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Oakes, Jeannie; And Others Multiplying Inequalities: The Effects of Race, Social Class, and Tracking on Opportunities to Learn Mathematics and Science. Rand Corp., Santa Monica, Calif. National Science Foundation, Washington, D.C. NSF-R-3928 Jul 90 SPA-8652467 152p.

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This study examines the way the nation's educational system distributes opportunities to learn mathematics and science among various groups of students. Participation and achievement in mathematics and science by women, minorities, and the poor is disproportionately low. Minorities and the poor, especially in inner cities, have considerably fewer opportunities to learn science and math, largely because of the kinds of schoois they attend. The section titles of this report are as follows: (1) "The Distribution of Opportunity"; (2) "The Effects of Student Characteristics on Opportunity"; (3) "Access to Science and Mathematics Programs"; (4) "Access to Qualified Science and Mathematics Teachers"; (5) "Access to Resources"; (6) "Classroom Opportunities: Curriculum Goals and Instruction"; and (7) "Implications." An appendix provides a classification of courses offered at the secondary schools included in the sample. A 133-item reference list is included. (DM)

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Multiplying Inequalities

The Effects of Race, Social Class, and Tracking on Opportunities to Learn Mathema!ics and Science

Jeannie Oakes

U.S. DEPARTMENT OF EDUCATION

Office ot Educational Research and improvement

EDUCATIONAL RESOURCES INFORMATION

CENTER (ERIC)

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The work described in this report was supported by the National Science Foundation under Grant SPA-8652467.

ISBN: 0-8330-1080-8

The RAND Publication Series: The Report k the principal publication documenting and transmitting RAND'S major research findings and final research results. The RAND Note reports other outputs of sponsored research for general distribution. Publications of The RAND Corpration do not necessarily reflect the opinions or imlicies of the sponsors of RAND research.

Published by The RAND Corporation 1700 Main Street, P.O. Box '2138, Santa Monica, CA 90106-2138

R-3928-NSF

Multiplying Inequalities

The Effects of Race, Social Class, and Tracking on Opportunities to Learn Mathematics and Science

Jeannie Oakes with Tor Ormseth, Robert Bell, Patricia Camp

July 1990

Supported by the National Science Foundation

RAN D

PREFACE

In its 1983 report to the nation, Educating Americans for the Twenty-First Century, the National Science Foundation (NSF) set an ambitious goal for precollege science and mathematics education: to provide "high standards of excellence for all studentswherever they live, whatever their race, gender, or economic status, whatever their immigration status or whatever language is spoken at home by their parents, and whatever their career goals." Of particular concern to the NSF was whether an uneven distribution of opportunities to learn science and mathematics might be contributing to unequal outcomes. It seems obvious that students won't learn what they are not taught, and that they won't learn well if they are not taught well. However, no comprehensive studies have investigated what various groups of students experience in their schools and classrooms; and no analyses have been performed that suggest how these experiences might re- strict learning opportunities. Without such analyses, educators and policymakers have found it difficult to frame initiatives that might help achieve the NSF's goal.

The NSF therefore asked RAND to undertake a study of the way the nation's educational system distributes opportunities to learn mathematics and science among various groups of students. The inequalities documented here should be of interest to policymakers and educators who are concerned with improving both the processes and outcomes of mathematics and science education.

Some education observers resist considering children's learning opportunities in the absence of other, often implicit variables. For example, some who see schools as meritocratic institutions consider achievement itself as the principal mediator of opportunity, arguing that children who achieve more are better able to benefit from and more deserving of the limited resources that are available. Others explain opportunity, achievement, and participation as a function of mental capacity; for them, the most important opportunities are con- ferred at birth or before (i.e., they believe that some groups of chil- dren, because of racial or class-linked heredity, simply do not have the mental capacity to be very high achievers). While the attribution of lower achievement and participation to an entire group's suppos- edly lesser capabilities has been thoroughly discreditedand is

clearly out of fashionproponents of this viewpoint remain active, though their arguments may be more subtle than in the past.

Other observers believe that children's physiological historypar- ticularly mothers' and children's nutrition and drug usemust be in- cluded in any discussion of children's opportunities to learn. Still others look to theories of cultural deprivation or to the nation's his- tory of racial and/or class biases. Finally, some see inequalities as a regrettable but inevitable consequence of a shortage of high-quality educational resources and an attempt to use those resources in ways that will bring what they consider the highest educational return.

This study in no way attempts to discredit, endorse, or debate these viewpoints; they are merely acknowledged as having the capac- ity to shape the reading and interpretation of the fmdings reported here. Certainly they constitute an important contey..1. for understand- ing school practices. For example, the use of tracking and ability- grouping in mathematics and science stems from the widespread be- lief that children's intellectual differences are so great that students with different perceived ability levels need to be taught in separate classes and that much of the curriculum, especially at the secondary level, is not appropriate for many students. Many see the coincidence of these differences with students' racial and socioeconomic status as distressing, but not a matter over which schools have much control. Furthermore, many ignore the overall ineffectiveness of such group- ing practices in increasing achievement.

Categorical differences in schooling opportunities are important, for both educational and political reasons. First, unequal learning opportunities provide some specific clues to how educational practices may help create and perpetuate differences in achievement and par- ticipation. Thus, the patterns that emerge suggest important targets for policies aimed at increasing students' clucational outcomes.

Second, whether or not opportunities push a particular group of children toward higher achievement may not be as important a con- sideration as the fact our nation views equal opportunity as a demo- cratic birthright. Yet the quality of the learning opportunities avail- able to different categories of children relates strongly to the social and economic circumstances of children's families and communities. That such inequalities have no place in a democratic society is unar- guable and should not be controversial.

SUMMARY

Widely published statistics document patterns of disproportion- ately low achievement and participation in science and mathematics by women, minorities, and the poor. These patterns are generating increasing concern as the nation's economic base shifts toward tech- nology and the traditional pool from which scientific workers have been drawn (i.e., young white males) continues to shrink. Without substantial increases in the educational achievement and participa- tion of currently underrepresented groups, the nation may not be able to meet its future scientific and technological needs. These human- capital issues converge with the long-standing policy objective of a fair distribution of economic and social opportunities. The specific policy issue of concern here is whether American schools give under- represented and low-achieving groups of students an equal opportu- nity to participate and achieve in these increasingly important fields.

STUDY APPROACH

This report examines the distribution of science and mathematics learning opportunities in the nation's elementary and secondary schools. It addresses four key questions:

1. What science and mathematics are being taught to which stu- dents?

2. How are these subjects being taught? 3. By whom are they being taught? 4. Under what conditions are they being taught?

The educational system in the United States does not allocate op- portunities directly to individuals; rather, it provides them to groups of students, first through schools and then through classrooms. We have examined opportunities that are available at different schools, opportunities available in different classrooms within schools, and fi- nally, the participation of various groups of students in those classes and schools. We have considered not only differential opportunities associated with students' race, social class, and neighborhood, but also the uniquely school-bound distinction of ability-group, or "track," level. In brief, we have investigated whether different types of stu-

dents have different opportunities to learn science and mathematics, and whether schools act on their judgments about students' academic abilities in ways that limit science and mathematics opportunities generally, and the opportunities of poor and minority students in par- ticular.

Cross-sectional data about science and mathematics programs, teachers, and classroom practices in elementary and secondary schools obtained through the National Science Foundation's 1985- 1986 National Survey of Science and Mathematics Education (NSSME) provided an unprecedented opportunity to describe the ac- cess of various groups to critical schooling elements. We have ana- lyzed the distribution of various features of science and mathematics programs through cross-tabulations, correlational analyses, and anal- ysis of variance. We have contrasted schools serving students of dif- ferent racial, ethnic, and socioeconomic backgrounds, and classrooms enrolling various types of students. We have used multivariate anal- yses to isolate the effects of particular school and classroom charac- teristics, and separate classroom analyses within schools of various types. These analyses provide important information about whether and how the distribution of specific features of schools and classrooms may affect the learning opportunities of different students.

FINDINGS

During the elementary grades, the science and mathematics expe- riences of children from low-income families, African-American and Hispanic children, children who attend school in central cities, and children who have been clustered in "low-ability" classes differ in small but important ways from those of their more advantaged and white peers. By the time the students reach secondary school, their science and mathematics experiences are strikingly different.

The Distribution of Judgments About Ability

Assessments of academic ability, placement in different tracks or ability-grouped classes, and the reduced educational opportunities that characterize low-track classes often parallel race and social class differences. At schools with large concentrations of low-income and non-Asian minority students, disproportionate percentages of teach- ers judge their science and mathematics students to have low ability. At schools with racially mixed student bodies, the proportion of

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classes judged to be high-ability diminishes as minority enrollment increases, and minority students are more likely than their white peers to be placed in low-track classes. Thus, to the extent that placement in classes at different ability levels affects students' oppor- tunities to learnand the evidence from our study suggests that the effects are quite profoundminority students disproportionately suf- fer whatever disadvantages accrue to students in low-track classes.

The inequitable practices related to ability-grouping that we have identified in this study are commonly viewed as natural responses to differences in student aptitudes and achievements. But even if sup- posedly objective ability groupings appear logical, they are easily confounded with race and social class. Moreover, the differences in opportunities they provide actually limit instruction, rather than fme- tune it. Disparities in secondary school opportunites may reflect ear- lier conditions that have reduced the skills of disadvantaged students. However, we also see significant effects of race, social class, and locale on opportunities at the elementary level, where the cumulative effects of discrimination are less strong and where tracks are less predicated on prior achievement.

Access to Science and Mathematics Programs

With the exception of slightly greater amounts of time allocated to mathematics instruction in elementary schools with high concentra- tions of low-income and minority children, students from groups that as adults consistently achieve and participate less in science and mathematics have less access to science and mathematics curriculum. Low-income African-American and Hispanic students enrolled in sec- ondary schools where they are the majority have less-extensive and less-demanding science and mathematics programs available to them. They also have fewer opportunities to take the critical gatekeeping courses that prepare them for science and mathematics study after high schoolalgebra and geometry in junior high school and calculus in senior high school. High-ability students at low-socioeconomic- status (SES), high-minority schools may actually have fewer opportu- nities than low-ability students who attend more advantaged schools. Moreover, overall differences in schools' science and mathematics programs are often compounded by inequalities in the opportunities available to various groups of students within schools. Students in low-track classes (disproportionately high percentages of whom are low-income and minority students) are far less likely than other stu-

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dents to be taking courses that emphasize traditional academic sci- ence and mathematics content. Although the differences are, in part, symptomatic of earlier conditions that fail to prepare disadvantaged students for rigorous courses, the net effect is that economically dis- advantaged and minority students have considerably less access to the knowledge considered necessary either to pursue careers in sci- ence and mathematics or to become scientifically literate, critical- thinking members of an increasingly technological workforce.

Access to Qualified Teachers

Several measures of teacher qualifications make clear that low- income and minority students have less contact with the best- qualified science and mathematics teachers. The frequency with which teaching vacancies occur and the difficulty principals have fill- ing vacancies with qualified teachers vary considerably among differ- ent types of schools. Teacher shortages appear most detrimental to low-income and minority students.

Most elementary and secondary school principals are fairly satis- fied with the caliber of their science and mathematics teaching staffs, but principals of racially mixed and high-minority schools more often complain that lack of teacher interest and/or inadequate preparation to teach causes serious problems at their schools. Principals at schools enrolling large concentrations of low-income or minority stu- dents or at schools in inner cities also report that fewer of their teach- ers are highly competent. Teachers are even less sanguine. Teachers at high-poverty, high-minority, and inner-city schools report most frequently that lack of teacher interest or insufficient background poses problems for science and mathematics instruction. Moreover, secondary teachers in inner-city and rural schools and schools en- rolling large concentrations of low-income children are less confident about their own science or mathematics teaching than teachers in more advantaged schools.

Evidence about teachers' formal qualifications reveals many of the same patterns. In this study, we found scant evidence of differences in certification status, academic background, and teaching experience among elementary teachers wcrking in different types of schools (possibly because the nature of quality differences is hard to quantify at the elementary level), but we found substantial differences at sec- ondary schools of different types. Schools whose students are pre- dominantly economically advantaged and white and suburban schools

employ teachers who are, on average, more qualified. Students at- tending these schools have greater access to science and mathematics teachers who are certified to teach their subjects, who hold bachelor's or master's degrees in those subjects, or who meet the standards set by professional associations.

Similarly, we found few differences in the qualifications of those teaching science and mathematics classes at different track levels at the elementary level, and substantial differences at the secondary level. Junior and senior high school students in low-ability classes are being taught by teachers considerably less well qualified than those teaching other levels. Nearly all types of secondary schools tend to place their least qualified teachers with low-ability classes and their most qualified teachers with high-ability classes. However, not all low- and high-track classes are equal, because of differences in the teacher pools available. In schools with less-qualified pools, teachers of low-track classes are less well qualified than those in schools with generally more qualified staffs. Students at the least advantaged schools must compete (through their class assignments) for teachers who are certified to teach mathematics and science or who have bachelor's degrees in these fields. In schools where teach- ers are generally more qualified, the sorting of teachers is evident on more eubtle or higher-level qualificationsteachers' perceptions of themselves Pe "master" teachers, years of teaching experience (which may represent either seniority or political clout in the school), and the holding of master's degrees. As a result, high-track students in the least advantaged schools are often taught by teachers who are less qualified than those teaching low-track students in more advantaged schools.

Access to Resources

Students' access to science and mathematics facilities and equip- ment appears to be similarly unequal. Students in low-income, high- minority schools have less access than students in other schools to computers and to staff who coordinate their use in instruction, to science laboratories, and to other common science-related facilities and equipment. Additionally, more principals and teachers at less- advantaged schools report that resource problems interfere with science and mathematics instruction. Finally, instruction in low- ability classes appears to be further constrained by science and mathematics texts that most teachers judge to be of lower quality.

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Classroom Opportunities

The curricular goals that teachers emphasize and the instructional strategies they use also differ in ways that further confirm the unequal opportunities of disadvantaged, minority, and inner-city stu- dents. Teachers serving large proportions of these students place somewhat less emphasis on such essential curriculum goals as devel- oping inquiry and problem-solving skills. These disadvantages are compounded by differences in the curricular emphases in classes at different track levels, with low-ability classes the object of less teacher emphasis on nearly the entire range of curricular goals. Similar double-layered differences appear in classroom instruction. Teachers in schools with large concentrations of low-income and mi- nority students are less likely to promote active involvement in math- ematics and science learning. Students who are classified as average- and low-ability are disadvantaged in their access to engaging class- room experiences and teacher expectations for their out-of-school learning. Consequently, unequal access to science and mathematics curriculum goals is exacerbated by discrepancies in instructional con- ditions in classrooms.

These fmdings do not suggest that schools are differentiating science and mathematics curricular goals and instructional strategies in ways that are appropriate to the needs of students at different ability levels. On the contrary, students in low-track classes simply have less exposure to the teaching goals and strategies that are most likely to generate interest and promote learning among students at all achievement levels. Since low-income and minority students are disproportionately assigned to low-track classes, these differences fur- ther disadvantage these groups.

IMPLICATIONS

Our evidence lends considerable support to the argument that low- income, minority, and inner-city students have fewer opportunities to learn science and mathematics. They have considerably less access to science and mathematics knowledge at school, fewer material re- sources, less-engaging learning activities in their classrooms, and less-qualified teachers. These inequalities are linked to both charac- teristics of the schools and characteristics of the classrooms. Because schools judge so many low-income and minority students to have low ability, many of these students suffer from being in classrooms that offer less, even if their schools, as a whole, do not. Moreover, our find-

ings are likely to be equally relevant for subject areas other than mathematics and science. The differences we have observed are likely to reflect more general patterns of educational inequality. As such, the implications of these findings extend beyond science and mathematics.

Our fmdings raise complex educational and ethical issues. Even though the data from this study do not link unequal opportunities di- rectly to differences in achievement and participation, they provide some important and specific clues about how educational practices may help create and perpetuate these differences. But whether or not equal opportunities push a particular group of children toward higher achievement, our nation rejects the view that we should provide less to those who are less advantaged or less able. Yet inner-city schools serving large concentrations of children from poor families or African- American and Hispanic minorities often lack the political clout to command resources equal to those of other schools. Teachers often view these schools as less-desirable places in which to teach, partly because of the economic and social disadvantages that shape their students' lives. Also, these schools often pay less than surrounding suburban schools and offer poorer working conditions.

Within schools, educators believe they base decisions about who teaches what science and mathematics, to whom, how, and under what conditions on egalitarian and educationally sound criteria. But the processes and outcomes of tracking are complex, subtle, often in- formal, and incremental. Although the decisions are usually well. intentioned, considerable evidn-tce suggests that tracking, especially at secondary schools, fails to increase learning generally and has the unfortunate consequence of widening the achievement gaps between students judged to be more and less able. Although schools may think that they ration good teaching to those students who can most profit from it, we find no empirical evidence to justify unequal access to val- ued science and mathematics curriculum, instruction, and teachers.

Moreover, the inequalities are not likely to be either self-correcting or easily changed by policymakers or educators. As long as high- quality educational opportunities are scarce and strategies for teach- ing diverse groups of students are largely untested, powerful con- stituencies of advantaged communities and parents will seek to pre- serve the educational advantages they now have. Consequently, it will be necessary for policymakers and educators to seek strategies that will ameliorate present inequalities and at the same time improve the science and mathematics education provided to all

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students. A multiple-strategies approach seems most appropriate for this complex and controversial policy issue.

RECOMMENDED STRATEGIES

Call Attention to the Problem

Policymakers would do well to expand their efforts to fuel public concern about educational opportunities as well as outcomes. Making better and more evenly distributed learning opportunities a focus of national concern can help clarify means for addressing issues of Pdu- cational quality, future economic competitiveness, and social and eco- nomic justice. Strong advocacy from Washington and the state capi- tals would go a long way toward establishing a receptive climate for policies and practices aimed at both improving opportunities and dis- tributing them more fairly.

Generate Additional Resources

Policymakers must seek new resources through new public fund- ing, creative uses of existing funding, and new alliances with the pri- vate sector. And these resources should be accompanied by policies that change priorities for their allocation. New resources for materi- als and staff should go first to those schools with the greatest need those that lag behind in computers, laboratories and materials, and well-qualified teachers. Like other affirmative-action strategies, how- ever, policies aimed at providing new resources for these schools will confront political opposition to what may be .seen as preferential treatment. The determination to ward off that opposition is often more easily sustained at the federal level. Nonetheless, state and lo- cal policymakers must also frame such farsighted policies.

Distribute Resources and Opportunity More Equitably

Many states are currently renewing their efforts to equalize fund- ing levels across districts and schools. Such efforts, if successful, could provide the resources low-income schools need to purchase the facilities, materials, and staffing they now lack, But financial incen- tives may need to be altered to prevent good teachers from abandon- ing schools that serve low-income and minority students,

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Policies are also needed that encourage a more equitable distribu- tion of resources and opportunities within schools. For example, the federal government, states, local education agencies, and universities can all initiate programs aimed at developing new knowledge and building staff capacity to work effectively with diverse groups of stu- dents.

New school organizational schemes must be developed. These might include flexible staffing patterns such as teams of teachers sharing responsibility for diverse groups of students and/or staggered working hours to provide some teaching staff extra instructional time after school or in the evening for students requiring additional help. Other arrangements could involve more flexible use of resources from categorical programs. But if schools hope to make greater science and mathematics learning opportunities accessible to diverse groups of students, they will also need to redesign science and mathematics curriculum and instruction. Such curricular developments will help ensure that any move away from ability-grouped classes will be ac- companied by higher-quality instruction for all students. Perhaps most important, improved curriculum and instruction should bolster the skills of currently disadvantaged children early on, so that they can more easily claim access to rigorous mathematics and science courses in junior and senior high school.

Hold States, Districts, and Schools Accountable for Equalizing Opportunity

Finally, given the difficulty and the potential political disincentives to equalizing educational opportunities, federal, state, and local ef- forts to reach this goal should be carefully monitored. As long as states view public accountability schemes as tools for encouraging lo- cal efforts to increase student outcomes, equalizing opportunities should be a part of what districts and schools are held accountable for. Educational data systems should be designed to report indicators of school resources, curriculum, teachers, instructional conditions, and outcomes by student race and SES. Such indicators could provide insights into how new educational policies could interrupt the patterns of unequal opportunities. Moreover, the public accounting could inform and energize communities and parents who may not otherwise realize that their children are getting less. Such monitor- ing effbrts should be supported by a hierarchy of financial incentives to develop programs for equalizing opportunity, beginning at the fed- eral level and extending to states, communities, and schools.

ACKNOWLEDGMENTS

Although responsibility for the analyses and interpretations in this study remains with the authors, the report has been enhanced by the generous involvement of a number of fine colleagues. Shirley Malcom and Audrey Champagne of the American Association for the Advancement of Science provided helpful comments on the initial questions and design of the study, as did Leigh Burstein of the University of California, Los Angeles, Thomas Romberg of the University of Wisconsin, and Kenneth Sirotnik of the University of Washington. Iris Weiss of Horizon Research provided ongoing guidance regarding the design and use of the 1985-1986 National Survey of Science and Mathematics Education (NSSME). Linda Darling-Hammond of Columbia University and RAND colleague Arthur Wise provided insightful reviews. Richard Berry and Ronald Anderson of the National Science Foundation gave encouragement and support. Finally, Janet De Land lent a fine editor's hand to the final report.

CONTENTS

PREFACE iii

SUMMARY

ACKNOWLEDGMENTS xv

FIGURES xix

TABLES xxi

Section I. THE DISTRIBUTION OF OPPORTUNITY 1

Organization of the Report 3 Dimensions of the Distribution of Opportunity . . 4 Study Approach 9 Limitations of the Study 10

II. THE EFFECTS OF STUDENT CHARACTERISTICS ON OPPORTUNITY 13

The Inseparability of Student Characteristics 13 The Relative Importance of Race and SES 16 The Relationships Between Ability Judgments

and Opportunity 17 Race, Social Class, and Ability Classifications 18

III. ACCESS TO SCIENCE AND MATHEMATICS PROGRAMS 26

Time Spent on Science and Mathematics in Elementary Schools 27

Science and Mathematics Programs in Secondary Schools 30

Access to Courses Within Schools 42 Summary 44

N. ACCESS TO QUALIFIED SCIENCE AND MATHEMATICS TEACHERS 46

Shortages of Qualified Teachers 47 Which Schools Have the Most-Qualified Teachers? . . 50 Which Classes Have the Most-Qualified Teachers? 62

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V. ACCESS TO RESOURCES 68 What Science and Mathematics Resources Are

Available? 69 Do Resource Problems Hamper Instruction? 75 How Good Are the Textbooks? 77 Summary 79

VI. CLASSROOM OPPORTUNITIES: CURRICULUM GOALS AND INSTRUCTION 80

Curriculum Goals and Expectations 80 Curricular Emphasis Across Schools and

Classrooms 82 Learning Approaches and Activities 88 Summary 100

VII. IMPLICATIONS 102 A Context of Diminished Resources and Low

Expectations 102 Three Scenarios for Righting Inequalities 106 Policies for Equalizing Opportunity and Improving

Science and Mathematics Education 107

Appendix: CLASSIFICATION OF COURSES 115

REFERENCES 121

FIGURES

2.1. Percentages of homogeneous ability classes, by school SES 20

2.2. Percentages of low-, average-, and high-ability classes in elementary schools, by school SES 20

2.3. Percentages of low-, average-, and high-ability classes in secondary schools, by school SES 21

2.4. Percentages of homogeneous-ability classes, by school racial composition 21

2.5. Percentages of low-, average-, and high-ability classes in elementary schools, by school racial composition 22

2.6. Percentages of low-, average-, and high-ability classes in secondary schools, by school racial composition 22

3.1. Time spent on science and mathematics in elementary schools serving different student populations 28

3.2. Mathematics and science classes per 100 students in grade 6-9 junior high schools, by school SES 33

3.3. Mathematics and science classes per 100 students in grade 6-9 junior high schools, by school racial composition 33

3.4. Mathematics and science classes per 100 students in senior high schools, by school SES 36

3.5. Mathematics and science classes per 100 students in senior high schools, by school racial composition 36

3.6. Junior high schools offering accelerated mathematics classes, by school SES and racial composition 38

3.7. Number of accelerated mathematics classes per 100 students in junior high schools offering accelerated mathematics classes, by school SES and racial composition 39

3.8. High schools offering calculus classes, by school SES and racial composition 40

3.9. Number of calculus classes per 100 students, by school SES and racial composition 41

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4.1. Percentages of eecondary schools where life science/ biology teacher vacancies were of concern to principals, by school SES, racial composition, and location 49

4.2. Percentages of secondary schools where principals reported difficulty filling mathematics teacher vacancies, by school SES, racial composition, and location 51

4.3. Percentages of secondary schools where principals reported difficulty filling life science/biology teacher vacan.cies, by school SES, racial composition, and location 52

4.4. Proportion of secondary school mathematics teachers considered highly competent by their principals, by school SES, racial composition, and location 54

4.5. Proportion of secondary school science teachers considered highly competent by their principals, by school SES, racial composition, and location 55

4.6. Percentages of secondary school principals who reported serious problems resulting from lack of teacher interest or preparation in science and mathematics, by school SES, racial compositi on, and location 56

4.7. Percentages of secondary school teachers who reported serious problems resulting from lack of teacher interest or preparation in science and mathematics, by school SES, racial composition, and location 58

4.8. Secondary teachers' qualifications, by school SES 60 4.9. Secondary teachers' qualifications, by school racial

composition 61 4.10. Secondary teachers' qualifications, by chool

location 61 4.11. Secondary teachers' qualifications, by ability level of

class to which they are assigned 63 4.12. Qualifications of secondary teachers in low-SES

schools, by ability level of assigned class 66 5.1. Percentages of elementary schools with computer

coordinators, by school SES and racial composition . . . . 70 5.2. Availability of science laboratories in elementary

schools, by school racial composition 72 5.3. Percentages of secondary schools with computer

coordinators, by school SES and racial composition . . . . 73

TABLES

2.1. Schools in various race, SES, and locale categories 15

2.2. Ability levels of classes in elementary schools, by racial composition of class relative to school enrollment 24

2.3. Ability levels of classes in secondary schools, by racial composition of class relative to school enrollment 24

3.1. Significance of SES, race, and locale differences for senior high school course offerings 37

3.2. Distribution of general, academic, and advanced science and mathematics courses in senior high schools, by ability level of class 43

3.3. Distribution of general, academic, and advanced science and mathematics classes, by class racial composition 44

4.1. Qualifications of secondary teachers in high- and low-ability classes in schools of different types 66

5.1. Percentages of secondary schools providing mathematics and science coordinators, by school SES, racial composition, and locale 74

5.2. Percentages of principals reporting resource problems, by school SES, racial composition, and locale 76

5.3. Percentages of teachers reporting resource problems, by school SES, racial composition, and locale 77

6.1. Elementary teachers' curricular objectives: relationship to class ability level 83

6.2. Secondary teachers' curricular objectives: relationship to class ability level 85

6.3. Secondary teachers' curricular objectives in high- and low-ability classes in schools of different types 87

6.4. Pementages of secondary teachers including various instructional activities in last science or mathematics lesson, by class ability level 97

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6.5. Percentages of time spent on various instructional activities in secondary science and mathematics lessons, by class ability level 97

6.6. Percentages of time spent on various instructional activities in high- and low-ability classes in secondary schools of different types 99

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I. ME DISTRIBUTION OF OPPORTUNITY

In 1983, the National Science Foundation (NSF) set an ambitious goal for precollege science and mathematics education: to provide "high standards of excellence for all studentswherever they live, whatever their race, gender, or economic status, whatever their im- migration status or whatever language is spoken at home by their parents, and whatever their career goals" (National Science Board (NSB), 1983:12). But the disproporfionately low achievement and participation in science and mathematics of women, minorities, the poor, and high school students who are not in college-preparatory programs reveals clearly that this goal is not being met.1

The lack of achievement and participation by these groups has generated considerable concern as the nation's economic base shifts increasingly toward technology. This concern is heightened by demo- graphic projections showing that the traditional pool from which sci- entific workers have been drawn, i.e., young white males, is shrink- ing. Future cohorts of workers will comprise increasing proportions of non-Asian minoritiesgroups that traditionally have not entered sci- entific and technological fields. These changes raise a number of specific policy questions: How can we ensure an adequate future sup- ply of highly trained mathematicians, scientists, and engineers? How can we provide the general labor force with the knowledge and skills needed for technological work? How can we attain the level of scien- tific literacy necessary for responsible, democratic decisionmaking about scientific and technological matters? There are no clear-cut an- swers to these questions. However, many observers suggest that if the educational achievement and participation of minorities do not increase substantially, the nation will not be able to meet its scientific and technological needs.

