# The predictors and consequences of eighth grade algebra success

TABLE OF CONTENTS

Dedication………………………………………………………………………… …ii

Acknowledgments………………………………………………………………..

…iii

List of Tables……………………………………………………………………...

…v

List of Figures…………………………………………………………………… …vii

Abstract…………………………………………………………………………

…viii

Chapter One:

Introduction……………………………………………………

…1

Chapter Two:

Review of the Literature……………………………………...

…17

Chapter Three:

Methodology…………………………………………………. …55

Chapte r Four:

Results………………………………………………………..

…68

Chapter Five:

Conclusions…………………………………………………

…133

References……………………………………………………………………… …149

Appendices

Appendix A:

Interview Letter of Introduction/Explanation………...

…154

Appendix B:

Counselor Interview Protoco l…………….......……….…156

v

LIST OF TABLES

Table 1.

Cohort Selection Criteria…………………………………………….

…60

Table 2.

Percentage of Students in Eighth Grade Algebra……………………

…81

Table 3.

Total Students by Parent Education Level…………………………..

…83

Table 4.

Participation in F ree and Reduced Lunch Program…………………. …85

Table 5.

Participation in GATE……………………………………………….

…86

Table 6.

Math Course Selection for GATE Students in Eighth Grade………..

…86

Table 7.

Special Education Student Participation…………………………….. …87

Table 8.

504 Accommo dation Plan Student Participation……………………. …87

Table 9.

Average Math CST Scaled Scores by Elementary School…………..

…90

Table 10.

Average CST Scores by Intermediate School……………………….

…91

Table 11.

Average 5th Grade Math and Algebra I CST Scales Scores………...

… 93

Table 12.

Average 7th Grade Math and Algebra I CST Scaled Scores………..

…94

Table 13.

Population of LAHS Graduating Classes 2008 - 2010……………….

…97

Table 14.

Total Students by Parent Education Level…………………………

…100

Table 15.

Weighted, Cumulative GPA (2008 - 201 0 LAHS graduates)……….

…102

Table 16.

Participation in the Free and Reduced Lunch Program……………. …103

Table 17.

Participation in GATE……………………………………………...

…103

Table 18.

Math Course Selection for GATE Students in the Eighth Grade…..

…104

Table 19.

Special Edu cation and 504 Accommodation Plan Student………… …104

Participation

Table 20.

Cohort Selection Criteria, Algebra I Variables…………………….

…107

vi

Table 21.

Math SAT Averages by Cohort…………………………………….

…108

Table 22.

Correlation Coefficients between Math SAT and Algeb ra I CST…. …108

Scaled Scores

Table 23.

Algebra II CST Scores and Averages by Cohort…………………..

…110

Table 24.

Correlation Coefficients between Math SAT and Algebra I CST…

…110

Scaled Scores

Table 25.

Grade Level of Last Math Course (shown in percentages)… ……...

…114

Table 26.

Average Cohort’s Final Mathematics Course and Grade Level…… …115

Table 27.

Accelerated Cohort’s Final Mathematics Course and Grade Level

…117

Table 28.

High Achiever Cohort’s Final Mathematics Course and Grade…… …118

Level

Table 29.

G rade Level of Final Science Course (shown in percentages)……..

…120

Table 30.

Average Cohort’s Final Science Course and Grade Level…………

…121

Table 31.

Accelerated Cohort’s Final Science Course and Grade Level……... …123

Table 32.

High Achiever Cohort’s Final Science Course and Grade Level…..

…124

vii

LIST OF FIGURES

Figure 1.

LAUSD Demographics…………………………………………….. …57

Figure 2.

Excerpt from the 6th Grade Math Recommendation Form………...

…72

Figure 3.

Multiple Measures for Pre - Algebra Identification: Grade 6……….

…74

Figure 4.

Math Course Sequence, 6th to 7th Grade…………………………..

…76

Figure 5.

Math Course Sequence, 7th to 8th Grade…………………………..

