Coursetaking & Achievement in Mathematics and Science:
Inequalities that Endure and Change

 Jeannie Oakes, Kate Muir, Rebecca Joseph
UCLA

Paper prepared for the National Institute of Science Education

July 2000

Abstract

A review of research on equity in mathematics and science coursetaking and achievement reveals that, in a decade of policies pressing for high standards in schools that remain separate and unequal, we’ve made some progress in raising the levels of coursetaking and achievement of all racial groups.  At the same time, however, we’ve done little to reduce the gaps among them.  While the increases are encouraging, they have served to raise standards for admission to competitive colleges in ways that prevent most low-income and minority students from translating their improved accomplishments into enhanced educational and life chances.  Our review also supports the claim made last year by the Task Force on Minority High Achievement that we have learned a great deal “about how minority educational outcomes can be improved, despite having made only modest investments in educational R&D” (The College Board, 1999, p. 14).  We concur with the Task Force’s recommendation that we must “redouble our efforts and our investments” to promote minority opportunities and high achievement (p. 14).  To forward this agenda, we offer a set of research questions about the general educational system as well questions specific to math and science education.  We believe that both types of questions are necessary as researchers and policy makers implement what we already know and mount new, vigorous initiatives to learn more and do more to achieve equitable course taking and achievement.

Introduction

 In July 1999, Rasheda Daniel and three of her fellow students at Inglewood High School in Southern California launched a legal challenge to achieve equitable access to Advanced Placement (AP) courses. Represented by the American Civil Liberties Union (ACLU) of Southern California, the Inglewood High School students filed a statewide class action lawsuit against their school district and the State of California.  (See Daniel v. California, No. BC 214156).  Their complaint states that this differential access to AP classes denies Rasheda Daniel and a class of primarily low-income students of color equal educational opportunity.   Like students at many other comprehensive urban high schools serving primarily poor, African American and Latino students, Rasheda Daniel and her schoolmates could not enroll in AP classes in math and science, because Inglewood High School did not offer AP courses in these core academic subjects.  Indeed, at the time of the suit’s filing, Inglewood High School offered only three AP courses, none in math or science.  By contrast, other California public high schools like Beverly Hills High School and Arcadia High School, which serve large numbers of White and affluent students, offered more than 14 different AP courses, including Calculus, Computer Programming, and Physics. Without such access, Rasheda and her lawsuit peers claim they would be severely disadvantaged when seeking admission to competitive universities.

The Daniel case demonstrates that unequal access to mathematics and science course taking and achievement remains a serious, self-evident problem in K-12 schools.  Moreover, the case also illuminates that the face of the problem has changed significantly over the past decade and that possible solutions are less than straightforward.  The case and its proposed remedy reveal both what we know and what we don't about the enduring, yet changing, relationship among diversity, mathematics and science course taking, achievement, and equity.

In what follows, we review research from the past decade that has examined various dimensions of this persistent and troubling problem.[1]  Our review reveals that, although both achievement and coursetaking have increased for all groups, serious gaps remain.  Those gaps relate, at least in part, to persistent race- and social class-linked inequalities in opportunities to learn between schools and within them.  This finding suggests that, while, continuing to add and/or require additional mathematics and science coursework may have some ameliorative effects in the future, these solutions won’t touch the core of the inequality problem. 

At the same time, considerable work studying curricular reforms and equity-minded interventions suggests a number of strategies for bridging the gaps in coursetaking and achievement.  We’ve also learned that translating effective strategies into wide-scale school change is enormously challenging.  In addition to new curricula, teaching strategies, and supplemental supports for low-income students and students of color, reducing inequality will require significant shifts in the current low educational expectations our culture holds for low-income students and students of color and in our political unwillingness to provide them high quality schooling.

We conclude from this review that we need to better understand the practices that will lead to more equitable patterns of course taking and achievement.  However, we also need far more knowledge of these cultural and political dimensions of the problem.  Because all of these areas would profit from further investigation, we offer a list of some questions that we find to be most promising for this future work.

We begin, however, by sketching the larger social and political context that helps us see how and why inequality has remained robust in the face of the increases in coursetaking and achievement.

Educational Equity in the 1990s--Broad Themes

Three themes emerged repeatedly in our examination of the past decade’s research on the relationship between equity, math and science coursetaking, and achievement: 1) the press for standards and accountability; 2) the still separate and still unequal K-12 education system; and 3) the redefinition of college eligibility.  We describe these themes to provide a context for our discussions of what we’ve learned from research and what we still need to know.

Press for Standards and Accountability

Despite the Reagan administration’s attempt to minimize the federal role in education, the late 1980s and 1990s witnessed an increased national emphasis on national goals and national standards for education, and, under the rubric of "systemic reform," the alignment of these national policies with state accountability systems.  Anxiety about potentially powerful competitors in the new global economy triggered a national conversation about what American students should know and be able to do to ensure our prosperity and pressed diverse groups of subject matter experts and policymakers to develop, implement, and adopt a standards-based approach to education reform.