These human-capital issues have converged with the long-standing policy objective of fair distribution of economic and social opportuni- ties. As technology becomes increasingly central to work and national life, the achievement of women and minorities in science and math-

1These discrepancies have been detailed in several reports over the past five years, including American Association for the Advancement of Science (AAAS), 1984; Achievement Council, 1985; Berryman, 1983; Chipman Thomas, 1984; Darling- Hammond, 1985; National Alliance of Black School Educators (NABSE), 1984; National Science Board, 1987; National Science Foundation, 1988; Oakes, 1990; and Task Force on Women, Minorities, and the Handkapped in Science, 1988.

ematics will be a primary factor in the ability of these groups to com- pete for employment, wages, and leadership positions. While not all students have the interests or aptitude to become scientists or math- ematicians, the disparities for African-American and Hispanic minori- ties and the poor are so great that considerable science and mathe- matics talent is undoubtedly being lost from these groups. Moreover, many minority and poor students are failing to reach even the levels of mathematics and science literacy believed to be necessary for knowledgeable participation in an increasingly technological society. Minorities have made important progress toward closing the achieve- ment gap in the past two decades, but appalling disparities in school achievement and occupational status remain.

The NSF was particularly concerned with the possibility that an uneven distribution of opportunities to learn science and mathematics might be contributing to unequal outcomes. It is obvious that stu- dents will not learn what they are not taught and that they will not learn well if they are not taught well. However, no comprehensive descriptions of what various groups of students experience in their schools and classrooms have been available, nor have analyses been performed to suggest how these experiences might restrict learning opportunities. Without such analyses, educators and policymakers have found it difficult to frame initiatives that could help to achieve the NSFs goal.

This report responds to these concerns by examining the distribu- tion of science and mathematics education in the nation's elementary and secondary schools. It provides information that should help to answer four key questions: What science and mathematics are being taught to which students? How? By whom? And under what condi- tions? The report has three broad objectives:

1. To 4.ocument the differences in science and mathematics cur- riculum, resources, classroom activities, and teacher quality among various groups of students in the nation's schools.

2. To provide insights into how those differences might shape the learning opportunities of groups that typically have low levels of achievement and participation in science and math- ematics.

3. To explore the implications of these findings for precollege science and mathematics education policy and practice.

Drawing primarily on data from the 1985-1986 National Survey of Science and Mathematics Education (NSSME), we explore whether

access to science and mathematics curriculum, resources, instruc- tional activities, and teachers relates to (1) characteristics of the school a student happens to attend, (2) characteristics of the class- room in which a student is enrolled, or (3) characteristics of school and classroom combined.

Our analyses reveal clear and consistent patterns of unequal op- portunities to learn mathematics and science. During the elementary grades, the science and mathematics experiences of large numbers of low-income children, African-American and Hispanic children, chil- dren who attend school in central cities, and children who have been judged to have "low ability" differ in small, but important ways from those of their more advantaged or white peers. By the time these students reach secondary school, the differences are striking. Low- income, minority, and low-ability students have considerably less ac- cess to science and mathematics knowledge; they have fewer material resources available to help them learn these subjects; their class- rooms offer less-engaging learning activities; and their teachers are less-qualified. These differences can be traced to characteristics of both the schools in which different groups of students are clustered and the classrooms in which they are taught. Because school officials judge so many low-income and minority students to have low ability, many of these students suffer the double disadvantage of being in schools that have fewer resources and classrooms that offer less ac- cess to knowledge.

ORGANIZATION OF THE REPORT

The remainder of this section describes a conceptual framework for understanding the distribution of opportunities. This framework suggests that distributional analyses must consider a comprehensive set of school, classroom, and student characteristics, and that the best way to assess individuals' opportunities is by examining the schools and classrooms in which particular groups of students are clustered. Finally, it describes the data and methods used in the study and their limitations. Section II describes how students' race and social class characteristics overlap with schools' assessments of their abilities and their placement in various types of science and mathematics classes. Section III examines the distribution of science and mathematics curricula, as evidenced by the types of courses schools offer. Section IV examines teachers' experience and qualifications and assesses how the distribution of these factors may influence students' learning and

participation. Section V analyzes the allocation of science and math- ematics resources to schools of various types. Section VI considers classroom processesthe emphasis teachers give to various curricu- lar objectives, the instructional activities they include in lessons, and how they use classroom time. Finally, Section VII discusses the im- plications of the distributional pitterns found in the study. Our focus on the specific dimensions of science and mathematics opportuni- tiesresources, teachers, curriculum, and instructional practices enables us to evaluate policies and practices that are likely to remedy discrepancies.

DIMENSIONS OF THE DISTRIBUTION OF OPPORTUNITY

Our educational system does not allocate opportunities directly to individuals; rather, it allocates them to groups of studentsfirst through states and school districts, and then through schools and classrooms. Consequently, distributional studies require comprehen- sive analyses at both the school and classroom levels, and the findings will undoubtedly reflect the resources made available by states and districts. It is necessary to describe, first, differences in the re- sources, instructional conditions, and teachers available to schools and, second, how schools distribute those resources to different class- rooms. While this departs somewhat from the usual approach of fo- cusing on individuals or groups to explain how their opportunities dif- fer, this institution-based rather than individual- or group-based ap- proach has several advantages. First, the clustering of students in schools and classrooms strongly influences the opportunities that they enjoy. Students' access to knowledge, resources, teachers, and classroom processes is shaped by the characteristics of the schools and classes in which they are enrolled. Moreover, this approach en- ables us to examine the availability of opportunities at several grade levels. This adds important information, since what students actually experience in their science and mathematics classrooms, from the earliest grades through senior high school, will cumulatively influ- ence both what they learn and whether they continue to participate in the pre-college mathematics and science pipeline.

At the school level, data are needed on the programs offered and the human and material resources available to deliver them. The courses that make up secondary schools' science and mathematics curricula suggest the programs' breadth, depth, and extent. In ele- mentary schools, the amount of instructional time spent in science

0 i)

and mathematics is critical. In both elementary and secondary schools, the ability composition of classes (heterogeneous or homoge- neous low-, average-, or high-ability) signals whether students have differentiated learning opportunities.2,3 Grouping of students within classrooms may indicate differential treatment, particularly in the el- ementary grades. Science and mathematics opportunities at a school are also shaped by the quality of the teachin,-; staff; materials and equipment available, and obst les teachers face as they teach these subjects.

School characteristics determine the conditions under which class- room teaching and learning occur, but how well students learn and how long they sustain an interest in the subjects they are taught are most influenced by day-to-day classroom experiences.4 In clasfrooms, we need to examine teacher quality, curriculum, and instructional activities and how these factors affect students' access to learning opportunities. Similar course titles at secondary schools can rep- resent quite different learning experiences, just as similar amounts of time allocated to instruction in elementary school subjects can mask substantial differences in how that time is spent. What students ex- perience in classrooms is determined largely by teachers' instruc- tional goals and objectives; the knowledge and processes teachers make available; the books, materials, and equipment teachers use; the classroom learning activities teachers arrange; the quality of teachers' background, training, and experience; and the support and resources available to teachers.

Distributional issues are not confined to general pazierns of varia- tion across the entire population, however; policym alters are increas- ingly concerned with the distribution of opportunities to particular groups, defined by where they live, race, gender, or economic status; immigration status; the language spoken at home their career goals (NSB, 1983:12). Therefore, it is necessary to ai yze the rela- tionship between student composition of schools and ( Assrooms, the types of communities in which the schools are located, and the re- sources and instructional conditions they provide.

2Throughout this report, we use the terms ability grouping and tracking inter- changeably to mean the clustering of students who are judged to be similar in their aca- demic ability into classes for instruction.

3At the elementary level, however, further differentiation often occurs when teach- ers form ability-based instructional subgroups.

4See Barr and Dreeben (1983) for a discussion of the importance of a multilevel ap- proach for understanding how schools work to produce student learning.

In 1983, the NSB also suggested that distributional inequalities are likely to be linked to beliefs about the abilities of students to learn and asserted that "the opportunity to learn mathematics, science, and technology is at present not fairly and evenly provided to all students, and that in the past, such inequalities have resulted from the failure to recognize and develop potential talent, from inadequate educa- tional programs in some communities or for certain groups of stu- dents, and from the erroneous belief that many students lacked the ability to learn mathematics and science" (NSB, 1983:13). Thus, dis- tributional analyses must consider the effects not only of race and so- cial class but also of teachers' judgments about students' abilities.

Ability classification is most useful in distributional analyses as a descriptor of the class as a whole, since it is a potentially important mediator of the resources and opportunities provided to all the stu- dents enrolled in the class. Teachers (particularly at the secondary level) typically make curricular and instructional decisions at the class rather than the individual level. Even in elementary schools, many teachers do not form instructtonal subgroups in mathematics, and teachers rarely use within-class ability groups for science instruc- tion (Oakes, 1985; Slavin, 1987). Therefore, in nearly all cases, the teacher's perception of a class's ability plays an important role in de- ciding what and how to teach it.

While most people (including many educators) assume that stu- dents will learn better if they are grouped together with those who have similar capabilities, 1.esearch has shown that putting children into separate classes to accommodate their differences from their ear- liest school years is neither necessary nor very effective. Tracking does not work well for students in the low- and middle-ability groups, who experience clear and consistent learning disadvantages. Perhaps more surprising, tracking does not necessarily promote achievement for high-ability children either: Many studies show that highly ca- pable students do as well in mixed-ability classes (Gamoran and Berends, 1987; Oakes, Gamoran, and Page, in press; Slavin, 1987; Slavin, 1990).

It is also well-established that tracking separates students by race and social class. African-American and Hispanic students are dis- proportionately assigned to low-ability classes and to non-college- preparatory high school programs, as are students from low-income families.

However, tracking is not only ineffective and segregative; it also leads to very unequal learning opportunities (see, e.g., Oakes, 1985, 1987). Students in different groups and tracks have access to very

different types of knowledgethose in high-track classes are more likely to study rich and meaningful topics and skills, while those in low-track classes get a low-level curriculum dominated by exercises, workbooks, and commercially produced basic-skills kits. Small-scale studies show these differences exist at nearly every grade level and in nearly every subject.

There are also important differences in classroom instruction. Students in higher-level classes spend more time on learning activi- ties and less time on discipline, socializing, or class routines. Teachers of these classes usually teach more enthusiastically, and they make their instruction clearer. They tend to organize tasks bet- ter and give children a greater variety of learning activities, and they expect their students to spend more time doing homework. In con- trast, students in low-track classes more often feel excluded from class activities and find their classmates unfriendly. Problems and arguments interrupt classes more frequently. Moreover, students in low-ability classes seem apathetic; being more likely to fail, they may feel that they risk much more by trying hard and giving the appear- ance that they care.

What prior work shows, then, is that tracking produces fundamen- tal schooling inequities. Students who need more time to learn get less; those who have the most difficulty learning experience less good teaching. In contrast to what is commonly assumedthat students are assigned to various ability-grouped classes because they belong there and that those classes serve their educational needsprior re- search suggests a very different conclusion. Designations of "ability" are suspect (given their links with race and social class), even though they may relate to students' prior school performance; and "ability- based" inf. rences about students' curricular and instructional needs are often wrong.

These findings and conclusions are particularly important for un- derstanding the underparticipation of minorities and low-income stu- dents in science and mathematics. Since patterns of enrollment and placement in ability-grouped classes have been found to be linked to race and social class, and since combinations of race, class, and track placements relate to the learning opportunities provided in clabd- rooms, four questions are particularly important:

1. What are the differences in the mathematics and science op- portunities schools provide based on judgments about stu- dents' ability?

2. Are these differences likely to constructively accommodate in- dividual differences in mathematics or science abilities?

3. How do judgments about ability and placements in various classes relate to other student background characteristics (e.g., race, class, and gender)?

4. What are the combined effects of race, class, and tracking on students' opportunities to learn mathematics and science?

To answer the fourth question, we must compare the resources and opportunities various types of schools (defined by socioeconomic sta- tus (SES), racial composition, locale, etc.) provide to students the schools perceive as most able, average, and least able.

In sum, distributional analyses must assess several kinds of distri- butional differences: those that seem to be a consequence of the schools students happen to attend (e.g., do students attending inner- city schools have different coursetaking options than those in subur- ban schools?), those that come about because of the classes in which students are enrolled (e.g., are students in high-track classes taught by different types of teachers than those in low-track classes"), and those that follow from combined school and classroom factors (e.g., do students in high-ability classes in affluent schools experience instruc- tion similar to that received by their high-track peers in schools with high proportions of low-income students?).

This framework for understanding the distribution of opportunities to learn science and mathematics looks at opportunities that are available at different schools, opportunities available in different classrooms within schools, and finally, the participation of groups of students in those classes and schools. To the more established con- cerns for differential opportunities associated with students' race, so- cial class, and neighborhood, we add the uniquely school-bound status distinction of perceived ability level. In brief, we ask whether stu- dents have different opportunities to learn science and mathematics, and if so, whether these opportunities are associated with students' race, class, and neighborhood. We also ask whether schools act on their judgments about students' abilities in ways that limit science and mathematics opportunities generally, and the opportunities of poor and minority students in particular.

; ( )

STUDY APPROACH

We approach our inquiry of the distribution of opportunities to learn science and mathematics from two perspectives, one reflecting research on school and classroom factors that relate to the participa- tion and achievement of women and minorities in science and math- ematics,5 and one reflecting our analyses of data from the NSSME, wnich provide an unprecedented amourt of information on the access of various groups to a whole constellation of critical schooling ele- ments. The juxtaposition of these two perspectives enables us to sug- gest whether and how the distribution of specific features of schools and classrooms observed in the data are likely to affect the learning opportunities of various groups.

The Database

The NSSME was administered to principals and teachers in a na- tional probability sample of 1,200 public and private elementary and secondary schools. The sample was designed to allow estimates of several dimensions of schools, teachers, and classroom practices in science and mathematics nationwide, as well as estimaWs for various subpopulations defined by region, type of community, and school type. Approximately 6,000 teachers of science and mathematics were ran- domly selected from within the sampled schools. One of the mathe- matics or science classes of each secondary teacher was randomly se- lected as the focus for the class-specific items.

Separate instruments were fielded for secondary and elementary school principals, secondary science and mathematics teachers, and two groups of elementary teachers. One elementary teacher sample responded about science teaching; the other responded about mathe- matics. The questionnaires focused on the school contexts of mathe- matics and science education, descriptions of programs in these sub- jects, and specifics about curriculum and classroom instruction. Data were also collected on the science and mathematics background, training, experience, and attitudes of teachers and administrators. Administrators reported the race and socioeconomic backgrounds of the students attending the schools; teachers detailed the race, gender (and gender breakdowns within racial and ethnic groups), and ability levels of students in their classes. The data thus permit analyses of between- and within-school differences for various groups of students

5This literature is reviewed in Oakes, 1 990.

(defined by race, social class,6 and track levels, both separately and in various combinations) at three levels of schooling (elementary, junior high/middle school, and senior high).7

Analytic Approach

We use cross-tabulations, correlational analyses, and analysis of variance to examine the distribution of mathematics and science pro- grams, teachers, facilities and equipment, and classroom experiences. We contrast schools serving students of different racial and ethnic groups and with varying socioeconomic backgrounds, and classrooms enrolling various types of students. We use multivariate analyses to help sort out the effects of school and classroom characteristics, and in some cases, we conduct separate classroom analyses within schools of various types.8

LIMITATIONS OF THE STUDY

While our findings provide new insights into the distribution of science and mathematics opportunities and the implications of that distribution for the participation and achievement of currently under- represented groups, the study also leaves many questions unan- swered. First, although research increasingly points to the impor- tance of school and classroom processes for learning, our Imderstand- ing of how various resources and opportunities enhance or constrain students' success is far from complete. Moreover, research on the rel- evance of particular school and classroom features to the success of women, minorities, the poor, and those identified as low-ability is far from unequivocal. Therefore, our selection of dependent variables for analysis was based on a less-than-perfect understanding of which fea- tures of schools and classrooms are most important to examine.

6The NSSME data provide SES information only at the level of the school. Therefore, we analyze classrooms of various racial/ethnic and ability compositions as "nested" within schools having different SES levels. Using this approach, we can examine how curriculum, resources, and classroom activities in low-track science and mathematics classes in low-SES schools or schools with all or predominantly nonwhite enrollments compare with similar classes in schools with different student population characteristics.

7For a more detailed discussion of of the survey sample designs, survey populations, and weighting process, see Weiss (1987).

8Except where noted, the General Linear Models analysis-of-variance program was used for the analyses of school- and class-level variables.

Moreover, the NSSME data contain no information about students' achievement. Consequently, we can draw no conclusions about how the distribution of learning opportunities relates to students' perfor- mance in science and mathematics. However, such relationships have been found in analyses of other datasets.

Second, the NSSME data cannot answer questions about certain important features of mathematics and science education. For exam- ple, girls' motivation to study mathematics appears to be adversely affected by several classroom characteristics, e.g., lack of opportunity for decisionmaking, emphasis on whole-group teaching and drill, less individualized instruction, concern with discipline and control, use of explicit and public criticism, and stress on competition (Eccles, Madver, and Lange, 1986; Fennema and Peterson, 1986; Lockheed, 1984; Lockheed, 1985; Parsons, Kaczala, and Meece, 1982; Peterson and Fennema, 1985). African-American and Hispanic students, too, may be disadvantaged under such classroom conditions (Armstrong, 1980; Kagan, 1980; Slavin, 1983). Both women and minorities have been shown to be more likely to persist in mathematics and science if they see these subjects as interesting, connected to everyday life, and relevant to their future careers (Casserly, 1979; Chipman and Thomas, 1984; Creswell, 1980; Fennema and Sherman, 1977; Lantz and Smith, 1981; Maccoby and Jack lin, 1974; Tobin and Fox, 1980).

Survey data simply dg not allow us to examine the subtleties of classroom interactions and learning experiences. When possible, however, we use variables in the NSSME data set that suggest the presence or absence of classroom characteristics that appear to influ- ence girls' and minorities' motivation and achievement in mathemat- ics. These include the time spent on whole-class versus small-group or individualized instruction, the use of discussion as a teaching strat- egy, and teachers' emphasis on developing an interest in mathematics and science, becoming aware of the usefulness of mathematics and science, and seeing the career relevance of these subjects. The data do permit us to examine the distribution of these features among large numbers of classrooms enrolling various grou?s of students and the extent to which more encouraging conditions are present in class- rooms of particular interest, e.g., those with large percentages of mi- norities.

Third, the NSSME survey data do not reflect the differences in the experience of various groups of students within the same classroom. Observational studies of teacher-student interactions and other, more subtle classroom features often find differential treatment within classrooms (for example, by student race, gender, or ability). This is

not a serious problem for our study, however, since most of the class- room variables included in the NSSME data reflect either tangible re- sources (computers, calculators, funding, teacher qualifications, class size) nr instructional decisions teachers typically make at the class level (such as how to deal with homework). Except possibly in upper elementary mathematics classes, where instructional subgroups may be formed according to ability levels, most of these factors will affect all of the Ptudents enrolled fairly evenly. Earlier work suggests that little individualization occurs within classrooms (e.g., Goodlad, 1984), so we can fairly safely assume that the broad patterns of experience reported in these data reveal class experiences shared by the students enrolled.

Fourth, we are unable to examine distributional differences related to gender. While we did not expect to find predominantly male or fe- male mathematics and science classrooms at the elementary and ju- nior high school levels, we thought we would find them at the senior high school level, since many classes at this level are optional. However, such distinct enrollment patterns did not appear in our analyses, so we were not able to explore whether there are systematic gender differences in access to resources and classroom experiences.

Other limitations that relate to particular constructs or variables are discussed in the context of specific analyses in subsequent sec- tions.

I. 4

II. THE EFFECTS OF STUDENT CHARACTERISTICS ON

OPPORTUNITY

Relating students' race, social class, neighborhood, and career goals to resource allocation and instructional conditions is complicated, be- cause while these classifications are individually important, they are also inseparableno student has only one of them. In this section, therefore, we first consider the interrelatedness of these characteris- tics. We then use data from the NSSME to argue that the judgments schools make about students' ability should also be considered an equally inseparable characteristic that influences students' access to educational opportunities.

THE INSEPARABILITY OF STUDENT CHARACTERISTICS

Every student is a member of a racial group, a social class, and a type of community, and each can be identified as having a particular ability status (e.g., low, average, or high). In the United States, these various memberships and categories cluster.

African-American and Hispanic students' tend to be clustered in inner-city schools. Low-income2 minority students are also concen-

1Our analyses of minority students focus on African-Americans and Hispanics. The small number of Native Americans in the sample does not permit us to extend our fmdings to that group, although we expect that their experiences parallel those of the African-Americans and Hispanics. We did not include the Asian students in our minority category, sines our purpose was to describe the experiences of minority groups that are underrepresented in science and mathematics. We grouped Asian students with whites in our analyses; separate analyses excluding Asians did not yield different results, however, because of the small size nf this group.

2At the school level, we created varlet les for SES based on principals' reports of school characteristics. Because recent ork has established its importance for a number of schooling outcomes (Orland, 1968), the concentration of poor students was used as the basis for our SES measure, with schools reporting low concentrations further differentiated by the proportion of students from wealthy backgrounds. We ere well aware that determining school and student SES is always difficult with surveys, and completely satisfactory proxies are rarely found. Our questionnaires asked principals to list the percentage of students with parents in the following occupational categories: (1) professional and managerial; (2) sales, clerical, technical, or skilled workers; (3) factory or other blue collar workers; (4) farm workers; (6) persons not regularly employed; (6) persons on welfare. We felt that while principals were likely to be fairly accurate in estimating percentages of students from families at the high and low ends of this occupational scale, they would be less able to discriminate among those

trated in other urban and rural schools, but they are not often in the majority there.3 On the other hand, middle- and upper-income white students are concentrated in and form a majority in suburban schools.4 Most rural schools tend to be populated by white students, most of whom are neither very poor nor very well off. Nevertheless, as Table 2.1 shows, there are exceptions. Noticeably absent from the exceptions are all-minority suburban schools and predominantly minority high-wealth schools. Moreover, disproportionately more African-American and Hispanic minority students, poor students, and inner-city-school students are classified by schools as being low in academic ability and not likely to attend college. (We shall look more carefully at these relationships later in this section.)

Not only do these patterns exist, the clustering of particular cate- gories is not serendipitous. Underlying social, political, and economic conditions provide substantive explanations for the fact that so many African-American and Hispanic youngsters are low-income, are living in inner-city neighborhoods, and are perceived to be less able than students from other backgrounds. These same dynamics also help to explain why such a large proportion of whites are economically better off, live in more affluent urban and suburban communities, and are more likely to be considered academically able.

