The 

Learning 

C u r v e

What We Are Discovering 

About U.S. Science and 

Mathematics Education

The 

Learning 

C u r v e

N A T I O N A L S C I E N C E F O U N D A T I O N

This document has been archived.
physical, medical, biological, social, and other sciences and to initiate and support

research fundamental to the engineering process and programs to strengthen engineering research potential and engineering education programs at all levels...”
The Learning Curve:

What We Are Discovering about 

U.S. Science and Mathematics Education

A Prefatory Report on the National Science Foundation’s

Indicators of Science and Mathematics Education 1995

January 1996

National Science

Foundation

REC Indicators

Series
Science and Mathematics Education. Edited by Larry E. Suter. Washington, DC:

National Science Foundation, 1996 (NSF 96-53).



Figure 1. Science and mathematics proficiency—percent of students 

at or above anchor point 250, by age: 1977 to 1992 . . . . . . . . . . . . . . . .8

Figure 2. Mathematics proficiency scores for 13-year-olds in 

countries and public school eighth-grade students 

in selected U.S. states: 1991 or 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Figure 3. Mean scores of 13-year-old public school students on

NAEP mathematics test, by race: 1992 . . . . . . . . . . . . . . . . . . . . . . . .10

Figure 4. Average number of minutes per day spent teaching 

each subject to self-contained classes, 

by grade range: 1977 to 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Figure 5. Percent of states imposing graduation requirements

in mathematics: 1974 to 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Figure 6. Mean number of credits earned by high school graduates 

in each subject field: 1982 to 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

Figure 7. Percent of science and mathematics teachers 

with undergraduate or graduate majors in science

or mathematics fields, by grade range: 1993 . . . . . . . . . . . . . . . . . . . . .12

Figure 8. Percent of science and mathematics teachers 

with various amounts of in-service education 

in these fields during the past 3 years: 1993 . . . . . . . . . . . . . . . . . . . . .13

Figure 9. Percent of classes using hands-on activities 

in most recent lesson, by subject and grade range: 1977 to 1993 . . . . .13

Figure 10. Science and mathematics proficiency—percent of students 

at or above selected anchor points, by age and sex: 1977 to 1992 . . . .14

Figure 11. Science and mathematics proficiency—percent of students 

at or above selected anchor points, by age, and race 

or ethnic origin: 1977 to 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Figure 12. Percent of high school graduates earning credits in science 

and mathematics courses, by subject and sex: 1982 to 1992 . . . . . . . . .16

Figure 13. Percent of high school graduates earning credits 

in science and mathematics courses, 

by race or ethnic origin: 1982 to 1992 . . . . . . . . . . . . . . . . . . . . . . . . .16

Figure 14. Ability composition of high school science and 

mathematics classes: 1986 and 1993 . . . . . . . . . . . . . . . . . . . . . . . . . . .17

Figure 15. Percent of high school sophomores aspiring 

to various levels of postsecondary education, 

by race or ethnic origin: 1980 and 1990 . . . . . . . . . . . . . . . . . . . . . . . .18

Figure 16. Percent of 1987 first-year undergraduate students 

in 4-year institutions who stayed in or switched to other 

(declared or intended) majors by 1991, by field of major: 1991 . . . . . .18

Figure 17. Number of bachelor’s degrees awarded, by sex 

and major field group: 1977 to 1991 . . . . . . . . . . . . . . . . . . . . . . . . . . .19

Figure 18. Science and engineering degrees awarded, by degree level: 

1971 to 1991 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19

List of Figures

Presenting the Indicators

According to data recently compiled by the National Science Foundation

(NSF), elementary schools in the United States today are devoting more

classroom time than ever before to science and mathematics instruction.

More high school students are undertaking advanced courses in these crucially

important areas of study. And U.S. colleges and universities are awarding more bachelor’s, master’s, and doctoral degrees in the natural sciences and engineering.

Moreover, members of all racial and ethnic groups are sharing in a number of the

notable gains made by the Nation’s science and mathematics students; for example,

a greater proportion of U.S. high school students, regardless of race or ethnic background, are now satisfactorily completing courses in science and mathematics.

Achievement scores in these fields are on the rise for students of all races. And there

is a discernible increase in the number of blacks, Hispanics, and Native Americans

earning bachelor’s degrees in science and engineering.

