90
Figure 3. Graphs of tracking means by SES and school poverty quartile.
ALGEBRA FOR ALL POLICY IMPACTS 91
In further illustration of the difference in General Mathematics tracking rates between
SES subgroups for eighth-graders in California, Table 16 contains calculations of the tracking
rate gaps between SED and NSED students across school poverty levels .
Table 16
Tracking Rate Gaps Between SES Subgroups by School Poverty Quartile
School Poverty
Quartile
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Diff.
1 Low .16 .18 .20 .22 .21 .21 .23 .22 .22 .22 .21 .05
2 .16 .17 .17 .17 .16 .15 .16 .17 .17 .17 .18 .02
3 .12 .11 .12 .13 .12 .11 .13 .13 .14 .14 .15 .03
4 High .05 .08 .08 .08 .08 .10 .08 .10 .07 .09 .11 .06
Note. Calculated differences are based on the raw data, not rounded data displayed. All
differences are statistically significant, p < .001 (see Table 17).
All schools increased the gap between their NSED and SED subgroups between 2003 and
2013 with a two to six percentage point increase in the difference between subgroup tracking
rates. However, despite a small increase over time, the smallest difference in treatment between
the SES subgroups i s observable in the data for quartile 4 high poverty schools, which means
California's poorest schools had the smallest differences in how their NSED and SED students
were placed in General Mathematics . The bottom line is poor students (SED) are more likely to
be placed in General Mathematics than their NSED peers; however, the difference is greater for
more affluent schools (quartile 1) than poor schools (quartile 4) and although these numbers
decrease over time, the statement holds true in all years between 2003 and 2013 .
All differences between subgroups by school poverty quartile were found to be
statistically significant using a Kruskal -Wallis analysis. The results of the analysis are located in
Table 17. Effect sizes (f) for the difference in tracking between SES subgroups (SED and
ALGEBRA FOR ALL POLICY IMPACTS 92
NSED) are large for poverty quartile 1 low poverty schools (f ≥ 0.4) between 2003 and 2008 and
then moderate sized ( f ≥ 0.25) between 2009 and 2013 . Quartile 2 schools started with large
effect sizes for differences between SES groups' tracking in 2003, however reduced the gap in
tracking between subgroups over time with moderate effect sizes . High poverty sch ools (quartile
4) schools maintained small effect sizes for all years in the sample, meaning that at quartile 4
schools (0.25 ≥ f ≥ 0.1) a student’s poverty status had smaller effects on placement in Algebra I
than at low poverty schools (quartile 1) . Looking back at Figure 3, visually, a smaller gap
between SES subgroups is apparent as school poverty goes down . These differences are
statistically significant with substantial effect sizes . See Table 17 for all results .
ALGEBRA FOR ALL POLICY IMPACTS 93
Table 17
Kruskal-Wallis—Tracking Between SES Subgroups Within Poverty Quartile
Year Poverty Quartile Result f
2003 1 Low x
2
(1)=63.965, p <.001 0.35
2 x
2
(1)=157.105, p <.001 0.42
3 x
2
(1)=97.374, p <.001 0.31
4 High x
2
(1)=13.728, p <.001 0.15
2004 1 Low x
2
(1)=108.596, p <.001 0.42
2 x
2
(1)=131.828, p <.001 0.38
3 x
2
(1)=67.613, p <.001 0.27
4 High x
2
(1)=10.640, p=.001 0.14
2005 1 Low x
2
(1)=119.641, p <.001 0.43
2 x
2
(1)=135.513, p <.001 0.39
3 x
2
(1)=42.550, p <.001 0.22
4 High x
2
(1)=16.028, p <.001 0.17
2006 1 Low x
2
2(1)=115.602, p <.001 0.42
2 x
2
(1)=107.972, p <.001 0.34
3 x
2
(1)=55.302, p <.001 0.25
4 High x
2
(1)=13.652, p <.001 0.15
2007 1 Low x
2
(1)=113.143, p <.001 0.40
2 x
2
(1)=89.899, p <.001 0.31
3 x
2
(1)=37.669, p <.001 0.21
4 High x
2
(1)=12.918, p <.001 0.15
2008 1 Low x
2
(1)=113.089, p <.001 0.41
2 x
2
(1)=58.971, p <.001 0.27
3 x
2
(1)=29.862, p <.001 0.18
4 High x
2
(1)=21.140, p <.001 0.15
2009 1 Low x
2
(1)=114.174, p <.001 0.39
2 x
2
(1)=67.443, p <.001 0.26
3 x
2
(1)=46.623, p <.001 0.22
4 High x
2
(1)=9.197, p=.002 0.12
2010 1 Low x
2
(1)=100.413, p <.001 0.37
2 x
2
(1)=85.211, p <.001 0.29
3 x
2
(1)=35.990, p <.001 0.20
4 High x
2
(1)=11.467, p=.001 0.14
2011 1 Low x
2
(1)=108.248, p <.001 0.39
2 x
2
(1)=70.262, p <.001 0.26
3 x
2
(1)=43.830, p <.001 0.22
4 High x
2
(1)=5.434, p=.02 0.09
2012 1 Low x
2
(1)=105.075, p <.001 0.37
2 x
2
(1)=70.815, p <.001 0.26
3 x
2
(1)=42.071, p <.001 0.21
4 High x
2
(1)=6.373, p=.012 0.10
2013 1 Low x
2
(1)=95.928, p <.001 0.36
2 x
2
(1)=83.865, p <.001 0.31
3 x
2
(1)=50.088, p <.001 0.24
4 High x
2
(1)=19.305, p <.001 0.15
ALGEBRA FOR ALL POLICY IMPACTS 94
Achievement—Research Questions 3 and 4
Research questions 3 and 4 were employed to analyze students' success in higher level
math courses in grade eight . Opponents to the Algebra for All movement, Tom Loveless for
example, argue that placing the majority of students in higher level mathematics courses dilutes
the curriculum and bring s down the achievement levels of eighth grade mathematics (Loveless,
2008). To examine these issues the following research ques tions were used:
3. To what extent, if any, have California high and low poverty schools increased
traditionally disadvantaged eighth grade students' success in Algebra I and above
between2004 and 2013?
4. To what extent, if any, have California high and low poverty schools decreased
the gap between non -disadvantaged and traditionally disadvantaged eighth grade
students' success in Algebra I and above between 2004 and 2013?
All students analyses by school poverty level. As a point of comparison, first the data
for all student subgroups across school poverty quartiles were examined . While schools in all
poverty quartiles increased proficiency rates, quartile 4 high poverty schools made the largest
gains with a 68% increase . Students at the poorest schools increased proficiency rates from 25%
in 2003 to 43% in 2013 . Although the gap between the most affluent and most poor schools is
still large (67% proficient versus 42% in 2013), quartile 4 schools decreas ed that gap
significantly from a 41 percentage point difference in 2003 to a 25 percentage point difference in
2013. Although 43% proficient is nowhere near NCLB's 100% proficient requirement by 2014,
this 43% also represents a larger number of students t aking the course . In 2003, quartile 4
schools had a mean of 25% proficient students representing 4,778 students . In 2013, quartile 4
schools had a mean proficiency rate of 43%, which represents 30,884 students . So, although
ALGEBRA FOR ALL POLICY IMPACTS 95
there was a 68% increase in t he proficiency rate, there was actually a 546% increase in proficient
students in quartile 4 schools . Adding all students together (all quartiles), in 2003 there were
58,256 proficient eighth-graders and 134,547 in 2013 —an overall increase of 131% . Proficiency
rates are important because they are the measure required by NCLB to determine AY P. A school
succeeds or fails in the public eye based on proficiency data . In addition, it is important that
students have mastered content in one course before moving on to the next . Students who fail to
master the concepts in Algebra I are less likely to be successful in subsequent courses and may
have to repeat the course . In Table 18 , the mean proficiency scores for eighth grade students
taking an Algebra I or hig her course are shown for students in all subgroups separated by school
poverty level.
ALGEBRA FOR ALL POLICY IMPACTS 96
Table 18
Proficiency Means for All Students by School Poverty Quartile
Year
School Poverty Quartile
1 Low 2 3 4 High
2003
M 0.65 0.49 0.35 0.25
SD 0.29 0.26 0.26 0.24
2004
M 0.63 0.43 0.32 0.22
SD 0.28 0.26 0.24 0.21
2005
M 0.62 0.45 0.32 0.27
SD 0.27 0.26 0.25 0.24
2006
M 0.67 0.50 0.37 0.32
SD 0.26 0.27 0.25 0.25
2007
M 0.64 0.45 0.34 0.30
SD 0.26 0.26 0.24 0.23
2008
M 0.65 0.47 0.36 0.34
SD 0.26 0.26 0.24 0.23
2009
M 0.66 0.49 0.38 0.36
SD 0.26 0.25 0.24 0.24
2010
M 0.65 0.51 0.40 0.37
SD 0.25 0.25 0.23 0.24
2011
M 0.65 0.51 0.43 0.37
SD 0.23 0.24 0.24 0.24
2012
M 0.65 0.51 0.43 0.37
SD 0.24 0.24 0.24 0.23
2013
M 0.67 0.54 0.43 0.42
SD 0.22 0.24 0.24 0.23
% Change 3% 10% 23% 68%
ALGEBRA FOR ALL POLICY IMPACTS 97
Ethnicity subgroup analyses by school poverty level. While the all student group
shows increases in student performance, the achievement gaps between student ethnic groups are
well established . African American and Latino students, in general, usually score at lower levels
on achievement tests than their white and Asian peers . The data in Table 19, for the most part, is
consistent with t his pattern. Table 19 contains proficiency means for eighth-graders taking an
Algebra I or higher course between 2003 and 2013 by ethnicity and further broken down by the
school poverty quartile . In addition to differences between ethnic subgroups in eve ry school
poverty quartile, there are differences between the scores of students of the same ethnic subgroup
attending schools of different poverty levels .
For example, in 2003, 22% of African American students in affluent schools (quartile 1 ,
low poverty ) scored proficient or higher on their CST that year, while less than half that many
(10%) of African American students attending the poorest schools (quartile 4 , high poverty )
score proficient or higher . This pattern continues across the year s. In 2013, for example,
although there were great differences in student performance —a 138% increase for African
students at quartile 1 schools and a 204% increase for African American students at quartile 4
schools—the difference in performance across s chool poverty level still remains .
ALGEBRA FOR ALL POLICY IMPACTS 98
Table 19
Proficiency Means by Ethnicity Subgroup and School Poverty Quartile
School
Poverty
Quartile
Subgroup
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
%
Change
M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD
1 Low AfAm .22 .22 .23 .26 .30 .23 .43 .26 .35 .27 .40 .25 .41 .26 .42 .23 .44 .22 .49 .23 .51 .24 137%
Asian .85 .16 .82 .18 .82 .19 .86 .16 .84 .17 .84 .17 .85 .15 .85 .14 .85 .14 .85 .15 .86 .13 2%
Fil .59 .24 .53 .31 .58 .23 .67 .24 .61 .25 .69 .23 .70 .22 .68 .19 .67 .20 .71 .17 .72 .20 23%
Lat .43 .28 .45 .27 .50 .26 .55 .28 .52 .28 .52 .27 .54 .28 .53 .25 .55 .24 .57 .25 .59 .24 36%
Wh .67 .27 .64 .26 .64 .24 .70 .24 .66 .25 .65 .25 .67 .24 .67 .23 .67 .22 .67 .22 .69 .21 3%
2 AfAm .19 .19 .20 .18 .19 .19 .26 .20 .24 .22 .32 .23 .31 .22 .36 .23 .36 .22 .36 .24 .37 .23 93%
Asian .66 .25 .59 .24 .61 .24 .69 .21 .63 .23 .70 .20 .68 .22 .70 .22 .71 .20 .72 .19 .74 .18 11%
Fil .50 .26 .42 .24 .40 .22 .54 .24 .43 .20 .54 .23 .55 .24 .58 .22 .55 .20 .59 .22 .65 .20 30%
Lat .34 .25 .32 .24 .34 .24 .39 .26 .35 .25 .40 .26 .40 .25 .44 .25 .44 .24 .46 .25 .47 .25 40%
Wh .50 .25 .46 .25 .49 .25 .53 .26 .48 .25 .51 .25 .53 .24 .56 .23 .55 .23 .55 .23 .58 .24 15%
3 AfAm .14 .17 .12 .13 .14 .17 .19 .20 .18 .18 .24 .21 .25 .20 .25 .20 .28 .21 .32 .24 .28 .21 98%
Asian .54 .28 .51 .27 .52 .26 .59 .24 .56 .24 .60 .23 .62 .23 .64 .21 .68 .20 .66 .22 .68 .22 28%
Fil .32 .23 .33 .21 .36 .21 .48 .23 .40 .23 .48 .19 .55 .19 .55 .19 .58 .21 .57 .22 .52 .23 66%
Lat .27 .24 .25 .22 .25 .23 .31 .24 .30 .23 .32 .22 .35 .23 .36 .22 .40 .24 .41 .24 .40 .24 50%
Wh .36 .24 .34 .24 .35 .25 .40 .25 .37 .24 .41 .23 .42 .24 .43 .23 .45 .22 .46 .23 .50 .24 40%
4 High AfAm .10 .13 .09 .12 .11 .16 .19 .24 .19 .21 .18 .19 .20 .21 .25 .22 .22 .22 .26 .23 .30 .22 203%
Asian .42 .30 .41 .26 .43 .23 .50 .23 .51 .24 .53 .21 .58 .21 .57 .21 .57 .23 .56 .26 .67 .21 59%
Fil .36 .29 .35 .24 .34 .23 .41 .23 .42 .25 .52 .21 .56 .18 .53 .23 .58 .22 .67 .17 .68 .10 87%
Lat .20 .22 .19 .20 .25 .23 .31 .25 .28 .22 .32 .23 .36 .23 .36 .24 .36 .23 .37 .23 .41 .23 102%
Wh .29 .20 .23 .22 .28 .23 .38 .23 .35 .19 .36 .21 .36 .21 .35 .20 .33 .21 .38 .22 .43 .23 52%
ALGEBRA FOR ALL POLICY IMPACTS 99
Despite the differences in student achievement across school poverty levels, the
proficiency rates of African American students increased dramatically between 2003 and 2013
for schools in all poverty quartiles. These gains, although dra matic, still leave room for growth
with the African American student subgroup scoring the lowest of all subgroups in all school
poverty quartiles. Similar results are observable for Latino students who improved mathematics
performance over time, although at lower levels —a 36% increase in quartile 1 low poverty
schools and a 104% increase at quartile 4 high poverty schools. Still, a gap continued to exist for
Latino students across school poverty levels . In 2003, there was a 24 percentage point difference
in the performance of Latino students across school poverty levels . While this gap decreased to
17% in 2013, a gap is still present .