While it has been argued that researchers should treat students' characteristics as inseparable, interactive influences on educational and occupational attainments (Grant and Sleeter, 1986), little is known about the simultaneous or combined effects of these character-

parents who held mid-level jobs (categories 2 and 3). Moreover, we considered "farm workers" an ambiguous category, which principals might interpret to include a wide range of occupational levels, from poor, itinerant field hands to owner-operators. We therefore constructed our SES categories from responses to the extreme categories (1, 5, and 6), devising measures that reflect the extent to which wealth and poverty are represented. The following school SES categories were defined: (1) high poverty (more than 30 percent of the students have parents who are either unemployed or on welfare); (2) moderate poverty (between 10 and 30 percent of the students have parents who are either unemployed or on welfare); (3) low poverty/low to moderate wealth (less than 10 percent of the students have parents who are either unemployed or on welfare, and no more than 30 percent have parents in professional or managerial occupations); (4) low poverty/high wealth (less than 10 pc-cent of the students have parents who ere either unemployed or on welfare, and more than 30 percent of the students have parents in professional or managerial occupltions).

3Categories of schools that differed in racial composition were defmed as follows: (1) mincsityless than 10 percent the of students are white; (2) mixed (mostly minority) 10 to 60 percent are white; (3) mixed (mostly white)-60 to 90 percent are white; and (4) whitemore than 90 percent are white.

4We did not defme new variables for determining a school's community type. Prin- cipals were asked to choose whether their school locations were beat described as (a) inner city, (b) urban, but not inner city, (c) suburban, or (d) rural.

3 6

Table 2.1

SCHOOLS IN VARIOUS RACE, SES,a AND LOCALE CATEGORIES (Percentage of all schools; N = 977)

Racial Composition

Inner City Other Urban Suburban Rural

High Mod. Pov. Pov.

Low High Pov. Wlth.

High Mod. Pov. Pov.

Low Pov.

High Wlth.

High Mod. Pov. Pov.

Low Pov.

High Wlth.

High Mod. Pov. Pov.

Law Pov.

High Wlth. Total

0-10% white Elementary 1.3 0.1 0.1 0 0.2 0.1 0.1 0 0 0 0 0 0.2 0.1 0 0 2.3 Secondary 1.3 0.5 0.1 0 0.4 0 0.3 0.1 0 0 0 0 0.4 0 0 0 3.2

10-50% white Elementary 1.2 0.1 0.1 0 0.9 1.0 0.2 0 0.4 0.3 0.3 0 0.3 0.2 0.1 0 5.2 Secondary 0.4 0.2 0.1 0 0.8 1.8 0.8 0.1 0.3 0.5 0.2 0 0.2 0.7 0.3 0 6.6

50-90% white Elementary 1.0 0.2 0.2 0 0.7 1.4 0.9 0.4 0.1 1.3 1.6 1.2 0.7 0.9 0.3 0.2 11.4 Secondary 0.6 0.9 0.6 0.1 0.5 2.3 2.2 1.2 0.5 1.9 2.2 2.5 0.8 3.2 1.5 0.3 21.3

90-100% white Elementary 0.1 0 0.5 0.2 0.4 0.7 0.4 1.0 0.1 1.4 2.3 2.6 1.0 2.4 2.5 0.7 16.3 Secondary 0.2 0.1 0.5 0.1. 0.3 1.2 1.9 1.4 0.3 2.2 4.3 7.4 0.8 5.8 6.1 1.1 33.9

Total 6.2 2.2 2.3 0.4 4.3 8.6 6.9 4.3 1.7 7.7 10.9 13.6 4.5 13.3 10.9 2.4 100

NOTE: Totals may not sum correctly due to rounding. SOURCE: 1985-1986 NSSME. aHigh poverty = more than 30 percent of students in school have parents who are either unemployed or on welfare; moderate

poverty = 10 to 30 percent have parents who are unemployed or on wehure; low poverty and low-to-moderate wealth = less than 10 percent have parents who are unemployed or on welfare, and no more than 30 percent have parents in professional or managerial occupations; low poverty and high wealth = less than 10 percent have parents who are unemployed or on welfare, and more than 30 percent have parents in professional or managerial occupations.

istics. For example, while there are extensive data on the experiences of minorities per se, data for minority subgroups are rarely collected or analyzed separately. There is little data, for exaMple, to document SES differences within minority groups, such as those between low- income and middle-class African-American students.

THE RELATIVE IMPORTANCE OF RACE AND SES

One of the most puzzling questions concerning atudent chEaacter- istics is whether race or SES has the greater effect on children's op- portunities for achievement and participation. Because these charac- teristics are nearly always studied separately, there is scant evidence with which to address this question. Race has received the bulk of the attention, since racial diswimination has been more often the sub- ject of court actions and federal programs. The experiences of poor children are often extrapolated from studies of racial differences, since many of the poorest children in the United States are African- American and Hispanic, and most of the affluent children are white. But inferring the status of poor children in this country trom the cir- cumstances of African-American and Hispanic children grossly and stereotypically oversimplifies matters. Race and class probably can- not be effectively disentangled in attempts to understand the lower rates of achievement and participation of African-American and Hispanic students, but, as Table 2.1 illustrates, the overlap is not per- fect. A significant disadvantaged sector of the school population children who are poor and whiteis often overlooked, as are middle- class minority students.

The importance of social class status in itself has been demon- strated in recent analyses. High School and Beyond (HSB) data illus- trate that with other school and student factors (including race and. ethnicity) controlled, students' SES accounts substantially for differ- ences in mathematics achievement (Rock, Braun, and Rosenbaum, 1985). Similar relationships are found in Scholastic Aptitude Test (SAT) scores (College Board, 1985).

These findings compel us not only to consider race and social class separately, but also to look at how combinations of student character- istics relate to schooling experiences. The objective should not be to determine which single characteristic is the most important; analyses that control for some characteristics in the attempt to determine the effects of any single characteristic may mask the fact that all of them are important. We need to know how race, social class, and neigh-

borhood independently affect students' learning opportunities. But we must also remember the overlaps among these characteristics, and whenever possible, we must explore how combinations of characteris- tics affect students' chances to learn.

THE RELATIONSHIPS BETWEEN ABILITY JUDGMENTS AND OPPORTUNITY

An often neglected key to understanding the distribution of critical features of science and mathematics education is the close connection between educators' judgments about students' intellectual ability and the educational experiences that follow from those judgments. The NSB has suggested that inequalities may stem from the "failure to recognize and develop talent" and "the erroneous belief that many students [lack] the ability to learn mathematics and science" (NSB, 1983:13).

Growing bodies of evidence show that assessments of students' in- tellectual abilities play a major role in the differential allocation of school experiences (Gamoran, 1987; Guthrie and Leventhal, 1985; Lee, 1986; Oakes, 1983, 1985, 1987). Judgments about academic abil- ity often lead to the segregation of students into separate elementary and middle-school classes and to enrollment in different senior high school courses. These placements, in turn, can mediate students' op- portunities to learn. In elementary and middle schools, students who appear to be slow are often placed in lower-level groups or remedial programs; students who seem to learn more eaaily are placed in high- ability groups. Research evidence suggests that these placements in- fluence the pace and content of instruction and contribute to achievement disparities (Barr and Dreeben, 1983; Hallinan and Sorensen, 1983). At the senior high school level, judgments about students' ability influence decisions about curriculum track enroll- mentwhether students take college-preparatory, general, or voca- tional courses of study. Track enrollment, in turn, is critical in coursetaking and achievement (Lee, 1986; Lee and Bryk, 1988; Rock et al., 1984, 1985), as well as in curriculum content, instructional practices, and classroom learning environments (Oakes, 1985).

Class and track placements and subsequent differences in learning experiences have traditionally been explained as appropriate, given the apparent differences in students' performance at school. How- ever, some evidence suggests that the ways elementary schools define ability and respond to students may help to solidify students' percep-

,r1

tions of their prospects for achievement and may eventually exagger- ate initial performance differences among them (Rosenholtz and Simpson, 1984). Slavin (1987) shows that the popular practice of whole-class ability grouping at elementary schools is ineffective in in- creasing student learning. Similarly, secondary school tracking does not increase schools' overall achievement. Some studies have found that tracking may raise achievement for high-track students slightly, but when these gains are found, students in low tracks suffer a corre- sponding loss. These fmdings raise the possibility that in trying to accommodate students' differences with different educational experi- ences, schools may actually limit most students' opportunities to learn.5

Judgments about students' ability and the corresponding place- ment in homogeneous ability groups can affect the quality of students' educational experiences and achievement; therefore, tracking must be considered an important mechanism for distributing science and mathematics opportunities.

RACE, SOCIAL CLASS, AND ABILITY CLASSIFICATIONS

Assessments of ability and placements in different classes appear ,) be particularly relevant to the educational experiences of poor and

minority students, since the assessments often parallel race and class differences (Persell, 1977; Oakes, 1985; 1987; Rose Zoaarn, 1980). Low-income and minority elementary and middle-school students are more likely to experience initial learning difficulties; as a result, they are more likely to be judged as "low-ability" and placed in low-track and remedial classes or in special education programs (Persell, 1977; Rosenbaum, 1980; Slavin, 1987). Whites and upper-SES elementary students are more likely to be identified as able learners (and more likely to be considered "gifted and talentec:'") anl placed in enriched or accelerated programs (Darling-Hammond, 1985). In senior high school, African-Americans, Hispanics, aud low-income students are enrolled more frequently in vocational and gerwral programs, while whites and high-SES students are more frequently enrolled in aca- demic programs (Rock et al., 1984, 1985).

There is a striking national pattern in the links between the track- ing phenomenon and students' race a.1 SFS in the NSSME data, consistent with earlier research. Teachers at schools enrolling poor

6See Oakes, Gamoran, and Page (in press) for a review of this literature.

stv dents and non-Asian minorities disproportionately judge their science and mathematics students to be of low ability.6 In mixed schools, science and mathematics classes in which disproportionate numbers of minorities7 are enrolled are highly likely to be perceived as low-ability classes.

Figure 2.1 shows that at both the elementary and secondary levels, schools in all four SES categories form classes that are homogeneous in ability, and that they do so to nearly the same extent.8

However, as Figs. 2.2 and 2.3 illustrate, despite the similarity in the percentages of homogeneous classes at both elementary and sec- ondary schools, the types of homogeneous groupings differ quite dra- matically in schools serving students of different SES levels, Schools that have large concentrations of low-income students have a sig- nificantly greater percentage of low-ability groups. The percentage of low-ability classes drops and the percentage of high-ability groups in- creases significantly with higher school SES.

The minority enrollment at schools relates similarly to the patterns of ability groupings (Figs. 2.4, 2.5, 2.6). Figure 2.4 shows only small

6The ability or track level of a class represents the teachers' categorization of the class as including (1) a wide range of ability levels, (2) predominantly low-ability students, (3) predominantly average-ability students, or (4) predominantly high-ability students. We must emphasize two limitations of analyses of ability groupings in the NSSME data. First, we are dealing with perceived ability as a characteristic of the classwe can legitimately talk about opportunities available to students in low-track classes, etc., but we can say nothing about individual ability. Second, we are dealing with teachers' perceptions of abilitywe cannot assume that ability means the same thing from teacher to teacher, or from school to school. Finally, while it is impossible to determine from the NSSME questionnaire whether a formal tracking system is in place at a school, the percentages of homogeneous groups reportPi by teachers agree very closely with the percentages of elementary schools reporting that they use whole-class ability grouping (Slavin et al., 1989).

7We used a variable created from principals' descriptions of school characteristics and teachers' descriptions of sampled classes to show the overrepresentation or underrepresentation of Mrican-American cnd Hispanic students. We developed three categories for this variable: (1) disproportionately whitesmaller percentage of mi- nority students in the classroom than in the school (differences can range from 10 percent to a theoretical 100 pervert); (2) proportionatesame percentage as in the school (within 10 percent in either direction); and (3) disproportionately minority larger percentage of minority students than in the school (differences can range from 10 percent to 100 percent).

Tthe most-affluent schools seem to group students homogeneously more frequently than the least-affluent schools, although the 5 to 10 percent difference is not statistically significant.

9Percentages in Figs. 2.2 through 2.6 do not sum to 100 because mixed-ability classes are excluded from these charts.

Fig. 2.1Percentages of homogeneous ability classes, by school SES

High poverty

Med. Low poverty poverty

Elementary school SES

High wealth

Fig. 2.2Percentages of low-, average-, and high-ability classes in elementary schools, by school SES (F = 11.05, P < 0.001)

4 2

Pig. 2.3Percentages of low-, average-, and high-ability classes in secondary schools, by school SES (F.= 3.92, P < 0.01)

0-10 10-50 5040 Percentage of White students

Fig. 2.4Percentages of ability classes,homogeneous- by school racial composition

90-100

60 0 Low ability II Averagq. abiMy 111 HO abilityi _50

0-10 10-90 50-00

Percentage of white students

90-100

Fig. 2.5Percentages of low-, average-, and high-ability classes in elementary schools, by school racial composition (F = 10.34, P < 0.001)

' Av ability gi Average ability II High ability

Fig. 2.6Percentages of low-, average-, and high-ability classes in secondary schools, by school racial composition (F = 10.70, P < 0.001)

I .1

differences in the percentages of mixed or homogeneously grouped classes across types of schools. However, as Figs. 2.5 and 2.6 make clear, the types of ability-grouped classes differ significantly across schools with different racial compositions. Students who attend high- minority elementary and secondary schools are far more likely than students attending other schools to be enrolled in low-track science and mathematics classes and far less likely to be in high-track classes. Elementary school students' chances of being viewed as ei- ther average- or high-ability increase somewhat with the proportion of white students, the largest concentration of high-track classes oc- curring at the all-white schools. At secondary schools, the proportion of high-track classes increases dramatically as the proportion of white students increases, and there is a corresponding drop in the propor- tion of low-track classes.

There is also a second type of association between minority status and tracking. Tables 2.2 and 2.3 show the distribution of classroom ability classifications across classrooms with greater, roughly equal, and lower proportions of minority students than the minority enroll- ment at the school as a whole. We can consider these classes to be overrepresenting minorities, representative of the student population, or underrepresenting minorities.10

The distribution of ability-grouped classes at racially mixed ele- mentary schools exhibited a highly significant pattern across the racial-composition categories." Although disproportionathly white classes were found to be about equally likely to be identified as low- or high-ability, disproportionately minority classes were seven times more likely to be identified as low-ability than as high-ability.

The association is even more dramatic in secondary schools: Not only were disproportionately minority secondary school classes far more likely to be judged low-ability (two-thirds of all such classes), disproportionately white classes were rarely judged this way. Dif- ferences in judgments about high ability were equally dramatic:

10For the school-level analysis, we used all secondary and middle schools in the data set. But because of the preponderance of 90 percent or more white schools in the sample, the classroom-level analyais was conducted for classes in schools with mixed racial composition (i.e., categories 2 and 3 of the school percentage-white variable). This analysis allows us to control for the racial composition of the schools when we consider the relationship between minority enrollment and ability classification at the classroom level.

"The tests of significance were conducted using class weights. For the school-level analysis, teachers' responses were averaged by school, and their weights were summed for each school, yielding a single observation. However, the data displayed in table form represent the teachers' responses directly.

Table 2.2

ABILITY LEVELS OF CLASSES IN ELEMENTARY SCHOOLS, BY RACIAL COMPOSITION OF CLASS

RELATIVE TO SCHOOL ENROLLMENT (In percent)

Class Ability Level

Class Enrollment* Relative to School Enrollment Low Average High

Fewer minorities 22 52 26 Same (within 10%) 14 74 12 More minorities 30 66 4

NOTE: Table includes classes at mixed-race elementary schools (10 to 90 percent minority) only.

aEffect of class racial composition (relative to school's) is significant at the 0.001 level (F = 8.54).

Table 2.3

ABILITY LEVELS OF CLASSES IN SECONDARY SCHOOLS, BY RACIAL COMPOSITION OF CLASS

RELATWE TO SCHOOL ENROLLMENT (In percent)

Class Ability Levels

Class Enrollmentm Relative to School Enrollment Low Average High Fewer minoritier 5 38 67 Same (within 10%) 21 50 29 More minorities 66 25 9

NOTE: Table 'icludes classe3 at mixed-race elementary schools (10 to 90 percent minority) only.

°Effect of class racial composition (relative to school's) is significant at the 0.001 level (F = 143.45).

More than half of the disproportionately white classes were judged high-ability, compared with fewer than 10 percent of the dispropor- tionately minority classes.

Our analyses of 3chools with different racial compositions and of classes at racially mixed schools show that African-American and Hispanic minorities face two potential barriers to science and math- ematics opportunities. First, their access to high-track science and mathematics classes diminishes as the rInority enrollment at their

schools increases. Second, those who attend racially mixed schools are more likely than their white peers to be placed in low-track classes. There is thus a "double jeopardy" effect for African-American or Hispanic students. These relationships suggest strongly that mi- nority students will suffer whatever disadvantages accrue to students in low-ability classes.12

Tracking is commonly viewed as a neutral, educationally sound re- sponse to a wide range of student aptitude and achievements, but the evidence we offer here confirms earlier work showing that such groupings are easily and commonly confounded with race and social class. Moreover, much prior research suggests that the differences in opportunities provided to ability-grouped classes limit instruction, rather than fine-tune it in ways that accommodate individual differ- ences and promote learning (Oakes, Gamoran, and Page, in press). We examined the distribution of opportunities by the track level of science and mathematics classes to further investigate the possibility that in their efforts to accommodate differences in ability with differ- ent educational experiences, schools actually limit some students' op- portunities to learn.

Because assessments of low academic ability and placements in nonacademic programs occur more frequently among low-income and minority students, the combined effects of ability and other back- ground characteristics are of special importance in attempts to un- cover factors related to underachievement and low participation among these groups. The recurrence of this relationship at both the school and classroom levels underscores the importance of considering ability grouping in any study of the relationship of students' charac- teristics to the distribution of opportunity.

12Because of the overlaps between minority status and poverty, a similar double disadvantage probably exists for low-income students. We were unable to test this hypothesis, however, because the NSSME survey collected no SES data at the classroom level.

III. ACCESS TO SCIENCE AND MATHEMATICS PROGRAMS

Obviously, the mathematics and science curriculum that is taught makes a difference in what students learn: When teachers teach particular mathematics and science topics, concepts, processes, and skills, students are more likely to learn them (Crosswhite et al., 1985; Husen, 1967; McKnight et al., 1987; Wolf, 1977). In this section, we examine the effects of school and classroom characteristics on the mathematics and science knowledge various groups of students have an opportunity to learn.

At the elementary level, the most basicalbeit limitedindicator of students' access to science and mathematics knowledge is the amount of time teachers spend teaching these subjects. An equiva- lent indicator at the secondary level is the number of science and mathematics courses schools offer. But to really understand the type of knowledge that students have an opportunity to learn, we also need to know the curricular goals that guide science and mathematics in- struction for different students; the topics and skills being taught and the depth of course coverage; the numbers of topics covered; the sci- entific accuracy of the content of science and mathematics lessons; and the suitability of the lessons to students' developing cognitive abilities. There is little reliable data available, since large-scale re- search on these issues is difficult and costly.

In this section, we present new evidence about the quantity and quality of the science and mathematics curriculum that different groups of students experience in schools and classrooms and place this evidence in the context of findings from other research. First, we look at the extent of programs, measured by the amount of time spent on science and mathematics in elementary schools and how many courses in these subjects are offered in secondary schools. Then we consider the depth and rigor of the content in secondary school pro- grams, as measured by the types of courses schools offer. We attempt to show the similarities and the differences in students' access to science and mathematics knowledge, and we examine the relationship of students' race, social class, community, and ability status to differ- ences in their curricula.

4 S 26

TIME SPENT ON SCIENCE AND MATHEMATICS IN ELEMENTARY SCHOOLS

As noted above, the amount of class time that elementary teachers devote to teaching science and mathematics is the most basic indica- tor of students' access to these subjects, but it indicates little about the time students spend engaged in lessons or about the pace, con- tent, and quality of instruction. Nevertheless, there is reason to be- lieve that the amount of time spent studying a subject does influence the amount of learning that takes place.' This relationship is strongest in mathematics and science, since these subjects, unlike reading and social studies, are rarely learned in informal settings (Husen, 1967).

The time devoted to various subject areas varies considerably among schools. Good lad (1984) surveyed teachers in thirteen elemen- tary schools and found that their reported time spent teaching math- ematics ranged from 45 minutes to 66 minutes per day. On average, mathematics occupied 20 percent of the total instructional time in these schools. Science typically occupied less time, but the variation among the schools was greater, with reported time ranging from 16 to 64 minutes. The average time devoted to science instruction was 28 minutes, about 10 percent of the total instructional time in these schools.

The NSSME data yield similar findings. Teachers of self-contained classes in grades K-3 reported spending an average of 43 minutes per day on mathematics instruction and 18 minutes on science.2 Their counterparts teaching grades 4-6 reported spending 52 minutes on mathemeics and 29 minutes on science. At both levels, the varia- tions in science were greater than those in mathematics. Schools us- ing "specialists" to teach science and/or mathematics typically devoted more time to science and slightly less time to mathematics (Weiss, 1987).

However, the variation in mathematics instructional time was not random. Schools and classrooms serving different groups of students spent significantly different amounts of time on mathematics lessons. Figure 3.1 shows that the number of minutes per day spent in math-

1See Carey (1989) for a review of the literature on this topic. 2Teachers reported the number of days per week they typically presented lessons in

science and mathematics and the approximate number of minutes they spent in an average lesson. To obtain an estimate of the average number of minutes per day in each subject, we multiplied the reported minutes per lessm by the number of lessons per week and divided the result by 5.

Fig. 3.1Time spent on science and mathematics in elementary schools serving different student populations (for science, no

significant differences; for math, F = 4.92, P < 0.01)

ematics instruction at the NSSME elementary schools differed by the percentage of low-income students enrolled.

Slightly more time per day was spent on mathematics at sc,lools enrolling large concentrations of low-income students than at other types of schools: 50 minutes, on average, compared with 47, 43, and 44 minutes at schools serving increasingly advantaged populations. Similar time differences occurred among schools serving different racial groups and in different types of communities. Schools with the largest percentages of African-American and Hispanic students and those in inner cities devoted the most time to mathematics. Inter- estingly, the small amount of additional time in mathematics in low- SES, high-minoety, and inner-city schools did not seem to be gained

at the expense of science instruction, for which time allotments were similar across school types. Because these schools tend to have longer school days, they can accommodate longer periods of mathematics instruction. For example, the low-SES schools averaged 171 instructional minutes per day, and the highest-SES schools averaged

5 o

156 minutes. The percentage of the school day spent on mathematics was a relatively constant 28 percent across schools.

On its face, it is not surprising that teachers at low-SES, high- minority, and inner-city schools would spend more time on mathematics, since most of these schools qualify for federal assistance in the form of Chapter 1 funds targeted at improving disadvantaged students' basic skills (95 percent of the schools in our low-SES category reported that they qualified for these funds). However, federal assistance did not seem to affect directly the time spent on mathematics instruction. What it did affect was the time teachers said they spent on science. In all but the most affluent group of schools (only 15 percent of which qualified for federal funding), schools with Chapter 1 programs spent more time on science.3 We speculate that raising students' mathematics achievement is thought to be important enough to command a large share of time with or without Chapter 1 funding. But the extra resourcesin the form of specialist teachers and instructional materialsmay enable partici- pating schools to free up more teacher time and resources for science instruction.

In contrast to these school differences, the track level of elementary science and mathematics classes does not seem to affect the allocation of instructional time. Within NSSME schools of different types, stu- dents in low-, average-, and high-ability classes spent equivalent amounts of time on lessons. Because schools often regulate the min- imtun amount of class time for various subjects, teachers may have little discretion about how much time they direct students of different ability levels to spend on lessons.4

Thus, elementary schools with large concentrations of -tudents who typically do poorly in mathematics seem to be attacking this problem by spending somewhat more time on mathematics lessons, presumably in hopes of giving disadvantaged and minority students a good start in mathematics. However, across all schools extra mathe-

3F = 5.05, P < 0.05. 4While we do not know with certainty that the homogeneous classes in our sample

were groups of students who remained together for the whole day or groups of students pulled from heterogeneous homerooms for science and mathematics instruction, we suspect many were the former. We base our speculation on the fact that many elementary schools regroup students from heterogeneous classes for mathematics instruction, but few do so for science (Oakes, 1985; Slavin, 1987). However, since only slightly smaller percentages of science than mathematics classes were identified as homogeneous (63 percent of science and 70 percent of mathematics), we suspect that most of thJ homogeneous classes in the sample stayed together for most or all of the school day.

matics time is not being provided in those classes for the students who are perceived to be the least able.5

Our cross-sectional data do not permit us to determine whether the increased time allocations in schools with large concentrations of low- income and minority students are long-standing or reflect recent changesperhaps in response to the press for additional time on ba- sic subjects in recent school reform proposals (e.g., A Nation at Risk). Nor can these data indicate whether the extra mathematics time in disadvantaged and minority schools is spent in ways that are likely to help students overcome their historic patterns of low achievement. We know, for example, that the time teachers allocate to lessons is far less important than the time students are actually engaged in appro- priate tasks (Berliner, 1979; Brophy and Good, 1986). Despite the limitations of these findings, however, achievement data showing a Slow but steady decrease in the black-white mathematics gap in the elementary grades over the past decade suggest that some factor in basic skills instructionperhaps even this small additional time allo- cationmay be having a modest benefit. However, other aspects of elementary school students' experiences, discussed in later sections, may offset this advantage.

SCIENCE AND MATHEMATICS PROGRAMS IN SECONDARY SCHOOLS

Secoadary students' access to mathematics and science can be judged roughly by the courses in these subjects that schools make available. In this section, we are interested in (1) the extent of science and mathematics programs, (2) the content and rigor of the courses that make up those programs, and (3) the extent to which schools offer typical "gatekeeping" courses, i.e., courses that are usu- ally prerequisites for participation in higher-level science and math- ematics.