These and an array of other encouraging findings are offered in an NSF presentation

of statistical data—or “indicators”—concerning the students, teachers, systems, curricula, learning environments, teaching methods, and other components of the

Nation’s science and mathematics education community. Titled Indicators of Science

and Mathematics Education 1995, the report was created in compliance with a 1991

mandate from the U.S. Congress. Like its 1992 predecessor, for which it serves as an

update, the latest volume is intended for use by anyone seeking qualitative and

quantitative information on trends in elementary, secondary, and postsecondary education. NSF expects the report’s readership to be broad in scope, including educators, elected officials, government policy makers, social commentators, professional

scientists and mathematicians, and the general public—all citizens, that is, who support the notion that significant improvement in U.S. science and mathematics education should rank among the Nation’s highest priorities.

For those who share in the hope that U.S. science and mathematics education is

effectively preparing our young people to live, work, and prosper in a technologyintensive, increasingly competitive global society, the report offers grounds for cautious optimism. Indeed, based on hundreds of statistical findings gathered by NSF

from a wide variety of authoritative national surveys, Indicators of Science and

THE LEARNING CURVE 1

What is an “Indicator”? 

An indicator is a statistic that describes the health 

of a system or the status of an important policy issue.
Mathematics Education 1995 suggests that considerable progress in science and mathematics education is being made at all grade levels.

◆ Particularly encouraging is the growing awareness among elementary school

teachers and curriculum designers that a familiarity with basic concepts in science and mathematics should be introduced to students at an early age.

Measured in blocks of time ranging from approximately 20 minutes to 100

minutes, the average amount of classroom time per day dedicated to science

and mathematics for grades 1 through 6 rose substantially between 1977 and

1993, according to a 1993 National Survey of Science and Mathematics

Education (NSSME), one of several sources for the Indicators of Science and

Mathematics Education 1995.

◆ Furthermore, students’ early exposure to science and mathematics is now being

parlayed beneficially through their high school years far more effectively than

it has been in the past, thanks largely to an increase in the number of states

that are imposing stricter graduation requirements in these areas of study. In

1974, about 15 percent of states required 2 or more years of mathematics for

graduation; in 1992, the figure was approaching 90 percent. Consistent with

elevated graduation requirements, the increased availability of advanced science and mathematics courses at the secondary level is evident nationwide.

Currently, nearly 100 percent of all U.S. high schools offer courses not only in

introductory algebra, geometry, and biology, but also in chemistry, physics,

algebra II, and trigonometry.

◆ Along with more stringent high school graduation requirements and the availability of advanced science and mathematics courses, the level of preparation

of postsecondary science and engineering students and the number of college

degrees being awarded in these areas are rising. Much of this progress has been

made within the very recent past. High school students who in 1993 planned

an undergraduate major in the natural sciences or engineering were, for the

most part, better prepared than were their counterparts just 3 years earlier.

Between 1990 and 1993, for example, the proportion of intended natural science or engineering majors who took calculus in high school rose from about

one-quarter to one-third, while the proportion of those taking physics

increased from about one-half to almost two-thirds.

◆ Among the most encouraging trends noted in the report is the increase in the

number of women with degrees in science fields. Between 1971 and 1991, the

percent of bachelor’s degrees in science and engineering fields awarded to

women increased from 29 to 44 percent and the percent of doctoral degrees

awarded to women increased from 10 to 28 percent. Steady increases occurred

over the past 20 years in the number of women receiving bachelor’s and doctoral degrees in science fields while the number of men receiving degrees did

not increase. While the number of women receiving doctorates in science

fields has increased by more than threefold since 1971, the number of men

receiving doctoral degrees is about the same in 1991 as in 1971.

2 PRESENTING THE INDICATORS
The Indicators of Science and Mathematics Education 1995 presents some less-encouraging indicators as well:

◆ While more high school students of all races are enrolling in and successfully

completing science and mathematics courses, and although test scores of all

students have improved during the past decade, scores for white students

remain significantly higher than those for black and Hispanic students. And

although more blacks, Hispanics, and Native Americans are earning bachelor’s

degrees in science and engineering today than ever before, all three minority

groups remain underrepresented in relation to their presence in the overall

U.S. college-age population.