Even for students not considered traditionally disadvantaged ( white and Asian, for
example), there are differences in performance across school poverty levels . While Asian
students in quartile 4 high poverty schools had the highest performance, in terms of proficiency,
across the ethnic subgroups (43% in 2003 and 65% in 2013), at quartile 1 low poverty schools
these numbers are much higher with 86% proficient in 2003 and 89% proficient in 2013 —a
difference of 53 percentage points in 2003 and 24 in 2013 . Again, the differences have shrunk
over time, but are still observab le. For quartile 4 schools though, the achievement gap between
white and Latino students has become quite small . In 2013, there was only a two percentage
point difference in proficiency rates between white and Latino students . Although the
proficiency r ates for both subgroups of students increased over time, Latino students increased at
a higher rate resulting in almost a complete closing of the ga p. A similar pattern is observable for
quartile 1 schools; however, a 12 percentage point gap still remains but is nearly half the gap of
23 points in 2003 .
ALGEBRA FOR ALL POLICY IMPACTS 100
Table 20 contains the Kruskal -Wallis analyses for the differences between poverty level
quartiles in the proficiency rates for the same subgrou p. For example, the proficiency rates for
the African American subgroups are compared to determine whether or not there are significant
differences in the proficiency rate s across school poverty levels . Only significant findings are
reported in the table . Effect sizes are in the moderate range for many subgroups; however, the
effect sizes for the Asian subgroup are quite large —meaning that there is a great amount of
variance between the differences in achievement for Asian students across school poverty
quartiles.
ALGEBRA FOR ALL POLICY IMPACTS 101
Table 20
Kruskal-Wallis Achievement Differences Between Poverty Quartiles by Ethnicity
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2003 AfAm x
2
(3)=11.71, p = .008 2 - 4 .008 0.22
Asian x
2
(3)=115.806, p <.001 1 - 2 <.001 0.58
1 - 3 <.001
1 - 4 <.001
2 - 3 .003
2 - 4 <.001
Fil x
2
(3)=18.902, p <.001 1 - 3 .013 0.42
2 - 3 .001
Lat x
2
(3)=65.735, p <.001 1 - 3 <.001 0.29
1 - 4 <.001
2 - 3 .004
2 - 4 <.001
3 - 4 .001
Wh x
2
(3)=212.367, p <.001 1 - 2 <.001 0.49
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
2004 AfAm x
2
(3)=24.328, p <.001 2 - 3 .006 0.29
2 - 4 <.001
Asian x
2
(3)=146.627, p <.001 1 - 2 <.001 0.66
1 - 3 <.001
1 - 4 <.001
2 - 4 .001
Fil x
2
(3)=9.919, p <.001 1 - 3 .018 0.27
Lat x
2
(3)=96.587, p <.001 1 - 2 .001 0.33
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 .014
Wh x
2
(3)=247.327, p <.001 1 - 2 <.001 0.52
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 .002
ALGEBRA FOR ALL POLICY IMPACTS 102
Table 20 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2005 AfAm x
2
(3)=25.152, p <.001 1 - 3 .006 0.28
1 - 4 <.001
2 - 4 .001
Asian x
2
(3)=159.745, p <.001 1 - 2 <.001 0.66
1 - 3 <.001
1 - 4 <.001
2 - 3 .028
2 - 4 <.001
Fil x
2
(3)=24.338, p <.001 1 - 2 .003 0.41
1 - 3 <.001
1 - 4 .002
Lat x
2
(3)=118.041, p <.001 1 - 2 <.001 0.35
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
Wh x
2
(3)=244.882, p <.001 1 - 2 <.001 0.51
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
2006 AfAm x
2
(3)=35.516, p <.001 1 - 2 .044 0.32
1 - 3 <.001
1 - 4 <.001
2 - 3 .009
2 - 4 .001
Asian x
2
(3)=168.839, p <.001 1 - 2 <.001 0.66
1 - 3 <.001
1 - 4 <.001
2 - 3 .009
2 - 4 <.001
Fil x
2
(3)=18.748, p <.001 1 - 3 .001 0.34
1 - 4 .002
Lat x
2
(3)=108.129, p <.001 1 - 2 <.001 0.32
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
Wh x
2
(3)=230.6, p <.001 1 - 2 <.001 0.48
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 103
Table 20 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2007 AfAm x
2
(3)=23.171, p <.001 1 - 2 .027 0.24
1 - 3 <.001
1 - 4 <.001
Asian x
2
(3)=168.607, p <.001 1 - 2 <.001 0.66
1 - 3 <.001
1 - 4 <.001
2 - 4 .017
Fil x
2
(3)=23.296, p <.001 1 - 2 .001 0.36
1 - 3 <.001
1 - 4 .013
Lat x
2
(3)=111.783, p <.001 1 - 2 <.001 0.31
1 - 3 <.001
1 - 4 <.001
2 - 4 .001
Wh x
2
(3)=222.555, p <.001 1 - 2 <.001 0.47
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
2008 AfAm x
2
(3)=50.39, p <.001 1 - 3 .001 0.36
1 - 4 <.001
2 - 3 .004
2 - 4 <.001
3 - 4 .036
Asian x
2
(3)=169.288, p <.001 1 - 2 <.001 0.65
1 - 3 <.001
1 - 4 <.001
2 - 3 .025
2 - 4 <.001
Fil x
2
(3)=23.784, p <.001 1 - 2 .008 0.35
1 - 3 <.001
1 - 4 .013
Lat x
2
(3)=93.196, p <.001 1 - 2 <.001 0.27
1 - 3 <.001
1 - 4 <.001
2 - 3 .001
2 - 4 <.001
Wh x
2
(3)=210.889, p <.001 1 - 2 <.001 0.45
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 104
Table 20 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2009 AfAm x
2
(3)=40.717, p <.001 1 - 3 <.001 0.31
1 - 4 <.001
2 - 4 <.001
Asian x
2
(3)=138.362, p <.001 1 - 2 <.001 0.57
1 - 3 <.001
1 - 4 <.001
2 - 4 .020
Fil x
2
(3)=21.018, p <.001 1 - 2 <.001 0.32
1 - 3 .001
Lat x
2
(3)=91.983, p <.001 1 - 2 <.001 0.27
1 - 3 <.001
1 - 4 <.001
2 - 3 .030
Wh x
2
(3)=203.884, p <.001 1 - 2 <.001 0.44
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
2010 AfAm x
2
(3)=46.147, p <.001 1 - 3 <.001 0.34
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
Asian x
2
(3)=131.92, p <.001 1 - 2 <.001 0.55
1 - 3 <.001
1 - 4 <.001
2 - 4 <.001
Fil x
2
(3)=14.13, p=.003 1 - 3 .009 0.25
1 - 4 .040
Lat x
2
(3)=100.388, p <.001 1 - 2 <.001 0.27
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
Wh x
2
(3)=212.876, p <.001 1 - 2 <.001 0.45
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 105
Table 20 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2011 AfAm x
2
(3)=56.393, p <.001 1 - 3 <.001 0.37
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
Asian x
2
(3)=115.465, p <.001 1 - 2 <.001 0.51
1 - 3 <.001
1 - 4 <.001
2 - 4 <.001
3 - 4 .016
Fil x
2
(3)=12.003, p=.007 1 - 2 .006 0.23
Lat x
2
(3)=100.926, p <.001 1 - 2 <.001 0.26
1 - 3 <.001
1 - 4 <.001
2 - 3 .035
2 - 4 <.001
Wh x
2
(3)=201.1, p <.001 1 - 2 <.001 0.44
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 .002
2012 AfAm x
2
(3)=44.955, p <.001 1 - 2 0.002 0.32
1 - 3 <.001
1 - 4 <.001
2 - 4 .001
Asian x
2
(3)=119.152, p <.001 1 - 2 <.001 0.53
1 - 3 <.001
1 - 4 <.001
2 - 4 .002
Fil x
2
(3)=19.905, p <.001 1 - 2 .002 0.31
1 - 3 <.001
Lat x
2
(3)=124.527, p <.001 1 - 2 <.001 0.29
1 - 3 <.001
1 - 4 <.001
2 - 4 <.001
3 - 4 .026
Wh x
2
(3)=184.177, p <.001 1 - 2 <.001 0.41
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 .035
ALGEBRA FOR ALL POLICY IMPACTS 106
Table 20 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2013 AfAm x
2
(3)=43.256, p <.001 1 - 2 .005 0.33
1 - 3 <.001
1 - 4 <.001
2 - 3 .018
Asian x
2
(3)=96.68, p <.001 1 - 2 <.001 0.47
1 - 3 <.001
1 - 4 <.001
Fil x
2
(3)=32.578, p <.001 1 - 3 <.001 0.40
2 - 3 .014
3 - 4 .030
Lat x
2
(3)=121.559, p <.001 1 - 2 <.001 0.29
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 .001
Wh x
2
(3)=161.384, p <.001 1 - 2 <.001 0.38
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 107
Table 21 contains a summary of the gaps between the highest performing and lowest
performing subgroups by school poverty quartile, which is a difference between the Asian and
African American subgroup s in all cases except for 2012 at quartile 4 high poverty schools
where the Filipino subgroup had the highest proficiency rates . For example, in 2003 , quartile 1
low poverty schools had a 65 percentage point gap in proficiency between their Asian subgroup
and African American subgroup but decreased this gap to a 38 percentage point difference in
2013—a de crease of 27 percentage points . Quartile 1 schools decreased their gap the most,
while quartile 2 through 4 schools only made small gains in closing the achievement gap.
Table 21
Proficiency Gaps Between Ethnicity Subgroups by School Poverty Quartile
School
Poverty
Quartile
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
1 Low .63 .59 .52 .43 .49 .44 .44 .43 .41 .36 .35
2 .47 .39 .42 .43 .39 .38 .37 .34 .35 .36 .37
3 .4 .39 .38 .4 .38 .36 .37 .39 .4 .34 .4
4 High .32 .32 .32 .31 .32 .35 .38 .32 .35 .3 .37
Note. All gaps are statistically significant, p < .001. See Table 22.
The gaps between ethnic subgroups' Algebra I (or higher) proficiency rates at each
poverty level are statistically significant and presented in Table 22. Effect sizes were large (f
>0.4) for nearly all analyses. Noteworthy for each year studied, effect sizes between ethnicity
subgroups decrease as school poverty level increases when comparing quartile 1 low poverty to
quartile 4 high poverty schools. The same does not hold true between quartile 2 and 3 schools.
ALGEBRA FOR ALL POLICY IMPACTS 108
Table 22
Kruskal-Wallis—Achievement Between Ethnicity Subgroups by Poverty Quartile
Year
Poverty
Quartile
Result f
Adjusted p Between Subgroups
Asian-
Fil
Asian-
Wh
Asian-
Lat
Asian-
AfAm
Fil-Wh
Fil-
AfAm
Fil-Lat
Wh-
AfAm
Wh-
Lat
AfAm-
Lat
2003 1 Low x
2
(4)=116.215, p <.001 0.57 .017 <.001 <.001 <.001 <.001 <.001
2 x
2
(4)=201.167, p <.001 0.52 .002 <.001 <.001 <.001
<.001 .001 <.001 <.001 .001
3 x
2
(4)=169.325, p <.001 0.46 <.001 <.001 <.001 <.001
<.001
<.001 <.001 <.001
4 High x
2
(4)=68.724, p <.001 0.42 <.001 <.001 .001 <.001 .004 .001
2004 1 Low x
2
(4)=145.095, p <.001 0.54 <.001 <.001 <.001 <.001 .040 <.001 <.001
2 x
2
(4)=178.327, p <.001 0.47 .001 <.001 <.001 <.001
<.001
<.001 <.001 .001
3 x
2
(4)=196.364, p <.001 0.51 .014 <.001 <.001 <.001
<.001
<.001 <.001 <.001
4 High x
2
(4)=92.816, p <.001 0.47 <.001 <.001 <.001 <.001 .01 <.001 <.001
2005 1 Low x
2
(4)=159.434, p <.001 0.52 <.001 <.001 <.001 <.001 .015 <.001 <.001
2 x
2
(4)=215.787, p <.001 0.52 <.001 <.001 <.001 <.001
<.001
<.001 <.001 <.001
3 x
2
(4)=196.916, p <.001 0.49
<.001 <.001 <.001
<.001 .002 <.001 <.001 <.001
4 High x
2
(4)=89.028, p <.001 0.45 .007 <.001 <.001 <.001 <.001 <.001
2006 1 Low x
2
(4)=152.150, p <.001 0.49 <.001 <.001 <.001 <.001 .011 <.001 <.001
2 x
2
(4)=229.503, p <.001 0.50 .001 <.001 <.001 <.001
<.001 <.001 <.001 <.001 <.001
3 x
2
(4)=200.592, p <.001 0.49
<.001 <.001 <.001
<.001 <.001 <.001 <.001 <.001
4 High x
2
(4)=86.626, p <.001 0.43 <.001 <.001 .001 <.001 <.001
2007 1 Low x
2
(4)=197.273, p <.001 0.52 <.001 <.001 <.001 <.001
.002
<.001 <.001
2 x
2
(4)=213.320, p <.001 0.48 <.001 <.001 <.001 <.001
<.001 .034 <.001 <.001 <.001
3 x
2
(4)=183.909, p <.001 0.47 .010 <.001 <.001 <.001
<.001 .011 <.001 .001 <.001
4 High x
2
(4)=93.971, p <.001 0.44
.013 <.001 <.001
<.001
<.001 .021 .002
2008 1 Low x
2
(4)=186.480, p <.001 0.52 <.001 <.001 <.001 <.001 <.001 .002 <.001 <.001
2 x
2
(4)=169.191, p <.001 0.46 .002 <.001 <.001 <.001
<.001 <.001 <.001 <.001 .044
3 x
2
(4)=191.782, p <.001 0.47
<.001 <.001 <.001
<.001 <.001 <.001 <.001 .001
4 High x
2
(4)=180.535, p <.001 0.50 <.001 <.001 <.001 .011 <.001 <.001 <.001 <.001
2009 1 Low x
2
(4)=214.542, p <.001 0.50 <.001 <.001 <.001 <.001
<.001 .001 <.001 <.001 .01
2 x
2
(4)=201.272, p <.001 0.46 .003 <.001 <.001 <.001
<.001 <.001 <.001 <.001 .003
3 x
2
(4)=192.815, p <.001 0.46
<.001 <.001 <.001 <.001 <.001 <.001 <.001 .005 <.001
4 High x
2
(4)=111.722, p <.001 0.48
<.001 <.001 <.001
<.001 <.001 <.001
<.001
ALGEBRA FOR ALL POLICY IMPACTS 109
Table 22 Continued
Year
Poverty
Quartile
Result f
Adjusted p Between Subgroups
Asian-
Fil
Asian-
Wh
Asian-
Lat
Asian-
AfAm
Fil-Wh
Fil-
AfAm
Fil-Lat
Wh-
AfAm
Wh-
Lat
AfAm-
Lat
2010 1 Low x
2
(4)=243.173, p <.001 0.56 <.001 <.001 <.001 <.001 <.001 .001 <.001 <.001
2 x
2
(4)=186.460, p <.001 0.42 .009 <.001 <.001 <.001
<.001 <.001 <.001 <.001 .043
3 x
2
(4)=219.961, p <.001 0.51
<.001 <.001 <.001 .001 <.001 <.001 <.001 .002 <.001
4 High x
2
(4)=90.407, p <.001 0.40 <.001 <.001 <.001 <.001 .034 .003 <.001
2011 1 Low x
2
(4)=233.858, p <.001 0.55 <.001 <.001 <.001 <.001
<.001 .003 <.001 <.001 .040
2 x
2
(4)=204.147, p <.001 0.44 <.001 <.001 <.001 <.001
<.001 .001 <.001 <.001 .006
3 x
2
(4)=210.160, p <.001 0.49
<.001 <.001 <.001 .001 <.001 <.001 <.001 .01 <.001
4 High x
2
(4)=111.328, p <.001 0.43
<.001 <.001 <.001 .004 <.001 .008 <.001
<.001
2012 1 Low x
2
(4)=232.361, p <.001 0.51 <.001 <.001 <.001 <.001 <.001 .001 <.001 <.001
2 x
2
(4)=194.742, p <.001 0.43 .002 <.001 <.001 <.001
<.001 <.001 <.001 <.001 .001
3 x
2
(4)=145.729, p <.001 0.40
<.001 <.001 <.001 .025 <.001 <.001 <.001 .033 <.001
4 High x
2
(4)=80.450, p <.001 0.36 .001 <.001 <.001 .001 <.001 <.001 .001 <.001
2013 1 Low x
2
(4)=218.560, p <.001 0.52 <.001 <.001 <.001 <.001 <.001 <.001 <.001 <.001
2 x
2
(4)=168.093, p <.001 0.44
<.001 <.001 <.001
<.001 <.001 <.001 <.001 .005
3 x
2
(4)=201.235, p <.001 0.47 .001 <.001 <.001 <.001
<.001 <.001 <.001 <.001 <.001
4 High x
2
(4)=133.59, p <.001 0.41 <.001 <.001 <.001 <.001 <.001 <.001 <.001 <.001
ALGEBRA FOR ALL POLICY IMPACTS 110
Although the Kruskal-Wallis indicates that differences in achievement between
subgroups continue to be statistically significant, there have been practical differences and
increasing proficiency, as reported in Table 21. Additionally, the Kruskal-Wallis and effect size
analyses do not provide a linkage to actual achievement scores as they are based on ranks. On
the following page, these reductions in gaps can be viewed visually in order to allow for
meaningful interpretation. Figure 4 shows line graphs for the years 2003, 2006, 2009, 2012, and
2013—every third year plus the final year. The ethnicity subgroups are defined by the colored
lines and the x-axis separates data by school poverty quartile.