The Extent of Programs Secondary schools vary considerably in the time they allocate to

science and mathematics. Good lad (1984) found that an average of 17

513ecause the survey reported only how much time the classroom teacher spent on lessons, we do not know the extent of additional time low-track students might have spent in pull-out, remedial programs that supplemented regular classroom instruction.

r y 0

percent of full-time teaching positions (equivalent to the percentage of instructional time) were devoted to mathematics in a sample ofjunior high schools. However, the range among the schools was 13 to 22 percent. In science, the average was 13 percent, but it ranged from 7 to 20 percent. Slightly less variability was found at the senior high school level, where, on average, 13 percent (with a range of 9 to 20 percent) of the teaching positions were allocated to mathematics, and 11 percent (with a range of 8 to 15 percent) were allocated to science.

What makes this variation worth noting is the connection between students' exposure to subjects and their achievement. Considerable evidence from national surveys (e.g., the National Assessment of Educational Progress (NAEP), National Longitudinal Study (NLS), and HSB) attests to the importance of high school coursetaking for mathematics and science achievement (Jones et al., 1986; Welch, Anderson, and Harris, 1982). Thus it is not surprising that the num- ber of courses offered relates to what and how much students learn (Peng, Owings, and Fetters, 1981; Rock et al., 1985).

The extent of programs in secondary schools is a rough corollary of the time devoted to classes in elementary schools. Here, we are inter- ested in the numbers of class sections offered in science and mathe- matics.6 The numbers indicate how much science and mathematics is available and the extent to which students are taking advantage of available opportunitieseither because of their own or their parents' wishes or because the school requires or presses students to enroll in science and mathematics courses. Of course, they reveal nothing about what kinds of courses are avi ilable. It is highly significant that differences in the extent of the programs at the NSSME secondary schools are not random, but rather are fairly consistently related to school population and community characteristics.7

6Class sections refers to the total number of classes offered by the school, not the number of discrete course offerings, For example, two schools may both offer 3 science courses: biology, chemistry, and physics. However, the first school may offer 3 sections of biology, 2 of chemistry, and 1 of physics, while the other offers 6, 6, and 2, respectively. While both schools offer 3 courses, the first offers 6 sections and the second offers 13. The importance of this is that it suggests greater participation rates for individual students if overall school enrollments are equivalent.

7The secondary and middle schools surveyed in the NSSME included schools with a variety of grade spans (9-12, 10-12, 7-9, 6-9, etc.). In this study, we usually used subsets of these schools. The 9-12 and 10-12 schools as a group represent high schools, and schools with maximum grades 8 or 9 represent junior high schools. The high school subgroup comprised about 860 schools; the junior high subgroup, roughly 200 schools. In some cases, we had to leave off the sampling weights because the schools were originally assigned a "senior" or a 'junior" weight, but not both. This became a problem, since some of the 9-12 schools were classified as junior highs (those in which only ninth grade teachers were sampled). Thus, for some of our school-level

Middle Schools and Junior High Schools. Figures 3.2 and 3.3 show the differences in the extent of the mathematics and science programs at the junior high schools in the NSSME sample by school SES and racial composition.8

These patterns are quite different from those related to time allo- cations in elementary schools. Students attending the junior high and middle schools with the largest concentrations of low-income stu- dents had access to considerably less-extensive programs in both science (approximately 2.5 classes per 100 students) and mathematics (approximately 3 classes per 100 students) than those attending the most affluent schools (slightly more than 4 classes per 100 students in each subject); differences in science exceeded those in mathematics. The Endings are only slightly different when the schools' racial makeup is considered. Science programs at schools whose student populations are more than 90 percent white were found to be signifi- cantly more extensive (nearly 4 classes per 100 students) than those at schoals with similar percentages of minorities (about 2.5 classes); no sigthficant race-related differences were found in the size of math- etnati es programs.

These findings, while perhaps disappointing, are not surprising. Many junior high school and middle school students are required to take only one semester or one year of science; additional science courses are either electives or recommended for high-achieving stu- dents. What the findings suggest is that high-SES and predomi- nantly white schools either have greater science requirements or offer greater numbers of optional science courses.

The finding that low-SES junior high schools offer fewer sections of mathematics raises more troubling questions. In nearly every state, junior high school and middle school students are required to take mathematics each year, so mathematics classes in low-SES schools may be consistently larger than those in other types of schools--large enough to reduce the relative number of mathematics sections offered. Our data, in fact, do show such a trend. The lowest-SES schools had significantly larger mathematics classes than did the most affluent schools (averaging 26 and 23 students per class, respectively).8 This

analyses, many of the more inclusive senior high schools (e.g., 9-12 schools) would not have the appropriate weights.

8To account for the size of the school and its grade span, which might affect the number of courses offered per student, we used an analysis of covariance to control for the logarithm of number of students per grade and the minimum and maximum grades in a school.

813 < 0.05.

5 4

111 Sdence I 111 Mathematics

Fig. 3.2Mathematics and science classes per 100 students in grade 6-9 junior high schools, by school SES (for mathematics,

F = 4.39, P < 0.01; for science, F = 13.69, P < 0.001)

0-10 10-50 50-90 90-100 Porcentsge of white students

Fig. 3.3Mathematics and science classes per 100 students in grade 6-9 junior high schools, by school racial composition (for mathe- matics, differences not significant; for scienr F = 3.64, P < 0.05)

means that the junior high schools serving the largest concentration of low-income students allocated less Vine and fewer teachers to mathematics, even though all students were probably enrolled. Community type had little effect on the extent of junior high school programs. This suggests that low-SES schools in both inner-city and rural areas (the communities where most low-SES schools are found) offer students fewer science and mathematics opportunities.

These findings suggest that the possible advantages of more time on mathematics instruction in elementary schools serving low-income and minority students may disappear when students reach middle school or junior high school.

Senior High Schools. Science and mathematics programs are similar in size at most senior high schools, but high-SES schools have significantly larger science programs than other types of schools, and rural schools have the least extensive mathematics programs.1°

Content and Rigor of Programs

Differences in the number of class sections reflect only the most general differences among programs. Data about the content and level of courses (e.g., advanced, general, or remedial) add considerable information, since programs at schools offering the same number of class sections may differ significantly in depth and rigor. For exam- ple, if a school offers no biology courses, no one at that school will have a chance to learn biology. These differences are important be- cause the particular courses students take affect their achievement (Jones, 1984; Jones et aL, 1987; Peng, Owings, and Fetters, 1981; Sells, 1982).

Because course offerings can constrain or encourage students' coursetaking in science and mathematics, differences in programs

10The subset of schools we used comprised all the schools with grade spans of 9-12 and 10-12. However, we considered only schools with more than 30 students in a grade to avoid the distortions extremely small schools can create. To account for school size and the presence or absence of a ninth grade (which can affect types of science offerings, for example), our model included the logarithm of number of students per grade and the minimum grade in a school. After controlling for these variables, we found that the distribution pattern by SES categories was significant at the 0.05 level for total science courses (F = 3.27, P 0.02), but not for total mathematics courses (F = 2.06, P = 0.11). Racial composition (percentage white) did not result in significant differences with respect to total course offerings in either mathematics or science (F = 1.22, P = 0.30 for science; F = 0.34, P = 0.80 for math). Significant differences in mathematics programs wine found in schools in different types of communities, however, with rural schools having the least-extensive programs (F = 3.05, P < 0.01).

may contribute to the achievement gaps among different student groups. I-ISB data show that senior high schools serving predomi- nantly poor students typically offer fewer advanced placement (AP) courses (Ekstrom, Goertz, and Rock, 1988) and enroll proportionately fewer students in those they offer (Jones, Burton, and Davenport, 1984), and that students in college-preparatory programs at low-SES schools (the schools most minorities attend) typically take fewer aca- demic courses (including mathematics and science courses) than their college-bound peers attending more-advantaged schools (Rock et al., 1985). These lower rates of academic coursetaking are linked to African-American students' lower levels of achievement in these sub- jects (Jones, 1984; Pallas and Alexander, 1983).

Figures 3.4 and 3.5 show the number of sections of general, college- preparatory, and advanced college-preparatory courses at the senior high schools in the sample.11

When the number of class sections is broken down by types of courses, the distribution patterns are significant or highly significant for all but general science classes. As the proportion of low-income and minority students at a school increases, the relative proportion of college-preparatory or advanced course sections decreases. Table 3.1 shows the significance of these differences.

The differences in the level of the classes offered cannot be ac- counted for by class size differences, as was the case among the junior highs. In fact, some of the differences in the sizes of various cate- gories of classes in different types of schools compound the difference in opportunities among schools. For example, while no overall SES-related differences were found in the number of students in science classes, the size of college-preparatory and advanced college- preparatory mathematics classes increased with the affluence of the school.12 This means that relatively more students were taking these courses at highly affluent schools than simple comparisons of the numbers of sections would indicate.

The Availability of Gatekeeping Courses

A third important dimension of students' access to science and mathematics knowledge is the extent of critical "gatekeeping" courses

11 The courses that were classified in each of these categories are listed in the Appendix,

12F = 3,03, P < 0.05; and F = 3.63, P < 0.05, respectively.

Fig. 3.4Mathematics and science classes per 100 students in senior high schools, by school SES

0 0-10 10-50 50-90

Percentage nt white students 90-100

Fig. 3.5Mathematics and science classes per 100 students in senior high schools, by school racial composition

Table 3.1

SIGNIFICANCE OF SES, RACE, AND LOCALE DIFFERENCES FOR SENIOR HIGH SCHOOL

CnURSE OFFERINGS

Independent Variable

Science Mathematics

F P < F P <

General Classes

SES 1.30 0.27 12.42 0.001 % White 2.02 0.11 7.80 0.001 Locale 1.51 0.21 3.71 0.02

College Prep Classes

SES 8.23 0.001 11.23 0.001 % White 5.48 0.001 3.00 0.03 Locale 3.45 0.02 7.32 0.001

Advanced College Prep Classes

SES 11.30 0.001 16.54 0.001 % White 6.97 0.001 6.67 0.001 Locale 4.08 0.01 10.49 0.001

All Classes

SES 3.27 0.02 2.06 0.11 % White 1,22 0.3 0.34 0,8 Locale 2.20 0.09 4.05 0.01

offered at their schools, that is, courses that are especially important in qualifying students for post-high-school work in science and math- ematics. At the senior high school level, the most critical course is calculus, because it is a prerequisite for entry into most science-, mathematics-, and technology-related majors at college. Without high school calculus, students must take beginning calculus classes in college. In many cases, this can make obtaining a baccalaureate de- gree in a quantitative field in four years very difficult. At the junior high school level, eighth grade algebra and ninth grade geometry are critical gatekeepers, since students who take these courses early are on track by grade 12 without having to double up classes or take mathematics courses during the summer.13

13The subsample of schools examined for calculus offerings was identical to that in the general mathematics and science offerings analysis, but the accelerated- mathematics analysis is based on our "junior high" grouping. The count of accelerated mathematics classes was determined by th3 number of algebra classes offered (in

0-10 10-50 50-90 90-100

Percentage of white students1M

Junior High Schools. We performed parallel analyses for the availew. v of algebra for eighth graders and geometry for ninth grader. lie junior high school sample and the availability of calcu- lus at - senior high level. Figure Z3.6 shows the percentages of ju- nior high schools, by SES and race, that offered at least one section of accelerated mathematics.

Despite what appear to be meaningful differences in the percent- ages of junior high schools offering accelerated mathematics classes far fewer of the sampled low-SES and predominantly minority schools offered these classesthe differences among all SES categories for ac- celerated mathematics offerings were not significant." A difference approaching significance, however, was found between the lowest-

20 High Med. Low High

PovellY PovertY PovertY wvalth

SES

NOTE: Overall differences due to SES and racial composition were not significalt, although groups 1 and 4 differed with P-values approaching significance (P = 0.086 f^r P = 0.08 for racial composition).

Fig. 3.6Junior high tools offering accelerated mathematics classes, by school SES and racial composition

schools whose fmal grade is 8), or by the number of geometry classes offered when algebra was also offered (in schools with a ninth grade).

14p = 1.30, P = 0.27.

and highest-SES schools.18 Similarly, the differences across per- centage white categories were not significant,18 but again, the dif- ference between high-minority and high-white schools approached significance."

Figure 3.7 shows the numbers of sections of accelerated mathemat- ics in schools of different types that offered these courses.18 The distribution of the number of sections offered is significant across SES categories,18 and it is highly significant across percentage-white cat- egories.20 S adents attending high-SES or all-white schools have

Fig. 3.7Number of accelerated mathematics classes per 100 students in junior high schools offering accelerated mathematics classes, by school SES and racial composition (for SES, F = 3.06,

P < 0.05; for racial composition, F = 4.54, P < 0.01)

15P = 0.09. 16F = 1.04, P = 0.38. 17P = 0.08. The lack of significance of these results may be attributable, in part, to

the small number of schools in some of the categories. 18As in the earlier analyses, course offerings were divided by the average number of

students per grade. 19F = 3.06, P < 0.05. 20F = 4.54, P < 0.01.

far greater opportunities to take critical gatekeeping courses that will prepare them for advanced mathematics and science courses in senior high school than students in low-SES and high-minority schools.

Senior High School. We were also interested in the percentage of senior high schools offering calculus classes.

Figure 3.8 shows the striking difference in students' opportunities to take calculus at schools of different SES levels. Predominantly white schools were found to be far more likely to offer calculus than high-minority schools,21 although the differences across all four racial groupings did not reach statistical significance. Eighty percent of the predominantly white schools offered at least one section of calculus, whereas only about 50 percent of the high-minority schools did. This means that students at low-SES or high-minority schools who are prepared to take calculus in high school have far less opportunity to do so than their peers at economically more advantaged or predom- inantly white schools.

Fig. 3.8High schools offering calculus classes, by school SES and racial composition (for SES, F = 4.21, P < 0.01; racial

composition had no significant effect overall, although groups 1 and 4 differed with P < 0.05)

21P > 0.05.

Among schoois offering calculus, a further dimension of opportunity is reflected in the number of sections offered relative to the size of the student body in various types of schools. Figi re 3.9 shows that the opportunity to take calculus increases considerably as the proportion of low-income students drops, and that while mixed schools have rela- ti*rely comparable numbers of calculus offerings, high-minority schools that offer calculus have far fewer sections. Moreover, the dif- ferences in students' access to calculus are minimized in these figures by the omission of schools that offered no sections.

It is difficult to determine exactly why schools offer the types of courses they do, Schools that offer few rigorous courses often do so because they have few students who are "qualified" to take those courses, that is, who meet test score or other criteria conventionally seen as prerequisites for learning content such as algebra, geometry, advanced mathematics, or mathematics-related science subjects. In fact, the most widely accepted explanation is that secondary schools'

Fig. 3,9Number of calculus classes per 100 students, by school SES and racial composition (for SES, F = 11.28,

P < 0.001; for racial composition, F = 3.05, P < 0.05)

progruns are constrained by earlier conditions that fail to develop the skills of disadvantaged students. But it should be noted that some schools bend conventional placement criteria and encourage lower- scoring students to take rigorous science and mathematics courses.

Some schools may simply place less emphasis on academic courses or, alternatively, more emphasis on more practical offerings, in the belief that such courses better meet their students' needs. Still other schools may lack staff who are able to teach certain courses, and this may be a significant factor in the paucity of curricular offerings in high-minority and high-poverty schools. Whatever the reasons, sec- ondary schools serving low-income, minority, and inner-city popula- tions offer fewer sections of college-preparatory or advanced courses and more general, applied, and remedial courses. The relatively small differences in the numbers of class sections offered in high school science and mathematics programs obscure substantial differ- ences in the depth and rigor of programs at different types of schools.

Moreover, differences in students' opportunities to take critical gatekeeping courses affect their access to continuing study in science and mathematics. Of course, some qualified students, especially in cities, can transfer to schools that offer advanced programs. In these cases, students' opportunities may not be as restricted as our data suggest. However, this does not contradict the clear finding that fewer schools serving low-income and minority students offer the op- portunity to begin the college-preparatory mathematics sequence in junior high school or to take calculus in senior high school. And among schools that offer these courses, the proportion of students who take them (as electives or as requirements) is far greater at high- income and predominantly white schools. These findings are quite disturbing: They are not simply consistent with the typically lower mathematics achievement of minority high school students, they strongly signal unequal access to valuable science and mathematics knowledge.

ACCESS TO COURSES WITHIN SCHOOLS

Schools' judgments about students' abilities and their likelihood of going to college affect access to various course offerings and shape the paths students take through the school curriculum. In most schools, fewer mathematics and science courses are available to low-track

. 4

students or required for them (Guthrie and Leventhal, 1985; Sanders, Stone, and La Follette, 1987; Vanfossen, Jones, and Spade, 1985).22

At the NSSME schools, traditional academic or standard college- preparatory courses and advanced college-preparatory courses are offered most often to students perceived as having high ability, somewhat less often to students thought to be of average ability, and hardly ever to students seen as having low ability (Table 3.2). Low- track students more often take general or applied science and math- ematics courses." While some of these courses include basic or ap- plied "versions" of standard academic subjects (e.g., pre-algebra or in- troduction to algebra, general biology, applied chemistry, basic or "fun" physics), the content in most is quite different from the standard fare in academic science and mathematics.

Since low-SES and minority students are disproportionately en- rolled in low-track classes and substantially underrepresented in high-ability classes, the likelihood of their being enrolled in academic and advanced courses decreases with the percentage of minority stu- dents in the class. Four-fifths of the predominantly white classes in the NSSME sample were taking traditional academic or advanced courses, whereas only 57 percent of the predominantly minority classes were taking such courses. Of course, these differences are

Table 3.2

DISTRIBUTION OF GENERAL, ACADEMIC, AND ADVANCED SCIENCE AND MATHEMATICS COURSES IN SENIOR

HIGH SCHOOLS, BY ABILITY LEVEL OF CLASS (Percentage of courses of each type taken)a

Type of Course

Class Ability Level General Academic Advanced Total

Predominantly low 74 25 1 100 Predominantly average 21 66 12 100 Predominantly high 5 40 55 100

aChi-square = 581.521, P < 0.001.

22However, access to courses and coursetaking varies among schools with different tracking policies (Rosenbaum, 1986; Oakes, 1985). For example, students enrolled in nonacademic tracks in Catholic high schools typically take more academic c,.,urses and fewer electives than do their counterparts in public schools; the Catholic schools also place more students in academic tracks (Lee, 1986; Lee and Bryk, 1988).

23Business mathematics, consumer mathematics, remedial mathematics, general mathematics, technical mathematics, applied mathematics, basic or remedial science, general science, agriculture, current issues, medical technology, plant science, electron- ics, aviation, ecology, environmental science.

shaped in part by the fact that fewer academic courses are offered at high-minority schools.

However, similar differences appear when we control for racial composition of the entire school. As shown in Table 3.3, those classes in which white students are clustered tend to be academic, and those in which minority students are clustered tend not to be.

Just as differences in course offerings at schools of different types result in unequal access to science and mathematics content, curricu- lum differentiation through ability grouping leads to further race- and class-linked inequalities. Students judged to have low ability (disproportionately large numbers of minority students) have far less access to the standard academic subject matter in science and math- ematics than do other students.

Table 3.3

DISTRIBUTION OF GENERAL, ACADEMIC, AND ADVANCED SCIENCE AND MATHEMATICS CLASSES, BY CLASS RACIAL COMPOSITION

(Percentage of courses of each type taken)a

Type of Course

Class Racial Makeup General Academic Advanced Total

Disproportionately minority 59 36 5 100 Racially proportionate (±10 percent) 23 51 25 100 Disproportionately white 15 49 36 100

NOTE: For these analyses, we considered only those schools with white populations greater that 10 percent, but less than 90 percent.

aChi-square 107.414, P < 0.001.

SUMMARY

This section has examined how students' access to science and mathematics knowledge varies with their race, social class, and neighborhood, and with the judgments educators make about their intellectual abilities. Except for slightly more time allocated for mathematics instruction in elementary schools with high concentra- tions of low-income and minority children, access to science and mathematics knowledge is limited for stud,nts from groups that con- sistently achieve and participate less in these areas. To the extent that they are enrolled in secondary schools where they are the major- ity, low-income students, African-Americans, and Hispanics have less-

I ' 6

extensive and less-demanding science and mathematics programs available to them, and they have considerably fewer opportunities to take the critical gatekeeping courses that prepare them to pursue sci- ence and mathematics study after high school. This disadvantage is compounded by differences in students' opportunities within schools. Students who are thought to be of low ability are far less likely to be placed in traditional academic courses than are students judged to be more capable. These disparities undoubtedly reflect earlier and broader conditions that fail to develop the skills of large numbers of disadvantaged students rather than overt discrimination in the course enrollment process. But the net effect is that disadvantaged and minority students have considerably less access to knowledge that is considered necessary either for science and mathematics ca- reers or for becoming scientifically literate, critically thinking citizens and productive members of an increasingly technological workforce.

Schools in the United States ration curriculum far more than those in many other countries. The Second International Math Study (SIMS) found that U.S. middle schools and junior high schools rou- tinely sort eighth graders into four types of mathematics classes (remedial, typical, enriched, and algebra); this ability grouping was more extensive than that practiced in any other country studied. The SIMS also found that different types of classes provided students with quite different access to mathematics topics. For example, only the small percentage of U.S. students who were enrolled in algebra classes spent much of their class time studying algebra topics. In con- trast, Japanese schools exposed nearly all their seventh graders to an intensive algebra curriculum. Only 13 percent of U.S. seventeen- year-olds were enrolled in advanced mathematics, and only about 20 percent of these advanced classes included calculus. This contrasts with many other countries where far greater percentages of students were enrolled in advanced mathematics (e.g., Hungary, Japan, Canada, Ireland, Scotland, Sweden, Thailand), nearly all of them in calculus courses (Travers and Westbury, 1989). Most surprising, the more exclusive populations of U.S. students who were taking calculus in the twelfth grade did not outscore the broader groups from other nations on advanced mathematics tests (McKnight et al., 1987). These data suggest that this highly selective system does not enhance achievement, even for those students enrolled in the most advanced courses.

W. ACCESS TO QUALIFIED SCIENCE AND MATHEMATICS TEACHERS

Another factor in the lower achievement of low-income and minor- ity students may be a lack of exposure to high-quality science and mathematics teachers. It has been widely believed, but not well doc- umented, that predominantly minority and poor schools are less able to attract and retain qualified and experienced teachers. A recent re- port of the California Commission on the Teaching Profession argues, in fact, that disproportionate numbers of poor and minority students are taught during their entire school careers by the least-qualified teachers. The Commission report cites high levels of teacher turn- over, large:: numbers of misassigned teachers, and classrooms staffed by teachers holding only emergency credentials as problems in schools serving these "at risk" groups (California Commission on the Teaching Profession, 1985). National data from the mid-1980s indi- cate that teachers in inner-city schools are more likely to be uncerti- fied than those who teach in the suburbs or rural areas (Darling- Hammond, 1985, 1987; Pascal, 1984). This problem has also been documented by anecdotes and some case-study work (Levy, 1970; Wise et al., 1987), but until now we have had little specific informa- tion about the distribution of science and mathematics teachers.

Schools enrolling large concentrations of low-SES students, African-Americans, or Hispanics are often perceived to be less desir- able places in which to teach, and teacher shortages are likely to be felt most in these schools. Some national evidence already supports this contention. In 1983, there were about three times as many un- filled teaching vacancies (including positions that were withdrawn or for which a substitute was hired) in central cities as there were in other types of districts (NCES, 1985).

Teacher shortages are greatest in mathematics and science, espe- cially in physical science. In 1981, more than half of the newly hired teachers in these fields either were not certified in science teaching or lacked certification in the specific courses they were to teach (NCES, 1983). Between 1972 and 1984, the number of newly graduating science and mathematics teachers decreased by 67 percent, and some estimates were indicating that as many as 30 percent of those teach- ing science and mathematics at the secondary level were unqualified or underqualified for their assignments (Johnston and Aldridge,

1984).1 These data suggest that canceled courses, overcrowded classes, teaching misassignments, and the use of substitute teachers in mathematics and science courses are far more likely to occur in inner-city schools.

While little hard evidence is available to document the effects of teacher quality on students' achievement or choices, teachers are considered by almost everyone to be an important part of the educa- tional process. Having well-prepared teachers who are knowledge- able in the subjects they teach is virtually a prerequisite to student learning (Darling-Hammond and Hudson, 1989). Thus, the teacher- quality gap among schools serving different student groups is in itself an important dimension of the distribution of opportunity to learn.

In this section, we first consider the extent of vacancies in the science and mathematics staffs of secondary schools of different types and the difficulties principals report in filling the vacancies that oc- cur, based on NSSME data.2 We next consider the principals' and teachers' perceptions of the competence of their mathematics and science staffs and the effects of teacher-related problems on the qual- ity of mathematics and science instruction at their schools. We alio consider the percentage of teachers employed at different types of schools who consider themselves to be "master" teachers in science and mathematics. Finally, we look at more tangible measures of teachers' backgrounds and qualifications: teaching experience, certi- fication status, and academic preparation.

SHORTAGES OF QUALIFIED TEACHERS

Few schools have classrooms that are not staffed by teachers. When vacancies occur, school administrators do not usually hold po- sitions open while they search for well-qualified replacements. If no qualified new hire can be immediately found, principals usually fill the opening with an unqualified teacher, use a substitute teacher, in- crease other teachers' class sizes or course loads, or cancel the course altogether.

The frequency with which vacancies occur and the difficulty princi- pals have finding qualified teachers, then, provide useful information

1More recent data, however, suggest that most science courses are taught by teachers who specialize in science, although perhaps not in the specific subject taught (National Science Teachers Association, 1987; Weiss, 1987).