The National Council of Teachers of Mathematics (NCTM) was both the first and the most recent group to release national goals and guidelines (NCTM, 1989, 2000).  In the field of science two organizations released documents that guide reform, the American Association for the Advancement of Science (AAAS) Project 2061’s Benchmarks for Science Literacy (AAAS, 1993) and the National Research Council’s (NRC) National Science Education Standards (NRC 1996).  Equity issues were salient, albeit contentious, in the framing of these documents, and the emerging foundation of these standards states that all students can learn high level math and science. For example the underlying principle of the National Science Education Standards reads:

Science is for all students.  This principle is one of equity and excellence.  Science in our schools must be for all students: All students regardless of age, sex, cultural or ethnic background, disabilities, aspirations, or interest and motivation in science, should have the opportunity to attain high levels of scientific literacy (NRC, 1996, p. 20).

While we do not yet know the full impact of the movement for high standards on equity in coursetaking and achievement, we’ve already seen a significant reduction in the number of low-level mathematics and science classes and an increased press for all students to complete Algebra 1 in high school. 

However, the same climate that produced an emphasis on higher educational standards also produced a rapid expansion of statewide accountability programs.  These programs feature high stake assessments to hold students, teachers, and schools accountable for meeting academic standards set by the states (Hanushek, 1994; Ladd, 1996; Millman, 1997).  To give these systems teeth, the accountability systems often include dire consequences for failure to meet the standards: grade retention or failure to earn a high school diploma for students and reconstitution or state-over for schools.  Increasingly, however, analysts worry that these programs will have a disproportionately negative effect on low-income minority students.  Recent studies suggest that standards-based accountability reforms can serve to widen the gap between these students and their more advantaged peers in their access to significant mathematics and science opportunities and achievement, even as the gap on basic skills tests may narrow.  For example, high stakes assessments, like those used in Texas, lead to students in low-income schools receiving significantly less science instruction and low-level math instruction at all levels in the K-12 educational system (McNeil & Valenzuela, 2000).

We will return later to the impact of reform on achievement and course taking.  Here, we simply note that the past decade’s standards and accountability reforms nearly affect every effort to achieve equity in opportunities and outcomes. 

Still Separate and Still Unequal

In the last 10 years, as our nation became more diverse and multicultural, different responses emerged to address these societal changes.  Increased segregation has been one.   Urban schools, for example, are more likely than ever to serve a population of low-income, minority students, given increased residential segregation and recent court decisions releasing schools across the country from desegregation orders (Orfield & Yun, 1999).

Segregated minority schools remain less likely to offer access to upper courses, despite considerable recent evidence of the benefit of rigorous curricula for all students, regardless of their educational backgrounds (Adelman, 1999).  Research in the past decade also demonstrates that, while a school’s ability to enable students to succeed in a rigorous curriculum depends on its teacher corps, schools serving minority and low-income students are least likely to have highly qualified faculties (Darling-Hammond, 2000; Ferguson, 1998, 1991; Greenwald, Hedges, & Laine, 1996; Murnane, 1996; Wright, Horn, and Sanders, 1997).  The very real teacher shortage in many parts of the nation, coupled with policies that discourage teachers from working in racially segregated minority schools, means that fewer well-qualified teachers are available to teach students of color in segregated schools.  Moreover, schools serving low-income students of color have yet to counter the growing "digital divide" that brings race and social class inequity in access to technology (Educational Testing Service Policy Information Report, 1997).

Additionally, counseling shortages in urban schools impact both the quality and quantity of advisement for low-income students.   This lack, combined with the pervasiveness of tracking, restricts these students access to challenging mathematics and science classes.  For, despite numerous efforts to detrack K-12 education institutions since the mid-1980s, tracking still exists and thrives in schools across the country (U.S. Commission on Civil Rights, 1999).  Within racially mixed schools, minorities are still disproportionately overrepresented in low-level courses and underrepresented in critical courses.  An ironic impact of the detracking movement may be the dramatic increase and emphasis on Advanced Placement courses and testing in the past decade (Oakes, Welner, Yonezawa, & Allen, 1998).  As schools began to eliminate some of their lower level courses, many middle class parents sought ways to maintain their children’s perceived competitiveness for college.  As a result, the math and science pipelines began earlier and became more extensive, with college-bound students taking Algebra I in eighth grade and ending their high school career in Advanced Placement courses, including calculus. 

College Eligibility—An Ever Rising Bar

Changes in college admissions make it far more difficult for students lacking access to rigorous K-12 mathematics and science education to qualify.  Most salient, the national movement to discredit and dismantle affirmative action in college admissions has increased the importance of K-12 academic achievement, particularly for low-income students of color.  Minority admissions to public universities in California and Texas have declined significantly since those states banned the use of racial preferences in their admissions’ processes (Orfield & Miller, 2000).   As a result, minority enrollment in college preparatory courses is even more important than ever.

Relevant here, too, is that AP classes have become an increasingly important factor in college admissions.  For example, in the past decade alone, the number of AP exams taken in California almost has tripled from 78,379 in 1989 to 203,523 in 1999. The increase in California can be traced to the decision of the University of California in 1984 to boost student grades in AP classes when calculating student grade point averages for university admission.  While California's rate of AP participation exceeds that of most other states, it is not alone in this trend.  Moreover as the demand for college increases, policy makers, educators, and members of the public now expect a highly competitive admissions process to elite universities.  Further, most people recognize that college preparatory curricula must now include AP courses.  Because these new expectations emerged without planning or publicity, only certain high schools—primarily those serving more advantaged populations—have been in the position to embrace them.  Without a plan for supporting schools to realize these new expectations, the state transformed the rules of the game in a way that negatively impacts its poorest and most vulnerable communities (Oakes et al, 2000).