The gaps between lines in Figure 4 represent achievement gaps in subgroups, whereas the
slope of the line represents the differences in performance between school poverty quartiles.
Looking across years there is a slight narrowing of the gaps between most subgroups and a
flattening of the lines across school poverty levels, which indicates that although gaps between
subgroups still existed they were becoming smaller and that the differences between poverty
quartiles lessened over time. Also of note is the very small achievement difference between the
white and Latino subgroups in quartile 4 high poverty schools. In 2013, Latino students at
quartile 4 schools performed at rates similar to those of Asian students in 2003; however, the gap
between Latino and Asian students has remained fairly consistent with the Asian subgroup
increasing performance by 26 percentage points.
It is promising that all groups have increased performance over time, but it is clear that
the differences between school poverty levels is correlated with performance of students beyond
the effects of ethnicity alone. In 2003, Asian students in quartile 4 schools (the highest
performing subgroup) scored at rates similar to Latino students in quartile 1 low poverty schools
(the second lowest performing subgroup). And in the years 2006 through 2013, African
ALGEBRA FOR ALL POLICY IMPACTS 111
American students at quartile 1 schools (the lowest performing subgroup at those schools) had a
mean proficiency rate higher than that of white students in quartile 4 schools, which suggests that
a school's poverty rate has effects greater than that of ethnicity. In essence, the more students
participating in FRPM, the worse the outcomes for students.
ALGEBRA FOR ALL POLICY IMPACTS 112
Figure 4. Proficiency mean line graphs by ethnicity subgroup and school poverty quartile .
ALGEBRA FOR ALL POLICY IMPACTS 113
Language subgroup analyses by school poverty level. Data for eighth grade proficiency levels
over time by language subgroup are presented in Table 23 . Bearing in mind the small sample of
quartile 1 low poverty schools, eighth grade students in all language proficiency subgroups grew
in mathematics proficiency over time with the exception of quartile 1 schools that star ted at
already high rates between 66% and 79% proficient . While students in the English Only group
grew by an increase of 2%, the RFEP and EL subgroups experienced a 4% and 34% decrease
respectively. Of note however, even with the decrease in proficiency rates, the students in all
language subgroups in quartile 1 schools scored higher than their counterparts at less affluent
schools (quartiles 2 -4) with the lowest achievement at quartile 4 high poverty schools, again
illustrating the impact of school pove rty level on achievement . Quartile 4 schools experienced
the greatest growth in achievement across poverty quartiles . The English Only subgroup of
quartile 4 grew the most overall with a 9 6% increase, which represents a change from 20%
proficient in 2003 to 39% in 2013 . Similarly, like the results by ethnicity, there are still
differences between school poverty levels, with a decrease in achievement levels with each
increase of poverty quartile —although there is little difference by 2013 between quartile 3 and 4
schools. Also of note, the RFEP subgroup outscored the English Only subgroup at each quartile
level with a difference of 3 to 10 mean percentage points in 2013 .
Data for quartile 1 schools must be evaluated with caution for this subgroup analysis as
very few affluent schools in California have significant numbers of English Learners taking
Algebra I or higher . In 2003, the quartile 1 sample includes 25 schools with significant numbers
of English Learners , while the quartile 2 -4 samples contains between 2.5 and 5.9 times more
schools. The same is true for the RFEP subgroup where there are 57 schools in the quartile 1
sample and 2.4 to 3.4 more schools in the quartile 2 -4 samples. When comparing the number of
ALGEBRA FOR ALL POLICY IMPACTS 114
quartile 1 schools in the Algebra I proficiency sample with the numbers of schoo l included in the
tracking file , there are 115 schools in the sample for both RFEPS and EL students, which mean s
that there are few affluent schools that place enough EL students into Algebra I or higher to
receive publicly available scores .
ALGEBRA FOR ALL POLICY IMPACTS 115
Table 23
Proficiency Means by Language Proficiency and School Poverty Quartile
School
Poverty
Quartile
Subgroup
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
%
change
M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD
1 Low RFEP .78 .24 .71 .26 .74 .23 .81 .18 .75 .23 .72 .24 .73 .23 .73 .21 .72 .21 .72 .21 .74 .20 -4%
EL .71 .28 .59 .31 .59 .31 .57 .31 .47 .30 .47 .32 .47 .34 .47 .32 .43 .29 .45 .29 .47 .31 -34%
Eng.
Only
.65 .28 .63 .28 .62 .26 .67 .26 .64 .26 .65 .26 .65 .25 .65 .25 .65 .23 .65 .23 .67 .22 2%
2 RFEP .48 .30 .43 .28 .47 .26 .51 .27 .46 .25 .52 .25 .52 .24 .57 .24 .55 .23 .57 .23 .57 .23 18%
EL .26 .27 .16 .21 .15 .18 .20 .23 .15 .18 .19 .22 .19 .19 .23 .21 .25 .23 .25 .21 .29 .21 12%
Eng.
Only
.49 .26 .44 .25 .46 .26 .51 .27 .45 .26 .48 .26 .49 .25 .52 .24 .51 .24 .51 .24 .54 .25 11%
3 RFEP .36 .28 .34 .26 .36 .26 .42 .25 .41 .24 .42 .24 .46 .23 .47 .23 .50 .23 .52 .24 .49 .24 36%
EL .19 .26 .12 .17 .13 .17 .16 .19 .14 .18 .16 .19 .20 .20 .20 .21 .21 .21 .21 .21 .21 .20 11%
Eng.
Only
.33 .25 .31 .24 .31 .24 .35 .25 .32 .23 .36 .23 .37 .24 .38 .23 .41 .24 .43 .24 .42 .24 27%
4 High RFEP .30 .26 .28 .23 .33 .24 .40 .25 .36 .23 .43 .24 .44 .24 .46 .24 .47 .23 .45 .23 .49 .23 62%
EL .13 .19 .08 .12 .11 .17 .14 .18 .15 .19 .14 .16 .20 .20 .21 .22 .21 .21 .18 .21 .20 .20 62%
Eng.
Only
.20 .19 .20 .21 .22 .22 .30 .26 .27 .22 .30 .22 .31 .23 .34 .24 .31 .23 .34 .22 .39 .23 96%
ALGEBRA FOR ALL POLICY IMPACTS 116
In Table 24, the Kruskal -Wallis results of achievement differences in language
proficiency subgroups across poverty quartiles are presented . Mainly the tests were looking for
the significanc e of differences in the achievement of a subgroup depending upon the poverty of
the school the students attended . The greatest variation across poverty levels is for the English
Only subgrou p. For most years, there is a significant difference between each of the poverty
quartiles. There are six poverty quartile comparisons possible: quartile 1 (low poverty) compared
to quartiles 2, 3, and 4 (high poverty); quartile 2 compared to quartiles 3 and 4; and quartile 3
compared to quartile 4 . For most years of t he comparisons between poverty quartile for the
English Only subgroup, all six comparisons were statistically significant ( p < .01) . The effect
sizes ( f) were all large falling between 0.49 and 0.58 . This demonstrates that poverty was a large
factor in a chievement for the English Only subgrou p. The RFEP subgroup also had great
variation between poverty quartiles . In most years under study, four or five of the six possible
poverty quartile comparisons were statistically significant ( p < .01) and effect si zes were medium
to large ranging from 0.38 to 0.48 . These data support that school poverty level has a large effect
on achievement for RFEP students . For the EL subgroup, the variation between quartiles 2, 3,
and 4 was not statistically significant, with the exception of 2003, 2004, 2012 and 2013 where
the differences between quartiles 2 and 4 were significant. Yet, for all years , the difference in
mean proficiency was statistically significant (p < .05) between quartile 1 low poverty schools
and quartiles 2, 3, and 4 . Quartile 1 school's mean proficiency rates were significantly higher
than the proficiency rates for quartile 2, 3, and 4 schools . The effect sizes ( f) of poverty quartile
for the EL subgroup were medium to large, between 0.25 and 0 .4 for all years, except for 2009,
which had a small effect size ( f = 0.23) . This provides evidence that the positive effects of being
at a low poverty school are quite high for EL students .
ALGEBRA FOR ALL POLICY IMPACTS 117
Table 24
Kruskal-Wallis—Achievement by Ethnicity Subgroup Within Poverty Quartile
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2003 RFEP x
2
(3)=99.63, p <.001 1 - 2 < .001 0.44
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
EL x
2
(3)=52.658, p <.001 1 - 2 < .001 0.40
1 - 3 < .001
1 - 4 < .001
2 - 4 .009
EO x
2
(3)=340.326, p <.001 1 - 2 < .001 0.58
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 < .001
2004 RFEP x
2
(3)=125.421, p <.001 1 - 2 < .001 0.46
1 - 3 < .001
1 - 4 < .001
2 - 3 .009
2 - 4 < .001
EL x
2
(3)=48.337, p <.001 1 - 2 < .001 0.35
1 - 3 < .001
1 - 4 < .001
2 - 4 .04
EO x
2
(3)=377.508, p <.001 1 - 2 < .001 0.59
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 < .001
2005 RFEP x
2
(3)=148.505, p <.001 1 - 2 < .001 0.47
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
EL x
2
(3)=64.374, p <.001 1 - 2 < .001 0.38
1 - 3 < .001
1 - 4 < .001
EO x
2
(3)=391.423, p <.001 1 - 2 < .001 0.58
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 < .001
ALGEBRA FOR ALL POLICY IMPACTS 118
Table 24 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2006 RFEP x
2
(3)=170.589, p <.001 1 - 2 < .001 0.48
1 - 3 < .001
1 - 4 < .001
2 - 3 .001
2 - 4 < .001
EL x
2
(3)=54.378, p <.001 1 - 2 < .001 0.33
1 - 3 < .001
1 - 4 < .001
EO x
2
(3)=354.001, p <.001 1 - 2 < .001 0.54
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
2007 RFEP x
2
(3)=183.039, p <.001 1 - 2 < .001 0.48
1 - 3 < .001
1 - 4 < .001
2 - 4 < .001
EL x
2
(3)=54.855, p <.001 1 - 2 < .001 0.31
1 - 3 < .001
1 - 4 < .001
EO x
2
(3)=376.412, p <.001 1 - 2 < .001 0.55
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 .031
2008 RFEP x
2
(3)=140.781, p <.001 1 - 2 < .001 0.39
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
EL x
2
(3)=59.167, p <.001 1 - 2 < .001 0.30
1 - 3 < .001
1 - 4 < .001
EO x
2
(3)=368.152, p <.001 1 - 2 < .001 0.52
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 .009
ALGEBRA FOR ALL POLICY IMPACTS 119
Table 24 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2009 RFEP x
2
(3)=150.256, p <.001 1 - 2 < .001 0.39
1 - 3 < .001
1 - 4 < .001
2 - 3 .017
2 - 4 .001
EL x
2
(3)=32.337, p <.001 1 - 2 < .001 0.23
1 - 3 < .001
1 - 4 < .001
EO x
2
(3)=363.194, p <.001 1 - 2 < .001 0.51
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 .018
2010 RFEP x
2
(3)=172.099, p <.001 1 - 2 < .001 0.40
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
EL x
2
(3)=49.604, p <.001 1 - 2 < .001 0.27
1 - 3 < .001
1 - 4 < .001
EO x
2
(3)=343.042, p <.001 1 - 2 < .001 0.49
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
2011 RFEP x
2
(3)=156.496, p <.001 1 - 2 < .001 0.37
1 - 3 < .001
1 - 4 < .001
2 - 3 .031
2 - 4 < .001
EL x
2
(3)=41.359, p <.001 1 - 2 < .001 0.25
1 - 3 < .001
1 - 4 < .001
EO x
2
(3)=374.041, p <.001 1 - 2 < .001 0.51
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 < .001
ALGEBRA FOR ALL POLICY IMPACTS 120
Table 24 Continued
Year Subgroup Result
Poverty Quartile Comparison
1 = Low; 4 = High
Adj. p f
2012 RFEP x
2
(3)=161.511, p <.001 1 - 2 < .001 0.38
1 - 3 < .001
1 - 4 < .001
2 - 3 .02
2 - 4 < .001
3 - 4 .002
EL x
2
(3)=61.618, p <.001 1 - 2 < .001 0.32
1 - 3 < .001
1 - 4 < .001
2 - 4 .001
EO x
2
(3)=331.288, p <.001 1 - 2 < .001 0.46
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 < .001
2013 RFEP x
2
(3)=175.073, p <.001 1 - 2 < .001 0.39
1 - 3 < .001
1 - 4 < .001
2 - 3 .001
2 - 4 < .001
EL x
2
(3)=47.009, p <.001 1 - 3 < .001 0.29
1 - 4 < .001
2 - 3 .009
2 - 4 .003
EO x
2
(3)=341.808, p <.001 1 - 2 < .001 0.47
1 - 3 < .001
1 - 4 < .001
2 - 3 < .001
2 - 4 < .001
3 - 4 < .001
In Table 25 on the following page, the percentage point difference (the gap) between the
highest performing subgroup and the lowest performing subgroup in language proficiency is
reported by school poverty quartile . Quartile 1 low poverty schools increased the gap between
their highest and lowest performing subgroups by 15 percent age points between 2003 and 2013 .