2Because most teachers in elementary schools teach all subjects, the issue of vacancies in the science and mathematics teaching staff is not relevant at that level.

about the quality of the teaching staff at different types of schools. And these data indicate that the teacher-shortage problem has the greatest effect on the access of poor and minority students to well-

qualified teachers.

Where Do Vacancies Exist?

Secondary school principals in the NSSME sample did not vary significantly in their reporting of concern with mathematics vacan- cies, whereas science vacancies were of substantially greater concern in low-SES, high-minority, and inner-city schools. One plausible ex- planation for this unexpected finding (we would expect principals with the least-qualified teachers to express the greatest concern) is that principals in disadvantaged schools are less likely to perceive a mathematics position as "vacant" if an unqualified teacher can be found to fill it. In contrast, because science is often perceived as somewhat more specialized and rich in content than the low-level, computation-oriented mathematics classes that dominate the curricu-

lum in low-income, minority schools, principals may be quicker to perceive a vacancy if a science course is taught by someone without science expertise.

Figure 4.1 shows the extent to which NSSME principals were concerned about filling biology or life science vacancies.3 Principals at all types of schools expressed concern about vacancies in science, but those at high-poverty, high-minority, and inner-city schools expressed this concern most frequently: 97 percent of the inner-city secondary school principals indicated that science vacancies were a problem, compared with 64, 67, and 70 percent of the principals of schools in other types of communities. Of course, the extent of vacan- cies often reflects high turnover and/or inadequate staffing.

How Hard Are Vacancies to Fill?

The extent of the difficulty principals report having in filling vacancies with well-qualified teachers also varies. Again, principals

3Principals of secondary schools were asked, Does your school find it difficult to hire

fully qualified teachers for vacancies in each of the following fields? They responded either yes, no, or no vacancies/does not apply. Separate responses were obtained for mathematics, several science subjects, and other school subjects. The percentages in Fig. 4.1 represent secondary school principals who answered either yes or no, since both answers indicate that staff vacancies are a problem.

1111.

HO Ma WO fth 0-10 10-00 OA 90-100 Irfor. Mot &b. RAW Povetti POI PowitY *NM Wien urban

SES Pementsge of white students Location

NOTE: Differences by SES are significant at the 0.01 level; differences by racial composition and location are significant at the 0.001 level.

Fig. 4.1Percentages of secondary schools where life science/biology teacher vacancies were of concern to principals, by school SES, racial composition, and location

at schools with the least-advantaged students, the highest proportions of minority students, and inner-city locations have the greatest difficulty. Figures 4.2 and 4.3 show the percentages of principals in schools of various types who reported difficulty filling vacancies in mathematics and biologythe two subjects most commonly taught in all types of secondary schools.

These fmdings suggest that low-income and minority students are seen as less desirable students to teach, and inner-city communities are thought to be less desirable places for teachers to work in. In addition, salaries at inner-city schools are often lower than in surrounding areas, working conditions are poorer, and there are fewer material resources to work with.

WHICH SCHOOLS HAVE THE MOST-QUALIFIED TEACHERS?

It is difficult to define teacher quality, since good teaching results from a combination of many characteristics, no one set of which works best for all students or all classrooms.4

Nevertheless, we can obtain a rough measure of teacher quality by considering the judgments that principals and teachers make about teaching staff quality and the judgments teachers make about their own competence, and by examining teachers' credentials, educational background, and years of experience.

The distribution of teachers across different types of schools pro- vides information about the overall level of human resources avail- able to implement the curriculum at various schools and about the level of success different types of schools have in attracting teachers who are well-qualified. It also reveals the access various groups of the nation's students as a whole have to well-qualified teachers. The distribution of teachers in various types of classes also provides information on the effects of judgments about students' abilities on access to well-qualified teachers. Finally, this information may indicate patterns of teacher assignment that relate to the racial composition of classes in racially mixed schools.

4See Darling-Hammond and Hudson, 1989.

High Med. Low High 0-10 1040 5040 00-100 Inner Olhw Sib PovolY fxoffY Pow ItY wealth thy urban urban

SES Percentage of whtle students Location

NOTE: Differences by SES are not significant; differences by racial composition are significant at the 0.01 level; differences by location are significant at the 0.05 level.

Fig. 4.2Percentages of secondary schools where principals reported difficulty filling mathematics teacher vacancies, by school SES, racial composition, and location

NOTE: Differences by SES, racial composition, and location are significant at the 0.001 level.

Fig. 4.3Percentages of secondary schools where principals reported difficulty filling life science/biology teacher vacancies, by school SES, racial composition, and location

Perceptions of Teacher Competence

In the NSSME, secondary school principals were asked to indicate how many of the science and mathematics teachers at their schools they considered to be highly competent, competent, and not compe- tent. While such judgments do not define quality, they do indicate the degree to which others perceive it. Figures 4.4 and 4.5 show the average percentages of teachers whose principals judge them highly competent at various types of schools.

Principals at schools with large concentrations of low-income or minority students and at inner-city schools reported that fewer of their teachers were highly competent. Principals at high-wealth, ra- cially mixed, predominantly white, and suburban schools were far more satisfied with the quality of their science and mathematics

, teachers.

We also looked for patterns in the percentage of principals who re- ported that teacher-related problems affect the quality of science and mathematics instruction at their schools. The NSSME principals were given a list of possible factors that may cause serious problems in science and mathematics, and were asked to indicate whether a lack of teacher interest and/or inadequate preparation to teach these subjects caused serious problems at their schools. Only 8 percent of the more than 1,000 elementary and secondary principals who responded said that this was the case. Among this small percentage, no significant patterns of differences appeared across all school types at the elementary school level, although principals at the most affluent schools reported these teacher problems far less often than did those at other types of schools. At the secondary school level, however, patterns of teacher problems do seem to be related to the racial mix in the student body and the type of community in which schools are located. The social class composition of the schools bore no apparent relationship to principals' judgments that teacher interest and/or preparation caused serious problems for their science and mathematics programs (Fig. 4.6).

Teachers may be more aware of the instructional problems caused by disinterested or underprepared teachers.5 Again, we see no pat-

51t is not possible to compare principals' and teachers' perceptions of problems with any certainty, since the NSSME questionnaires worded these questions differently for the two groups. While principals were asked to mark factors that cause "serious" prob- lems, teachers were allowed a broader range of responses. For each factor--including lack of teacher interest and lack of teacher preparationteachers were asked whether it was a "serious problem," "somewhat of a problem," or "not a significant problem."

IMO,

8070 I_

1 1

. 40

. 1.! 10 a

0 I I High M. Low High 0-10 10-50 50-90 90-100 Yaw Calw Sub- Rural

PovertY PovoitY Moth' mai citif urban utan

SES Percent/pa of whits students Location

NOTE: Differences by SES are significant at the 0.01 level; differences by racial composition are not significant; differences by location are significant at the 0.001 level.

Fig, 4.4Proportion of secondary school mathematics teachers considered highly competent by their principals, by school SES, racial composition, and location

High Med. Low High 0-10 10-50 50-00 00-100 ilinsf Other Sub. Rural Po Veity PovedY POWlY wsalth tity urban Wan

SES Percentage of white students Location Ilalr-

NOTE: Differences by SES and location are significant at the 0.001 level; differences by racial composition are significant at the 0.05 level.

Fig. 4.5Proportion of secondary school science teachers considered highly competent by their principals, by school SES, racial composition, and location

7 '7

1 10

1111 1111 I MI 111 High Med. Low ligh 0-10 10-50 5040 03-100 biper Othst Sib- Rural

Pei Pert/ WM/ wuith or/ Aso utbsn

SES Petcentaoe of *tits students Location

NOTE: Differences by SES are not significant; differences by racial composition are significant at the 0.001 level; differences by location are significant at the 0.05 level.

Fig. 4.6Percentages of secondary school principals who reported serious problems resulting from lack of teacher interest or preparation in science and mathematics, by school SES,

racial composition, and location

tern of differences at the elementary school level, but quite dramatic differences among secondary schools (Fig. 4.7).

Teachers at high-poverty, high-minority, and inner-city schools re- ported far more frequently than teachers at other types of schools that a lack of teacher interest or insufficient background posed prob- lems for science and mathematics instruction. In each category of schools, teachers in the least-advantaged schools reported problems at least twice as often as those in other types of schools.

Finally, teachers were asked to indicate the degree to which they considered themselves "master" teachers in science or mathematics.6 On the whole, elementary teachers seemed less confident about their science and matilematics teaching than their counterparts in sec- ondary schools, especially in science. Only 12 percent of the elemen- tary teachers reported that they were master science teachers, while 37 percent of those asked about mathematics said they were. In nei- ther subject did teachers in schools of various types differ, on average, in their confidence levels. In contrast, the distribution of highly confi- dent secondary teachers was not so even: More than half of them in both science and mathematics agreed that they were master teachers. But far fewer teachers in inner-city and rural schools and schools en- rolling large concentrations of low-income children perceived them- selves to be this competent.7

In sum, then, the perceptions of principals and teachers converge around the issue of teacher quality. Schools serving disadvantaged and minority students reported suffering from teacher shortages and teacher quality problems far more than other types of schools.

Teachers' Formal Qualifications

Elementary Schools. Teachers' formal qualifications follow many of the same distributional patterns as teacher shortages and perceptions of teacher competence. There is little evidence of differ- ences in the certification status, academic backgrounds, and teaching experience of elementary teachers working in different types of

6Teachers were asked to respond to the statement, "I consider myself a 'master' science (or math) teacher," by checking either strongly agree, agree, no opinion, disagree, or strongly disagree.

7As the concentration of low-income students decreased at schools, the average level of perceived competence rose (F = 4.98, P < 0.01). Similarly, teachers at schools in urban (outside the inner city) and suburban schools were more self-confident (F = 4.88, P < 0,01).

i30

I I, 20

I 10 0 .A...111.

High Med. Low High 0-10 10-60 50.40 20-100 km CS* 20). Rural PovertY FovortY PosertY wolith dt/ tsban titan

SES Percentage of *bite students Location

NOTE: Differences by SES, racial composition, and location are all significant at the 0.001 level.

Fig. 4.7Percentages of secondary school teachers who reported serious problems resulting from lack of teacher interest or preparation in science and mathematics,

by school SES, racial composition, and location

schools. However, there is one striking exception: While few elemen- tary teachers were found to have a bachelor's degree in either math- ematics or science or a degree in education with a mathematics or science emphasis (only 4 percent over the entire sample), teachers at elementary schools with the highest concentrations of minority stu- dents were more likely to have such degrees than were teachers at schools with other racial mixes (16 percent in high-minority schools; 3, 5, and 6 percent in the other categories based on racial composi- tion).8 The large percentage of minority teachers with degrees ac- counts for the overall higher level of teacher qualifications at the pre- dominantly minority schools. These schools employ the largest per- centages of minority teachers,8 who are more likely to have mathe- matics and science degrees than their counterparts at other types of schools. At predominantly minority schools, minority teachers are also more likely than whites to have mathematics and science bache- lor's degrees. The number of well-qualified minority teachers was large enough to counter the smaller proportions of degree-holding white teachers at these schools.

A major reason for the presence of well-qualified teachers at Chapter 1 schools is that these schools are more likely than others to have mathematics specialists. Many of these teachers are specially trained and certified in elementary mathematics education, and city schools were among the first to train and hire specialists. Also, many highly qualified minority teachers became committed to these schools years ago. Young, inexperienced white teachers who teach in high- turnover, imier-city schools are generally "paying their dues" before they can transfer out to other schools.

One interesting exception to the pattern of more highly qualified minorities being employed at high-minority schools was found in the all-white elementary schools. The few minority teachers at these schools had more science and mathematics degrees than minority teachers at any other type of school (22 percent held these degrees); however, their overall numbers were so small that their presence did not give the schools a relative advantage on this dimension.

Secondary Schools. In contrast to the similarities in teacher qualifications at elementary schools, the qualifications of secondary school teachers at schools of different types differ substantially. Teachers at schools with predominantly economically advantaged white students and suburban schools are, on average, more qualified. There are significant differences in the average amount of teaching

8F = 3.64, P < 0.05.

experience at different types of schools, but students attending pre- dominantly white, high-SES, and suburban schools have greater ac- cess to well-qualified science and mathematics teachers.

Teachers at high-minority, high-poverty, inner-city schools are slightly less likely to have state certification in any subject.9 And as shown in Figs. 4.8, 4.9, and 4.10, the differences among types of schools become more pronounced as the level of qualification increases beyond basic certification. Teachers in schools serving minority and disadvantaged students are less likely to be certified to teach science and mathematics or to hold bachelor's and/or master's degrees in these fields. They are also less likely to meet the standards of the National Science Teachers Association or the National Council of Teachers of Mathematics.

El High poverty

El Med. poverty

Low poverty

High wealth

Cedloallon BA ova& MAcOLS, NSTA NCT1A quallicica q.altaice

Qualification measures

Fig. 4.8Secondary teachers' qualifications, by school SES (for certification, master's degree, NSTA qualification, P < 0.001;

for bachelor's degree, P < 0.01; differences for NCTM qualification were not significant)

9For racial composition, F = 5.19, P < 0.01; for locale, F = 2.69, P < 0.05. No significant differences were found related to schools' SES.

I 70

I 320° 10

0 0%-10% white

0 10%-50% white

50%-90% white

90%-100% white

Cereacallon BA or B.S. MAorM.S NSTA NCT1A qualrolice quacation

Qualificalion measures

Fig. 4.9Secondary teachers' qualifications, by school racial composition (for certification and bachelor's degree, P < 0.001; for NSTA qualification, P < 0.05; differences for master's degree and

NCTM qualification were not significant)

0 Inner city

0 Other urban

III Suburban

Rural

rf- Gdicsimi BA 001 MA oat& NCT1A

qualiftion qualicabon

Qualification measures

Fig. 4.10Secondary teachers' qualifications, by school location (for certification, bachelor's degree, maser's degree, P < 0.001;

differences for NSTA and NCTM qualification were not significant)

Formal qualifications are not the only standards on which teachers at different types of schools vary. There are also significant differ- ences in the amount of formal computer training teachers have re- ceived: Those at high-poverty schools," predominantly minority schools,n and inner-city and rural schools" have received substan- tially less than those at other types of schools. Clearly, the small ad- vantage in teaching quality enjoyed by students participating in mathematics programs in high-minority elementary schools disap- pears by junior or senior high school.

WHICH CLASSES HAVE THE MOST-QUALIFIED TEACHERS?

While there are few differences in the qualifications of science and mathematics teachers in elementary school classes at different ability levels, there are considerable differences in secondary schools. Teachers of low-track classes in junior and senior high school are considerably less well-qualified than are teachers of other classes.

The Relationship Between Judgments About Student Ability and Teacher Qualifications

Students in science and mathematics classes who are judged to be low in ability tend to be taught by teachers with less teaching experi- ence than those teaching average- or high-track classes." Addi- tionally, as shown in Fig. 4.11, teachers of low-track classes rank lower on most formal qualifications.

In addition to differences in certification and degrees, relationships can be found between tracks and the amount of computer training teachers have received. While there are few differences in the overall amount of computer training (self-taught, inservice training, and coursework) experienced by teachers, there are differences in the amount of college coursework in the use of computers completed by teachers working with different types of classes. Teachers of high- ability classes were found to be more likely than others to have had such coursework."

1OF = 4.37, P < 0.01. 11F = 3.35, P < 0.06. 12F = 9.28, P < u.01.

= 5.47, P < 0.01. 14F = 6.40, P < 0.01.

El Low ability

1111 Average ability

High ability

BA or B.S. MA or 1LS. NSTA NCTM quelkellon qualkdon

Fig. 4.11Secondary teachers' qualifications, by ability level of class to which they are assigned (for certification, bachelor's degree, master's degree, P < 0.001; for NCTM qualification, P < 0.01;

for NSTA qualification, P < 0.05)

Finally, we found significant differences in the extent to which science and mathematics teachers of different ability-level classes perceive themselves to be highly competent. Teachers of high-track classes felt most strongly that they were master teachers; teachers of average-track classes were somewhat less likely to characterize themselves as master teachers; and teachers of low-track classes had the poorest image of their abilities.15

The Effects of School Type and Class Type

The finding that secondary students in classes of different track levels differ in their access to well-qualified teachers must not be in- terpreted simplistically, since some class-level differences are con- founded by large school-level differences in teacher qualifications. Low-SES, high-minority, and inner-city junior and senior high schools have, on average, the least-qualified teachers and have dispropor-

15F 27.92, P < 0.01

tionate percentages of low-track classes (as discuosed in Section II), so some track-level differences may result from the disproportionate percentages of students in low-ability classes who attend schools where access to well-qualified teachers is constrained by overall staff deficiencies. thio does not invalidate the finding that students judged to be low in ability are being taught by less-qualified teachers, it is important to determine the extent to which the matching of teachers and tracks is a function of school staff resources and the ex- tent to which it results from a differential distribution of qualified teachers within schools. That is, we need to know whether low-track students have the least-qualified teachers simply because more of them go to disadvantaged, minority schools where the teachers are less-qualified or whether the schools themselves. contribute to this matching by systematically assigning their least-qualified teachers to the students they consider the least able.

Even when school-type differences in teacher qualifications are ac- counted for, most track-level differences remain significant, and others that were obscured by school differences emerge. For example, when community type is controlled for, teachers of low-ability classes have fewer years of experience than teachers of average- and high- ability classes (2 years less, on average).16 When school SES is ac- counted for, teachers of classes at lower track levels are less likely to be certified in mathematics and science or to hold bachelor's degrees in these fieldsthe lowest-ability groups have the fewest qualified teachers, and in all but the highest-SES schools, the highest-ability groups have the most.17 When racial composition is accounted for, high-track classes have significantly greater exposure to teachers with mathematics or science ceAification and to teachers with bache- lor's degrees than do low-track classes.18 When community type is accounted for, low-ability classes have less access to teachers with mathematics or science certification and to teachers with either bach- elor's or master's degrees in these fields.16 School differences do not

16F = 11.67, P < 0.01. 17For certification, F = 10.40, P < 0.01; for bachelor's degrees, F = 13.37, P < 0.01.

At the highest-SES schools, we found no significant differences in ability groups' access to teachers with bachelor's degrees.

18For teacher certification, P < 0.05; for teachers' degrees, P < 0.01. Average classes did not differ significantly from low-track classes on teacher certification, but they were more like high-ability groups in their access to teachers with degrees.

19For certification, F = 6.18, P < 0.01; for bachelor's degrees, F = 5.96, P < 0.01; and for master's degrees, F 8.79, P < 0.01. In suburban schools, low- and average-track classes had fairly equal access to teachers with bachelor's degrees in science and mathematics, whereas high-ability classes were more likely to have teachers with these degrees.

explain the differences in computer training of teachers of different ability-level classesagain, teachers of high-ability classes are the best qualified in this area.2° Clearly, secondary schools of all types systematically allocate their most-qualified teachers in ways that dis- advantage the students who are thought to be less able in science and mathematics.

While nearly all types of schools place their least-qualified teachers in low-ability classes and their most-qualified teachers in high-ability classes, schools of different types cannot provide students in comparable tracks with teachers who have comparable qualifications. In schools with less-qualified teacher pools (low-SES, high-minority, inner-city schools), teachers of low-track classes are less well- qualified than teachers of low-track classes in schools with generally more qualified staffs (higher-SES, white, suburban, and rural schools). Thus, students at the least-advantaged schools more often compete (through their class assignments) for teachers who are certified to teach mathematics and science or who have bachelor's degrees in these fields. We found that in schools with the highest concentration of low-income students, the teacher qualifications at different track levels differed considerably, as shown in Fig. 4.12.

In contrast, schools whose teachers were generally more qualified exhibited the same patterns of differences, but far more classes had access to certified teachers and teachers with bachelor's degrees. The assignment patterns of teachers at these schools are most evident in terms of the subtle or higher-level qualificationsteachers' percep- tions of themselves as master teachers, years of teaching experience (which may represent seniority or political clout in the school, as well as a feeling of high competence), and the holding of master's degrees. These differences are vividly illustrated by contrasting teachers' qualifications in classes of similar ability levels in a subset of different type8 of schools (see Table 4.1). The qualifications of teachers of vari- ous track levels at high-minority, low-SES, inner-city schools differed substantially from those of teachers at high-wealth, predominantly white, suburban schoolsP

20For computer training, F = 3.09, P < 0.05. 21The first group of schools includes those at which at least 30 percent of the

students are from unemployed families or families on welfare, those with minority populations exceeding 50 percent, and those located in inner-city or other urban neighborhoods. The second group includes those at which at least 30 percent of the students have parents in professional or managerial occupations, those with white populations exceeding 60 percent, and those located in suburban neighborhoods.

El Low ability

II Average ability

High ability

Fig. 4.12Qualifications of secondary teachers in low-SES schools, by ability level of assigned class

Table 4.1

QUALIFICATIONS OF SECONDARY TEACHERS IN HIGH- AND LOW- ABILITY CLASSES IN SCHOOLS OF DIFFERENT TYPES

Low-Ability Classes High-Ability Classes

Teacher Qualifications

Low-SES, Minority,

Urban

High-SES, White,

Suburban

Low-SES, Minority,

Urban

High-SES, White,

Suburban

Certified in science/math 39 82 73 84 Bachelor's in science/math 38 68 46 78 Master's in science/math 8 32 10 48 NSTA qualified 11 36 6 47 NCTM qualified 23 26 4 16 Computer coursework 41 61 69 62

Importantly, however, the differences are somewhat greater for low-track classes than for Mgh-track, especially in terms of teacher certification.

Teachers also differed in their years of teaching experience. Teachers of low-track classes in disadvantaged schools averaged 11.5 years of experience, whereas their counterparts at more-advantaged

schools had 15 years of experience. Teachers of high-track classes at disadvantaged schools averaged 13 years, while their peers at advan- taged schools averaged 15 years. Interestingly, however, teachers of classes of the same ability level at different types of schools were quite similar in their perceptions of themselves as master teachers: Teachers of high-track classes at both types of schools agreed far more strongly that they were in this category.

Perhaps the most striking finding in this area is that while ail types of schools provide high-track students with the best-qualified teachers, the scarcity of highly qualified teachers at disadvantaged schools has enormous implications: Although high-track students na- tionwide have access to the best-qualified teachers, low-track students in the most advantaged schools are likely to have better-qualified teachers than high-track students in the least-advantaged schools. This pattern constitutes a double disadvantage for students judged to be low in ability who attend low-income, predominantly minority schools. Their schools have scarce resources to begin with, and as those schools follow the national pattern of uneven distribution of re- sources by ability level, low-track students end up with the least of the least. Moreover, their schoolmates who have been judged to be promising fare little better. The "advantages" that accrue to them as the result of being judged able do not even equal those of students judged to be least able and provided the fewest teacher resources at more-advantaged schools.

V. ACCESS TO RESOURCES

This section considers the distribution of resources and materials among different types of schools: computers and special staff to coor- dinate their instructional use; science laboratories and other science- related equipment and materials; and textbooks. It also examines principals' and teachers' perceptions of whether inadequate resources pose problems for science and mathematics instruction. While there is little evidence that the actual quantity of resources available to schools, teachers, and students has a direct effect on learning or will- ingness to persist in science and mathematics, resources are enablers. They provide the context in which schools and classrooms operate; they often define the outer limits of what is possible. For example, if a school has no science laboratory facilities, even the best-prepared teachers will be unable to engage students in laboratory work.

There are two dimensions of resource availability that seem likely to affect the quality of the instructional program in science and math- ematics: the number and type of resources that are available, and the perception of educators about whether or not they have sufficient resources for carrying out their instructional programs. Countable science and mathematics resources would include specialist teachers or coordinators for overseeing programs or providing additional teach- ing; laboratory facilities; computers and calculators; textbooks; and specialized equipment such as greenhouses, darkrooms, or weather stations.

By counting the number of resources available at different types of schools and comparing those counts across schools, we can determine how evenly some common resources are allocated. Then, by compar- ing perceptions of how resource adequacy varies across schools, we can identify real inequalities that a simple count of equipment and materials may miss and can show whether schools of different types feel more or less constrained by resources. Different types of schools may perceive their resource needs quite differently, but educators' perceptions of resource adequacy should be taken seriously as indica- tors of the degree to which resource problems constrain instructional programs.

!")1) 68

WHAT SCIENCE AND MATHEMATICS RESOURCES ARE AVAILABLE?

Recent work has documented inequities in the numbers of micro- computers available for student use at different schools and in the ways computers are used for different subpopulations of children (Becker, 1983, 1986; Furr and Davis, 1984; Winkler et al., 1984). In 1986, only about 40 percent of middle schools in low-SES communi- ties had as many as 15 microcomputers, whereas two-thirds of the middle schools in high-SES communities had at least this number (Becker, 1986). The fewest microcomputers were available in elemen- tary schools serving predominantly poor and/or minority children; and at these schools, smaller percentages of children actually used the computers. Moreover, fewer poor and minority schools had teach- ers who were computer specialists.

The NSSME data permit a broader look at the availability of science and mathematics resources at different types of schools.' The data indicate that elementary schools of different types are more similar in terms of availability of science and mathematics resources than are secondary schools.