What We Know from Research about Course Taking and Achievement

Whether you view the glass as half empty or half full, positive trends exist in mathematics and science coursetaking and achievement.  First, we will note these positive trends and then describe other patterns that have developed over the past 10 to 15 years. Then we analyze coursetaking patterns.  Within these positive trends, patterns of differential access both between schools and within schools to math and science coursetaking continue to disadvantage poor children.

Trends in Achievement

As Rodriguez (1997a) states, “There is cause for cautious celebration regarding student achievement in science” (p. 13). Positive patterns occurred in mathematics achievement as well.  Over the last 20 years, scores on the science and math portions of the National Assessment of Educational Progress (NAEP) have increased for all student populations.  From 1973 to 1996, all ethnic groups increased their NAEP math and science with the greatest increases for all tested age groups in both subject areas occurring in the 1970s and 1980s (Synder & Hoffman, 2000).  Figures 1 and 2 display NAEP scores for thirteen-year-olds in math and science respectively. 

INSERT FIGURES 1 & 2

 Other positive trends in NAEP assessments include the steady disappearance of a gender gap in science achievement and the almost non-existent gender gap in math achievement.  For example, 1996 male and female students’ science scores in grades 4 and 8 “did not differ to a statistically significant degree” (O’Sullivan et al., 1997, p. 28).  And even though 1996 students in grade 12 males on average scored higher on the NAEP science assessment than their female peers (National Science Foundation [NSF], 1999), the gender gap is one of the smallest internationally as reported by the Third International Mathematics and Science study (U.S. Department of Education, 1998). 

Despite these science and math gains in NAEP, performance gaps persist between white students and Hispanic students (National Science Board, 2000; NSF, 1999; Rodriguez, 1997a; Synder & Hoffman, 2000).  In fact,  13 year olds scored slightly lower in science than white 9 year olds” (Synder & Hoffman, 2000).  A gap also exists in achieving advanced scores on NAEP tests.  Table 1 displays the 1996 math and science NAEP test scores for twelfth graders.   and Hispanic students do not score at the advanced level in math, and only one percent of Hispanic students score at the advanced level in science.  Socioeconomic gaps occur as well; Title I students and students receiving free or reduced lunch score lower than students ineligible for these benefits.

Table 1 Percentages of twelfth-grade students within the Proficient and Advanced achievement ranges on the NAEP 1996 math and science tests.

Source: The College Board, 1999

Moreover, minority groups exhibit gender gaps that raise troubling questions about the overall patterns of decreasing gaps that we noted earlier.  Underrepresented minority males fall far behind their female counterparts in achievement and attainment.  That males earned only 36 percent of the bachelor’s degrees accorded to African Americans in the mid-1990s attests to a pattern of differential achievement among males and females from the earliest grades (The College Board, 1999).

Trends in Course Taking

Who has access to mathematics and science courses and who is taking them?  These are the questions to which we now turn.  Minority enrollment and completion of advanced level math and science courses dramatically increased during the past twenty years.  The percentages of  and Hispanic high school graduates taking Algebra II more than doubled from 1982 to 1994.  As Figure 3 demonstrates, Calculus course taking doubled as well.  In science almost all high school graduates take biology (93 percent in 1994) as compared to only 77 percent in 1982 (NSF, 1999).  Changes in chemistry enrollment are shown in Figure 4. 

INSERT FIGURES 3 & 4

Despite these tremendous gains, great differences still exist among racial/ethnic groups. Aggregated data from 1998 show similar patterns in advanced mathematics (an aggregate of trigonometry and calculus) and advanced science (Chemistry II and Physics II) coursetaking.  Asian students take advanced mathematics (56 percent of high school graduates who took these courses) and advanced science (17 percent) more often then their high school peers (see Table 2).

                                                                                                           Source: NSF, 1999

On the remedial end, “Black and Hispanic high school graduates in 1994 were far more likely than white and Asian students to have taken remedial mathematics courses: 31 percent of Blacks, 24 percent of Hispanics compared to 15 percent of whites and Asians” (NSF, 1999, p. 16).  On the honors or advanced end, Asians far outpaced other racial/ethnic groups in advanced mathematics coursetaking (NSF, 1999, p.16).

Similar patterns occur in science coursetaking.  Moreover, an apparent gender gap occurs in the type of science enrollment—“Females were slightly more likely than males to have taken biology and chemistry and males were more slightly more likely than females to have taken physics” (NSF, 1999, p. 12).  Madigan (1997) also notes that males were more likely to have taken physics than their female peers.

These gaps among groups in Table 2 are actually far larger than these numbers show.  Low-income students of color, and particularly Latino youth experience far higher dropout rates than their more white and Asian peers.  The Latino dropout rate, for example, hovers around 50 percent.  Consequently, figures showing the participation of students of high school age in the population at large would show significantly greater gaps in participation.

These achievement and coursetaking gaps are unnecessary and dangerous (Education Trust, 1998).  They are unnecessary because low income students and minority students will achieve at the highest levels, given appropriate learning opportunities and support, and dangerous because we cannot afford the loss of these students’ talents and future efforts.  While the gaps narrowed in the late 1970s and 1980s, they stagnated in the 1990s.  We turn now to explanations of why these tenacious gaps remain.