For all school quartiles, the gap between subgroups increased over the 11 years studied . This is
ALGEBRA FOR ALL POLICY IMPACTS 121
due to little change in mean proficiency rates across time for EL students while the English Only
and RFEP subgroups increased proficiency rates.
Table 25
Achievement Gaps Across Language Proficiency by Poverty Quartile
School Poverty
Quartile
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Low 1 .13 .14 .16 .25 .30 .27 .27 .26 .30 .28 .28
2 .24 .29 .33 .32 .32 .33 .34 .35 .32 .33 .29
3 .18 .23 .24 .27 .27 .27 .27 .28 .29 .31 .29
High 4 .18 .20 .22 .25 .22 .29 .25 .26 .27 .28 .30
To examine the achievement differences between subgroups within each poverty level,
Kruskal-Wallis tests were conducted for the years 2003 – 2013. In Table 26, the results along
with pairwise analyses comparing the differences between subgroups are presented . Only
significant results appear in the table . The data illustrates that the differences between language
proficiency subgroups is significant between the EL subgroup and RFEP and English Only
subgroups at nearly all school poverty levels and over nearly all years . The effect sizes of these
differences increase as school poverty increases . There are small to insignificant effect sizes ( f <
0.25) at quartile 1 low poverty schools, medium to large effect sizes ( f > 0.25 ) for quartile 2 and
3 schools, and large effect sizes ( f < 0.4 ) for quartile 4 high poverty schools. The effect of
subgroup across poverty quartiles actually increases over time, until 2008 when a tapering off
occurs and effect sizes remain fairly stable through 2013 .
ALGEBRA FOR ALL POLICY IMPACTS 122
Table 26
Kruskal-Wallis—Achievement Between Language Proficiency by Poverty Quartile
Year
Poverty
Quartile
Result f
Adj. Significance Between Subgroups
RFEP - EO RFEP - EL EL- EO
2003 1 Low x
2
(2)=266.306, p <.001 0.18 .004
2 x
2
(2)=38.704, p <.001 0.25
<.001 <.001
3 x
2
(2)=73.435, p <.001 0.32
<.001 <.001
4 High x
2
(2)=67.076, p <.001 0.38 <.001 <.001 <.001
2004 1 Low x
2
(2)=7.771, p=.021 0.13 .023
2 x
2
(2)=84.991, p <.001 0.37
<.001 <.001
3 x
2
(2)=139.741, p <.001 0.44
<.001 <.001
4 High x
2
(2)=111.272, p <.001 0.47 <.001 <.001 <.001
2005 1 Low x
2
(2)=17.796, p <.001 0.19 <.001 .026
2 x
2
(2)=111.381, p <.001 0.42
<.001 <.001
3 x
2
(2)=160.089, p <.001 0.45 .026 <.001 <.001
4 High x
2
(2)=128.782, p <.001 0.49 <.001 <.001 <.001
2006 1 Low x
2
(2)=32.796, p <.001 0.26 <.001 <.001
2 x
2
(2)=130.175, p <.001 0.43
<.001 <.001
3 x
2
(2)=174.789, p <.001 0.47 .001 <.001 <.001
4 High x
2
(2)=145.187, p <.001 0.50 <.001 <.001 <.001
2007 1 Low x
2
(2)=42.942, p <.001 0.27 .001 <.001 <.001
2 x
2
(2)=174.777, p <.001 0.50
<.001 <.001
3 x
2
(2)=221.358, p <.001 0.54 <.001 <.001 <.001
4 High x
2
(2)=137.952, p <.001 0.47 <.001 <.001 <.001
2008 1 Low x
2
(2)=29.384, p <.001 0.23 .004 <.001 <.001
2 x
2
(2)=127.362, p <.001 0.45
<.001 <.001
3 x
2
(2)=179.177, p <.001 0.48 .001 <.001 <.001
4 High x
2
(2)=305.543, p <.001 0.60 <.001 <.001 <.001
2009 1 Low x
2
(2)=28.583, p <.001 0.21 .004 <.001 .001
2 x
2
(2)=170.795, p <.001 0.48
<.001 <.001
3 x
2
(2)=198.488, p <.001 0.47 <.001 <.001 <.001
4 High x
2
(2)=145.104, p <.001 0.47 <.001 <.001 <.001
2010 1 Low x
2
(2)=38.440, p <.001 0.24 .001 <.001 <.001
2 x
2
(2)=165.596, p <.001 0.45 .023 <.001 <.001
3 x
2
(2)=224.634, p <.001 0.50 <.001 <.001 <.001
4 High x
2
(2)=173.527, p <.001 0.48 <.001 <.001 <.001
2011 1 Low x
2
(2)=53.743, p <.001 0.29 .001 <.001 <.001
2 x
2
(2)=146.536, p <.001 0.41
<.001 <.001
3 x
2
(2)=221.703, p <.001 0.49 <.001 <.001 <.001
4 High x
2
(2)=200.908, p <.001 0.51 <.001 <.001 <.001
2012 1 Low x
2
(2)=47.223, p <.001 0.25 .001 <.001 <.001
2 x
2
(2)=143.109, p <.001 0.40 .003 <.001 <.001
3 x
2
(2)=213.747, p <.001 0.49 <.001 <.001 <.001
4 High x
2
(2)=219.910, p <.001 0.54 <.001 <.001 <.001
2013 1 Low x
2
(2)=43.069, p <.001 0.25 <.001 <.001 <.001
2 x
2
(2)=79.890, p <.001 0.33
<.001 <.001
3 x
2
(2)=175.615, p <.001 0.46 <.001 <.001 <.001
4 High x
2
(2)=274.751, p <.001 0.52 <.001 <.001 <.001
ALGEBRA FOR ALL POLICY IMPACTS 123
On the following page , Figure 5 illustrates the change in mean proficiency over time for
the language proficiency subgroups across school poverty quartiles . Similar to the data reviewed
for the ethnicity subgroups, school poverty quartile matters . There is a difference in performance
between the lowest and highest poverty schools across all subgroups . Unlike the ethnicity data
though, there is one subgroup that seems to least affected by school poverty in quartiles 2
through 4. With the exception of quartile 1 schools that have very high proficiency rates
compared to other quartiles, there is little difference between the performance of EL students
across school poverty levels 2-4. Again, there are many fewer schools in quartile 1 with
signficiant EL and RFEP subgroups, so this must be viewed with caution . The graphs look very
similar with small increases in achievement means over time for the RFEP and English Only
subgroups but very little change for the EL subgrou p.
ALGEBRA FOR ALL POLICY IMPACTS 124
Figure 5. Proficiency line graph by language proficiency and school poverty quartile.
ALGEBRA FOR ALL POLICY IMPACTS 125
Socioeconomic status subgroup analyses by school poverty level. To analyze eighth
grade achievement in mathematics at or above Algebra I, student socioeconomic subgroup and
school poverty level achievement means were compared . The means ( M) and standard
deviations ( SD) are presented in Table 27. The "% Change" column is a calculation of the
percent increase between 2003 proficiency and 2013 proficiency rates . For example, the NSED
subgroup in quartile 4 schools had the highest change with a 93% increase in mean proficiency
rate between 2003 and 2013 . The NSED subgroup began at a rate of 2 4% and increased to 46%
in 2013, in essence the proficiency rate nearly doubled . Both quartile 1 and 4 schools made
gains with the SED subgroup with increases of 52% and 74% respectively . Both SED and
NSED subgroups increase d achievement over time across poverty quartiles . The NSED
subgroup at quartile 1 (low poverty) schools made the least gains (only 4% increase) but
continued to be far and above the highest achieving subgrou p. The next highest achieving
subgroup in 2013 w as the NSED subgroup ( M = .59) at quartile 1 schools followed closely by
the SED subgroup ( M = .58) at quartile 1 schools . Like other analyses on achievement described
previously, school poverty level seems to matter quite a bit.
ALGEBRA FOR ALL POLICY IMPACTS 126
Table 27
Proficiency Means by SES Subgroup and School Poverty Quartile
School
Poverty
Quartile
Subgroup
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
%
Change
M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD M SD
1 SED .38 .29 .43 .27 .48 .27 .51 .29 .47 .29 .50 .28 .50 .28 .52 .27 .54 .25 .56 .25 .58 .24 52%
Low NSED .67 .27 .64 .27 .64 .26 .69 .25 .66 .25 .67 .25 .68 .24 .67 .24 .68 .21 .68 .22 .70 .21 4%
2 SED .38 .27 .32 .24 .35 .25 .41 .26 .36 .27 .39 .27 .41 .26 .45 .25 .45 .25 .46 .25 .48 .25 25%
NSED .50 .26 .45 .25 .49 .25 .54 .26 .49 .25 .52 .25 .54 .23 .56 .23 .56 .23 .57 .23 .59 .23 17%
3 SED .30 .26 .27 .24 .28 .24 .34 .25 .31 .24 .34 .24 .36 .24 .38 .23 .41 .24 .43 .24 .41 .24 35%
NSED .36 .26 .34 .24 .35 .25 .41 .25 .38 .24 .41 .23 .43 .23 .45 .22 .46 .22 .49 .23 .50 .23 37%
4 SED .24 .24 .22 .22 .26 .24 .32 .25 .29 .23 .33 .23 .36 .24 .37 .24 .37 .24 .37 .23 .41 .23 74%
High NSED .23 .23 .23 .22 .28 .25 .33 .26 .34 .24 .36 .23 .37 .24 .42 .25 .41 .25 .39 .24 .46 .24 95%
ALGEBRA FOR ALL POLICY IMPACTS 127
Students in all socioeconomic subgroups across school poverty quartiles improved in
terms of proficiency between 2003 and 2013 . NSED students in quartile 4 schools experienced
the most growth with a 93% increase in proficiency ; however this increase is still 22 percentage
points lower than the performance of the NSED subgroup at quartile 1 (low poverty) schools in
2003. The poorest stu dents in the poorest schools (SED students in quartile 4 schools)
experienced the second largest increase with 76%, from 24% proficient in 2003 to 42%
proficient in 2013 . Despite these increases differences between school quartile groups persist .
Additionally, proficiency levels decrease as the school poverty level increases . For example, in
2013, the SED subgroup decreases from 58% proficient in quartile 1 schools to 42% proficient in
quartile 3 and 4 (high poverty) schools.
To further examine the gap s between subgroups, Table 28 contains a calculated difference
(gap) between the NSED and SED subgroup in mean proficiency across school poverty quartiles .
Quartile 1 schools decreased the gap in performance between t he NSED and SED by 16
percentage points over all years (between 2003 and 2013) , while quartile 4 schools increased the
difference by 4 percentage points (from M = .00 to M = .04). Overall, however, quartile 4
schools have the smallest gap between the subg roups with only a four percentage point
difference in mean proficiency . Quartile 4 schools consistently had the smallest achievement
gap between their SED and NSED subgroups .
ALGEBRA FOR ALL POLICY IMPACTS 128
Table 28
Proficiency Gaps Between SES Subgroups by School Poverty Quartile
School Poverty
Quartile
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
1 Low .30 .23 .17 .20 .20 .18 .19 .17 .16 .15 .14
2 .13 .15 .15 .14 .15 .14 .14 .13 .13 .13 .13
3 .07 .07 .08 .08 .07 .08 .07 .08 .06 .07 .10
4 High .00 .01 .03 .01 .05 .03 .01 .05 .03 .01 .04
To determine the strength of the differences between subgroups and school poverty
quartiles, a Kruskal -Wallis test was performed . The results follow in Table 29. The table only
contains the results of significant ( p < .01) findings where the differences between mean
achievement are different between the subgroups SED and NSED . The results are prese nted by
school poverty quartile for each year . As stated previously, quartile 4 has only small differences
between the achievement means for SED and NSED . The only years where the means were
statistically significant between SES subgroups at quartile 4 s chools was 2007 ( f = 0.11), 2010 ( f
= 0.1), and 2013 ( f = 0.08); effect sizes were small to insignificant . For quartile 3 schools, the
differences between the SED and NSED subgroups were significant for all years with small
effect sizes (0.11 < f < 0.2). For quartile 1 (low poverty) and 2 schools though, differences in
the achievement means between SED and NSED subgroups were significant ( p < .001) with
medium effect sizes ( f > .2) . These results show a greater difference in achievement gaps for
SES subgroups as the poverty level in the school goes down . Over time, this pattern changed
little. There were only small decreases in quartile 1 schools coming down by the year 2012 to
match the gaps of quartile 2 schools (as also seen in Table 28).