◆ Despite some modest gains since 1988, women and minorities continue to be

underrepresented on U.S. higher education science and engineering faculties.

◆ While today’s students have parents with higher levels of education—a factor

that many experts consider a positive influence on academic proficiency—

these students are more likely to be members of one-parent families and to be

living in poverty—factors that many experts consider a negative influence on

performance.

◆ Eighth-grade mathematics achievement in some states (Iowa, North Dakota,

and Minnesota) was the same as in top-performing countries (Taiwan, Korea,

and former Soviet Union), while achievement in the lowest performing states

(Arkansas, Alabama, Louisiana, and Mississippi) was about the same as in the

lowest performing country (Jordan).

◆ Despite increases in the time and attention being devoted to science and

mathematics, the high school graduation requirements for these subjects in

many states still fall short of the 4 years of each that has been recommended

by education reform advocates.

These and a wealth of other significant revelations emerge from the array of indicators presented in the report, a sampling of which appears in Highlights (page 8 of

this summary report). In creating Indicators of Science and Mathematics Education

1995, NSF has focused on collecting, synthesizing, analyzing, evaluating, and presenting relevant data.

Standards and the Quest for Reform

Over the past decade, science and mathematics education standards have been articulated by a number of prestigious organizations, such as the National Council for

Teachers of Mathematics, the National Research Council, the National Science

Teachers Association, and the American Association for the Advancement of

Science. While differing in details, the standards are consistent in providing guidelines for instruction, calling for improvement in teacher qualifications and the learning environment, and setting levels of expectation for student achievement. The

standards reinforce the notion that the pursuit of excellence must be open to all students, regardless of their sex, race, or the community in which they live. 

THE LEARNING CURVE 3
The standards have, in turn, yielded a widely endorsed set of specific goals, such as

the following:

◆ All students should be expected to attain a high level of scientific and mathematical competency.

◆ Students should learn science and mathematics as active processes focused on

a limited number of concepts.

◆ Curricula should stress understanding, reasoning, and problem solving rather

than memorization of facts, terminology, and algorithms.

◆ Teachers should engage students in meaningful activities that regularly and

effectively employ calculators, computers, and other tools in the course of

instruction.

◆ Teachers need both a deep understanding of subject matter and the opportunity to learn to teach in a manner that reflects research on how students learn.

One way the standards and goals of excellence and equity in science and mathematics education have been implemented is through efforts to reform many aspects of

the school system at once—an approach entailing a coordinated national initiative,

as opposed to piecemeal remedial efforts, to address all critical components of the

prevailing educational system. Dr. Luther S. Williams, Assistant Director of NSF’s

Directorate for Education and Human Resources, says that systemic reform “...is a

revolutionary vehicle to ameliorate the performance gap—which demographics dictate we must do in order to achieve Goals 2000 for all of our students.”

4 PRESENTING THE INDICATORS

What are the “Standards”?

National standards provide an explicit set of expectations for teaching

and learning. Stressing the importance of mathematics and science

for all students, they provide a vision that is based on our best

understanding of teaching and learning. Standards provide the basis

for guiding educational programs and for measuring the

accomplishments of our educational institutions.
Systemic science and mathematics education reform is built on the following

elements:

◆ Curricular reform for all students at all grade levels, including the establishment of achievement standards based on the ability to master scientific

processes rather than memorization of facts or formulas.

◆ Changes in the learning environment, including pedagogic reform, with teachers emphasizing active student involvement through discussion, problem solving, hands-on activities, and small-group work.

◆ More opportunities for all students to use calculators and computers in the

classroom and for homework.

◆ More exposure of low-achieving students to the full range of educational

opportunities and demands.

◆ Assessment reform that replaces tests based on factual knowledge with tests

that measure the ability to reason, solve problems, and use scientific principles.

THE LEARNING CURVE 5

What is “Systemic Reform?”

“Systemic reform” is a process of educational reform based on the

premise that achieving excellence and equity requires alignment of

critical activities and components. It is as much a change in infrastructure as in outcomes. Central elements include—

◆ High standards for learning expected from all students;

◆ Alignment among all the parts of the system—policies,

practices, and accountability mechanisms;

◆ A change in governance that includes greater school site

flexibility;

◆ Greater involvement of the public and the community;

◆ A closer link between formal and informal learning experiences; 

◆ Enhanced attention to professional development; and

◆ Increased articulation between the precollege and postsecondary

education institutions.
In light of prevailing concerns about U.S. students’ comparatively low academic

achievement in science and math, and considering the commitment of the Federal

Government and state governments to reverse the situation by the year 2000, it follows that policy makers, congressional leaders, parents, and others are looking for

answers to a number of questions, including the following:

◆ Are current reform efforts succeeding in improving science and mathematics

education?