Why Do Inequalities Persist?  Between School Differences

A student can only take a high level class in science and mathematics if his or her school offers such classes or if his or her school opens up access to these courses to all students.  In other words, how far a student can go down either the mathematics or science pipeline depends on his or her access to particular courses.  We will focus on high-level gatekeeping courses such as Algebra II and calculus in math and physics and chemistry in science to elucidate patterns of access and non-access to such courses.  We find that, despite the standards movement, segregated minority schools remain less likely to offer access to upper level math and science courses.  Many schools do not offer math beyond Algebra II.  Many schools do not offer three basic lab science classes.  Poor and minority students form a disproportionate number of students affected by these differences in coursetaking opportunities (Oakes, 1990a).

For example, participation in advanced courses differs by a school’s SES level (Ma & Willms, 1999). “With all factors being equal, students were more likely to pursue advanced mathematics if they attended a high SES school than if they attended a low SES school” (Ma and Willms, 1999, p. 379).  Similarly, using data from two sources—the National Education Longitudinal Study of 1988 (NELS: 88) and the High School Effectiveness Study (HSES)—Lee, Burkham, Chow-Hoy, Smerdon & Geverdt (1998) define types of schools based on average pipeline completion. Two types relate to our discussion: “low-progress schools” (15.8 percent of the sample) and the “high-progress schools” (17.4 percent of the sample).  Low-progress schools, all public schools, include schools in which the average progress through the mathematics pipeline ends at algebra.  Most of these schools feature high minority enrollments (40 percent or more minority students), and on average have lower achieving students.  High-progress schools, of which 14 percent are public, are defined as schools where all students reach calculus.  All high progress schools offered calculus “but less than half of the low-progress schools offer this course” (Lee et al., 1998, p. 21).  Low- progress schools offered “nearly twice as many math courses below algebra as high-progress schools” (Lee et al., 1998, p. 21).

Similar patterns occur in science course offerings.  Differentiating schools by community type, Matti and Weiss (1994) found that students in disadvantaged urban schools along with many of their rural peers "were less likely to have the opportunity to take advanced science courses” (p. 37).  Students from low SES backgrounds in NELS: 88 were clearly less likely than those from high SES backgrounds to take eight or more semesters of science or to take physics” (Madigan, 1997, p. 11). 

            These gaps extend to Advanced Placement courses.  Oakes and her colleagues (2000) found that high schools across the state of California vary greatly in their AP offerings.  Some high schools offer multiple sections of more than 14 different AP courses.  Many other California high schools offer only a single section of 2 or 3 different AP courses with 177 California high schools not offering any AP classes.  While these differences in AP offerings correlate to several factors including school size and location, they clearly correspond to a high school’s racial composition.  Comprehensive urban high schools that serve predominantly poor Latino and African American students typically offer far fewer AP courses than suburban high schools of comparable size serving predominantly White and middle class students.  Regardless of high school size, the availability of AP courses decreases as the percentage of African Americans and Latinos in the school population increases (Oakes et al., 2000).  Moreover, differential access to AP classes is most stark and most consequential in mathematics and science.  The following table shows that schools that enroll a predominately African American and Latino student population offer far fewer offerings than schools that serve predominantly white and/or Asian students.

Table 3: Disparities in Math and Science Offerings

                                                                                        Source: Tomas Rivera Center, 1999

The Same Courses Differ Between Schools

As early as 1980 researchers commented on the curricular differences in schools with varying levels of socioeconomic status (SES).  These differences continue, and may be made worse, ironically, by standards-based accountability systems.

Content Differences.  High poverty elementary school curricula often focus on basic facts and skills, while affluent school curricula provide access to richer, problem-based learning and "enrichment" activities.  For example, Anyon noted differences in elementary school curricula between what she termed a “Working Class School” and an “Executive Elite School” (Anyon, 1980).  In particular science and math instruction differed at these two types of schools.  Teachers at the Working Class School used procedure driven techniques in their classes and often failed to gauge whether their students understood what they were making or doing.  In science, “children were never called upon to set up experiments or to give explanations for facts or concepts” (Anyon, 1980, p. 75).  In contrast at the Executive Elite School, teachers expected students to develop ”analytical intellectual powers” (p. 83).  In math, teachers encouraged students to evaluate each other’s decision making strategies; in science, as an Executive Elite School teacher explains, students “generate hypotheses and devise experiments to solve the problem” (p.86 ). 

Later studies confirm Anyon’s findings, of teachers in low SES elementary schools emphasizing less on problem solving and inquiry skills than their higher SES peers. (Matti & Weiss, 1994; Oakes, 1990a).  Increased emphases on standardized testing in many states exacerbate these differences, with teachers teaching towards basic skills necessary to achieve well on statewide assessments (McNeil & Valenzuela, 2000).  Often, elementary teachers in low SES schools eliminate most science instruction to focus on basic reading and math skills (McNeil & Valenzuela, 2000).  In states that mandate performance based assessments including portfolios, some improvements in access to higher level math and science instruction and curriculum do occur in low-income elementary schools (Darling-Hammond, 1997; Koretz, Mitchell, Barron & Keith, 1996; Stecher & Mitchell, 1995).

In high-poverty and high-minority secondary schools, courses offer less content coverage, depth, and laboratory.  In a recent study, for example, Lee and her colleagues, determined that “disadvantaged students . . . are often found in classrooms that emphasize lower-order skills, basic knowledge, drill and practice, recitation, and desk work” (Lee, Smith and Croninger, 1997, p. 130).  Similarly, Weiss (1994), replicating Oakes' 1990 findings, found that math and science teachers in classes with high proportions of minority students are more likely than others to emphasize standardized test preparation (these tests often focus on low level skills) and less likely to attempt to prepare students for further study in these fields.  For example, examining High School and Beyond data, Adelman concluded that Algebra II classes in high poverty schools often resemble Algebra I classes found in more affluent schools (Adelman, 1999).