ALGEBRA FOR ALL POLICY IMPACTS 129
Table 29
Kruskal-Wallis—Achievement Between SES Subgroups by Poverty Quartile
Year Poverty Quartile Overall Diff. Between Subgroups f
2003 1 Low x
2
(1)=31.815, p <.001 0.34
2 x
2
(1)=31.324, p <.001 0.22
3 x
2
(1)=15.644, p <.001 0.14
2004 1 x
2
(1)=33.663, p <.001 0.30
2 x
2
(1)=52.518, p <.001 0.27
3 x
2
(1)=18.869, p <.001 0.16
2005 1 x
2
(1)=28.420, p <.001 0.25
2 x
2
(1)=56.860, p <.001 0.28
3 x
2
(1)=20.819, p <.001 0.16
2006 1 x
2
(1)=39.672, p <.001 0.29
2 x
2
(1)=51.173, p <.001 0.25
3 x
2
(1)=23.035, p <.001 0.17
2007 1 x
2
(1)=50.458, p <.001 0.30
2 x
2
(1)=64.463, p <.001 0.28
3 x
2
(1)=20.566, p <.001 0.16
4 x
2
(1)=5.301, p=.021 0.11
2008 1 x
2
(1)=39.795, p <.001 0.27
2 x
2
(1)=46.846, p <.001 0.26
3 x
2
(1)=24.774, p <.001 0.18
2009 1 x
2
(1)=62.365, p <.001 0.31
2 x
2
(1)=54.364, p <.001 0.26
3 x
2
(1)=19.678, p <.001 0.15
2010 1 x
2
(1)=51.38, p <.001 0.28
2 x
2
(1)=54.3, p <.001 0.25
3 x
2
(1)=27.080, p <.001 0.18
4 x
2
(1)=5.483, p=.019 0.10
2011 1 x
2
(1)=49.547, p <.001 0.28
2 x
2
(1)=56.531, p <.001 0.25
3 x
2
(1)=12.179, p <.001 0.12
2012 1 x
2
(1)=42.725, p <.001 0.24
2 x
2
(1)=59.167, p <.001 0.25
3 x
2
(1)=15.247, p <.001 0.13
2013 1 x
2
(1)=42.146, p <.001 0.25
2 x
2
(1)=39.582, p <.001 0.23
3 x
2
(1)=31.479, p <.001 0.19
4 High x
2
(1)=4.495, p=.034 0.08
ALGEBRA FOR ALL POLICY IMPACTS 130
Additional analyses were conducted on the differences in mean proficiency differences of
the SES subgroups across school poverty levels . Kruskal-Wallis test results are located in Table
30. In the table, f or all years of the study the differences between all poverty quartiles were
significant for the NSED subgrou p. Though in the years 2009 – 2011 and in 2013, the differences
between quartile 3 and 4 for the NSED subgroup are not significant . The effect siz es of poverty
quartile on the mean achievement of the NSED subgroup were quite large ( f between 0.4 and
0.54). For the SED subgroup, school poverty also varied by school poverty level meaning that a
SED student at a high poverty school (quartile 4) had significantly lower achievement than a
SED student at quartile 2, 3, and 4 schools . The effect sizes for the differences were lower than
they were for the NSED subgroups with small effect sizes ( f) between 0.2 and 0.27.
ALGEBRA FOR ALL POLICY IMPACTS 131
Table 30
Kruskal-Wallis—Achievement Between SES Subgroups by Poverty Quartile
Year Subgroup Result
Poverty Quartile Comparison
(1 = Low; 4 = High)
Adjusted p f
2003 SED x2(3)=46.957, p <.001 1 - 4 .009 0.23
2 - 3 .001
2 - 4 <.001
3 - 4 .003
NSED x2(3)=286.234, p <.001 1 - 2 <.001 0.53
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 <.001
2004 SED x2(3)=54.078, p <.001 1 - 2 .024 0.23
1 - 3 <.001
1 - 4 <.001
2 - 3 .034
2 - 4 <.001
3 - 4 .012
NSED x2(3)=309.463, p <.001 1 - 2 <.001 0.54
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 <.001
2005 SED x2(3)=79.852, p <.001 1 - 2 .001 0.27
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
NSED x2(3)=283.874, p <.001 1 - 2 <.001 0.50
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 .05
2006 SED x2(3)=59.894, p <.001 1 - 2 .009 0.22
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
NSED x2(3)=270.732, p <.001 1 - 2 <.001 0.53
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 .018
ALGEBRA FOR ALL POLICY IMPACTS 132
Table 30 Continued
Year Subgroup Result
Poverty Quartile Comparison
(1 = Low; 4 = High)
Adjusted p f
2007 SED x2(3)=51.311, p <.001 1 - 2 <.001 0.20
1 - 3 <.001
1 - 4 <.001
2 - 4 .01
NSED x2(3)=281.35, p <.001 1 - 2 <.001 0.49
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 <.001
2008 SED x2(3)=57.148, p <.001 1 - 2 <.001 0.20
1 - 3 <.001
1 - 4 <.001
2 - 4 .006
NSED x2(3)=280.478, p <.001 1 - 2 <.001 0.48
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 .02
2009 SED x2(3)=49.884, p <.001 1 - 2 .001 0.18
1 - 3 <.001
1 - 4 <.001
2 - 3 .027
2 - 4 .02
NSED x2(3)=280.478, p <.001 1 - 2 <.001 0.47
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
2010 SED x2(3)=75.173, p <.001 1 - 2 .009 0.22
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
NSED x2(3)=206.744, p <.001 1 - 2 <.001 0.40
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 133
Table 30 Continued
Year Subgroup Result
Poverty Quartile Comparison
(1 = Low; 4 = High)
Adjusted p f
2011 SED x2(3)=83.43, p <.001 1 - 2 <.001 0.23
1 - 3 <.001
1 - 4 <.001
2 - 4 <.001
3 - 4 .018
NSED x2(3)=224.559, p <.001 1 - 2 <.001 0.42
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
2012 SED x2(3)=94.913, p <.001 1 - 2 <.001 0.24
1 - 3 <.001
1 - 4 <.001
2 - 4 <.001
3 - 4 .004
NSED x2(3)=210.253, p <.001 1 - 2 <.001 0.40
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
3 - 4 .002
2013 SED x2(3)=94.555, p <.001 1 - 2 <.001 0.24
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
NSED x2(3)=204.188, p <.001 1 - 2 <.001 0.40
1 - 3 <.001
1 - 4 <.001
2 - 3 <.001
2 - 4 <.001
ALGEBRA FOR ALL POLICY IMPACTS 134
In the line graphs in Figure 6 on the following page, mean proficiency rates for SES
subgroups are represented by the colored lines and the x -axis separates the proficiency rates by
the school poverty quartile . Graphs for the years 2003, 2006, 2009, 2012, and 2013 are
provided. Like data presented previously, the graphs show data for each three years plus the
final year of analysis as there are small differences in the last year of data . As a school increases
in FRPM participation (school poverty quartile), the mean achievement in te rms of proficiency
goes down. Additionally, the distance between the two lines, representing SES subgroups,
narrows. There is a smaller difference (for all years studied) between SES subgroups as the
poverty level of the school increases . Further, the effect of school poverty is stronger than the
effects of SES subgroup alone. For example, in 2013, the NSED (not socioeconomically
disadvantaged) subgroup at quartile 2, 3, or 4 (high poverty) schools were outscored by the SED
(disadvantaged) subgroup at quartile 1 (low poverty) schools.
ALGEBRA FOR ALL POLICY IMPACTS 135
Figure 6. Line graphs of proficiency means by SES subgroup and school poverty quartile .
ALGEBRA FOR ALL POLICY IMPACTS 136
Equity in Placement—Research Question 5
The final research question was used to further delve into t he issue of tracking based on
previous mathematics success and whether or not students are placed equitably across school
poverty levels and student demographic subgroups . The final question was:
5. Between 2003 and 2013, how are previous mathematics achiev ement (as
measured by the seventh grade mathematics CST), student demographics
(ethnicity, language proficiency, socioeconomic status), and school poverty levels
(as measured by FRPM participation rates) related to placement in eighth grade
Algebra I?
All students analyses by school poverty level. Placement rates were calculated by taking the
percentages of students proficient in a previous year (grade seven mathematics CST) and
subtracting the percentages of students taking the CST for Algebra I or higher the year under
study. A positive placement rate indicates over-placement of students (using previous year's
proficiency as a benchmark), whereas a negative placement rate indicates under-placement. The
means of these calculations were used for the following analyses. The graph in Figure 7 displays
the mean placement rate for schools across the years 2003 through 2013 and by school poverty
quartiles.
The graph shows that quartile 1 (low poverty) schools over all are least lik ely to over
place students into courses Algebra I and above and the only schools that under placed students
(years 2003 -2006). Quartile 4 schools are the most likely to over place students into courses
Algebra I and higher . Interestingly there is a stron g drop in over-placement in the 2012 -13 data
set for all school quartile groups, represented by a dark green bar on the graph .
ALGEBRA FOR ALL POLICY IMPACTS 137
Figure 7. All subgroups placement by school poverty quartile .
In further examination of the drop in over-placement in 2013, Table 31 contains the mean
placement rates by school poverty quartile for the years 2003 through 2013 . School quartile
groups 2 through 4 (high poverty) decreased their over-placement rates in 2013 to rates lower
than they were in 2003 . In addition, there is a clear and persistent trend that student over-
placement increases as the school poverty level increases .
ALGEBRA FOR ALL POLICY IMPACTS 138
Table 31
All Subgroups Placement Means by School Poverty Quartile
School
Poverty
Quartile
2003-
04
2004-
05
2005-
06
2006-
07
2007-
08
2008-
09
2009-
10
2010-
11
2011-
12
2012-
13
1 Low M -1.84 -0.57 -1.21 -2.08 2.76 3.13 6.55 2.68 5.30 1.37
SD 23.69 22.83 23.12 24.40 24.96 23.58 23.17 22.18 23.29 22.54
2 M 9.23 8.61 9.46 10.47 13.00 13.71 14.91 12.31 13.25 4.95
SD 25.81 24.77 27.40 28.02 28.62 29.85 27.95 27.47 28.13 27.12
3 M 17.75 22.53 19.26 22.13 23.31 25.44 25.84 21.66 20.73 15.57
SD 28.86 30.78 28.16 30.35 29.28 30.95 29.96 28.95 29.87 28.98
4 High M 23.74 24.53 25.15 23.49 26.54 27.24 28.33 28.11 29.31 20.27
SD 29.66 32.47 32.15 30.42 30.39 30.21 30.68 30.06 32.15 30.74
Ethnicity subgroup analyses by school poverty level. The previous data showed that
students are placed in Algebra I or higher using different benchmarks across school groups and
that in 2012 -13 there was a return to practices similar to those before the Algebra for All policies.
In order to analyze whether or not schools placed students differentially by subgroup, the data
need to be disaggregated . Table 32 contains the placement means for ethnic subgroups by school
poverty quartile.
Similar to the all students data presented in Table 31 there is a trend present across
subgroups where over-placement generally increases across the years and across school poverty
levels. Again, in 2012 -13, there is a large change in practice with less over-placement for all
poverty quartiles and for all subgroups . In terms of ethnicity, subgroups most traditionally
disadvantaged (African American and Latino) were over placed more often than the Asian and
white subgroups.