◆ Has overall achievement improved?

◆ Do students in each state and region of the country perform equally?

◆ Are achievement levels among ethnic groups converging?

◆ Have differences in the achievement levels of the United States and other

countries narrowed?

◆ Is a reduction occurring in the practice of grouping students by ability level?

◆ Is there an increase in the number of teacher-development programs that

emphasize new methods of science and mathematics instruction?

◆ Is there an increase in the number of teachers with undergraduate-level

coursework in science and mathematics?

◆ Is there an increase in the number of teachers who belong to racial and ethnic

minorities, especially in schools with large minority student populations?

Data Sources

Since its establishment in 1950, one of NSF’s missions has been to provide research,

guidance, and support for U.S. science and mathematics education. NSF’s role

extends into the compilation of statistical data about science and mathematics programs gathered by Federal agencies, such as the National Center for Education

Statistics. NSF analyzes statistical information from outside sources as well and

develops appropriate methods for evaluating the effectiveness of programs and initiatives. Creation of the biennial indicators report, therefore, builds on the agency’s

leadership as compiler, reviewer, and interpreter of complex data. 

While the 1992 Indicators of Science and Mathematics Education report primarily

described science- and mathematics-related trends from 1970 to 1990, the latest document focuses wherever possible on information regarding student proficiency, curricula, learning environments, demographics, and so forth, that has been gathered

through 1993. Therefore, the 1995 report serves as an update on the ways in which

the important issues in science and mathematics education that were analyzed in the

1992 edition continue to change.

6 PRESENTING THE INDICATORS

Highlights

To reflect the content of the full Indicators of Science and Mathematics

Education 1995, the following sampling of the report highlights significant

findings regarding student achievement, curriculum, teachers and the learning environment, equity, demographic changes, and postsecondary education.

Student Achievement

Science and mathematics proficiency among high school students, regardless of race,

gained between 1977 and 1992 (see figure 1)—a change that may be attributed in

part to the fact that many more students are taking advanced science and mathematics courses in high school as a result of changes in requirement policies within each

state.

However, while a higher percentage of 13-year-old students scored 250 or higher on

the NAEP science and mathematics proficiency test in 1992 than in 1977, recent

comparisons of achievement show 13-year-old U.S. students scoring below students

of other countries. (See figure 2.) These latter data, based on a 1991 study, substantiated results from earlier studies that provided the impetus for efforts to improve science and mathematics education in the United States.

Notwithstanding, a recent reanalysis of data shows that there are sharp differences

in student mathematics performance among states in the United States that match

differences among countries. (See figures 2 and 3.) A comparison of international

and state proficiencies shows, for example, that eighth-grade performance in the

highest ranking states (Iowa, North Dakota, and Minnesota) was the same as in the

8 HIGHLIGHTS

1977 1982 1986 1990 1992

0

20

40

60

80

100

Percent at or above 250

Science

Age 17

Age 13

Age 9

1977 1982 1986 1990 1992

0

20

40

60

80

100

Percent at or above 250

Mathematics

Age 17

Age 13

Age 9

SOURCE: Mullis, I.V.S., et al. (1994). NAEP [National Assessment of Educational Progress] 1992 trends in academic progress (Report No. 23-TR01). 

Washington, DC: National Center for Education Statistics.

FIGURE 1

Science and mathematics proficiency—percent of students

at or above anchor point 250, by age: 1977 to 1992
THE LEARNING CURVE 9

FIGURE 2

Mathematics proficiency scores for 13-year-olds in countries and 

public school eighth-grade students in selected U.S. states: 1991 or 1992

NOTES: International data are 1991. All U.S. data are 1992. Only 41 states and

the District of Columbia volunteered to participate in the study. 

SOURCE: National Center for Education Statistics (NCES). (1993). Education in states 

and nations: Indicators comparing U.S. states with the OECD countries

in 1988 (NCES 93-237). Washington, DC: NCES. 