Elementary Schools

The most obvious finding is that few elementary schools have sub- stantial science and mathematics resources. The nation invests little in elementary mathematics, science, or computer instruction. Over- all, there is considerable equality in the kick of resources, but elemen- tary schools with large percentages of minority students (i.e., more than 50 percent) are even less likely to have computers available for stucknt use than are schools with majority white populations. How- ever, at the time of the NSSME, most schools of both types did have computers& percent of the high-minority schools and 94 percent of

1Principals in the NSSME sample indicated whether their schools had microcom- puters; terminals connected to mini/mainframe computers; a greenhouse; a telescope; a darkroom; a weather station; hand-held calculators; microscopes; cameras; scientific models; a small-group meeting room; a learning resource center; mathematics and sci- ence laboratories; an outdoor study area; a vivarium; a portable planetarium; a video- cassette recorder; and a videodisc player. They also reported the number of computer terminals and microcomputers available for student use and whether anyone on their staff was specifically designated to coordinate or supervise mathematics, science, and computer instruction. Teachers were asked about the availability of computers for use in their classes.

the predominantly white schools.2 There were no significant differ- ences in the number of computers relative to the size of the student body among schools of different socioeconomic or racial composition, but locale did make a difference: Rural elementary schools had more computers available per student than did other schools.3 This may be attributable to the fact that rural schools typically have fewer stu- dents, but they need the same number of computers to set up a com- puter laboratory that can serve a classroom of children.

As shown in Fig. 5.1, high-SES schools were far more likely than other schools to provide a computer coordinator, and high-minority schools were far less likely to have such a staff person.4 Urban schools not located in inner cities were also more likely than other

1 I t 60 1

E 8 Z 40 .1

1 20 I01 0 it High Mod. Lao High 0-10 10-60 50-00 90-100

PovertY PliodY PovertY naliti

SES Percentage of white students

Fig. 5.1Percentages of elementary schools with computer coordinators, by school SES and racial composition (for SES,

F = 3.48, P < 0.05; for percent white, F = 4.18, P < 0.01)

2F = 3.51, P < 0.05. 3Rural schools, on average, had 4.88 computers per 100 students, while inner-city,

other urban, and suburban schools averaged about 3 computers per 100 students (F = 9.87, P < 0.01).

4These ana!yses were performed controlling for school size.

schools to have computer coordinators (70 percent, compared with 53 percent of inner-city schools, 56 percent of suburban schools, and 47 percent of rural schools).5

Overall, the availability of a staff coordinator for mathematics and science instruction did not differ at schools of different social class or racial composition (slightly more than a third of all elementary schools had such coordinators). However, urban schools, both inner- city and other urban, were more likely than either suburban or rural schools to have mathematics coordinators-49 percent, compared with 37 and 22 percent.6

i3oth location and racial composition relate to the availability of science facilities, equipment, and materials. However, racial compo- sition stands out in this respect. Elementary schools with a majority of African-American and Hispanic students reported having, on aver- age, only two different types of science-related resources, while schools with majority white populations reported having three.7 Inner-city schools had fewer materials than schools in other locations, but other urban, suburban, and rural schools had similar resources.5 While many elementary schools have no science laboratories, some types of schools are more likely to have them than others. Figure 5.2 shows that predominantly white schools are about twice as likely to have science laboratories as predominantly minority schools.

Secondary Schools

Larger differences in the distribution of science and mathematics resources exist at the secondary level.9 Only 77 percent of the prin- cipals of low-SES high schools said that they had computers available for instructional use, whereas 95 percent of the principals of schools in higher SES categories did.19 Moreover, teachers at low-SES and inner-city schools reported that computers were less readily available at their schools, or, if they were available, they were difficult to se- cure for use in instruction.11 Students at high-minority, inner-city

5F = 3.03, P < 0.05. 8F = 6.22, P < 0.01. 7F = 6.70, P < 0.01. 8There were an average of 2.4 resources in inner-city schools, 2.6 in other urban

schools, 2.8 in suburban schools, and 2.7 in rural schools (F = 3.36, P < .05). 9Each of the analyses of the distribution of resources controlled for the size of

schools' student population. 10F = 12.48, P < 0.01. 11For school SES, F = 5.22, P < 0.01; for school location, F = 6.56, P < 0.01.

Fig. 5.2Availability of science laboratories in elementary schools, by school racial composition (F = 3.13, P < 0.05)

schools had access to far fewer computers, even when computers were

available. Schools with 90 percent or greater minority populations had an average of 1 .76Tomputers per 100 students; schools with less than 90 percent minorities averaged about 2.70.12 Inner-city schools averaged 1.88; other urban schools, 2.48; suburban schools, 2.80; and

rural schools, 2.86.13 And, as Fig. 5.3 illustrates, both SES and location affected whether schools were likely to have a staff person designated to supervise or coordinate the instructional use of computers.

Secondary schools also differed in the extent to which they pro- vided a special staff person to supervise or coordinate science and mathematics instruction, with the greatest differences occurring in science (see Table 5.1).

High-SES schools were most likely to have specially designated co- ordinators for science and mathematics programs. While predomi-

12F = 4.96, P < 0.01. 13F = 8.42, P < 0.01.

9 1

High Met Low High !my 011w Sub- Rural powety poverty poverty we* dty urben urban

SES Location

Fig. 5.3Percentages of secondary schools with computer coordinators, by school SES and racial composition (for SES, F = 13.43, P < 0.001; for percent white,

F = 6.59, 13 < 0.001)

nantly white schools were shown to be less likely than minority schools to have such coordinators, the nonwealthy rural schools prob- ably account for this finding. Other interesting differences appear among all types of schools, but wealth and locale seem to be the major factors determining the availability of these human resources.

Secondary schools with large concentrations of low-income or African-American and Hispanic ot.1.1ents and schools located in inner cities have far fewer facilities ay._ luipment available, e.g., green- houses, telescopes, darkrooms, weather stations, calculators, micro- scopes, cameras, scientific models, outdoor study areas, resource cen- ters, vivariums, or planetariums. An average of 2.33 different types of science equipment were available at the lowest-SES schools, com- pared with 3.77 at the highest-wealth schools.14 Schools with the highest concentration of minority students averaged 2.52, and schools

14F = 3.93, P < 0.01.

Table 5.1

PERCENTAGES OF SECONDARY SCHOOLS PROVIDING MATHEMATICS AND SCIENCE COORDINATORS,

BY SCHOOL SES, RACIAL COMPOSITION, AND LOCALE

School Characteristic Mathematics Coordinators

Science Coordinators

SES° High poverty 67 59 Medium poverty 61 60 Low poverty 64 63 High wealth 93 91

Racial compositionb 0-10% white 77 77 10-50% white 83 81 51-90% white 73 67 90-100% white 63 63

Locationc Inner city 74 55 Other urban 75 74 Suburban 76 77 Rural 54 53

°Significance of SES: for mathematics, F = 13.13, P < 0.001; for science, F = 13.38, P < 0.001.

bSignificance of racial composition: for mathematics, F = 4.21, P < 0.01; for science, F = 2.69, P < 0.05.

cSignificance of location: for mathematics, F = 9.60, P < 0.001; for science, F = 11.59, P < 0.001.

with the lowest, 3.72.18 Schools in inner cities averaged 2.83; other urban schools, 3.48; suburban schools, 3.56; and rural schools, 379.16

As at the elementary level, schools with the fewest minority stu- dents had slightly more science laboratories than racially mixed or all-minority schools.° Location was a far more important factor in this case than any other school characteristic. Inner-city schools re- ported an average of less than one laboratory; schools in other urban communities, 1.26; suburban schools, 1.34; and rural schools, 1.40.18

16F = 14.77, P < 0.01. 16F = 17.20, P < 0.01. 17F = 2.65, P < 0.05. 18F = 8.09, P < 0.01.

DO RESOURCE PROBLEMS HAMPER INSTRUCTION?

Given the differences in the availability of countable resources, it is not surprising that principals and teachers in schools of different types also differed in their perceptions of the effects of resource inade- quacy on science and mathematics instruction. In the NSSME, prin- cipals and teachers were asked to indicate whether inadequate facili- ties, insufficient funds for purchasing equipment and supplies, lack of materials for individualizing instruction, insufficient numbers of textbooks, poor quality of textbooks, and/or inadequate access to com- puters posed instructional problems." The findings are shown in Tables 5.2 and 5.3.

Principals clearly perceived fewer resource problems than teachers did. Principals of elementary schools of different SES composition and locale reported problems at a similar rate. The differences are as expected but are not statistically significant. But when schools were compared in terms of racial composition, principals differed signifi- cantly in their perceptions of problems. Principals of high-minority schools reported problems far more often than principals of majority white schools. Differences in secondary school principals' perceptions were more pronounced and were affected by SES, racial composition, and location.

Teachers reported numerous resource problems at both the ele- mentary and secondary levels at all types of schools. This stands to reason, since they experience the problems first-hand as they attempt to teach. Even so, high-poverty, high-minority, and inner-city schools have greater resource constraints that affect teachers' judgments about the quality of their science and mathematics programs.

Taken together, the patterns in the NSSME data are unmistak- able. Students in high-poverty, high-minority, and inner-city schools, more than others, have resource constraints that affect the quality of their science and mathematics programs.

19The wording of the items for principals was slightly different from that for teachers and may contribute to differences in the percentages reporting that resources were a proble.a. Principals were asked to "indicate if [each of the factors listed above] is a serious problem in [mathematics and/or science]." Teachers were asked to indicate whether each of the factors was "a serious problem," "somewhat of a problem," or "not a significant problem."

Table 5.2

PERCENTAGES OF PIUNCIPALS REPORTING RESOURCE PROBLEMS, BY SCHOOL SES,

RACIAL COMPOSITION, AND LOCALE

School Characteristic Elementary

Schools Secondary "Schools

SES' High poverty 19 19 Medium poverty 21 13 Low poverty 16 9 High wealth 15 7

Racial compositionb 0-10% white 23 18 10-50% white 28 13 51-90% white 19 15 90-100% white 16 10

Locationc Inner city 20 17 Other urban 16 15 Suburban 18 10 Rural 19 12

aDifferences between elementary schools by SES are not significant. For secondary schools, F = 12.36, P< 0.001.

bSignificance of racial composition: for elementary schools, F = 4.34, P < 0.01; for secondary schools, F = 4.21, P < 0.01.

cDifferences between elementary schools by location are not significant; for secondary schools, F = 4.51, P < 0.01.

TaiAe

PERCENTAGES OF TEACHERS REPORTING RESOURCE PROBLEMS, BY SCHOOL SES,

RACIAL COMPOSITION, AND LOCALE

School Characteristic Elementary

Schools Secondary

Schools

SESa High poverty 68 61 Medium poverty 65 57 Low poverty 55 54 High wealth 53 46

Racial compositionb 0-10% white 86 64 10-50% white 72 64 50-90% white 59 54 90-100% white 55 53

Locationc Inner city 71 74 Other urban 59 52 Suburban 60 53 Rural 59 53

aSignificance of SES for elementary schools: F = 4.77, P < 0.01. For secondary schools, F = 5.45, P < 0.01.

bSignificance of racial composition for elementary schools: F = 9.41, P < 0.001; for secondary schools, F = 2.81, P < 0.05.

cDifferences for elementary schools by location are not significant. For secondary schools, F = 9.89, P < 0.001.

HOW GOOD ARE THE TEXTBOOKS?

While teachers at low-SES, high-minority schools feel the overall pinch of inadequate resources more keenly than do teachers at other types of schools, all of them expressed similar judgments about the quality of the textbooks they have available. However, teachers of low-track classes were generally more dissatisfied with their text- books than were teachers of higher tracks.

In the NSSME, science and mathematics teachers were asked to rate available texts in terms of appropriateness of reading level; in- terest to students; clarity and organization; helpfulness in developing problem-solving skills; quality of explanations of concepts; inclusion of

examples to reinforce concepts or exercises to practice skills; quality of suggestions for activities and assignments; and quality of supple- mentary materials.° Of particular interest were teachers' ratings of the quality of presentation in the text,21 whether they thought texts helped students develop problem-solving abilities, and their judgments about the texts' suggestions for activities and assignments and the supplementary materials provided. These aspects of text- books speak to the quality of the texts per seindependent of the particular students with which they are used.

We aggregated teachers' ratings of textbooks at the school level and then compared the responses from different types of schools. We found no significant differences across schools. However, within schools, teachers of classes of different track levels rated their text- books somewhat differently. At the elementary level, teachers of low- ability classes rated textbooks (except for supplementary materials) significantly lower than did teachers of average- and high-ability classes.22 At the secondary level, teachers were generally in agree- ment about the quality of their texts' suggestions for classroom activ- ities, but on other dimensions, those working with different groups of students had divergent opinions. Teachers of low-track classes gave lower overall ratings for quality of presentation of material in their texts than did teachers of high-track classes.23 However, on help- fulness in developing students' problem-solving skills and quality of the supplementary materials included with the text, teachers of low- track classes rated their textbooks higher than did other teachers." The more highly qualified teachers of high-ability classes were more critical of texts on these dimensions, perhaps because they know more about their subjects.

20Teachers rated the textbook they use most often in class by indicating the strength of their agreement or disagreement with various statements (e.g., "Is not very interesting to my students') on a five-point scale.

21We combined three of the statements ("Is unclear and disorganized," "Explains concepts clearly," and "Needs more examples to reinforce concept? (science only) and "Needs more exercises for practice of skills" (mathematics only)) into a single measure of teachers' perception of the quality of the presentation of content. Responses to negatively worded statements were reversed to obtain a positive rating for the texts.

22For overall quality of presentation, F = 9.54, P < 0.01; for development of problem- solving skills, F = 6.42, P < 0.01; for quality of suggestions for activities, F = 3.21, P < 0.05.

23F = 4.37, P < 0.05. Secondary teachers of average classes and low-ability classes gave similar ratings; teachers of high-ability classes, however, rated texts higher than either of these two groups.

24For development of problem-solving skilla, F = 10.71, P < 0.01 (again, high-ability teachers stand outthis time for their distinctly lower ratings); for the quality of supplementary materials, F = 3.48, P < 0.01.

In sum, the quality of available texts appears to be similar across both elementary and secondary schools. However, the opportunities to learn afforded by textbooks differ for students in different track levels. Most significant, textbooks for low-ability classes appear to present science and mathematics content less well than the textbooks used in higher-level classes.

SUMMARY

Our examination of the differences in the distribution of instruc- tional resources that support science and mathematics teaching and learning revealed disturbing patterns of unequal opportunities that parallel our findings concerning science and mathematics programs and teachers. Low-income and minority students who are clustered in schools with others like them and those in inner-city schools have less access to computers, staff to coordinate the use of computers in instruction, science laboratories, and other common science-related facilities and equipment than do students in other schools. Additionally, more principals and teachers at low-SES, high-minority schools report that resource problems create problems for science and mathematics instruction. Finally, across all schools, instruction in low-track classes (again, comprising disproportionate numbers of low- income and minority students) appears to be constrained by science and mathematics texts that teachers judge to be of lower quality in most respects.

40 I

VI. CLASSROOM OPPORTUNITIES: CURRICULUM GOALS AND

INSTRUCTION

Thus far, we have considered the distribution of opportunities that create boundaries around what students can learn in science and mathematicsextensiveness, content, and rigor of school programs; access of students judged to be of different abilities to science and mathematics courses; allocation of well-qualified teachers; and the availability of important enabling instructional resources. In each case, we have found distressing patterns of fewer opportunities for students who typically exhibit patterns of lov, achievement and minimal participation in science and mathematicslow-income, African-American, Hispanic, and inner-city students. In this section, we step inside classrooms to examine whether schools and classes of different types also differ in the curricular goals teachers set for their students and in the type of instruction they provide and explore the implications of differences for students' learning opportunities.

CURRICULUM GOALS AND EXPECTATIONS

Some case-study research suggests that even when course titles are the same, the curriculum taught in predominantly poor and minority schools is essentially different from that taught in predominantly white middle- and upper-class schools. These differences suggest that advantaged, white children are more likely to be exposed to essential concepts (as opposed to isolated facts) and to be taught that academic knowledge is relevant to their future lives (Anyon, 1981; Carnoy and Levin, 1986; Hanson, in press). For the most part, however, these is- sues have received little research attention.

In contrast, there is considerable evidence of differences in the op- portunities to learn science and mathematics content in different classrooms within the same school: On average, high-ability groups in elementary schools progress further in a school curriculum over the course of the year (Rist, 1973; Hanson and Schultz, 1978; Barr and Dreeben, 1983; Rowan and Miracle, 1983; Gamoran, 1986). While we know of no systematic studies of content differences in ability- grouped science and mathematics instruction at the elementary level, low-ability reading groups have been shown to spend more time on

I 80

decoding activities, whereas in high-ability groups more emphasis is placed on the meanings of stories (Alpert, 1974; Hiebert, 1983). High- ability-group students do more silent reading and are interrupted less often when reading aloud (Allington, 1980; Eder, 1981). The high- ability-group advantage is presumably cumulative over the years, and as a result, students with a history of placement in high-ability groups cover considerably more materialand distinctively different materialin elementary school.

Differences in pace and quantity of coverage have also been de- tected at junior and senior high school levels (Ball, 1981; McKnight et al., 1987; Metz, 1978; Page, 1984). McKnight et al. (1987) used data from the SIMS to examine differences in content for eighth graders enrolled in different types of mathematics classes (e.g., remedial, typ- ical, honors, or algebra). Not only did the lower-level courses provide students with access to fewer mathematics topics and skills, students in lower-level clasaes in the United States had much narrower cur- riculum opportunities than their counterparts in many other nations (see Kifer, in press). Not surprisingly, the lack of opportunity to learn various topics was reflected in these students' performance on test items.

Low-track classes not only typically offer a limited array of topics and skills, they consistently emphasize less-demanding topics and skills, whereas high-track classes typically include more complex material and more difficult thinking and problem-solving tasks (Burgess, 1983, 1984; Hargreaves, 1967; Metz, 1978; Nystrand and Gamoran, 1988; Oakes, 1985; Powell, Farrar, and Cohen, 1985; Sanders, Stone, and LaFollette, 1987).

In an earlier study of 300 junior and senior high school English and mathematics classes, quantitative and qualitative analyses of data from teacher and student questionnaires, teacher interviews, class- room observations, and content analyses of curriculum packages re- vealed that high-track students were more often presented with tra- ditional academic topics and intellectually challenging skills (Oakes, 1985). Additionally, teachers in high-track classes more often cited having students learn to be competent and autonomous thinkers as among their most important curricular goals. Teachers of low-track classes more often emphasized basic literacy and computation skills and presented topics commonly associated with everyday life and work. Their important curricular goals focused on conformity to rules and expectations.

CURRICULAR EMPHASIS ACROSS SCHOOLS AND CLASSROOMS

The NSSME data provide useful information about the importance teachers place on central goals of science and' mathematics education and about how their expectations vary for different groups of stu- dents.

Teachers were asked to rate, on a scale from "none" to "very heavy," the emphasis they placed in a particular class on having stu- dents achieve the following objectives:

Become interested in science/mathematics. Learn basic science concepts (science only). Know mathematical facts, principles, algorithms, or proce- dures (mathematics only). Prepare for further study in science/mathematics. Develop inquiry skills. Develop a systematic approach to solving problems. Learn to communicate ideas in science/mathematics effec- tively. Become aware of the importance of science/mathematics in daily life. Learn about the applications of science/mathematics in tech- nology. Learn about the career relevance of science/mathematics. Learn about the history of science/mathematics. Develop awareness of safety issues in the lab (science only). Develop skill in laboratory techniques.

Because both school and classroom characteristics can affect stu- dents' access to science and mathematics courses, it is important to understand the emphasis teachers place on various curricular objec- tives both at schools of different types and in classes of different track levels. Then, to evaluate the relative influence of the school and the classes a student is enrolled in within the school, we must compare the emphasis in classes of the same abilitylevels in different types of schools.

Elementary Schools. At the elementary school level, about the only differences we found were in the emphasis teachers placed on developing awareness of safety issues in the science laboratory. Teachers in inner-city and rural schools reported emphasizing labora- tory safety more than teachers in other urban and suburban settings.

There were no school-level differences related to the racial or socio- economic makeup of the school population.'

However, across the sample of elementary schools, we found con- siderable differences in teachers' emphasis on various objectives in classes that differed in ability level. Table 6.1 shows the strength and direction of these differences.2

Table 6.1

ELEMENTARY TEACHERS' CURRICULAR OBJECTIVES: RELATIONSHIP TO CLASS ABILITY LEVEL

Objectives Showing No Significant Positive Relationship with

Class Ability Level

Objectives Showing Significant Positive Relationship with High

Class Ability Level

Math, facts and principles Math, computations Importance in life Technology applications History Career relevance Science, lab safety

Science, lab technique

Interest * Science, basic concepts**

Preparation for further study** Inquiry skills**

Problem-solving approach**

Communicate ideas**

NOTE: * = significant at 0.05 level; ** = significant at 0.01 level.

In many respects, teachers have considerably higher expectations for students in high-ability classes. They clearly place more emphasis on some goals that have been widely heralded as critical, not only for future scientists, but for scientifically literate citizens and productive workers in an increasingly technological economy. Such goals as in- terest in science and mathematics, inquiry skills, and problem-solving are believed to promote essential adult knowledge and competencies; indeed, many science educators suggest that they constitute the core

'Where curriculum objectives (or other classroom-level-dependent variables) were analyzed with respect to school characteristics, teachers' responses were averaged within each school and the class weights were summed. In these cases, the number of observations was equal to the number of schools, not the number of teachers surveyed.

2The analysis of track level applies only to classrooms with homogeneous grouping; mixed-ability classes were omitted. Class weights were used to provide nationally representative information about differences among classes at different ability levels. Within each category of the respective independent variables, we calculated the teachers' mean response, but because of the difficulty of interpreting the question- naire's Liked scale responses in absolute terms, we focused primarily on the relative differences in emphasis between categories.

of science and mathematics education.3 Moreover, teachers place greater emphasis on preparing high-track students for further study in science and mathematicsa goal that might be seen as equally important for the low-track students who are at risk for continuing low achievement and nonparticipation in science and mathematics courses in later grades.

Compounding this unequal access to some important curricular goals, students in low-ability classes are not receiving correspond- ingly greater emphasis on other curriculum objectives. Teachers of low-ability classes simply seem to set their sights lower than teachers of classes at other track levels.

Secondary Schools. At the secondary level, there are both school and classroom differences in t.he emphasis teachers place on various objectives. Teachers at high-SES schools emphasize preparing stu- dents for further study in mathematics and science, developing in- quiry skills and laboratory skills, and acquiring a systematic ap- proach to solving problem8.4 Teachers at lower-SES schools empha- size becoming aware of the importance of science and mathematics in daily life and recognizing the career ilelevance of these subjects.6

We found racial composition to have relatively little effect on teachers' curriculum objectives. At predominantly white schools, teachers place more emphasis on learning basic science concepts; at predominantly minority schools, they place more emphasis on becom- ing aware of the importance of science and mathematics in daily life.6

There are far more differences among classes than among schools. As Table 6.2 illustrates, teachers' emphasis on curriculum objectives differs considerably with the ability composition of their classes. Students in low-track or disproportionately minority classes are dis- advantaged in the degree to which teachers emphasize most curricu- lum objectives. Teachers of low-track classes were found to give less emphasis to every curriculum objective except becoming aware of the importance of science and mathematics and performing computations. As at the elementary level, these differences distance students in low- ability classes from some of the most important goals of science and mathematics. Moreover, there is a certain irony to the greater em-

3See, for example, Bybee et al., 1989; Champagne and Hornig, 1987. 4For preparing students for furthe.. study in mathematics and science, F = 3.63, P <

0.06; for developing inquiry skills, F = 4.73, P < 0.01; for laboratory skills, F .2 4.32, P < 0.01; for acquiring a systematic approach to solving problems, F = 6.45, P < 0.01.

6For students becoming aware of the importance of science and mathematics in daily life, F = 6.97, P < 0.01; for the career relevance of these subjects, F 4.48, P < 0.01.

6For basic science concepth, F = 3.11, P < 0.05; for becoming aware of the importance of science and mathematics, F = 3.07, P < .05.

Table 8.2 /

SECONDARY TFACHERS' CURRICULAR OBJECTIVES: REIATIONSHIP TO CLASS ABILITY LEVEL

Objectives Showing Significant Negative

Relat4onship with High Class Ability Level

Objectives Showing No Significant Monotonic

RelaUonship with Class Ability

Objectives Showing Significant Positive

Relationship with High Class Ability Level

Importance in daily life" Career relevance Math, computations"

Interest* Science, basic concepts" Math, facts and principles" Preparatiou for further study Inquiry skills" Problem-solving approach" Communicate ideas" Technology applications" History" Science, lab safety' Science, lab techniques"

NOTE: = significant at 0.05 level; " = significant at 0.01 level.

phasis teachers of low-ability classes place on developing an appreci- ation of the importance of science and mathematics in daily life. While few would question the importance of this goal, teachers be- have as if they believe that this is all low-track students can do. One might speculate that teachers of low-ability classes work for student appreciation rather than helping their students become knowledge- able and competent.

These track-level differences reveal important nationwide differ- ences in the types of goals teachers emphasize and their expectations for different groups of students. However, because of the uneven dis- tribution of track levels among different types of schools, it is impor- tant to understand whether low-track classes receive different cur- ricular emphases partly because they tend to be at schools that em- phasize different objectives. In fact, school differences do not appear to account for the ability-level differences noted above. With the in- fluence of school-SES differences accounted for, ability-group differ- ences in teachers' emphasis on preparing students for further study remain.7 The same is true for developing inquiry skills,8 laboratory

7F = 95.47, P < 0.01. 8F = 27.83, P < 0.01.

techniques,9 and a systematic approach to problem solving." How- ever, there is an interesting interaction between school type and track level on some objectives. At the lowest-SES schools, teachers of low- ability classes placed somewhat greater emphasis on inquiry skills and laboratory techniques than did teachers of average classes. In all cases, however, teachers of these two types of classes placed less importance on these objectives than did teachers of high-ability classes.

School differences did not affect the greater emphasis in low-track classes on appreciating the importance of science and mathematics in daily life, but low-SES schools' greater emphasis on the career rele- vance of these subjects is responsible for ability-group differences. That is, this objective appeared to receive greater emphasis across the sample of low-track classes because it was given greater weight in low-SES schools, and low-track classes were found in far greater numbers in these schools. Thus, track level alone did not produce these differences. Once the differences among schools of different ra- cial compositions were taken into account, ability-group differences in the emphasis placed on learning basic science concepts disappeared. Low-track classes received greater emphasis because there are dis- proportionately more of them in high minority schools that place more emphasis on this objective in all types of classes.