…77

Figure 6.

Math Course Sequence, 8th Grade to 12th Grade………………….

…78

Figure 7.

Percentage of Students in Eighth Grade Algebra… ………………..

…82

Figure 8.

Ethnicities of the Overall Eighth Grade Student Population……….

…82

Figure 9.

Parent Education Level of Students (shown in percentages)………

…84

Figure 10.

Ethnicity of Students that took Eighth Grade Algebra I…………… …98

(2004 - 2006)

Fig ure 11.

Ethnicity of the Overall Student Population that Graduated……….

…99

High School (2008 - 2010)

Figure 12.

Parent Education Level of Students (shown in percentages)……... …101

viii

ABSTRACT

This study examined predictors of success in eighth grade Algebra a nd the consequences of that success in high school. There has been a nationwide push to enroll more eighth grade students in Algebra in order to allow access to advanced mathematics in high school. The increase of students enrolling in Algebra has not on ly resulted in more minority students having access to a more academic track in math classes, but has also resulted in a group of students that may not have been prepared to take Algebra in the eighth grade. This study sought to find viable, accurate and reliable predictors of success in eighth grade algebra as well as what that success means in terms of later academic achievement.

Using the Los Amigos Unified School District as a model for this case study, it was found that fifth and seventh grade CST sco res have a strong correlation coefficient to success in eighth grade Algebra. The study also found that students of particular elementary schools and intermediate schools perform significantly better than students from other schools in the district. The study also found that eighth grade Algebra I CST scores have a strong relationship not only to Algebra II CST scores, but also to math SAT scores.

This study lends supportive evidence to the belief that success in Algebra I is of more importance than the g rade level at which Algebra I is taken. The nature of Algebra, and the essential fundamentals that children master through studying Algebra serve as an essential building block of further mathematical studies. This study underscores the importance of suc cess in Algebra.

1

CHAPTER ONE

INTRODUCTION

The ability of the United States to adequately educate and prepare its students in the use of quantitative ideas is critical to its standing as a world leader in economics, technology and scientific innovation. Hi story is full of examples of civilizations that have thrived and flourished as a direct result of their ability to understand and apply mathematical concepts. “Leading societies have commanded mathematical skills that have brought them advantages in medic ine and health, in technology and commerce, in navigation and exploration, in defense and finance and in the ability to understand past failures and to forecast future developments” (NMAP, 2008, p. 1). An understanding of mathematical principles is necess ary in order to preserve the quality of life to which the citizens of the United States have become accustomed. “Although the need for mathematics within science and technology fields is significant, its role goes beyond career preparation; mathematics re asoning is an indispensable tool for informed participation in a democracy” (Gine & Kruse, 2007, p. 1). Mathematical preparation is also a vital component of the United States’ ability to adequately prepare a workforce that is able to keep pace with and a dapt to the challenges of the 21 st century global economy. Job growth in the mathematics, science and engineering workforce are outpacing overall job growth and that trend is sure to continue. Mathematic proficiency is an essential element if the United States is to maintain its position as a world leader.

2

Since World War II, the government and educators of the United States have recognized the need for its citizens to obtain mathematic proficiency and have made it the focus of a number of reports, reform s and initiatives designed to raise mathematical achievement in the nation’s schools. Herrara & Owens (2001) suggest that the 1957 launch of the Soviet satellite Sputnik helped to create the perception that the United States trailed the Soviet Union in sc ience and technology. Sputnik

helped to refocus the nation’s attention on math and science education as an integral component to success and security. The result was an educational reform known as the “New Math Movement.” This movement of the 1960s focu sed predominately on preparing students for higher level courses such as calculus and analytical geometry mathematics at the university level. The discovery and problem solving techniques of the New Math Movement eventually gave way to the “back to basics ” era of the 1970s in which educators employed procedures and principles backed by behavioral psychology (Herrara & Owens, 2001). Students were drilled in the basics and learned the procedures for solving complex mathematical problems. During both decade s, neither reform resulted in substantial gains in student mathematics achievement.