Teacher Quality Differences.  Teacher quality differences accompany course-offering differences.  Generally, students in high poverty schools often have less qualified teachers than their suburban peers, and these trends are most extreme in math and science.  Forty percent of math teachers and 20 percent of science in high poverty schools teach out of field as compared to 28 percent and 14 percent, respectively, in low poverty schools (Ingersoll, Han & Bobbitt, 1995). Out-of-field teachers and uncertified teachers are more likely to have onerous teaching loads.  Their lack of experience and expertise makes them more likely to rely heavily on textbooks and short answer questions.  Consequently, they spend less time developing students’ critical thinking skills and attending to students’ interests.

Importantly, districts with low-income students often pay less and offer poorer working conditions (larger class sizes, more bureaucratic regulations, and less teacher autonomy) that make them less able to attract and retain qualified urban teachers (Darling-Hammond, 1997; Gilford & Tenebaum, 1995; Ingersoll, 1999).  Ineffective and uncoordinated hiring practices also contribute to qualified math and science teacher shortages in urban districts.  Applicants to urban schools offer encounter unwieldy personnel offices, which routinely lose files, answer questions incorrect or not at all, and ignore qualifications in favor of compliance.  Late budget decisions and seniority transfer policies often make it impossible for urban recruiters to specify to which school prospective teachers will be assigned  (Darling-Hammond, 1997; Gilford & Tenebaum, 1995).  Rather than conducting full job searches, urban schools often fill mid-year vacancies with out of field teachers or substitutes (Ingersoll, 1999).  All these policies mean that urban districts hire less qualified teachers, whom are assigned to their neediest schools.

Making matters worse, math and science teachers often do not feel prepared to teach students from diverse cultural backgrounds.  Results of the 1993 National Survey of Science and Math demonstrate that only 29 percent of these teachers feel comfortable teaching English language learners (Weiss, 1994).[2]

Within School Differences: Tracking

We’ve known for years that tracking has allocated quite different instruction to students in different tracks, socialized them to accept their position in the school’s status hierarchy, and signaled their appropriate futures to the outside world.  And American schools have quite consistently assigned children from privileged families (usually white) to academic tracks, and those who are poor and non-white to the others.  Despite numerous efforts to detrack K-12 education institutions since the mid- 1980s, tracking still exists and thrives in schools across the country.  Recent efforts at raising student achievement paradoxically may exacerbate tracking. Also the content coverage and teaching objectives vary within the different levels/ ability grouped courses.  Through tracking policies, then, students have differential access to high-level courses and, in turn, to science and math achievement.  (Hoffer, 1992; Lee, Smith & Croninger, 1997; Mason & Good, 1993; Oakes, 1990b; 1995; Oakes, Gameron, & Page, 1992).

Prevailing norms about the desirability of tracking underlie its persistence.  Interestingly, while more than 75 percent of science and math teachers believe that almost all children can develop mathematical and scientific thinking skills; most teachers do not believe they can bring about such learning in heterogeneous classes.  Approximately 30 percent of elementary school teachers and 70 percent of high school teachers favor ability grouping for effective math and science instruction (Weiss, 1994).  Perhaps ironically, the movement away from tracking and toward high standards for all students has increased emphasis on Advanced Placement courses.  As schools eliminate their lower level courses, middle class parents often look to Advanced Placement as a way to maintain their children’s perceived competitiveness for college (Oakes, 1998).  As a consequence, increasing numbers of students are taking Algebra I in eighth grade and hoping to complete Advanced Placement courses, including calculus, during high school.

Track Level Differences in Content

Although national standards call for high expectations for all students, teachers set different objectives for students depending on the perceived academic composition of the class.  High ability classes focus on skill building, while low ability courses focus on the importance of science/math in daily life.  Teachers of low level classes are more likely to emphasize awareness of the importance of math and science in daily life, while they focus more on developing reasoning and inquiry skills in their high level classes.  “Instructional activities follow similar patterns; low ability science classes spend more time reading from textbooks and completing worksheets than high ability classes, and they spend less time than high ability participating in hands-on activities or being asked to write about their reasoning about solving a math problem” (Weiss, 1994, p. 20; see also, Oakes, 1990a).  Figure 5 demonstrates the significant differential between math and science objectives in low and high ability classes (Weiss, 1994, p. 21).

Insert Figure 5

Raudenbush, Rowan, and Cheong (1993) multi-level analyses of data about secondary teachers’ instructional goals found that the variation in emphasis on teaching higher order thinking across subjects (and most strongly in mathematics and science) was a function of hierarchical conceptions of teaching and learning related to perceived ability group (track).  That is, teachers who taught classes at more than one level varied their instructional goals among those classes.  Teachers placed much greater emphasis on higher order thinking and problem solving in their high-track classes than in others.  These goals included generic thinking and problem solving skills, as well as advanced academics topics and skills.