Most striking, however, is the finding that teachers of classes at the same track levels in very different types of schools appear to place similar emphasis on various curriculum objectives.

As shown in Table 6.3, even when the most widely different school types are compared, the curricular emphases in classes at various ability levels are more alike than they are different.11

The similarities are particularly noticeable among low-track science and mathematics classes. On only two curricular objectives

9F = 20.01, P < 0.01. 10F 19.91, P < 0.01. 11For these analyses we used two groups of schools: The first included those with at

least 30 percent of the students from families that were unemployed or on welfare, those with minority populations exceeding 50 percent, and those located in inner-city or other urban neighborhoods. The second group included those in which at least 30 percent of the students had parents in professional or managerial occupations, those with white populations exceeding 50 percent, and those located in suburban neighborhoods.

Table 8.3

SECONDARY TEACHERS' CURRICULAR OBJECTIVES IN HIGH- AND LOW-ABILrTY CLASSES lN SCHOOLS OF DIFFERENT TYPES

More Emphasis in Disadvantaged Schools

than in Advantaged Schools' No Significant Difference

More Emphasis in Advantaged Schools

than in Disadvantaged Schools"

Low-Ability Classes

Inquiry skills* History"

Interest Science, basic concepts Math, facts

Preparation for farther study Problem-solving approach Communicate ideas Inportance in daily life Technology applications Career relevance Science, lab safety

Science, lab technique

High-Ability Classes

Importance in daily life**

Technology applications"

Career relevance** History"

Interest Science, lab safety" Science, basic concepts Science, lab technique" Math, facts

Preparation for further study Inquiry skills Problem-solving approach

Communicate ideas

NOTE:* = significant at 0.05 level; " = significant at 0.01 level. °Disadvantaged schools are low-SES, inner-city or urban, and 50-100% minority

schools; advantaged schools are high-SES, suburban, and 0-50% minority schools.

did teachers of low-ability classes in low-SES, predominantly minor- ity, urban schools deviate from their counterparts in high-SES, pre- dominantly white, suburban schools. The curricular focus in high- ability classes was also quite similar across school types. The teach- ers of these classes in the widely different schools differed on only one objective rated high by more than half of the science teachers and about half of the mathematics teachers: The goal of having students become aware of the importance of science and mathematics in daily

life was considered more important in schools serving disadvantaged, minority students.

While school cl..!,racteristics do influence the curriculum emphases at secondary schools, considerably greater differences result from the judgments educators make about the abilities of their students and the types of class groupings they forTrt. While the NSSME data do not permit causal inferences, school differences appear to stem largely from the disproportionate number of students at high-SES, white schools who are judged to be able learners and the disproportionate number at low-SES, minority schools who are judged to be less able. Howerz, high- and low-track students are generally thought to need much the same curricular focus regardless of where they go to cchool. The one exception is the more applied and historical curriculum that is offered to low-track students in low-SES, minority schoolsa dif- ference that may result from having a less-qualified staff and fewer instructional resources.

LEARNING APPROACHES AND ACTIVITIES

The types of instructional activities that take place in classrooms are useful indicators of how teachers go about engaging students in learning. We know of no prior research that has examined differences in instructional practices at the school level or among ability-grouped science and mathematics classes at the elementary level, although considerable case-study and some survey research has investigated the variation in instructional activities with the track level of sec- ondary school classrooms.

Evidence from both American and British ethnographers indicates that teachers describe their expectations for high- and low-track stu- dents' classroom participation in different terms (Hargreaves, 1967; Lacey, 1970; Rosenbaum, 1976; Metz, 1978; Ball, 1981; Schwartz, 1981). Hargreaves, for example, found a high-track blackboard with the sign, "We must always remember to behave as an A class," whereas a teacher of a low-ability-level class remarked, "You just can't afford to trust that lot." Such comments seem to be typical of many schools.12

Not surprisingly, these differences parallel differences in teaching practices. High-track teachers report spending more time preparing for class, and they appear to be more enthusiastic and more willing to

12We grateful to Reba Page for reminding us of this study.

push their students to work harder (Rosenbaum, 1976; Metz, 1978; Schwartz, 1981; Oakes, 1985). Instruction in low tracks, on the other hand, has been characterized as oversimplified, repetitive, and frag- malted. Observers report that teachers of low-track classes use recitation and worksheets to break topics down into minute bits of information, causing lessons to lack overall coherence (Hargreaves, 1967; Keddie, 1971; Metz, 1978; Oakes, 1985; Page, 1987a). Low- track assignments require more rote memory and less critical think- ing than work in high-track classes (Hargreaves, 1967; Oakes, 1985). In high-track classes, teachers sometimes pursue serious understand- ing of complex themes; in low-track classes, instruction is often lim- ited to basic, surface-level understanding of simplified materials (Keddie, 1971; Oakes, 1985; Page, 1987a, 1987b). Even when osten- sibly similar materials are used, low-track classes "caricature other classes in their abbreviated discussions and simplification of ideas. Page (1987b:21) quoted one teacher as saying, "In this particular ninth grade history class, we're less concerned about history and more concerned about improving your reading skills " Thus, students find the "main idea" of a paragraph about the American Revolution, but they do not discuss the implications of the idea itself.

Using national data, Vanfosaen, Jones, and Spade (1987) found that college-track students were more likely than others to describe their teachers as patient, respectful, clear in their presentations, and enjoying their work. In earlier work, we found that the use of time also varied by track: In high-track classes, more time and emphasis were devoted to learning activities, and less to behavior management; high-track students also spent slightly more time on-task and were expected to spend more time on homework (Oakes, 1985). In another study, Gamoran (1987) found that high-ability classes were character- ized by more open-ended questions, more higher-order cognitive tasks, and more student control over work.

Thus there is strong and consistent evidence of differences in the implementation of curriculum across tracked classes. Reports of fragmentation and rote tasks in low-track classes indicate a consis- tent pattern of low-quality instruction. This probably also relates to teacher ability and qualifications. Less-qualified teachers have a more limited instructional repertoire and tend to rely on worksheets more often. However, many of the criticisms that have been leveled at low-track classes have also been listed as concerns for the average American classroom. Not only low-track, but also regular classes are described as lifeless, emotionally flat, having fragmented curricula, and including little critical thinking or cognitive challenge (Goodlad,

1984; Powell, Farrar, and Cohen, 1985). Consequontly, these differ- ences must be seen within the context of across-the-board classroom instruction that is not very engaging (Gamoran and Berends, 1987).

The NSSME data provide additional insights into how schools and classes enrolling different groups of students vary in the learning ac- tivities they provide. The data include the percentages of teachers who used particular types of activities in their last science and/or mathematics lesson and the percentages of class time teachers say students spend on these activities.13

Do Learning Activities Differ Among Elementary Schools and Classes?

Elementary teachers were asked which of the following activities they included in the last science or mathematics lesson they taught:

Lecture Discussion Student use of computers Student use of hands-on materials Students doing seatwork assigned from textbook Students completing supplemental worksheets

Those reporting on science were also asked whether the following additional activities were included in their most recent lesson:

Teacher demonstration Students working in small groups

Teachers reporting about mathematics lessons were also asked about the following activities:

13Teachers were asked to report the instructional activities that took place during the last science or mathematics lesson they trught. While data about a single lesson cannot provide a full picture of time use and activities in any one class, the weighted data can be aggregated to provide representative deseriptions for various types of schools (as defmed by SES, racial/ethnic composition, and locale). The data also reveal patterns of time use and learning activities among classes of various types (e.g., ability levels). However, all114 alio limited in that the types of activities listed (e.g., lecture, seatwork, quiz) arb gross categories, the specific nature of which may differ consider- ably from class to class. Therefore, analyses of these data cannot begin to portray the subtle differences in the activities or in the teacher-student interadions that take place during instructionsubtleties that can make a tremendous difference in the quality of the instructional opportunities made available to students.

112

Student use of calculators Teets or quizzes

Teachers at all types of schools reported using basically similar ac- tivities in their lessons. Perhaps the most important difference was that a larger proportion of teachers at high-poverty schools used tests or quizzes in their mathematics lessons." Test use also differed among schools of different racial composition, with predominantly minority schools using tests most often.15 Elementary schools of dif. ferent types diverged on only one other instructional activity, discus- sion. A slightly greater proportion of teachers at high-minority schools said that discussion was a part of their most recent lesson.16

In addition to reporting the types of learning activities included in their most recent lesson, teachers also indicated how much time they spent on learning activities, daily routines, interruptions, and other noninstructional activities." Science teachers also estimated the time spent on:

Teacher lecturing Students working with hands-on, manipulative, or laboratory materials Students reading about science Students taking tests or quizzes Other science instructional activities

In contrast, mathematics teachers also estimated the time spent in various types of instructional groupings:

Teacher working with the entire class as a group (e.g., lecture, test, etc.) Teacher working with small groups of students

14Twenty-three percent, as compared with 17 and 15 percent (F = 2.90, P < 0.05). Because teacher reports were aggregated at the school level, these percentages repre- sent the average percentages of teachers within schools of each type.

16Twenty-five percent of the teachers in high-minority schools and 29 percent of those in schools with between 50 and 90 percent minority populations reported that they used tests or quizzes, compared with 18 and 19 percent, respectively, in majority white and 90 percent or more white schools (F 2.94, P < 0.05).

16Teachers at high-minority schools included discussion somewhat more often (96 percent) than did teachers at other majority-minority schools (88 percent), majority- white schools (85 percent), or predominantly white schools (90 percent) (F = 3.23, P < 0.05).

ineachers were asked to report the number of total minutes spent on the last lesson and then divide those minutes among the list of activities.

I 3

Teacher supervising students working on individual activities

Although we found few differences in the total amount of time spent on instruction,18 science teachers at high-minority schools assigned students only about half as much hands-on and laboratory work as teachers at schools with predominantly white enrollments,19 and those in predominantly minority schools spent twice the time on testoo Also, mathematics teachers at predominantly minority schools had students spend more time working in small groups than did teachers at majority-white schools.21 While greater amounts of small-group time may appear to provide students greater opportuni- ties for active, engaged learning interaction, in most cases, small- group work actually decreases the amount of instructional time indi- vidual students spend with teachers, since the teacher can work with only one group at a time. Individual students, although grouped, often work alone at seatwork while they are waiting for their group's turn with the teacher. Moreover, these findings may well reflect the slightly smaller percentage of homogeneous ability classes in predom- inantly minority schools, noted in Section II. The greater percentage of class time spent in small groups in these schools probably repre- sents more within-class ability grouping for mathematics instruction.

School location was not a factor in either the distribution of types of activities or the way time was spent.

We found no differences in the types of activities that elementary teachers of high-, average-, and low-track classes included in science and mathematics lessons. However, we did find some small differ- ences in their allocation of class time; for example, low-track classes spent the most time in class routines.22 These differences largely reflect the larger number of low-ability classes in low-SES schools,

18For example, teachers at high-poverty and low-poverty schools spent slightly more time on routines and other noninstructional activities (12 and 11 percent of lesson time, respectively) than did those at moderate-poverty and high-wealth schools (9 percent each) (F 111 4.24, P < 0.01).

18Twenty-four percent at schools with between 60 and 100 percent minority; 30 percent at schools with 50 to 90 percent white students; and 48 percent at schools with more than 90 percent white students (F is 2,89, P < 0.05).

20 Twelve percent at each of the predominantly minority school types, compared with 6 percent at each of the two types of nitority-white schools (F = 3.44, P < 0.06).

21 Twenty-two and 26 percent for schools with minority populations greater than 90 percent and 60 to 90 percent, respectively. This compares with 17 percent in schools with between 60 and 90 percent white students and 19 percent for schools with more than 90 percent white students (F = 3.25, P < 0.05).

22Teachers of elementary low-track classes said they spent slightly more time on classroom routines (11 percent) than did teachers of average- (9 percent) or high-track groups (10 percent) (F = 2.93, P < 0.05).

where routines generally consume more time. Even when we con- trolled for school differences, however, we found that students in low and average-ability science classes spent less time on testing" and more time on reading than high-ability groups did."

Low-track mathematics classes spent considerably less time than did average- and high-track groups in whole class instruction" and considerably more time working with the teacher in small groups.26 However, once again, these differences are largely a reflection of school differences, although the greater time low-ability classes spend in small groups is not entirely explained by the greater small-group time spent in high-minority schools, where disproportionate percent- ages of low-ability classes are found.

In summary, we find that teachers in high-minority elementary schools less often involve students in hands-on or laboratory activi- ties. And students in such schools spend more lesson time on rou- tines, testing, and working in small groups than do students in other types of schools. Together, these findings suggest that students in less-advantaged schools have less access to active, engaging learning activities. Track-level differet.ces suggest additional instructional disadvantages for students n low-track classes at these and other types of schools, who spend less time than their peers in other classes actively engaged with the teacher in science and mathematics lessons. In racially mixed schools, because of the placement of large numbers of minority students in low-ability classes, these class-level differences have a disproportionate effect on the opportunities of mi- nority students.

Do Learning Activities Differ in Secondary Schools and Classes?

There is little school-related variation in the types of activities sec- ondary teachers include in their lessons. Neither the composition of the student body nor the location of the school has a noticeable effect on the strategies teachers use in science and mathematics classes. In

23Five and rt percent, compared with 12 percent for high-track classes (F = 3.79, P < 0.05).

24Eighteen percent for low-ability, 22 percent for average-ability, and 13 percent for high-ability groups (F = 5, P < 0.05).

25Thirty-five percent, compared with 45 and 47 percent (F = 8.04, P < 0.01). 26F = 2.96, P < 0.05.

all types of schools, most teachers lecture and few use computers,27 and most activities specifically related to science or mathematics classes. such as teacher demonstrations,28 small-group science ac- tivities,28 or the use of calculators in mathematidsare similar across school types.3°

However, the differences we do find are telling. For example, the percentage of teachers who ask their students to do seatwork is strik- ingly higher at schools with large concentrations of low-income stu- dents-65 percent, compared with 48 percent of teachers at low- poverty/high-wealth schools.31 Also, nearly half of the teachers in inner-city schools said that they used worksheets in their last lesson, compared with about a third of the teachers in other types of commu- nities," and nearly twic3 the percentage of teachers in high- minority schools said that their last lesson included a test." The use of hands-on laboratory activities also differed at schools of different SES levels, and seatwork differed with school location. However, the direction and meaning of these relationships are muddy.34

There is also considerable divergence in how much time students spend on different types of activities at different types of schools. The higher the minority population at schools, the more time teachers spend on daily routines, interruptions, and noninstructional activi- ties, although the size of these differences is smrll (ranging from 13 percent at schoole with minority populations greater than 90 percent

27For example, 87 percent of all secondary teachers said they lectured during their last lesson; 86 percent said they included discussion; and only 6 percent reported using ampputers.

29Reported by 44 percent of the science teachers. 29Thirty-seven percent. 30Twenty-one percent. 31F = 6.3, P < 0.01. 32Forty-seven percent of the teachers in inner-city schools, compared with 37

percent of suburban teachers, 35 percent of rural, ard 31 percent of other urban (F = 4.47, P < 0.01).

33Thirty-one and 26 percent in high-minority and majority-minority schools, com- pared with 21 percent and 16 percent in majority-white and nearly all-white schools (F = 6.20, P < 0.01).

34High-poverty and high-wealth schools had the lowest percentages of teachers who said that hands-on or laboratory activities were a part of their most recent lesson (24 and 25 percent, respectively); 33 percent of teachers at moderate-poverty and 28 percent at low-poverty schools reported using such activities (F = 3.86, P < 0.01). Inner-city and suburban schools had the fewest teachers indicating that their students did seatwork (63 percent at each type of school, compared with 61 and 63 percent, respectively, at rural and other urban schools) (F = 6.99, P < 0.01). However, the low incidence of seatwork in inner-city schools may be accounted for by the greater use of worksheets, as noted above.

if)

to 11 percent at schools with 90 percent or more white populations).35 More significant, science teachers in schools with higher concentrations of low-income and minority students have their stu- dents spend more time reading than do teachers in other schools. Students in the lowest-SES schools spent 14 percent of their class time reading, while those in the high-wealth schools spent only 4 percent. Consistent with this pattern, students in inner-city schools spent more time reading in science classes than did students in other communities.38 Additional science time spent on reading may come at the expense of instruction delivered directly by the teacher; teachers at the highest-SES schools spent 43 percent of their time lecturing, while those at the lowest-SES schools spent only 33 percent."

Mathematics teachers in high-poverty and majority-minority schools also have their students spend somewhat more time working alone and less time working with the whole class than do teachers with more-advantaged students. Students in high-poverty schools spent, on average, 53 percent of their class time working with the whole class (e.g., listening to teachers' lectures) and 24 percent working alone; students in high-wealth schools spent 60 and 21 per- cent of their class time, respectively, in these ways.38

Overall, then, while there are more similarities than differences in science and mathematics instruction in various types of schools, the pattern of differences is revealing. Students at higher-income and majority-white schools spend more instructional time on whole-class activities and less time working alone, i.e., reading or doing work- sheets, than do those at lower-SES, high-minority schools.

The Links Between Tracking and Classroom Activities

Far more striking than the differences between schools of various types are the differences among tracks within schools. Here, too, the differences in how time is spent are greater than the differences in the types of activities teachers include. But, taken together, the dif- ferences reveal quite distinct patterns of students in low-track classes spending more time on routine, less engaging, perhaps even less in-

35F = 3.03, P < 0.05. 36For reading and SES, F = 10.61, P < 0.01; for reading and racial composition, F =

8.52, P < 0.01; for reading and school location, F = 7.60, P < 0.01. 37For lecturing and SES, F = 3.11, P < 0.05; for lccturing and racial composition, F =

2.75, P < 0.05. 38For SES and individual activities, F = 3.18, P < 0.05; for SES and whole-class

activities, F = 4.05, P < 0.01; for racial composition, F = 4.20, P < 0.01.

structional activities. Table 6.4 shows that although teachers of the three class levels include most types of instructional activities at the same rates, the pattern of more isolated, routine activities in low- track classes is clear. Students in these classes are more often given seatwork, worksheets, and tests.

Table 6.5 shows how time is divided in classes of different track levels. Students in high-track science classes are advantaged by spending less class time on routines and reading and more time on hands-on activities and receiving instruction from teachers. Students in high-ability mathematics classes spend more time on whole-group instruction and less time working alone.

Considerable literature suggests that the instructional patterns we have observed reflect an overemphasis on control processes and a concomitant deemphasis on educative processes in lower-track classes. In an earlier study where similar instructional differences were found, teachers spent more time disciplining than teaching in lower-track classes (Oakes, 1985). :These classes focused on passive drill and practice with trivial bits of information, whereas the upper- track classes included more imaginative, engaging assignments. Other studies describe a similar balance between education and order in high-, average-, and low-track classes, both in the United States and in other industrialized nations, and at the elementary as well as the secondary school level (e.g., Ball, 1981; Eder, 1981; Goodlad, 1984; Hargreaves, 1967; Page, 1987a; Powell et al., 1985; Schwartz, 1981). These findings, combined with evidence that active learning strategies are most likely to promote student achievement in science and mathematics (Bredderman, 1983), suggest that the instructional patterns observed in the NSSME data restrict opportunities to learn in low-ability classes.

The track-level differences remain, even when we control for in- structional differences among different types of schools. With the ef- fect of school location accounted for, low-ability groups were found to do seatwork as a part of their lessons far more often than students in other track levels.39 With school differences in racial composition accounted for, low- and average-ability classes were more often made to complete worksheets,4° and more teachers of low-ability classes gave tests and quizzes.41

39An average of 63 percent of the lesson time in low-ability classes was spent on seatwork, compared with 45 percent in high-ability classes (F = 12.44, P < 0.01).

40The contrasts between low- and high-track classes and between average- and high- track classes were both significant at the 0.01 level.

410verall ability-group differences were significant at the 0.05 level, F = 3.04.

Table 6.4

PERCENTAGES OF SECONDARY TEACHERS INCLUDING VARIOUS INSTRUCTIONAL ACTIVITIES IN LAST SCIENCE OR MATHEMATICS LESSON, BY CLASS ABILITY LEVEL

Instructional Activity

Class Type Significance of Differences

Low Average High F P <

All classes Lecture 89 85 88 2.25 (not significant) Discussion 88 86 85 1.45 (not significant) Seatwork 63 61 52 10.20 0.001 Worksheets 43 37 29 16.11 0.001 Small groups 41 37 40 1.17 (not significant) Hands-on 23 26 27 1.08 (not significant) Test or quiz 21 18 16 3.07 0.05 Calculators 13 12 25 29.02 0.001 Computers 8 5 6 2.47 (not significant)

Science classes Demonstration 46 39 46 3.36 0.05

Table 6.5

PERCENTAGES OF TIME SPENT ON VARIOUS INSTRUCTIONAL ACTIVITIES IN SECONDARY SCIENCE AND MATHEMATICS

LESSONS, BY CLASS ABILITY LEVEL

Class Type Significance of Differences

Instructional Activity Low Average High F P <

All classes Routine 12 12 10 14.08 0.001

Science classes Lecture 36 36 41 4.98 0.01 Hands-on 20 20 26 5.85 0.01 Reading 12 10 5 22.58 0.001 Test or quiz 7 7 6 0.26 (not significant) Other activities 13 14 12 0.96 (not significant)

Mathematics classes Classlecture, teat, etc. 48 55 59 18.71 0.001 Small groups 10 9 10 0.65 (not significant) Individual 29 25 20 14.57 0.001

n !)

Ability-group differences in how class time is spent also remain when school characteristics are controlled. The high-track advantage in the smaller amount of time spent on routines remained,42 as did the greater exposure to teacher-led instruction in these classes." Clear instructional disadvantages for low-track classes also remained after we accounted for school differences. Students in low-track classes across all school types spent greater amounts of their science class time reading.44 Similarly, low-ability groups spent more time working alone in mathematics and less time doing whole-class activities."

The combined effect of being in a low-track class in a low-SES, high-minority, inner-city school is that lessons tend to be considerably more passive than those in higher tracks at any school. The contrasts shown in Table 6.6 between the most extreme caseslow-track classes in high-poverty, minority, inner-city schools and high-ability classes in high-wealth, white, suburban schoolsare particularly striking.

Do Expectations About Homework Differ Among Schools and Class Types?

Finally, we examined how expectations about homeworkthe in- structional time students spend outside of schooldiffer among schools and classes of different types. We first considered the per- centage of teachers who assign homework as a part of their science and mathematics lessons. Then we compared the amount of time teachers in different settings expect students to spend doing home- work.

Among elementary schools, neither the concentration of low-income students nor the location of schools made any difference in whether teachers assigned homework or how much time they expected stu- dents to spend on it. However, while about a third of the elementary teachers at mixed-race and all-white schools included homework as a part of their science and mathematics lessons, 54 percent of those in

42For location and time on routines, F = 13.77, P < 0.01; for racial composition and routMes, F = 8.48, P < 0.02.

OF . 6.78, P < 0.01. 44For SES and reading, F = 18.96, P < 0.01; for racial composition and reading, 'F .

12.07, P < 0.01; for school location and reading, F = 18.17, P < 0.01. 45For racial composition and working alone, F = 3.94, P < 0.05; for SES and whole-

class activity, F = 9.25, P < 0.01; for SES and working alone, F = 8.27, P < 0.01; for SES and class activities, F = 10.74, P < 0.01.

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Table 6.6

PERCENTAGES OF TIblE SPENT ON VARIOUS INSTRUCTIONAL ACTIVITIES IN HIGH- AND LOW-ABILITY CLASSES IN

SECONDARY SCHOOLS OF DIFFERENT TYPES

Instructional Activity

Class and School Types

Low-Ability Classes in Low- SES, Minority, Urban Schools

High-Ability Classes in High-SES, White, Suburban Schools

All classes Routine 17 9

Science classes Lecture 28 51 Hands-on 20 26 Reading 21 1 Test or quiz 10 4

Mathematics classes Classlecture, test, etc. 48 63 Small groups 7 8 Individual 26 20

schools with predominantly minority enrollments assigned home- work." We also found large differences in the time teachers expect students to spend on their homework. While teachers in schools with predominantly white populations expected students to spend about 8 minutes on an average day, teachers in high-minority elementary schools expected students to spend twice that much-16 minutes per day.47 Within elementary schools, the track level of classes made no difference in whether or not teachers assigned homework, but the class ability level did relate to the amount of homework assigned. Teachers in high-track classes assigned students an average of 14 minutes per day, slightly more than the 13 minutes assigned to low- track classes. Teachers assigned average-track classes somewhat less homework, an average of about 10 minutes.48

At the secondary level, school type made no difference in the per- centage of teachers assigning homework (63 percent across the sam- pled teachers) or in the amount of time students were expected to spend on homework (an average of 27 minutes per day). Teachers of

46F = 2.85, P < 0.05. 47F = 9.13, p < 0.01. 48F = 8.95, P < 0.01.

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classes at all levels were equally inclined to assign homework, but teachers of high-ability classes assigned considerably more homework than other teachers. High-ability classes were assigned an average of 33 minutes of homework per day; average-ability classes, 26 minutes; and low-ability classes, 24 minutes."