In 1983, the National Commission for Excellence in Education brought renewed attention to the need for adequate mathematics preparation in its Nation at Risk report. The d evelopment of standards by the National Council of Teachers of Mathematics (NCTM) was one of the outcomes of this report. “Mathematical curriculum standards refer to the set of learning goals articulated across grades that

3

outline the intended mathematics content and process goals at particular points in time throughout the K – 12 mathematics program” (Reys, Reys, Lapan, Holliday & Wasman, 2003, p. 75). The use of standards - based curricula has now become the accepted standard for mathematics instruction a cross the nation. Many studies have shown that student achievement in mathematics has significantly increased with the use of a standards - based curriculum, including students with varying ability levels and backgrounds (Briars, 2001; Griffin, Evans, Timms & Trowell, 2000). Currently state and federal laws require that all public schools teach to approved standards and that students’ proficiency of the standards is assessed.

Despite advances made in content and pedagogy, student achievement in mathematics remains dismal. According to the 2007 National Assessment of Educational Progress (NAEP) scores, only 39% of students in grade 8 and only 23% of students in grade 12 are at or above the proficient level (Lee, Grigg & Dion, 2007). Several measures of stud ents’ mathematical understanding show that American students do not fare well compared to the youth of other industrialized nations. In the Trends in Mathematics and Science Study (TIMSS), 38% of the fourth graders in Singapore scored at an advanced level while only 7% of the fourth graders in the United States did so (NMAP, 2008). Another study by Baldi, et al. (2007) showed that American 15 year old students’ understanding of math literacy and problem solving ranked 25 out of 30 among developed nations. Even more alarming are 2003 NAEP scores that showed many eighth grade students lack the fundamental skills required for algebra including familiarity with fractions and word

4

problems (Braswell, et al., 2005). These examples illustrate a much larger prob lem: students in American public schools are not acquiring the mathematical knowledge necessary to maintain America’s position of leadership in the global community.

Algebra has become a major focus for increasing students’ mathematical achievement. The N CTM (2008) describes algebra as “… a way of thinking and a set of concepts and skills that enable students to generalize, model and analyze mathematical situations. Algebra provides a systematic way to investigate relationships, helping to describe, organ ize and understand the world” (p. 1). Algebra is seen as a gatekeeper course that teaches students skills that will enable them to be successful in higher level mathematics courses. Students who complete high advanced math courses such as Algebra II have more success in high school and college mathematics courses and eventually have a higher earnings potential (NMAP, 2008, p. xii). “Algebra offers a way to generalize mathematical ideas and relationships, which can then be applied in a wide variety of mat hematical and nonmathematical settings” (NCTM, 2008, p. 1). Thus, algebra is seen as an integral component to raising students’ math achievement. It was observed on both the 2003 and the 2008 California Standards Test (CST) in mathematics that students d emonstrated a marked decline in mathematics achievement during their intermediate school years; close to the same time that they enter or are preparing to enter their first formal algebra course (EdSource, 2009). Many educators are concerned that poor mat h achievement during students’ middle school years will discourage students in their first algebra course contributing to less future success in

5

and a general dislike for mathematics (NMAP, 2008). As one of the primary and most important mathematical skil l sets, algebra equips students to pursue higher mathematics contributing to greater mathematical achievement.

There has been a significant ground swell of support to teach algebra in the eighth grade. The emphasis on algebra in the eighth grade was broug ht to national attention when President Clinton declared it a national goal in Goals 2000. Many states such as California now insist that students take Algebra in the eighth grade by employing assessment and accountability measures. The body of literatur e suggests that earlier algebra completion will result in greater chances of taking advanced mathematics courses, higher mathematical achievement and greater likelihood of college admission and graduation (Loveless, 2008). Along these lines, educators and

policy makers have pushed for students to take algebra before entering high school. Middle school mathematics course selection has real academic consequences: often placing students on a track that predicts their course placement at the high school level (Oakes, Gamoran & Page, 1992). “Eighth grade mathematics generally is considered to be the gatekeeper to advanced mathematics learning, entry into physical science courses, and post secondary opportunities” (Wang & Goldschmidt, 2003, p. 14). Current res earch suggests that the earlier algebra has been taught, the greater the students’ mathematical achievement and policy makers have decided that algebra should be taught in the eighth grade.