ALGEBRA FOR ALL POLICY IMPACTS 139
Table 32
Placement Means by Ethnic Subgroup and School Poverty Quartile
School
Poverty
Quartile
Subgroup
2003-
2004
2004-
2005
2005-
2006
2006-
2007
2007-
2008
2008-
2009
2009-
2010
2010-
2011
2011-
2012
2012-
2013
1 Low AfAm M 2.62 2.95 -0.05 1.56 2.36 9.64 12.90 11.31 10.82 4.88
SD 25.21 26.39 28.38 29.02 29.03 31.27 31.16 29.61 30.89 26.14
Asian M -6.45 -5.57 -5.28 -5.05 1.08 2.16 5.07 3.10 3.88 1.52
SD 16.55 16.99 17.23 16.75 19.04 17.20 17.09 15.11 13.22 13.12
Fil M -6.91 -4.37 -9.13 -8.01 -3.61 5.42 7.18 6.15 5.47 3.34
SD 22.68 26.90 23.89 27.41 24.65 25.05 24.57 21.84 23.73 22.69
Lat M -1.91 0.39 -0.67 -2.23 3.56 4.93 8.11 2.14 3.55 0.50
SD 23.66 24.27 25.66 27.91 28.96 30.43 30.16 28.54 29.80 27.71
Wh M -5.12 -2.67 -3.99 -5.18 0.51 1.21 4.26 1.14 2.73 -0.93
SD 22.72 22.60 22.41 24.30 24.86 23.85 22.98 22.55 23.00 20.72
2 AfAm M 16.16 16.71 18.04 21.36 20.80 20.21 21.24 20.01 21.65 10.66
SD 26.42 28.17 31.41 32.05 32.40 34.59 35.05 32.98 33.33 31.98
Asian M 4.98 5.54 4.37 6.67 9.18 11.16 13.15 10.87 13.01 9.42
SD 21.39 22.43 20.54 22.78 22.16 22.25 20.74 18.02 18.85 16.79
Fil M 9.11 9.19 8.45 10.79 13.05 14.25 16.59 17.46 13.72 11.94
SD 24.34 24.45 26.71 26.93 27.10 28.06 24.08 23.17 23.77 17.49
Lat M 12.38 12.73 14.08 15.00 15.80 18.06 16.97 14.95 15.05 8.61
SD 25.94 26.60 29.58 31.15 32.01 32.29 31.26 31.33 30.75 29.44
Wh M 7.37 6.57 8.02 8.06 9.97 9.94 11.99 8.95 9.58 2.77
SD 25.07 24.47 27.03 27.24 27.54 27.17 26.00 24.87 25.79 25.53
3 AfAm M 24.63 28.14 24.14 29.93 27.47 31.74 34.28 26.74 28.37 28.02
SD 30.78 33.81 31.81 34.22 32.73 33.57 35.09 34.17 34.67 34.93
Asian M 11.05 13.86 13.12 11.09 16.77 22.60 22.11 16.33 18.01 13.41
SD 25.00 28.86 24.96 23.24 22.33 21.89 20.06 17.79 20.45 17.92
Fil M 17.98 18.42 13.21 16.04 22.12 20.91 29.36 22.11 23.67 22.87
SD 23.70 28.01 27.80 27.51 27.10 25.79 24.84 20.36 23.12 24.61
Lat M 21.25 24.46 22.86 23.72 25.83 26.21 28.09 23.39 23.13 18.72
SD 30.33 32.14 30.12 31.07 30.27 31.63 30.48 30.96 31.14 30.54
Wh M 14.42 19.22 16.84 17.13 19.59 19.84 20.94 16.76 13.27 10.15
SD 26.32 29.31 27.39 27.24 27.54 28.27 28.74 27.74 27.35 27.73
4 High AfAm M 28.56 29.04 32.58 25.61 30.04 28.86 30.77 28.79 29.88 20.25
SD 30.70 35.17 33.47 29.82 32.51 35.68 35.60 34.74 35.26 34.43
Asian M 20.04 22.66 20.57 14.80 22.62 20.76 22.45 22.97 23.61 12.66
SD 24.74 25.13 23.94 23.02 22.78 24.28 21.31 23.76 22.78 21.89
Fil M 26.46 21.22 23.63 13.22 19.07 16.41 23.87 23.72 27.96 18.29
SD 28.87 29.00 28.77 27.62 27.36 20.82 22.29 23.50 17.91 17.64
Lat M 25.53 26.83 25.59 24.88 28.74 27.65 29.68 29.22 31.13 21.61
SD 30.68 33.46 32.18 30.95 31.99 30.11 30.98 30.72 31.99 31.03
Wh M 22.09 17.51 15.59 11.17 18.41 20.81 24.58 22.29 19.69 10.12
SD 31.17 25.35 26.39 23.41 27.06 28.35 29.96 26.70 31.48 28.90
ALGEBRA FOR ALL POLICY IMPACTS 140
The two -way ANOVA results for placement means by ethnicity and poverty level are
located in Table 33. The main effects for poverty quartile are significant with small effect sizes
for all years except 2013 . The main effects for ethnic subgroup are significant for all years with
small effect sizes with the exception of 2004 -5 and 2006 -7, which are statistically significant ( p
< .001) but without significant effect sizes ( f < 0.1). Interaction effect of poverty and ethnicity
subgroup are significant for all years ( p < .05), but considering e ffect size calculations , the
interactions are only pertinent for the years 2011 -12 and 2012 -13 where the effect sizes are f =
0.1. Controlling for the differences in proficiency rates between school poverty quartiles (the
lower the poverty, the higher the proficiency), an ANCOVA analysis provided different results
with significant interactions for all years between subgroup and school poverty quartile ( p < .05);
however, Cohen's f effect sizes were insignificant for all years except for 2011 -12 (F(12,4478) =
3.97, p < .001, f =0.1 ) and 2012 -13 (F(12,4539) = 3.81, p < .001, f = 0.1). For Cohen’s f,
effect sizes of 0.1 are considered small (Parke, 2010). Further analysis of the interaction results
through the use of post -hoc Bonferroni tests and pairwise comparison, revealed that the
interaction effects were significant only in quartile 2, 3, and 4 (high poverty) schools and
between ethnic subgroups Africa n American and Asian (p = .03 at quartiles 2 and 3) and between
the white and Latino subgroups (p = .02 at quartile 2 and p < .01 at quartile 3 and 4) .
ALGEBRA FOR ALL POLICY IMPACTS 141
Table 33
ANOVA Results Placement by Ethnicity and Poverty Level
Year Factor df F p f
2003-04
Subgroup 4 11.32 <.001 0.10
PovLvl 3 32.76 <.001 0.15
Subgroup * PovLvl 12 1.84 .037 0.07
Error 4482
2004-05
Subgroup 4 9.08 <.001 0.09
PovLvl 3 32.76 <.001 0.15
Subgroup * PovLvl 12 1.77 .047 0.07
Error 4434
2005-06
Subgroup 4 12.02 <.001 0.10
PovLvl 3 34.84 <.001 0.15
Subgroup * PovLvl 12 2.37 .005 0.08
Error 4498
2006-07
Subgroup 4 8.20 <.001 0.08
PovLvl 3 42.82 <.001 0.17
Subgroup * PovLvl 12 2.89 .001 0.09
Error 4589
2007-08
Subgroup 4 15.73 <.001 0.12
PovLvl 3 29.95 <.001 0.14
Subgroup * PovLvl 12 2.51 .003 0.08
Error 4656
2008-09
Subgroup 4 13.04 <.001 0.11
PovLvl 3 22.41 <.001 0.12
Subgroup * PovLvl 12 1.97 .023 0.07
Error 4646
2009-10
Subgroup 4 21.31 <.001 0.14
PovLvl 3 22.50 <.001 0.12
Subgroup * PovLvl 12 2.09 .015 0.07
Error 4460
2010-11
Subgroup 4 17.08 <.001 0.13
PovLvl 3 17.63 <.001 0.11
Subgroup * PovLvl 12 2.43 .004 0.08
Error 4366
2011-12
Subgroup 4 21.19 <.001 0.14
PovLvl 3 15.19 <.001 0.10
Subgroup * PovLvl 12 3.97 .000 0.10
Error 4478
2012-13
Subgroup 4 26.17 <.001 0.15
PovLvl 3 13.55 <.001 0.09
Subgroup * PovLvl 12 3.81 .000 0.10
Error 4539
Note. *Effect sizes of f ≥ 0.1 are considered small.
ALGEBRA FOR ALL POLICY IMPACTS 142
An additional analysis of the change in mean placement between 2011 -12 and 2012 -13
was performed using a two -way ANOVA. The results of the ANOVA show that the differences
in placement mean between the two years were statistically significant for each poverty quartile .
By splitting the data file by ethnic subgroup, the treatment of a particular subgroup and analysis
of a subgroup across poverty quartiles by year was possible . The results are reported in Table 34.
Looking at the African American subgroup for the placement means between 2011 -12
and 2012 -13, the difference in the placement means betwee n the two years is statistically
significant ( p < .001) and has a small effect size ( f = 0.1). Plus, the difference across poverty
levels in those two years is not only significant ( p < .001) but also has a small (approaching
medium) effect size ( f = 0.22). This means that for African American students, there was a
significant change in placement between the 2011 -12 and 2012 -13 school years and there was a
difference in treatment of the subgroup across poverty quartiles . Referring to the means table
(Table 32), over-placement decreased across all school poverty quartiles (although there was
very little difference in quartile 3 schools) .
ALGEBRA FOR ALL POLICY IMPACTS 143
Table 34
ANOVA Results for Placement in 2011-12 and 2012-13 by Poverty Level
Subgroup Factor df F p f*
AfAm Year 1 10.81 <.001 0.10
PovLvl 3 18.24 <.001 0.22
Error 1161
Asian Year 1 23.32 <.001 0.14
PovLvl 3 46.85 <.001 0.35
Error 1132
Fil Year 1 2.50 .11 0.07
PovLvl 3 23.00 <.001 0.36
Error 540
Lat Year 1 30.81 <.001 0.09
PovLvl 3 97.59 <.001 0.29
Error 3416
Wh Year 1 28.10 <.001 0.10
PovLvl 3 33.68 <.001 0.19
Error 2770
Note. *Effect size of f ≥ 0.1 is considered small, f ≥ 0.25 is considered medium, and f ≥ 0.4 is
considered large.
Language subgroup analyses by school poverty level. The placement means ( M) data
with standard deviations ( SD) by language proficiency and school poverty quartile between 2003
and 2013 by are provided in Table 35. Again, placement rates are highest for California's poorest
schools, meaning that quartile 3 and 4 schools place more students in Algebra I and high er than
were proficient on the previous year's CST . Somewhat concerning however is the under-
placement of the RFEP and EL subgroups at quartile 1 schools between the 2003 -4 and 2008 -9
school years—quartile 1 (low poverty) schools were placing fewer studen ts into Algebra I than
were proficient on their previous mathematics CST . After 2008 -9 this number increased;
ALGEBRA FOR ALL POLICY IMPACTS 144
however, in a trend similar to what has been observed in previous placement analysis, in 2013,
placement rates decreased and the placement rate for the RFEP and EL subgroups again fell into
a state of under-placement.
Table 35
Placement Means by Language Proficiency and School Poverty Quartile
School
Poverty
Quartile
Subgroup
2003-
2004
2004-
2005
2005-
2006
2006-
2007
2007-
2008
2008-
2009
2009-
2010
2010-
2011
2011-
2012
2012-
2013
1 Low RFEP M -3.01 -6.40 -9.76 -8.67 -2.99 -0.72 2.02 0.67 1.76 -0.20
SD 23.38 18.50 20.04 21.82 23.23 24.58 24.57 22.32 23.23 21.89
EL M -2.06 -2.65 -0.14 0.34 6.04 3.94 5.82 3.69 1.99 -0.89
SD 22.12 20.05 24.48 25.90 27.40 32.31 33.53 35.48 35.06 34.42
Eng.
Only
M -2.74 -1.37 -1.91 -3.09 2.04 2.56 5.93 2.14 4.67 0.23
SD 23.74 22.78 23.55 24.68 25.11 23.95 22.95 22.36 22.89 22.24
2 RFEP M 9.58 7.16 7.04 5.22 9.27 12.62 13.71 11.48 13.16 7.01
SD 27.84 27.40 29.25 29.18 30.54 28.24 28.12 25.96 26.08 26.18
EL M 11.10 10.64 14.08 17.70 17.91 16.86 16.12 12.10 10.74 4.40
SD 26.69 26.30 31.25 34.69 34.69 37.79 37.95 36.69 34.88 33.63
Eng.
Only
M 8.71 7.94 8.43 10.44 12.39 13.21 13.95 11.71 12.70 4.72
SD 25.70 24.99 27.09 28.42 28.35 29.00 27.76 26.78 28.04 26.74
3 RFEP M 16.30 18.45 17.83 16.12 19.35 20.70 24.92 19.78 18.39 17.12
SD 28.37 30.26 30.09 27.65 27.49 26.66 25.21 25.46 26.33 26.45
EL M 18.70 24.61 24.69 26.19 25.26 25.78 26.44 21.35 20.76 17.95
SD 30.08 35.05 35.04 35.11 34.55 38.51 38.80 40.33 40.28 39.44
Eng.
Only
M 17.26 23.39 19.59 22.05 22.45 25.07 24.88 21.78 19.92 14.49
SD 28.55 31.37 28.69 30.11 28.99 31.33 30.15 29.61 30.52 28.68
4 High RFEP M 25.20 24.48 24.19 20.91 24.73 24.83 27.44 23.78 25.59 19.97
SD 31.71 30.56 27.68 27.29 28.03 25.81 25.51 23.77 26.10 26.34
EL M 24.32 26.43 27.68 25.42 31.37 27.05 29.39 29.26 31.53 20.73
SD 31.97 36.88 34.98 34.18 37.39 37.22 38.13 40.23 41.55 39.93
Eng.
Only
M 24.55 23.48 26.58 23.23 27.48 28.62 27.87 29.41 29.95 19.58
SD 29.92 31.89 33.86 30.10 30.88 31.16 30.94 31.21 33.38 30.90
ALGEBRA FOR ALL POLICY IMPACTS 145
A two -way ANOVA for the difference between years and school level poverty was
performed to analyze this change between 2012 and 2013 . The difference in placement means
across poverty quartiles between the school years 2011 -12 and 2012 -13 was statistically
significant for all language proficiency subgroups ( p < .01), but the effect size was only
noteworthy for the English Only subgroup (F(1,3911) = 61.09, p < .001, f = 0.13).
Additionally, a two-way ANOVA also showed that for each year, the differences between
subgroups were insignificant within each poverty quartile; however, they were significantly
different between poverty quartiles . Therefore, there was a main effect for poverty quartile but
not for subgrou p. Additionally, there were no interaction effects between language proficiency
subgroup and poverty quartile . The ANOVA results of the main effects for school poverty
quartile are provided in Table 36. The Cohen's f effect sizes for all years measured were medium
sized effects.
ALGEBRA FOR ALL POLICY IMPACTS 146
Table 36
Main Effect of Poverty Quartile for Placement by Language Proficiency
Year
df F p f
2003-04 School Poverty 3 111.521 < .001 0.30
Error 3685
2004-05 School Poverty 3 144.960 < .001 0.34
Error 3750
2005-06 School Poverty 3 148.885 < .001 0.34
Error 3839
2006-07 School Poverty 3 140.846 < .001 0.32
Error 4008
2007-08 School Poverty 3 128.207 < .001 0.30
Error 4202
2008-09 School Poverty 3 113.644 < .001 0.28
Error 4211
2009-10 School Poverty 3 107.126 < .001 0.28
Error 4181
2010-11 School Poverty 3 112.808 < .001 0.28
Error 4167
2011-12 School Poverty 3 114.684 < .001 0.28
Error 4349
2012-13 School Poverty 3 92.490 < .001 0.25
Error 4453
Note. *Effect size of f ≥ 0.10 is considered small, f ≥ 0.25 is considered medium, and f ≥ 0.40 is
considered large.
ALGEBRA FOR ALL POLICY IMPACTS 147
To further illustrate this difference in placement across poverty quartiles (for the language
proficiency subgroups) line graphs of placement means by school poverty quartile and subgroup
for the years 2003 -04, 2009 -10, and 2012 -13 are presented in Figure 8. The lines in the graph
are virtually on top of one another, which demonstrates that within each school poverty quartile
placement means were similar; however, the stee p slope of the lines showed an increasing over-
placement across school quartiles —the higher the poverty the higher the over-placement.
Figure 8. Placement means across language proficiency and school poverty quartile.
ALGEBRA FOR ALL POLICY IMPACTS 148
Socioeconomic status subgroup analyses by school poverty level. The data for the
SES subgroups were also very similar . The placement means (M) and standard deviations ( SD)
over the years 2003 -2013 by school poverty quartile are available in Table 37.