Track-level Differences in Teacher Quality

In tracked schools, students in lower tracks are more likely to have out of field math and science teachers than students in higher tracks (Ingersoll, 1999).  Using data from the High School and Beyond (another national database) study's 1984 Teacher and Administrator Survey, Talbert and Ennis (1990) also found track-related teacher differences.  Their analyses suggest that, while teachers of high-track students also teach other ability groups, teachers of low-track students are more often "tracked" themselves.  Twenty-four percent of the teachers in the national sample indicated that they teach predominantly low-ability students in tracked classes, compared with only 14 percent reporting that they are comparably "tracked" into classes with high-ability students.

The extent of teacher tracking (inequalities in the distribution of teachers among high- and low-tracks) is partly a function of social inequalities among students and teachers (e.g., social class background, race, and ethnicity) (Talbert & Ennis, 1990).  Teacher tracking is far less extensive in schools with relatively high-SES student populations and more extensive in schools with relatively high proportions of minority students, minority teachers, and women teachers.  Women teachers are more likely than men to be tracked into low-ability classes are.  Talbert and Ennis also found that teachers with low-track assignments had less influence over school policies and less administrative and collegial support.  Finally, teachers' track assignments were related to their instructional efficacy, with high-track teachers feeling more efficacious than others.  Talbert and Ennis concluded,

Regardless of whether relatively ineffective teachers are assigned to teach low-track classes or teachers assigned to teach low-tracked classes come to feel inefficacious, teacher tracking practices exacerbate student inequalities.  Students in low-track classes are more likely than their academic- or general-track peers to have teachers with low status in the school, with fewer resources for personal growth, and who feel relatively ineffective in promoting student learning (p.30). 

Racial Consequences of Tracking

Within racially mixed schools, minorities remain disproportionately overrepresented in low level math and science courses and underrepresented in critical gatekeeping math and science courses.  For example, Braddock and Dawkins’ (1993) analyses of the base-year and first follow-up data from the National Educational Longitudinal Study of 1988 (NELS:88) found African American, Latino, and American Indian 8th and 10th grader to be significantly under-represented in high ability classes and significantly over-represented in low ability classes.  This disproportionate placement is a product of two somewhat distinct dynamics.  First, schools with predominantly low-income and minority student populations offer relatively smaller numbers of high track classes and larger number of low-track, remedial and vocational programs than do schools serving whiter, more affluent student bodies (Oakes 1990a).  Second, in racially mixed schools that offer upper level math and science courses, low SES students and student of color are much less likely to enroll in them (Atanda, 1999; Horn, Nunez, & Bobbitt, 2000; Ma & Willms, 1999). 

Low SES students and non-Asian minorities are less likely than others to take math and science courses beyond mandated graduation requirements (Ma & Willms, 1999; Weiss, 1994).  Nationwide, while 20 percent of high school biology takers are African American and Latino, only 10 percent of high school physics students are from these groups (Weiss, 1994).  Similarly, while 34 percent of students in remedial or review math classes are non-Asian minorities, they comprise only 8 percent in Algebra II and more advanced math classes (Weiss, 1994).

A relaxing of the rigid three-track structure (academic, general, and vocational) of high schools over the past 20 years may have actually disadvantaged students from lower class families (Lucas, 1999).  Currently, course titles usually suggest that classes at different ability levels are simply modified versions of the same course, and few make clear their consequences for college eligibility.  Lower-income families lack the experience of middle and upper-class families to recognize and negotiate placements that provide better opportunities (Yonezawa, 1997).  Moreover, Oakes and Guiton (1995) found educators did not compensate for parental lack of access to knowledge, but rather justified the disproportionate enrollment of whites and Asians in high-track classes as the result of meritocratic selection or from student choice.  Some faculty members brushed aside the disproportionate representation of Hispanics—even those whose test scores were comparable to high-track white and Asian students—attributing these disparities to differences in students’ motivation and choices, or to racial differences in educational values or family support.  Oakes' (1995; 2000) studies of Rockford, Illinois and San Jose, California found that course placement practices consistently skewed enrollments in favor of whites over and above that which can be explained by measured achievement.  African American and Latino students were much less likely than comparably scoring White or Asian students to be placed in accelerated courses.  Table 4 illustrates the placement disparities in mathematics and English.

Table 4.  Placement of Majority and Minority High School Students with Comparable Math/Reading Achievement in Regular and Advanced Classes 1998-1999, Rockford, IL

*NCE:  Normal Curve Equivalent

The table shows discrimination at both high and low levels of achievement.  Even minority students in the highest scoring groups fared worse than majority students scored, and the combined impact across the ranges is considerable.

Other studies suggest how this discriminatory effect occurs.  Increasingly, school systems do not use fixed criteria to assign students to particular course levels.  Teacher and counselor track-placement recommendations include, in addition to test scores and grades, highly subjective judgments about students’ personalities, behavior and motivation, especially at critical transitions between elementary, middle, and high schools (Paul, 1995).  Some schools allow considerable student choice, and many routinely honor parent requests.  Not surprisingly, parent involvement often increases students’ chances of taking higher level math and science courses (Ekstrom, Goertz, & Rock, 1988; Horn, Nunez, & Bobbitt, 2000; Useem, 1992b).

These aspects of course placement interweave with race and social class.  Dornbush (1994) analyzed track assignment practices and tracking consequences in a stratified random sample of students in six diverse, northern California senior high schools.  Using a combination of survey and longitudinal record data (beginning in grade 5), Dornbush compared the impact of course taking, grades, attendance and disciplinary patterns and test scores on college preparatory course taking of comparable students in different racial groups.  Dornbush found marked differences in science and math, with Asians and non-Hispanic white student groups enrolling in college prep courses at more than twice the rates of African American and Latino peers with comparable high school grades.  While parent education differences explained some of these group differences, having highly educated parents did not have nearly as strong a positive impact on disadvantaged minority students' coursetaking as it did on whites’ coursetaking.