Student access to and success in algebra has been shown to differ across ethnic and gender lines. The number of mathematics courses taken differs according

6

to ethnicity and gender. “Girls and underrepresented minorities, especially African Americans and Hispanics, tended to take few mathematics courses” (Wang & Goldsch midt, 2003, p. 3). In 2003, only 23% of black students and 26% of Latino students took Algebra in the eighth grade limiting most of these students’ chances of completing Algebra II by the end of high school (EdSource, 2009; Tietelbaum, 2003). Students ta king fewer mathematics courses are often at a disadvantage when applying for college admission. The NMAP Final Report (2008) demonstrated that mathematics success is related to college success which in turn is related to higher earnings and a higher quali ty of life. Thus, access to algebra courses for all students in eighth grade is an equity issue. “The push for universal eighth - grade algebra is based on an argument for equity … democratizing eighth - grade algebra promotes social justice” (Loveless, 2008 , p. 3).

While the immediate objective of increasing access to algebra for eighth grade students has succeeded, the long term goals of increasing student math achievement and access to higher level mathematics have yet to be realized. The math achievement of California students, as measured by the CST in 2003 and 2008, has shown that even though algebra enrollment in the eighth grade increased by 43% over five years, nearly the same percentage of students is scoring at or above proficient level (EdSource, 2009). Thus, while student participation in algebra at the eighth grade level has increased, student success has remained fairly stagnant. The 2007 NAEP scores showed that from 2000 to 2007, the achievement of eighth grade students in advanced classes su ch as Geometry and Algebra II has decreased by four

7

points (Lee, Grigg & Dion, 2007). Across gender, ethnicity, linguistic background and learning ability, the increase in the number of students taking Algebra in the eighth grade does not yield greater st udent success in math. Data also show that many eighth grade algebra students repeat algebra in their first year of high school. As EdSource claims more than one - third of students taking Algebra in their ninth grade year are repeating the same course tha t they took in eighth grade (EdSource, 2009). Loveless (2008) attributes these concerning trends to students that are inappropriately accelerated and subsequently misplaced in Algebra courses in the eighth grade. Eighth grade students that are misplaced in advanced algebra courses were shown to score significantly lower than their peers on the 2007 NAEP (Loveless, 2008). While the increasing number of eighth grade students taking algebra courses is encouraging, their lack of success is cause for concern.

Schools must weigh the pressure to accelerate all students to take algebra in the eighth grade, keeping in mind the mathematic preparation and scholastic well being of the child. Some scholars worry that a continuous lack of success in math can have the effect of convincing students that they are unable to learn the material and will create general dislike of mathematics (EdSource, 2009). Loveless (2008) suggests that NAEP scores show that eighth grade students misplaced in advanced algebra courses are a ctually seven grade levels of mathematical achievement below their appropriately placed peers in the same mathematics courses. Additionally, many high schools will not recognize Algebra courses taken at the middle school level, questioning its rigor and f orcing students to repeat the course in the ninth grade

8

year (EdSource, 2009). The push to accelerate students to take Algebra in eighth grade may result in unintended consequences for student achievement while not progressing towards the primary goal of putting students on track to take higher level mathematics courses in high school.