Table 37
Placement Means by SES Subgroup and School Poverty Quartile
School
Poverty
Quartile
Subgroup
2003-
2004
2004-
2005
2005-
2006
2006-
2007
2007-
2008
2008-
2009
2009-
2010
2010-
2011
2011-
2012
2012-
2013
1 Low SED M -.72 .44 .40 .46 4.30 4.39 6.05 .31 2.86 -1.13
SD 23.26 22.77 25.49 29.80 28.34 30.34 29.53 29.72 31.61 29.02
NSED M -3.93 -2.15 -2.06 -3.94 1.58 3.03 6.27 2.95 5.57 .95
SD 21.92 21.93 22.89 23.40 24.00 22.67 22.17 21.52 21.68 20.78
2 SED M 11.11 10.50 12.67 13.46 16.55 16.13 16.93 13.84 13.31 4.99
SD 26.34 26.24 30.13 30.60 32.50 33.04 30.90 30.90 31.22 30.95
NSED M 8.48 8.92 7.96 8.93 10.68 13.15 14.69 11.32 12.27 5.31
SD 25.54 24.93 25.74 27.03 26.41 26.53 26.13 23.83 25.50 25.18
3 SED M 19.34 23.59 21.58 23.21 25.99 25.99 27.14 22.31 21.96 16.83
SD 28.33 31.40 29.94 31.25 30.12 32.23 30.81 30.59 30.78 30.55
NSED M 17.13 23.08 19.13 18.85 21.63 25.83 25.47 22.07 20.51 15.77
SD 27.88 30.13 27.55 27.23 26.84 28.23 26.44 25.59 26.88 25.25
4 High SED M 23.94 25.32 26.27 23.68 27.71 27.29 28.98 29.08 29.86 20.74
SD 29.72 33.08 32.15 30.59 31.02 30.15 30.55 30.45 32.05 31.03
NSED M 24.54 24.77 22.74 20.81 26.02 27.59 28.57 24.52 24.47 19.00
SD 29.48 30.63 30.62 26.54 29.33 28.09 28.60 28.42 29.26 28.80
Again looking at the means alone , placement increases with increases in school poverty;
the differences between the SES subgroups means (within school poverty quartiles) are small but
significant. There was again a change in practice in 2012 -13, which was statistically significant,
ALGEBRA FOR ALL POLICY IMPACTS 149
p < .001, where schools began to reduce over-placement and in the case of quartile 1 (low
poverty) schools revert to under-placement. Although statistically significant, the effect sizes
were only notable for quartile 2 (F (1,1958) = 35.2, p < .001 f = 0.13) and quartile 4 (F(1,1360)
= 14.36, p < .001, f = 0.1) schools.
A two -way ANOVA showed that at each poverty quartile, for each year between 2003and
2013 there was a significant main effect in placement by SES subgroups. In addition, there was
a significant main effect of poverty quartiles. The results of analyses are found in Table 38.
Between the years 2004 -05 and 2007 -08, the differences between SES subgroups (overall),
although statistically significant, did not have significant effect sizes . Post-hoc analysis showed
a significant difference ( p < .01) between all quartiles for each year (except between the bottom
quartiles 3 and 4) . However, there were no interaction effects between school poverty level and
school quartile level . A possible confounding variable in th e placement values is that proficiency
decreases as school poverty increases . Therefore a bootstrapped two -way ANCOVA was
performed controlling for the variable of proficiency . These data revealed that, when controlling
for proficiency rate, there was a significant interaction effect between school poverty and SES
subgroup for the school years 2005 -2006 ( F(3,3035) = 3.01 , p = .03, f = .05) , 2010-2011
(F(3,3182) = 5.61 , p = .001, f = .07), 2011 -2012 ( F(3,3328) = 6.56 , p < .001, f = .08) and 2012 -
2013(F(3,3324) = 2.98, p = .03, f = .05) . The Cohen's f effect sizes of greater than .1 are
considered small and therefore, although the interaction effects are statistically significant the
effect sizes are not .
ALGEBRA FOR ALL POLICY IMPACTS 150
Table 38
ANOVA Results for SES Placement
Year Independent Variable df F p f*
2003-04 Poverty Quartile 3 27.74 <.001 0.17
Subgroup 1 33.20 <.001 0.11
Error 3005
2004-05 Poverty Quartile 3 45.11 <.001 0.21
Subgroup 1 25.88 <.001 0.09
Error 3031
2005-06 Poverty Quartile 3 32.03 <.001 0.18
Subgroup 1 24.62 <.001 0.09
Error 3035
2006-07 Poverty Quartile 3 36.45 <.001 0.19
Subgroup 1 14.12 <.001 0.07
Error 3104
2007-08 Poverty Quartile 3 42.16 <.001 0.20
Subgroup 1 14.76 <.001 0.07
Error 3235
2008-09 Poverty Quartile 3 36.91 <.001 0.19
Subgroup 1 37.92 <.001 0.11
Error 3231
2009-10 Poverty Quartile 3 36.23 <.001 0.18
Subgroup 1 40.00 <.001 0.11
Error 3192
2010-11 Poverty Quartile 3 47.88 <.001 0.21
Subgroup 1 32.75 <.001 0.10
Error 3182
2011-12 Poverty Quartile 3 31.38 <.001 0.17
Subgroup 1 36.01 <.001 0.10
Error 3328
2012-13 Poverty Quartile 3 31.09 <.001 0.17
Subgroup 1 51.06 <.001 0.12
Error 3324
Note. *Effect sizes of f ≥ 0.1 are considered small.
ALGEBRA FOR ALL POLICY IMPACTS 151
To illustrate the significant effects of placement means across subgroups an d school
poverty quartiles, Figure 9 shows the means plots for the years 2005 -2006, 2010 -2011, 2011 -
2012, and 2012 - 2013. Graphs are presented to show the directionality of the interactions . Of
note in the graphs below is that (although not significant) quartile 1 (low poverty) schools have
the largest gap between the placement of their NSED and SED subgroups . Additionally, for the
first time since 2006, in 2012 -13, quartile 1 schools under placed SED students ( M = -1.13, 95%
CI [ -3.87,1.61]) and over placed NSED students ( M = .945, 95% CI [ -1.29,3.19]).
Figure 9. Interaction effects of school poverty quartile and SES on placement.
ALGEBRA FOR ALL POLICY IMPACTS 152
Chapter 5: Discussion
A brief summary of the results by research question are presented below . Conclusions,
practical implications, limitations and suggestions for future research follow . The research
questions were:
1. To what extent, if any, have California high and low poverty schools increased
enrollment in early algebra for traditionally disadvantaged students between 2003 and
2013?
2. To what extent, if any, have California high and low poverty schools decreased the
gap between non -disadvantaged and traditionally disadvantaged students' access to
early algebra between 2003 and 2013?
3. To what extent, if any, have California high and low poverty schools increased
traditionally disadvantaged eighth grade students' success in Algebra I and above
between 2003 and 2013?
4. To what extent, if any, have California high and low poverty schools de creased the
gap between non -disadvantaged and traditionally disadvantaged eighth grade
students' success in Algebra I and above between 2003 and 2013?
5. How are previous mathematics achievement (as measured by the seventh grade
mathematics CST), student demographics (ethnicity, language proficiency,
socioeconomic status), and school poverty levels related to placement in eighth grade
Algebra I in California between 2003 and 2013?
Tracking—Research Questions 1 and 2
Many studies have shown that students have not had equal access to advanced
mathematics courses at instances predictable along ethnic, language proficiency, and SES lines
ALGEBRA FOR ALL POLICY IMPACTS 153
(Bozick, Ingles, & Owings, 2008; EdSource, 2008; Smith, 1996; Wang & Goldschmidt, 2003;
Coleman, et al., 1966). In order to narrow the achievement gap, it is necessary to at a minimum
provide increased access to courses. Research questions 1 and 2 on the topic of tracking, were
used to determine if California schools have made progress in reducing tracking and opening up
access to students of all subgroups (in particular those from traditionally disadvantaged
subgroups), and also to evaluate if there have been reductions in the differences (gaps) in access
by subgroup. Moreover, an evaluation of the role of a school’s poverty level was also a factor in
analysis to determine differences between high and low poverty schools’ tracking data .
First, eighth grade algebra enrollment between 2003 and 2013 increased for students in
all subgroups across all school poverty quartiles ranging between 33% to 43% (67% to 57%
enrollment in Algebra I) down from a high of 72% (28% enrollment in Algebra I). Schools in
California greatly increased access to Algebra I moving from a time when most students were
enrolled in General Mathematics in 2003 to the majority of students enrolled in Algebra I by
2013. Looking at school poverty quartile alone, the tracking rates decreased over time for all
quartiles. Quartile 1 (low poverty) schools started with the lowest numbers of tracking (most
students enrolled in Algebra I) and continued to enroll the most students in Algebra I across all
years studied. Quartile 2 (moderately low poverty) through 4 (high poverty) schools, on other
hand, reduced tracking consistently up until 2012. In 2012, tracking rates were similar across all
poverty quartiles (mean difference of only 0.05). In 2013 though, for quartile 2, 3, and 4 schools,
tracking rates went up (mean difference between quartile 1 and 4 of 0.1). These were
statistically significant (p < .05) but only had an effect size of f = 0.07, only a minor effect (f >
0.1 is considered a small effect). The difference is important to mention because it was the only
year that tracking rates went back up. This coincided with the SBE's decision in 2013 to remove
ALGEBRA FOR ALL POLICY IMPACTS 154
the penalties for student enrollment in General Mathematics and withdraw the algebra standards
originally added to the eighth grade Common Core course. Most concerning is that the quartile 4
(high poverty schools) tracking averages went up for Filipino students (7 percentage points),
African American students (6 percentage points), and Latino students (4 percentage points),
while white students only increased 1 percentage point, and Asian students were tracked at
exactly the same rate as the previous year (no change). This caused an increase in the gap for
tracking rates and portends a future problem for discrepancies in treatment across ethnic lines.
Although the tracking rates are still significantly lower than they were in 2003, schools must
carefully monitor their decisions to place students in mathematics courses and not move
backwards in terms of equity in opportunity to learn.
The gap in access between traditionally disadvantaged student subgroups and non-
disadvantaged student subgroups also decreased significantly between 2003 and 2013. This was
true for both high and low poverty schools. However, most notable was that the factor of a
school’s poverty level had a large effect on the gap between subgroups—mainly that the higher a
school's poverty the greater the gap between subgroups. This effect decreased over time between
2003 and 2013; however, significant gaps in the tracking rates between traditionally
disadvantaged minority subgroups and non-traditionally disadvantaged subgroups persist. As the
tracking rates for Latino and African American students decreased over time, so did the other
subgroups and sometimes at higher rates. So, although tracking decreased overall for all ethnic
subgroups, the gap was not reduced. This was also true for language proficiency subgroups and
SES subgroups. For language proficiency subgroups, there was even less change in the tracking
rate gaps between the highest and lowest tracked subgroups at each poverty level. The tracking
rates for EL students remained the highest of all subgroups—between 64% and 72% in 2013.
ALGEBRA FOR ALL POLICY IMPACTS 155
The next highest tracked subgroup were the African American subgroup (M = 0.39 to 0.49, in
2013) and the SED subgroup (M = 0.42 to 0.49, in 2013).
Although tracking rates for SED subgroups decreased (32% - 42% decrease), tracking
rates for NSED subgroups decreased at higher rates (46% - 53% decrease). Plus, the NSED
subgroup started at lower tracking rates to begin (see Table 14). This resulted in very little
change in the gap between the SES subgroups over time. Gaps between subgroups were
statistically significant for all years in the study with small to large effect sizes (f).
Achievement—Research Questions 3 and 4
Previous studies on the impact of taking Algebra I in eighth grade have found mixed
results in terms of achievement . Some found that givin g students the chance to take algebra
increased achievement (Gamoran & Hannigan, 2000; Ma , 2005b). While other studies found
that opening up access to all students was not beneficial (Allensworth, Nomi, Montgomery, &
Lee, 2009; Loveless, 1999) . In this study, a ll student subgroups in schools of all poverty
quartiles increased achievement rates significantly in Algebra I (and higher course) CST
proficiency rates between 2003 and 2013 . A significant difference in achievement existed
between high and low poverty schools in 2003 and persisted through 2013; however, while
quartile 1 (low poverty) schools experienced very little change in their mean achievement scores
(M =0.65 in 2003 and M =0.67 in 2013), quartile 4 schools experienced significant growth ( M
=0.25 in 2003 and M =0.42 in 2013) . Schools with the highest rates of poverty (q uartile 4)
improved Algebra I (and higher course) achievement rates by 68%. Paired with tracking data,
this shows that not only has the proficiency rate gone up, it has gone up with significantly more
students taking the course than ever before —an increase of 546% in the number of eighth grade
students proficient in Algebra I (and higher courses) in quartile 4 schools. These results are
ALGEBRA FOR ALL POLICY IMPACTS 156
contrary to the findings of Loveless (2013) who stated, "boosting the percentage of student in
higher level courses is associated with decreases in the mean scores of those courses —
suggesting a watering down effect" (p.30) . These results refute Loveless' finding in that not only
did more students get to take Algebra I, more students were proficient at all school poverty
quartiles. While low poverty schools ( quartile 1) made very little ga ins in achievement (their
scores still remained the highest overall) , the schools increased access to Algebra I by 45% and
kept achievement rates steady , illustrating that there was no watering down of the course and
many more student had access than ever before.
Gaps in achievement still existed, as of 2013, between ethnicity subgroups across all
school poverty quartiles. Even as the highest achieving subgroups in eighth grade increased their
success on the Algebra I (and higher courses) CST, African American and Latino students
increased proficiency rates enough to decrease the gap by 28 percentage points (mean difference
of 0.63 in 2003, compared to a mean difference of 0.35 in 2013) at low poverty (quartile 1)
schools. Quartile 1 schools had the largest achievement gap in 2003 and had the lowest gap in
2013. Quartile 2 schools decreased the achievement gap slightly (mean difference of 0.1), but
quartile 3 schools made no progress, and quartile 4 (high poverty) schools actually increased the
achievement gap between ethnic subgroups by a small mean difference of 0.05.
When comparing language proficiency subgroups, the RFEP subgroup outperformed the
English Only subgroup in all years and at all poverty quartiles. This was most likely due to the
inclusion of African American and non-EL SED students in the English Only subgroup whose
scores on average are the lowest in comparison with other subgroups. Comparing 2004 to 2013,
the difference in performance of the EL subgroup between quartile 1 (low poverty) schools and
the others decreased from a huge 41 mean percentage point difference in achievement (between
ALGEBRA FOR ALL POLICY IMPACTS 157
quartile 1 and 4) to a 27 mean percentage point difference, which demonstrates the large
correlation between school poverty level and performance. An additional component to the
difference may be in the composition of the EL subgroup at affluent school versus schools with
high poverty. In California, the majority of EL students' primary language is Spanish. Of those
Spanish-speaking eighth grade EL students, in 2013, 83% of them were also SED, whereas only
50% of the EL students who speak an Asian language (including Filipino) are SED (CDE, 2013).
