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



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 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.

 


 

Proficient

Advanced

 

Math

Science

Math

Science

White

18

24

2

3

 

4

4

0

0

Hispanic

6

6

0

1

Asian

26

19

7

3

Native American

3

10

0

0

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).



 

Table 2 Percentage of high school graduates who took advance mathematics or science courses 1998

 


Race-Ethnicity

Advanced Mathematics

Advanced Science

White

45

7

 

30

5

Hispanic

26

6

Asian/ Pacific Islander

56

17

American Indian/ Alaskan Native

27

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.

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