The opportunity for an eighth grade student to take algebra means nothing if that student has not been adequately prepared in the prerequisite skills necessary to be success ful in that course. The increase of students taking algebra courses has resulted in a situation in which students are taking courses for which they are not prepared. The NCTM (2008) remarks:

Only when students exhibit demonstrable success with prerequisi te skills –

not at a prescribed grade level – should they (students) focus explicitly and extensively on algebra, whether in a course titled Algebra I or within an integrated mathematics curriculum. Exposing students to such coursework before they are rea dy often leads to frustration, failure and negative attitudes towards mathematics and learning (p. 1)

The California Mathematics Framework explicitly states that students should be prepared to study algebra by the eighth grade. However, student learning must be the primary goal, not course completion. The practice of placing all eight grade students in algebra may not be the best way to increase student math achievement.

Given that preparation is crucial to success in algebra courses, schools and distric ts are looking to find effective means of assessing student algebra preparedness in order to place students in the most appropriate math course in the eighth and ninth grades. Students placed in courses that are appropriate for their skill level will bene fit more than students who are accelerated and misplaced (Loveless,

9

2008). Therefore, a school’s ability to adequately assess students’ algebra preparedness and to place students in challenging yet appropriate math courses may ultimately determine that sc hool’s math achievement. The numerous, current predictors for a students’ success in algebra are as follows: standardized test scores, academic marks, placement test results and teacher recommendations are commonly used to place students in the appropriat e math class. Not only must schools and districts be able to rely on accurate and consistent predictors of student success in algebra, they should understand the effect that taking algebra in the eighth grade can have on students’ college readiness.

State ment of the Problem

Achievement of the primary goal of increasing student math achievement and a greater aptitude for problem solving and technical skills is critical to the United States’ ability to meet the upcoming challenges of the 21 st century. The p ush for algebra in the eighth grade has reached a sort of academic crossroads, carefully attempting to weigh the increased likelihood of future success by taking advanced math courses with the preparation necessary to enroll in such a course. Teachers and

administrators in public schools are under pressure to enroll eighth grade students in algebra courses from state and federal governments; however, increased enrollment in eighth grade algebra has contributed to lower student math achievement and more stu dents repeating the course. Many observers feel that these trends are the consequences of eighth grade students misplaced in advanced algebra courses without adequate preparation. In order to realize the greater goals of accelerating

10

students to take Alg ebra in eighth grade, schools must ensure that students are adequately prepared for Algebra prior to placing students in courses that they are destined to fail and repeat.

The teachers and administrators of individual schools must make math course placemen t decisions that affect their students’ future, their school’s achievement and yet must meet the demands of educational policy makers. The factors and guidelines to determine this placement vary greatly between schools and districts. Given that the Unite d States’ standing as a scientific and technological leader in the world is greatly dependent on its ability to educate its population and workforce in mathematical ideas, it is critical that teachers and administrators are adequately informed to make such placement decisions. Research is needed to show which factors are reliable and accurate predictors of algebra readiness, to what extent those factors contribute to a student’s success and how to best assess these factors. It is necessary to evaluate whi ch practices in student placement have lead to increased student success and which have lead to failure. Teachers’ and administrators’ understanding of these factors is crucial to raising the math achievement of America’s students.

Purpose of the Study

Th e purpose of this study is to research the predictors and consequences of eighth grade algebra success. A better understanding of the predictors of algebra success will allow schools to more appropriately place students in their eighth and ninth grade mat h courses. The study will use a medium sized suburban school

11

district to analyze student performance on previous assessments of student achievement in math and their corresponding success in algebra. The study will also relate eighth grade algebra achiev ement to college readiness factors such as course rigor and SAT scores among three cohorts of students. Another goal of this study is to gain a working knowledge of current eighth grade math course selection practices in the above mentioned district.

With a firm grasp of the current course selection practices and a better understanding of the validity of certain predictors, the study will be able to offer suggestions to this district and others like it as to the best practices for placement in eighth grade algebra. The study will also demonstrate the effects of taking algebra prior to students gaining adequate preparation. With the information that results from this study, educators will be able to make more informed math course selections for students in the eighth grade. More informed math course selection in the eighth grade will allow students to take the course that will most benefit their progression of mathematical skills and thinking.