This might contribute to the higher scores of EL in more affluent schools as the effects of student
SED and school poverty levels are so high—being that populations of EL students at affluent
schools are more likely also to be affluent and may additionally be of Asian descent. The EL
subgroup overall made only small gains in achievement over the course of the 11 years studied.
At quartile 1 (low poverty) schools, EL students perform about as well as the highest achieving
subgroup (RFEP) at quartile 4 schools, but at quartile 2, 3, and 4 (high poverty) schools the EL
subgroup has only achieved proficiency rates of 20 – 29%, similar to the achievement rates of
African American students. Although this is an improvement over previous rates, these rates still
leave a large gap in achievement between the RFEP and English Only subgroups.
Finally, it is clear that school level poverty matters. Additionally, the SES of individual
students within different schools matters as well. In this study, quartile 3 and 4 (high poverty)
schools began with very small differences in the achievement rates of their SED and NSED
students in 2003. Quartile 3 schools started at achievement rates higher than that of quartile 4
schools, but the quartile 4 schools nearly caught up by 2013. At quartile 4 (poorest) schools,
both subgroups gained ground and improved proficiency rates, but the rates of the NSED
subgroup increased at rates higher than that of the SED subgroup, 95% increase versus 74%
increase respectively at quartile 4 schools. Quartile 1 (low poverty) and 2 schools had larger
ALGEBRA FOR ALL POLICY IMPACTS 158
gaps in achievement between SES subgroups but decreased the gap by more than half between
2003 and 2013. The SED subgroup at quartile 1(low poverty) schools, for instance, increased
proficiency rates by 52%. Remember these increases also coincide with the increases in access
for all subgroups in all poverty quartiles, so as access increased so did proficiency—even for
students traditionally disadvantaged and underperforming. For all student subgroups (ethnicity,
language proficiency, and SES) the school's poverty rate was highly correlated to achievement.
As the poverty level of the school increased, achievement decreased for all students.
Equity in Placement—Research Question 5
In 2010, Waterman found that several school districts in the Bay Area of California were
under placing proficient eighth grade students in Algebra I . Especially problematic was th at the
misplacement was correlated across subgroups; traditionally disadvantaged sub groups were
found to be more likely to be under -placed in algebra . Under-placement indicates that there are
students not receiving a fair and equitable opportunity to learn . Research question 5 was used to
look at these same patterns of placement for all schools in California between 2003 and 2013 .
Although this study cannot state that the Algebra for All policy caused the noted impact on
placement, there is a correlation between the years of the policy implementation and a change in
placement practices across all middle schools in California. Over time, schools increased the
numbers of students taking Algebra I regardless of previous mathematics (seventh grade)
proficiency.
First, placement rates increased over time between 2003 and 2013 and decline d
significantly in 2013 . In 2013, the California SBE removed the penalty to API scores for
placement of students in General Mathematics and also adopted an eighth grade math curriculum
aligned to CCSS to be implemented in the 2014 -15 school year . These two decisions together
ALGEBRA FOR ALL POLICY IMPACTS 159
ended the Algebra for All movement. When looking at placement data, there is a correlation
between this decision and a change in mean placement practices across CA —namely, a reduction
of over -placement in quartile 2, 3, and 4 schools and a return to slight under -placement at
quartile 1 (low poverty) schools.
Secondly, placement rates were significantly influenced by a school's poverty quartile .
Chiefly, the higher a school's participation rate in the FRPM program (high poverty) the higher
the over-placement of students into Algebra I . The higher the school’s poverty rate the more
likely that the schools were to place non -proficient students into Algebra I. This was true even
when controlling for the effect of achievement —as achievement rates at quartile 1 (low poverty)
schools are significantly higher than they are at quartile 4 (high poverty) schools. Interaction
effects for subgroup and poverty quartile were statistically significant only for ethnicity and SES;
however effect siz es for these interactions were only small for the last two years of the analyses
on ethnicity (2011-12 and 2012 -13). These interactions were significant for the bottom three
quartiles but not for quartile 1 schools . Paired with the correlation between th e end of the
Algebra for All policy this may reveal a pattern that the effects of school poverty are more
significant than those of other student factors on placement and that new algebra policies (mainly
that it is up to the local level to decide) may be more of a concern for high poverty schools . For
example, the analysis of 2011 -12 and 2012 -13 placement across poverty quartiles for specific
subgroups (Table 34) shows that there is a small to moderate effect size for a school poverty
level on placement by ethnic subgrou p.
This was also true for the analysis by language proficiency . Placement rates were not
affected by language proficiency —analyses between language proficiency subgroups did not
have significant effect sizes; however, the effect sizes for school poverty level across the
ALGEBRA FOR ALL POLICY IMPACTS 160
subgroups revealed moderate effect sizes ( f > 0.25). Again, school poverty level had a larger
effect on placement th an did the language proficiency subgroups .
An analysis of student SES did reveal effects of subgroup on placement but only with
small effect sizes ( f > 0.10) at quartile 2 and 4 (high poverty) schools. However, an analysis
across poverty level treatmen t of SES did again reveal statistically significantly different
placement means across poverty levels with small approaching moderate effect sizes ( f between
0.17 and 0.21) for all years studied . Of note for the SES analysis is that although the differenc es
were not significant, quartile 1 schools had much larger gaps in their placement rates of students
by SES with SED subgroups being placed at lower ratios that NSED s tudents. And in 2012 –
2013, quartile 1 schools under placed SED students and over placed NSED students . It will be
important to keep an eye on this in future analyses of practice especially when the Common Core
eighth grade course is made available as the standard.
Implications
While long known differences still exist between student s ubgroups (ethnicity, language
proficiency, and SES), the differences in achievement for these groups was strongly affected by
school poverty . A school cannot affect change in their poverty rate . Giving additional funding
to schools with high levels of po verty may help, but there are greater implications . Rather than
looking at the school level, funding of community resources and services may be the lever for
change. Schools provide breakfast, lunch, and sometimes even dinner . After school programs
provide homework help and enrichment into the evening . Some schools even have Saturday
programs. At some point, the circle of influence on achievement must move beyond what a
school can provide and look to changes that need to occur in whole communities .
ALGEBRA FOR ALL POLICY IMPACTS 161
Moving to a conversation about tracking practices in the future, it appears that the
Algebra for All policies had an impact on reducing tracking . What will happen beginning as
soon as the next school year with the introduction of CCSS? NCLB requires that a ll students are
proficient. Because California's eighth grade course was Algebra I, all eighth-graders had to be
proficient in Algebra I . Obviously, the schools in the state did not achieve that goal, although
significant progress was made . With the imp lementation of CCSS, the new course for eighth-
graders is the eighth grade Common Core class, with Algebra I being a ninth grade course .
Although the SBE hopes that schools will continue to place students into Algebra I at the eighth
grade "when they are ready," the pressures of reaching the lofty 100% proficient for AYP are
high. What is the incentive for schools to place students into Algebra I? Will the divide between
high and low poverty schools increase? Schools with the lowest levels of achievement (high
poverty schools) are most likely to place students into the lower Common Core Grade Eight
course. For students that are nowhere near ready for Algebra I (those scoring Far Below Basic
for example), this will probably be a good move . The new course is not a repeat of grade six and
seven standards as the old General Mathematics course was .
The greatest concern though is for the students that could be successful with support . As
schools have to now offer two options for eighth grade mathematics, thi s reduces their ability to
provide support courses . For example, at a small school with only one eighth grade mathematics
teacher, that teacher now must teach two courses —Algebra I and Grade Eight Mathematics . The
addition of a support or intervention co urse would require this teacher to now teach three
courses. Most schools do not require teachers to take on three preparations, or at least they try to
avoid it. Additionally, there may be contractual issues that prevent this . Even if the teacher does
take on three courses, that teachers attention is now split across three different lesson plans for
ALGEBRA FOR ALL POLICY IMPACTS 162
each day, possibly affecting teacher effectiveness . Furthermore, some schools may find that
rather than provide a support class it may be better for that st udent to instead take Grade Eight
Mathematics where they will not need support . Schools may be tempted to think of this as a
win-win situation. The student can be successful in mathematics and, hopefully, the schools AYP
will increase . The incentives to put a student in Grade Eight Mathematics are much higher than
the incentive to enroll them in Algebra I .
Limitations
By far the largest limitation of this study is the inability to tie any of these results directly
to the Algebra for All policies. What can be said is that during the time these policies were in
place, tracking was reduce d and achievement went up and in 2013 , when news of the dissolution
of the policy was announced tracking increased slightly . Additionally, these findings are limited
to the population under study —California eighth-graders—and cannot be generalized to other
grades or other places . Finally, by using means to analyze data, the differences between districts
and schools are lost . By aggregating the data for analysis, the inf ormation about how different
locales implemented Algebra for All is not measured . For example, while one study found that
there were placement discrepancies across several districts in the Bay Area of California, another
analysis did not reveal these disc repancies statewide (Liang, J.H., Heckman, & Abedi, 2012) . In
order for schools and districts to utilize the results of this study, they must conduct their own
analysis of their practices to determine whether or not they have i ncreased access to algebra
equitably (tracking) and successfully (achievement).
Suggestions for Future Research
First, there were some limitations in the detail of subgroups because of the size and scope
of this large analysis. Future researcher may want to look closer at student subgroups
ALGEBRA FOR ALL POLICY IMPACTS 163
particularly the combination subgroups. For example, i n the analyses of achievement, the
English Only subgroup performed at rates lower than the RFEP subgroup. The English Only
subgroup includes all ethnicities and SES subgroups, which may have led to the differences
between the English Only and RFEP groups. To further del ve into these achievement differences,
using the multiple subgroup data provided by the CDE might provide clearer detail. For
example, the Dataquest files (available from the CDE) provide combination subgroups —English
Only and African American, English Only and White, etc. This combined subgroup data could
provide additional detail with the differences in the language proficiency and student poverty
analysis.
Secondly, w ithin the first few years of implementation of CCSS, careful analyses must
take place at local levels to ensure that placement decisions for eighth-graders are equitable and
fair. Within a few short months of the end of Algebra for All, changes in tracking and placement
were evident. Because this study included all schools in the state, these effects may be greater
for some districts than for others . Local school districts should analyze their own tracking
practices over the last 10 years alongside their proficiency rates to determine whether or not they
have achievement and tracking gaps. Further, schools and districts have access to matched
scores, which allows for the local analysis of student pathways and placement practices. Th is
will not only provide data for the analysis of past practice but will also allow local agencies to
determine what trailing indicators were most likely associated with success in Algebra I. Clearly,
between 2007 and 2012, schools across the state over -placed students in Algebra I (especially
high poverty schools). Despite this over -placement, achievement in Algebra I continued to
increase. Therefore, proficiency in seventh grade mathematics may not be the best indicator for
success in Algebra I. It is possible that a scale score somewhere between Basic and Proficient
ALGEBRA FOR ALL POLICY IMPACTS 164
may be associated with success in Algebra I. Additionally, districts and schools may have other
assessment and achievement results (common assessments, district benchmarks, diagnostic tes ts)
that they have access to that can be analyzed to determine appropriate placement. As the current
recommendation for placement in Algebra I in California is to place students “when ready,” there
is a large responsibility on local education agencies to create a readiness profile for students that
includes multiple data points. Schools and districts must implement practices to monitor their
readiness benchmarks, placement practices, achievement, and tracking by subgroup each year to
self-audit. The SBE has put the decision about Algebra I at the eighth grade on local education
agencies, and therefore these agencies have a duty to critically review their own practices to
ensure equity and access .
Finally, a year after the implementation of CCSS, the tra cking rates for Algebra I
statewide should be examined . It is likely that many high poverty schools will place the majority
of their eighth graders into the CCSS Grade Eight Mathematics. While many students at high
poverty schools have not been successfu l in Algebra I at the eighth grade , Algebra for All
policies opened up access to many students (successfully) that never would have been given
access before the policies. These successes and the increased access experienced by poor and
minority students c ould disappear without close scrutiny and constant pressure to maintain
equity. Achievement should be examined statewide as well; however, if schools place large
numbers of students in Grade Eight Mathematics, achievement may be artificially inflated .
Therefore, achievement rates must be examined alongside tracking and placement practices to
get a true picture. Overall, the CCSS and its emphasis on depth of understanding should provide
a better mathematics education for students; however, the implementat ion of the new standards
should not mean decreased access to Algebra I for students that are ready.
ALGEBRA FOR ALL POLICY IMPACTS 165
Conclusion
Over the course of the Algebra for All policy implementation in California between 2003
and 2013, California eighth-graders across subgroups an d across school poverty levels
experienced increased access to Algebra I . In addition, Algebra I achievement increased . With a
new set of standards, the policy regarding eighth grade mathematics placement is changing .
While the efforts to improve educat ion should continue and sharing common benchmarks across
the country has benefits , future outcomes for students need to be analyzed . If indeed schools
begin to limit access to Algebra I at the eighth grade, there will be effects on higher mathematics
course taking and subsequent preparation for college . Although many questioned the wisdom of
requiring all eighth-graders to take Algebra I, it is unquestionable that access to the course was
provided to many that did not have access previously and achievemen t rates increased . Schools
and districts should carefully consider these findings before making local policy decisions on
what course their eighth grade students will take with the implementation of CCSS.
ALGEBRA FOR ALL POLICY IMPACTS 166
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Abstract (if available)
Abstract
Algebra for All policies in California were designed to open the barriers to the courses that correlate to college achievement and wage increases. Previous findings have so far been mixed, revealing both successes and work still to be done. It is important to determine whether these policies had the effects intended and to consider practical implications of the policy before the next big change in California mathematics—the implementation of Common Core State Standards in 2014-15. This study contains data from all California middle schools between 2003 through 2013 with a focus on the differences between high and low poverty schools' outcomes across student demographic subgroups. The focus of the study was on the impact of early algebra policies on California eighth‐graders with regard to tracking, achievement, and placement practices. Kruskal‐Wallis and two-way ANOVA were used to analyze results. The data studied revealed that between 2003 and 2013, enrollment into Algebra I at the eighth grade was increased for all students in all subgroups and proficiency rates in Algebra I went up for all students across all subgroups and school poverty levels.
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Raymundo, Natalie Ann
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The impact of Algebra for all policies on tracking, achievement, and opportunity to learn: a longitudinal study of California middle schools
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University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
CST
education policy