According to Dornbush, this disproportionality resulted partially from overt discrimination against African American and Latino students in high school class placement.  To a much larger extent, the differences resulted from a combination of racial and ethnic differences in eighth grade math test scores, grades, attendance records in elementary school, and negative comments about their behavior.  In contrast, Asian enrollment patterns were greatly affected by positive discrimination during the high school enrollment process, in that Asians enrolled in college track classes at rates greater than expected, given the predictor variables.

Other studies also find that counselors play a role in the lower participation rates of low-income and African American and Latino students in higher level math and science courses.  For example, Paul noted that while counselors used test scores or current math placements to bar these students from high level courses, they permitted middle class students with similar qualifications to enroll when their parents intervened on their behalf (Paul, 1995; Romo & Falbo, 1996).  Similarly, controlling for student achievement levels, McDonough (1997) found that students in middle class schools get significantly more supportive guidance counseling than do their peers in lower income schools.  Additionally, counselors in the latter schools more often steered students toward post secondary programs for which they are overqualified.

Finally, in a recent study using the NELS 88/94 data, Horn, Nunez, & Bobbitt (2000) compared the high school academic performance of students who would be first-generation college goers[3] (a group in which minorities and low-income students are disproportionately represented) with peers from college-educated families.  Controlling for academic achievement, family income, family structure, the researchers found the “first-generation” students less likely to participate in college preparatory programs and much less likely to enroll in college within two years of high school graduation.  However, for both groups parent participation in college preparation activities and high school assistance in application process increased students’ college-going chances.

The influence of middle class parent interventions appear as early as middle school (Horn, Nunez, & Bobbitt, 2000; Useem, 1992b), as students vie for eighth grade algebra placements.  Useem (1992a), for example, found a strong relationship between parents’ education levels and placement in middle school mathematics, with college-educated parents involved in school programs and parent information networks, intervening in placement decisions, and influencing their children’s course choices.  Horn, Nunez, & Bobbitt (2000) findings mirror these patterns, even after controlling for students’ math ability.  Thirty-one percent of parents of “first generation” students encouraged their students to take algebra compared to 53 percent of college graduate parents. 

To better understand the relative contributions of between-school differences, tracking, and individual student characteristics on high school math and science course taking, Hoffer and Nelson (1993) used Hierarchical Linear Modeling (HLM) to examine the LSAY data.  Doing so, they found that about 80 percent of course taking differences occurred within schools.  Although students' prior achievement and aspirations accounted for much of the differences in participation, lower socioeconomic status and minority status had independent negative effects.  The influence of between-school differences on course taking was much smaller; students attending high schools with large concentrations of low-income, minority students took fewer demanding math and science courses than did comparable students at schools with more advantaged students.  Additionally, higher rates of course taking took place at schools where greater proportions of the students with comparable ability levels were placed in high-level math and science classes.

Differences Between and Within Schools Matter

 In this section, we examine the impact that differences in access to and participation in math and science courses has on students’ achievement and post secondary opportunities.  The relevant body of research yields five conclusions: (1) advanced course taking enhances achievement; (2) advanced course taking determines eligibility for competitive colleges; (3) completion of a rigorous high school program is the strongest predictor of college success, and it has a particularly strong impact on under-represented students of color; 4) taking courses from qualified teachers increases achievement; and 5) a school’s tracking policies play an important role in all of these outcomes.

Advanced Course Taking Enhances Achievement

        A straightforward relationship exists between course taking and: the more academic courses high school students take, the more positive their schooling outcomes.  Advanced courses, in particular, positively affect student achievement, particularly in science and mathematics, in students’ preparedness for college, and in their success in college-level work. 

Recent NAEP data, for example, show that 8^th graders who take algebra perform considerably better in mathematics and that the more math they take the better they do (U.S. Department of Education, 1997).  Similarly, evaluations of the 1993 decision requiring all New York City public high schools students to take tougher Regents-level math and science courses (courses traditionally reserved for college-bound students) showed the number of Hispanic students passing Regents Science tripled in a single year and the number of African American students passing doubled (Education Trust, 1997). 

A clear link also exists between twelfth grade NAEP math achievement and highest mathematics course taken (Synder & Hoffman, 2000).  Students who take precalculus or calculus score higher than students in lower level classes.  This trend is consistent across gender and race. 

Similar patterns occur in science.  Using NELS: 88 data to investigate the link between science course taking and achievement, Madigan (1997) found “that students who take higher level science courses are more likely to gain in science proficiency” (p. 12), as measured on the NELS scientific achievement measure.  Madigan compared scores from the same set of students twice- when they were in 8^th grade and then again in 12^th grade. 

Table 5 below summarizes Madigan’s findings.  More students at all three levels of 8^th grade science proficiency increased their scores if they took physics.