Research Questions

The following research questions guided this study:

1.

What criteria do intermediate school counselors use to place eighth grade students in their math course?

2.

What student information helps to predict success in eighth grade algebra?

12

3.

How do eighth grade algebra CST scores relate to math SAT scores and

Algebra II CST scores?

4.

Are students more likely to take advanced math and science courses during high school if they have success in eighth grade algebra?

Importance of the Study

The findings of this study will give educators and policymakers alike a bett er understanding of the predictors and consequences of eighth grade algebra achievement. While all stakeholders may claim that their decisions are based on the best interests of students, a closer examination of the practices that yield the greatest stude nt achievement will allow educators to make more appropriate decisions on the behalf of students.

Educators need to be armed with information that allows students to be placed in the most appropriate math course. It is of paramount importance that all stu dents not only have an opportunity to take and learn algebra but also to develop a working conceptual and procedural knowledge of algebraic principles. Furthermore, basic algebra serves as a foundation upon which a myriad of advanced mathematical skills a re based. Research has shown a clear link between algebra preparedness and algebra success. Schools must be aware of the characteristics of students that are prepared to take algebra and those that are not. By using one of these factors, or a combinatio n of them, schools may be able to better place students in the most appropriate math course, leading to greater math achievement over the course of their academic career. Educators will also be able to determine the reasons that

13

students are not ready to take algebra and address deficiencies in the curriculum and instructional practices. This study will allow schools to best place students in math courses that are best suited to meet their academic needs.

The push to enroll students in algebra in the eigh th grade has been driven by the need to see increased math achievement among all students. Policymakers saw that students who took algebra in the eighth grade were more college ready as demonstrated through a more rigorous course load and achieved better SAT scores. However, pushing all students to enroll in eighth grade algebra did not result in increased student achievement. Instead, it placed many students in a course for which they were unprepared. This study will lend support to the notion that inc reased math achievement is not always manifested through more difficult courses at an earlier age. Math achievement increases through a better understanding of and a genuine interest for learning the subject matter. When this study is finished, policymak ers will be able to see that students placed in the appropriate math course for their preparation level show higher math achievement than students who are accelerated into algebra courses prior to being fully prepared.

Increased math achievement amongst Am erican students is an appropriate and important goal for the public education system in the United States. There are differing views on what would be the most effective and efficient way to boost this achievement. This study will help to show educators a nd policymakers that eighth grade math course selection is a critical decision that has a direct relation to student’s

14

college readiness and give educators suggestions as to the best predictors of algebra success.

Assumptions

This study assumes that the qu antitative measurements of student success are the result of the students’ best efforts to demonstrate their knowledge and mastery of the information to be assessed. It is further assumed that students are currently placed in their eighth grade math cours e based upon seventh grade teacher recommendation. In this district, teacher recommendations are the default course placement criteria and are based on students’ performance in their previous math course. The study also assumes that the instruction and c urriculum in Algebra courses follow the California State Standards for Algebra.

Limitations

This study is set in a high performing, medium sized suburban school district. There is a strong emphasis on college readiness in the homes of the students, at sch ool and in the community.

The first limitation is that quantitative results of this study are limited by the small sample size as well as the characteristics of the participants. Certain students may have incomplete academic records for a variety of diffe rent reasons and there is a moderate degree of transiency in the district which makes comparisons between students more difficult. Variables such as ethnicity, socioeconomic status and family background will not be taken into account in this study.

15

The se cond limitation is that student assessments that are used to determine preparedness and student achievement are only snapshots of student learning and may not reflect the true level of the students’ knowledge of the California State Standards.

Thirdly, the qualitative aspects of this study acquired through interviews and surveys are limited and open to interpretation of the researcher and participants. Thus they may be subject to a certain level of bias. Although measures will be taken to collect data fro m multiple viewpoints, a small level of bias is still a concern of the researcher. This is to be expected in any qualitative study.