The fact that students in low-track classes were expected to spend less time on their homework than other students points to a funda- mental irony found in earlier studies of track-level differences in homework (Oakes, 1985). That is, those students who probably need to spend the most time engaged in learning activities to overcome their current deficiencies in science and mathematics are the ones of whom less out-of-school learning time is expected. In contrast, the students who achieve most easily in these subjects are expected to spend the most time learning at home. Thus, teachers have unequal expectations about homework that are likely to further distance high- and low-track students' learning

SUMMARY

This section has examined two central dimensions of classroom learning opportunities: the curriculum goals that teachers emphasize and the instructional strategies they use to achieve them. Once again, we find patterns that suggest that disadvantaged, minority, inner-city students have more-limited learning opportunities than their more-advantaged, white peers. In the elementary years, differ- ences in curricular goals and instruction are small, but not unimpor- tant. In high-minority elementary schools, there are some small ex- ceptions to the patterns, including higher teacher expectations con- cerning the amount of homework assigned to students. We must caution, however, that at the elementary level, our measures of oppor- tunity are few and gross in nature, and more work needs to be done on measuring what goes on at this level. It is also possible that the increased investment in instructional time and homework may be having perverse, unintended effects: The additional time may not in fact impart the types of knowledge that encourage participation at a later stage in students' academic careers, The evidence from recent achievement assessments appears to bear this out. Finally, there may be processes at work in middle schools or in the early high school years that undo gains made at the elementary level. Our data show

49F = 80.09, P < 0.01.

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that the differences in curricular and instructional opportunitiesas in the areas investigated in earlier sections of this reportgrow con- siderably wider in secondary schools.

Again, we find evidence of a double disadvantage for low-income and minority students, particularly in secondary schools. Teachers in schools serving large proportions of these students place somewhat less emphasis on such essential curriculum goals as developing in- quiry and problem-solving KAls. Moreover, teachers in low-ability classes (where disproportioi e percentages of minority students in mixed schools are found) place less emphasis on nearly the entire range of curricular goals.

Schools with large concentrations of low-income and minority stu- dents offer fewer classroom conditions that are likely to promote ac- tive engagement in mathematics and science learningsuch as op- portunities for hands-on activities and time working with the teacher. These differences are also compounded by differences in the experi- ences of students classified as high-, average-, and low-ability. The latter group are disadvantaged in their access to engaging classroom experiences and in their teachers' expectations for out-of-school learn- ing. Because low-income and minority students are disproportion- ately assigned to low-ability classes, these track-related differences further disadvantage these groups. Thus, our evidence suggests that unequal access to science and mathematics curriculum goals is fur- ther exacerbated by discrepancies in instructional conditions in schools and classrooms. Together, the data reveal striking differences in classroom opportunities.

VII. IMPLICATIONS

This study addresses four specific questions about students' oppor-. tunities to learn science and mathematics: What science and mathe- matics are being taught to which students? How? By whom? And under what conditions? The educational system funnels curriculum, resources, instruction, and teachers to students through the schools they attend and the classrooms in which they sit, and this process re- sults in disturbingly different and unequal opportunities to learn differences that are clearly related to race, social class, community, and the judgments that schools make about students' abilities. At elementary schools, and even more dramatically at junior and senior high schools, science and mathematics programs, teachers, resources, curricular goals, and instructional activities are allocated in ways that disadvantage low-income students, African-American and His- panic students, and students in inner cities. Those students whom schools judge to have "low ability' and place together in low-track classes are likewise disadvantaged. While each of these char- acteristics leads to diminished opportunities, students' background characteristics and schools' use of tracked classes combine in ways that place low-income and minority students doubly at risk. Because of the overlap of race, SES, and placement in low-track classes, mi- nority and low-income students' access to learning opportunities is limited beyond what would be expected from being enrolled in either a disadvantaged school or a low-track class.

A CONTEXT OF DIMINISHED RESOURCES AND LOW EXPECTATIONS

Perhaps we should not be surprised by these findings. Children living in communities with low levels of property wealth and personal income typically attend schools that spend fewer dollars on schooling. These relationships appear to persist even in states where school fi- nance reforms have attempted to equalize schooling resources (Carroll and Park, 1983). In fact, per-pupil expenditures between some neighboring high- and low-wealth districts differ by as much as a factor of three or more (Neu. York Times. 1990; Wise and Gendler, 1989).

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Unequal funding patterns are particularly relevant to race- and social-class equity concerns, since most minority and poor children at- tend schools in low-wealth communities or in central cities, where the competing demands for tax dollars are greatest. Also, costs of main- taining inner-city schools may be greater even when funding is equiv- alent. For example, expenditures for building maintenance, replacing items lost or damaged through vandalism, and providing "basic" sup- plies such as pencils and paper may be greater in older, inner-city schools. In 1983, 71 percent of the African-Americans and 58 percent of the Hispanics in the United States lived in inner-city areas (American Council on Education, 1983). The proportion of minority enrollments in large city school districts has increased dramatically in the past fifteen years (in some cases it has doubled), and current projections suggest that this trend will continue. As a result, the pattern of unequal funding in the nation's schools means that poor and minority children will have progressively less access than their more advantaged counterparts to well-maintained school facilities, highly qualified teachers, small classes, and instructional equipment and materials.

Moreover, poor and minority children have been more negatively affected than others by recent changes in educational funding poli- cies. Changes in the method of distributing federal funds have dimin- ished programs and services for disadvantaged children. The Educa- tional Consolidation and Improvement Act (ECIA) of 1981 lessened the regulation and monitoring of Chapter 1 compensatory funds with respect to both targeting aid for particular populations and ensuring comparable spending in target and nontarget schools. Additionally, by combining the Emergency School Assistance Act program (which was aimed at assisting desegregating school districts) with a number of other programs into enrollment-based block grant funding, the ECIA further reduced funds and programs for urban schools and minority children (Darling-Hammond, 1985).

At the state level, decreased public willingness to provide support for schooling (best exemplified by the "tax revolt" that began with the passage of California's Proposition 13 in 1978) has led to substantially fewer dollars being available for education overall. In many advan- taged school districts, community groups have offset some of these re- ductions by establishing educational foundations to raise additional funds. These, however, are not the districts where most poor and mi- nority children live. Even though some state funding is being in- creased in conjunction with educational reforms, urban districts re- main hard-pressed.

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Declining enrollments, particularly in urban schools, have further reduced dollars, since state funding is typically allocated on a per- pupil basis. Pressures on educational budgets have caused many ur- ban districts to cut back on the maintenance of facilities and pur- chases of textbooks and equipment, and some schools have closed al- together. Under these circumstances, we would expect science and mathematics programs in high-poverty, high-minority, and inner-city schools to be adversely affected.

Our findings also underscore the National Science Board's concern that inequalities may stem from the "failure to recncgnize and develop talent" and "the erroneous belief that many students lack the ability to learn mathematics and science" (NSB, 1983:13). The distribution of opportunity can be understood not only by looking at students' race and social class characteristics, but also by tracing the links between these characteristics, schools' judgments about students' intellectual ability, and the different educational experiences that follow from these judgments.

Educators have historically concluded that track-related differ- ences in teacher expectations, types of knowledge, learning experi- ences, and even the assignment of teachers were appropriate, given quite apparent differences in students' readiness for particular sci- ence and mathematics curricula and instruction. However, our anal- yses suggest that these differences may reflect something other than appropriate adjustments for differences in aptitude. Students judged to have low ability may get less because they are thought to need less (they are considered unable to benefit) or deserve less (they are con- sidered unwilling to benefit). But one could also argue that they need moremore able teachers, more instructional resources and supports. Here, we suggest that in their efforts to accommodate differences in ability with different educational experiences, schools actually limit some students' opportunities to learn. And given the disproportion- ately high proportion of students judged to have low ability in schools serving large concentrations of low-income and/or African-American and Hispanic minority students and the disproportionate assignment of minorities to low-track classes in mixed-race schools, these stu- dents experience a double disadvantage.

In addition to attending schools with less extensive and less rigor- ous science and mathematics programs, less-qualified teachers, fewer resources, and less-engaging classroom environments, low-income and minority students often find themselves in low-track classes that focus on "general" mathematics and science content and provide less access to the topics and curricular obje 'lives that could prepare them

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for successful participation in academic courses in these subjects. They, more than other students, learn in classrooms where instruc- tional activities appear to be directed toward control rather than ed- ucative purposes. They interact with less well-qualified and less- confident teachers. In fact, students in high-track classes at high- poverty and high-minority schools may have fewer opportunities than students in low-track classes at more advantaged schools; for exam- ple, they may have less access to highly qualified teachers.

These findings raise complex educational and ethical issues. Many schools servMg large concentrations of poor children, non-Asian mi-

er-city children lack the political clout to command re- sources &fail to those of other schools (although parity with relatively better-funded schools may be too low a standard, given the dire straits inner city and many suburban schools are in). Teachers often view these schools as less desirable places in which to teach, partly because the ever-present difficulties of teaching are compounded by the economic and social disadvantages that shape the students' lives and partly because such schools are often far from the middle-class teachers' homes. Many cities pay less, and inner-city schools have less desirable physical plants (many of them are literally crumbling) and fewer resources for teaching. These factors are often particularly important in teachers' decisions about where to teach. As a result, schools serving disadvantaged and minority students have far greater difficulty attracting and retaining well-qualified teaching staffs.

Within schools, many educators believe they base their decisions about who teaches what science and mathematics, to whom, ho, and under what conditions on egalitarian and educationally sound crite- ria. Although many realize that some decisions are political, rather than educational, and most educators are unhappy about the hiring of unqualified teachers, the processes and outcomes of curriculum dif- ferentiation and ability grouping are complex, subtle, often informal, incremental, and usually well-intentioned. For example, high schools with an uneven teaching staff often decide that students studying traditional college-preparatory mathematics content need teachers with stronger preparation in mathematics than do students strug- gling to understand fundamental mathematics processes. Of course, this assumption can be challenged. Uncertified or unprepared teach- ers are also least equipped to diagnose students' learning problems or to design activities that will help overcome them.

Nevertheless, considerable evidence suggests that this differentia- tion, especially at secondary schools, fails to increase learning gener- ally and has the unfortunate consequence of widening the achieve-

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ment gaps betweeu students judged to be more and less able. Thus, we find no instrumental value that might justify unequal access to valued science and mathematics curricula, instruction, and teachers.

THREE SCENARIOS FOR RIGHTING INEQUALITIES

The inequalities we have documented are not likely to be either self-correcting or easily changed. As long as high-quality educational opportunities are scarce and strategies for teaching diverse groups of students are largely untested, powerful constituencies of advantaged communities and parents will seek to preserve their educational ad- vantages. Policymakers and educators must therefore seek strategies to ameliorate the inequalities and, at the same time, improve the science and mathematics education provided to all students.

We can describe three scenarios for remedying the uneven distri- bution of science and mathematics resources and teachers. First, through legislative action and local district decisions, policymakers and educators could redistribute the available resources to schools by shifting equipment, materials, and staff away from schools that now have more to those that have less. Second, policymakers at the fed- eral, state, and local levels could attempt to increase the overall levels of educational resources so that all schools could command sufficient facilities, equipment, materials, and qualified staff to develop and sustain high-quality programs. Third, policymakers and educators could work together to both increase educational resources and frame resource allocation policies so that any new resources would go first to those schools serving economically disadvantaged and minority stu- dents.

We believe that the first scenario would be politically disastrous, since powerful constituencies would undoubtedly work to prevent a withdrawal of resources from currently advantaged schools. The sec- ond also holds little promise, since even as resources increased, the communities and parents who are now more advantaged would un- doubtedly use their political clout to garner the lion's share of those resources for their schools and children, absent any policies regulat- ing their distribution. Furthermore, the notion ofadvantage is a rela- tive, rather than an absolute, designation. Schools with better science and mathematics programs may still have legitimate needs for additional resources.

Only the third approach stands a chance of meeting the dual tests of political acceptability and potential effectiveness. Even at that, the

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extent to which policymakers and educators could marshal support for the preferential distribution of new resources is doubtful. We therefore believe that such an approach stands the best chance of suc- ceeding if it is linked with other policies aimed at improving science and mathematics education at all schools. We suggest some specific targets for such policies below.

POLICIES FOR EQUALIZING OPPORTUNITY AND IMPROVING SCIENCE AND MATHEMATICS EDUCATION

Focusing on the Importance of All Students' Opportunities

In the past decade, policymakers and educators have come to rec- ognize the effectiveness of federal and state "bully pulpits" for draw- ing public attention to educational problems. National and state leaders have generally used their pulpits to decry poor educational performance and to call for schools to improve student achievement and demonstrate, through accountability indicators, that they have made efforts to do so. However, attention is increasingly turning to the achievement and participation of low-income, minority, and inner- city students. Policymakers worry that an increasingly technological workplace and an increasing percentage of non-Asian minorities in the population portend critical labor-force shortages. Moreover, these human-capital concerr converge with concerns for social and eco- nomic equality. As science- and mathematics-related occupations in- crease in importance in terms of labor-market opportunity, the typi- cally lower attainments of low-income and minority students will in- creasingly influence their ability to compete for employment and good wages. These concerns have thus focused a great deal of attention on the educational "bottom line," i.e., achievement outcomes.

Policymakers would thus do well to fuel public concern about science and mathematics opportunities as well as outcomes. Focusing national concern on better and more evenly distributed learning op- portunities could clarify the means by which issues of economic prospects and social and economic justice can be addressed. Strong advocacy for such efforts on the part of the federal and state govern- ments could help to establish a receptive climate for policies and prac- tices aimed at better opportunities and fairer distribution of those op- portunities.

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Generating Resources and Devising Improvement Strategies

Generating new resources inevitably requires money. Additional funding is needed to upgrade science awl mathematics facilities and to provide laboratory and computer equipment. Extra money is also needed to raise teachers' salaries to levels that will make science and mathematics teaching more competitive with private-sector science- and mathematics-related careers, as well as to retain experienced teachers who might be attracted to more lucrative jobs outside of schools. With a strong commitment from the White House and the Congress, Washington could probably convince the public that addi- tional federal monies cou1 .1 profitably be allocated to schools serving the most needy children. One example of such funding emerged from recent deliberations regarding the reauthorization of the Carl D. Perkins Vocational Education Act, which will probably channel re- sources to schools serving large concentrations of disadvantaged stu- dents and enable them to integrate vocational and academic studies. Science and mathematics are obviotis subjects for such integrated programs. Another current effort is the Kennedy and Pell legislative initiative that addresses teacher shortages and distribution. Other creative avenues for generating new public funds could undoubtedly be found if national and state policy leaders turned growing public concern about outcomes toward the importance of educational oppor- tunities. The federal government and individual states might both supplement compensatory education programs targeted specifically toward science education.

Other sources for increased commitment and new resources include the new affiances between business and public education in many cities and states. As it becomes convinced that good public schools play an important role in local and state economic development, busi- ness can be effective by generating enthusiasm for new public funding and providing seed money for developing new avenues to equalize sci- ence and mathematics opportunities.

Opportunities to learn can also be increased by upgrading the sci- e e and mathematics knowledge of current teachers and improving the training of new entrants to teaching. State departments of educa- tion and universities can play a central role by developing new cur- ricula and instructional strategies that can serve diverse groups of students, and by supporting research and development on methods of restructuring school organization and curriculum to promote equi- table access to resources, knowledge, and teachers. State department staffs, business leadership, and university faculty can also play an

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important role in upgrading teachers' skills. Building on successful teacher inservice training models such as the University of Califor- nia's Bay Area Writing Project, science and mathematics faculty could come together with engineers from the private sector in summer workshops with science, mathematics, and vocational teachers to de- velop new teaching strategies for improving the learning opportuni- ties of low-income and minority students. Scholarships or stipends for participation might be provided to teachers who teach in disad- vantaged schools. These new strategies could then be disseminated through networks of school3 serving disadvantaged students. Addi- tionally, universities could incorporate training in equitable ad- ministrative and teaching practices into education programs for teachers and administrators. Finally, science and mathematics in- struction occurs in the context of whole schools. It is unlikely that opportunities in these two subjects can exceed those available throughout the whole schooling enterprise. High expectations and support for children succeeding in all academic areas, parent educa- tion, and professional conditions for teaching must accompany specific attention to mathematics and science opportunities (Oakes and Lipton, 1990).

Changing Priorities for Resource Acation

While strategies for improving science and mathematics teaching and learning should be made available to all schools, policies are needed to allocate new material and staff resources first to schools with the greatest needthose that lag behind in computers, labora- tories and materials, and well-qualified teachers. Such policies, like other affirmative-action strategies, must be backed by people with the determination to ward off political opposition to what may be seen as unwarranted preferential treatment. Moreover, educational "payoffs" from increased resources to the most troubled schools will not be im- mediate. Months, years, and terms of office may elapse before the in- vestment in opportunity produces significant returns.

Such determination often is more easily sust Lined at the federal level. However, state and local policymakers must also frame far- sighted policies, since it is at these levels that most educational re- sources are generated and allocated. For example, successful new ef- forts to equalize intradistrict funding could send considerable new re- sources to the most disadvantaged schools. States might also provide incentives for attracting and retaining highly qualified staff at schools

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serving large concentrations of disadvantaged and minority students. These incentives might include additional funding, technical support for new program development, and public recognition. Local districts can alter resource allocation and teacher assignment policies in ways that keep resources at the most disadvantaged schools. Teacher as- signment policies would probably need to be devised cooperatively with teachers' unions and might include rescinding teachers' transfer privileges based on seniority.

Improving the Use of Resources Within Schools

Policies that will equalize and improve opportunities within schools are far more difficult to frame than policies regulating opportunities between schools. Much of what happens inside schools is based on in- tangible factors such as expectations, beliefs about individual differ- ences and ways to accommodate them, and educators' preferences about which students they want to teach. However, state and local policies aimed at building staff capacity to work effectively with dif- ferent groups of students should support efforts to restructure schools so that opportunities are equalized for students in the same school who are judged to differ in ability.

As we have shown, tracking in science and mathematics, particu- larly in secondary schools, channels very different opportunities to different groups of students. Because the differential opportunities that result from ability grouping are related to students' race and so- cial class, and because there is little evidence to support the educa- tional effectiveness of tracked classes, effective alternatives should be sought. Such alternatives will require the development of new school organizational schemes that support efforts to provide equal class- room opportunities. Such schemes might include flexible staffing pat- terns, such as teams of teachers sharing responsibility for diverse groups of students and/or staggered working hours so that some teaching staff are available to provide extra instructional time after schcfol for students requiring additional help. Other arrangements could involve more flexible use of resources from categorical programs to enable more effective mainstreaming of students with mild learn- ing handicaps who are now served under Special Education programs or educationally disadvantaged students who are now served under Chapter 1 programs, and their teachers.

In addition, if schools hope to make science and mathematics learning opportunities accessible to diverse groups of students, they

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will have to redesign both curriculum and instruction. Help from state departments of education and universities should be an integral part of this process, for both technical and political reasons. Promising curricula and instructional strategies for heterogeneous groups of students already exist and can form the basis for new devel- opment. Knowledge gained from research in education, cultural an- thropology, and sociolinguistics can support new approaches that may be especially appropriate for low-income and minority students. Non- traditional instruction can be more effective than conventional tech- niques for minority children. African-American and Hispanic chil- dren tend to succeed better in classrooms featuring cooperative, small learning groups (Au and Jordan, 1981; Cohen and De Avila, 1983; Slavin and Oickle, 1981; Slavin, 1985) and experience-based instruc- tion (Cohen and De Avila, 1983). Recent analyses of the effectiveness of activity-based science curricula (e.g., the Elementary Science Study, ScienceA Process Approach, and The Science Curriculum Improvement Study) have concluded that while all students profit from such curricula, disadvantaged students make exceptional gains in their understanding of science processes, knowledge of science con- tent, and logical development when these methods are used (Bredderman, 1983). Attention to new curricular findings can help ensure that any move away from ability-grouped classes will be ac- companied by higher-quality science and mathematics instruction for all students. Such efforts should increase the skills of disadvantaged students and provide the knowledge that will allow them access to rigorous courses in junior and senior high school.

Monitoring the Distribution of Opportunities and Accountability for Equal Opportunity

Finally, given the difficulty of equalizing educational opportunities and the potential political disincentives, federal, state, and local ef- fors to reach this goal should be carefully morAtored. As long as states view public accountability schemes as mechanisms for encour- aging local efforts to increase student outcomes, districts and schools should be held accountable for working toward equalizing opportuni- ties. Data systems should be designed to report indicators of school resources, curriculum, teachers, instructional conditions, and out- comes by student race and SES. These indicators could provide in- sights into the possibilities for new educational policies to interrupt the patterns of unequal opportunities. Monitoring efforts should be

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complemented by a hierarchy of fmancial incentives for developing programs that will equalize opportunity, beginning at the federal level and extending to states, communities, and schools.

The following indicators should be useful for monitoring national progress toward equal educational opportunities and holding schools accountable:

Key resource indicators, by school type (e.g., schools serving different race and SES student populations): per-pupil ex- penditures, teacher salaries, pupil/teacher It otos, class sizes. Instructional time in science and mathematics at elementary schools of different types. Course offerings in science and mathematics at secondary schools of different types. Ratios of enrollment in different mathematics and science courses to student groups' representation in the school popu- lation. (For example, African-American students may repre- sent x percent of the student population, but only y percent of the enrollment in calculus classes.) Science, mathematics, and technology resources available at schools of different types. Teacher quality at schools of different types. Curriculum in science, mathematics, and technology available to diffe rent groups of students (e.g., classes serving different race and SES student populations). The instructional processes in science, mathematics, and technology that are available to various groups (e.g., in class- rooms serving different race and SES student populations).

The experience of schools and districts across the nation clearly shows that accountability systems are powerful tools. Teachers, ad- ministrators, and local communities respond both to the data these systems produce and to the implicit message embedded in the nature of their indicators. But such systems are only as good as their design. Indicators and accountability systems directed at monitoring progress toward equal opportunities to !nun science and mathematics should be designed not just to reward and/or punish schools, but to enable policymakers to describe and state problems more clearly; to recog- nize new problems more quickly; and to obtain clues about promising educational programs. Such systems should provide a direct contri- bution to policymakers' and educators' thinking about issues of equal-

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ity and educational opporturitics, rather than prescriptions for ac- tion.'

1 See Oakes (1989a) for a more detailed discussion of the use of educational indicators for monitoring equity in science and mathematics education.

Appendix CLASSIFICATION OF COURSES

This appendix lists the courses offered at the secondary schools in our sample, by title, and explains the basis on which we categorized them as either general, academic/college preparatory, or advanced academic/college preparatory.

The general category includes courses in mathematics and science that focus on content not usually considered necessary or appropriate for preparing students for college: remedial courses, applied or voca- tionally oriented courses, and courses that are either titled General or take a broad, nonrigorous approach to science and mathematics top- ics. Examples include basic life science, electricity, general science, computational mathematics, business mathematic? general mathe- matics, and pre-algebra.

Academic courses are defined as those that offer science and mathematics content that is typically considered preparation for college. At the junior high school level, the availability of such ourses may enable students to move more quickly into advanced

courses when they reach high school. For example, a student who has an opportunity to take algebra in the eighth grade or g..anistry in the ninth may be on a fast track in high school mathematics and may be able to complete advanced algebra, trigonometry, and calculus before graduation. Similarly, a student who has the opportunity to take biology in junior high school may be able to take more advanced science courses in high school. High school level academic courses are those that make up the standard approved sequence of core courses or electives that satisfy minimum college and university entrance requirements.

Advanced academic courses are those (1) whose titles designate them as being both standard academic subjects and designated for advanced, accelerated, honors, or "gifted and talented" students or (2) that go beyond the typical minimum requirements for college en.. trance (e.g., chemistry II, calculus).

To clarify ambiguous course titles, we consulted other researchers who have recently categorized courses for transcript analyses and officials in state departments of education. If no clear category was

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apparent, we classified courses conservatively, placing them in the lowest categories they qualified for.

The following lists specify the courses in each category across both elementary and secondary school levels.

SCIENCE

General Courses

General Science 7-9 Life Srience Earth Science Physical Science General Science 7 General Science 8 General Science 9 General Science 10-12 Ecology, Environmental Science Other Science 9th & 8th Grade Science Life/Physical Science General Science 9-12 Biology/Physical Science General Biology Agriculture Current Issues Science, grade 6 or under Earth/Physical Science General Science, grade unspecified Medical Technology Plant Science Electronics Applied Chemistry Life/Earth Science Aviation Life/Earth/Physical Science General Chemistry Basic Remedial Science Basic/Fun Physics

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Academic/College-Preparatory Courses

Biology I Chemistry I Astronomy Anatomy Zoology Earth/Space/Physical ScienceAcademic Anatomy/Physiology Marine Biology Geology Oceanography Meteorology Chemistry/Physics II Human Biology Research Botany Microbiology Cell Biology Genetics Embryology Other Chemistry Chemistry/Physics I

Advanced Academic/College-Preparatory Courses

Physics I Biology II Chemistry II Physics II Physiology AP Biology AP Chemistry AP Science AP Physics Chemistry/Physics II

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MATHEMATICS

General Courses

Mathematics 7 Mathematics 8 General Mathematics 9 General Mathematics 10-12 Business Mathematics Consumer Mathematics Remedial Mathematics Pre-Algebra/Introduction to Algebra Other Mathematics Mathematics 7 & 8 Computer Mathematics General Mathematics 7-9 Mathematics, grade unspecified General Mathematics 9-12 Mathematics, grade 6 or under Technical Mathematics Applied Mathematics

Academic/CC.lege.Preparatory Courses

Algebra I Algebra II Geometry Integrated Mathematics Sequential Mathematics Advanced Computer Mathematics

Advanced Academic/College-Preparatory Courses

Accelerated Mathematics 7/8/9 Integrated Sequence Accelerated Trigonometry Probability/Statistics Senior Mathematics (no Calculus) Advanced Senior Mathematics (some Calculus) Calculus AP Celculus

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Pre-Calculus Mathematics Analysis Advanced Mathematics Honors/Advanced Algebra I Integrated MathematicJTrigonometry/Algebra III Honors Geometry Integrated Mathe4iadcs Senior Mathematics/Analysis/Calculus Calculus/SW

I ( )

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