Table 5:  Percent of Students gaining science proficiency between grades 8 and 12

Source: (NELS 88 Data) Madigan, 1997

Recent tracking studies find similar effects on student achievement.  Oakes' (1995; 2000) studies of San Jose and Rockford schools, for example, found that high-track placement led to greater achievement gains than low track participation for students at all ability levels.  In San Jose, for example, “average” students (with prior math achievement between 50 and 59 Normal Curve Equivalents (NCEs), placed in low-tracks course students lost an average of 2.2 NCEs after one year and had lost a total of 1.9 NCEs after three years.  By contrast, students in the same group who were placed in a regular-track gained 0.1 NCEs after one year and had gained 3.5 NCEs after three years.  Most striking, the students in this average group who took an accelerated course experienced the greatest gain—gaining 6.5 NCEs after one year, and a total of 9.6 NCEs after three years.  Oakes found similar results across prior achievement levels.  That is, whether students began with relatively high or relatively low achievement, those who were placed in lower-level courses showed lesser gains over time than similarly-situated students who were placed in higher-level courses.

            Dornbush's (1994) work demonstrates an overall low correlation between 8th grade test scores and subsequent math and science grades--a relationship that is especially low for students in the low-track.  However, students who scored above the 50th percentile as 8th graders and who were placed in low-track classes did poorly in those classes and did worse in terms of grades than comparably scoring peers who were placed in high track classes.  Such findings contradict the belief that low-track classes permit students to earn higher grades than they would earn if they were placed in more challenging classes.

Advanced Course Taking Determines Eligibility for College

Enrollment alone in upper level courses also correlates to long-term benefits.  Paul (1995) found, for example, that placement in general math or Algebra I in junior high highly corresponds to counselors’ recommendations for high school placement.  Those students taking 8^th or 9^th grade algebra were much more likely to be placed in college prep programs.  Similarly, a US Department of Education analysis showed that 83 percent of students taking Algebra I and geometry went to college within two years of their high school graduation compared to 36 percent of students who did not take these two courses (U.S. Department of Education, 1997).  Almost 89 percent of students taking chemistry in high school attend college, while 43 percent of those not taking chemistry (U.S. Department of Education, 1997).

These results are explained, in part, by the fact that college prep students receive more information and help in developing four-year high school plans and long term educational and career plans than general education students (McDonough, 1997; Paul, 1995).  Counselors use academic program placement to determine how much potential students have for college and how strongly to recommend students for post-secondary and career opportunities.

Differences in access to AP courses in math and science are particularly important in access to highly competitive colleges.  For example, discrepancies in AP participation have a major impact on student competitiveness for admission to California’s universities.  The University of California counts the total number of AP courses students take as indicators of a rigorous curriculum and student potential when evaluating applications.  Student performance on AP tests is used as an important marker of student achievement.  Moreover, it allows students to boost their grades in AP classes (by one point on a four-point scale) for the purpose of calculating their grade point averages (“GPAs”).  Since students can receive a 5 on the 4 point scale for an A in an AP class, the median GPA of students admitted to UCLA and UC Berkeley is now well over 4.0.  Students who lack meaningful access to AP classes, thus, find themselves at a competitive disadvantage in the UC admissions process (Oakes et al, 2000). 

The disadvantage to students without AP is particularly pronounced in a post-affirmative action era.  Prior to the 1994 passage of Proposition 209 (which prohibits the University of California from taking race into account in college admissions), African American and Latino students who did not take AP classes could gain admission to UCLA or UC Berkeley through affirmative action policies.  In the wake of Proposition 209, students at low AP availability high schools are expected to compete for admission with students from more advantaged schools that offer extensive AP programs. 

In addition to shaping college competitiveness in general, AP courses in biology, calculus, and physics also serve as “gates” though which prospective science, mathematics, and engineering majors must pass.

A Rigorous High School Program Is The Strongest Predictor Of College Success, Particularly for Minority Students

In his analysis of the new restricted 1998 edition of the High School and Beyond sophomore cohort files, Adelman (1999) found that finishing a course beyond Algebra II more than doubles the chances of students who go to college will complete it.  In fact, the highest level of math studied in high school impacts bachelor’s completion more than any other pre-college variable.  As with Algebra II, advanced placement course-taking strongly correlate with bachelor’s degree completion, even more so than they do to college access (Adelman, 1999). 

Taking calculus in high school has tremendous consequences.  Students who persist through calculus are much more likely to pass college calculus courses, which serve as the gateway to more than half of college majors (Burton, 1989)

The cumulative effects of rigorous middle and high school math and science courses are particularly strong for low-income students.  Low-income students who take algebra and geometry are almost three times as likely to attend college as those who do not (Atanda, 1999).  When low-income students take rigorous courses, income effects on college entrance decrease significantly (Horn, Nunez, & Bobbitt, 2000; U.S. Department of Education, 1997). 

Taking Courses from Qualified Teachers Promotes Achievement

Students learn more in courses taught by teachers who’ve majored in the academic subjects they and who are certified (Darling-Hammond, 2000; Ferguson, 1998; 1991; Greenwald, Hedges, & Laine, 1996; Murnane, 1996; Wright, Horn, & Sanders, 1997).  These benefits have been documented in math and science specifically.  Analyzing eighth grade scores from the 1996 NAEP, for example, Hawkins, Stancavage, and Dossey (1998) found that students who are taught by teachers with either an undergraduate or graduate mathematics major scored higher than their peers taught by other teachers.  Teachers with teaching certificates in mathematics, moreover, impacted student achievement more than teachers certified in other areas (Hawkins, Stancavage, and Dossey, 1998).  In a study of Stanford 9 test scores in California, Fetler (1999) repli