Mean (average) District of Columbia

Mississippi

JORDAN

Louisiana

Alabama

Arkansas

Hawaii

West Virginia

Tennessee

North Carolina

New Mexico

Georgia

Florida

South Carolina

California

Kentucky

UNITED STATES

Delaware

SPAIN

Texas

Maryland

Rhode Island

Arizona

SLOVENIA

New York

Virginia

Oklahoma

Ohio

Michigan

SCOTLAND

IRELAND

Indiana

Missouri

CANADA

Pennsylvania

New Jersey

Massachusetts

 ITALY

ISRAEL

Colorado

FRANCE

Connecticut

Wyoming

Utah

Idaho

Wisconsin

Nebraska

HUNGARY

New Hampshire

Maine

SWITZERLAND

SOVIET UNION

Minnesota

North Dakota

KOREA

Iowa

TAIWAN

170 190 210 230 250 270 290 310 330 350

Score

Mean score

Range of scores (between 5th and 95th 

percentile) within U.S. states

Range of scores (between 5th and 95th 

percentile) within countries
281 or higher

274 to 280

267 to 273

Nonparticipant*

260 to 266

273

277

277

276

275 272

276

278

279

272

281

284

284

284

275

265

263

282

274 273

262

264

266

264

260 275

266

270

273

276

276

279

279

278

272

283

283

278

271

277

FIGURE 3

Mean scores of 13-year-old public school students 

on NAEP mathematics test, by race: 1992

265

251 or higher

244 to 250

237 to 243

Nonparticipant*

220-236

245

240

238

247

253

261

254

257

253

253

248

248

252

254 251

228

228

246

249 245

223

220

227

231

230 254

238

233

233

248

246

243

240

239

247

241

232

Hispanic

240

258

DC=225

251 or higher

244 to 250

237 to 243

Nonparticipant*

230-236

236

233

251

241

243

238

236

241

230

232

246

234 243

230

231

234

241

243 244

238

241

241

232

237

232

239

241

242

242

240

Black

243

DC=233

*This category also includes states where there were too few sample cases for a reliable estimate.

SOURCE: National Center for Education Statistics. (1993). Data almanac: NAEP's 1992 assessment in 

mathematics [CD-ROM]. Princeton, NJ: Education Testing Service [Producer]. Washington, DC: U.S. 

Department of Education [Distributor].

1 0 HIGHLIGHTS
THE LEARNING CURVE 11

top-performing countries (Taiwan,

Korea, and the former Soviet Union),

and achievement in the lowest performing states (Arkansas, Alabama,

Louisiana, and Mississippi) was about

the same as in the lowest performing

country (Jordan).

Within the United States, differences

in student mathematics achievement

are not simply a reflection of the concentration of racial or ethnic groups in

some regions. For example, large differences in state mathematics scores exist

for white and Hispanic students across

regions and small differences exist for

black students across regions. Overall,

students in the Midwest had the highest NAEP mathematics scores, and students in the Southeast had the lowest

scores. (See figure 3.)

Curriculum

Elementary schools are placing more emphasis on science and mathematics education by devoting more classroom time to it. (See figure 4.) Since 1977, the time

devoted to science and mathematics has been more in line with recommendations

incorporated in the standards delineated by various organizations.

1977* 1986 1993 0

20

40

60

80

100

Number of minutes per day

Grades 1–3

Reading

Mathematics

Science

1977 1986 1993 0

20

40

60

80

100

Number of minutes per day

Grades 4–6

Reading

Mathematics

Science

FIGURE 4

Average number of minutes per day spent teaching each subject

to self-contained classes, by grade range: 1977 to 1993 

* 1977 data include kindergarten.

SOURCES: Weiss, I.R. (1987). Report of the 1985–86 national survey of science and mathematics education. Research Triangle Park, NC: Research 

Triangle Institute; Weiss, I.R., Matti, M.C., & Smith, P.S. (1994). Report of the 1993 national survey of science and mathematics education. Chapel Hill, 

NC: Horizon Research, Inc.

74

0

10

20

30

40

50

60

70

80

90

100

Percent of states

No state requirements

2 or more years of math

80 83 85 87 89 92 90

SOURCES: Stecher, B. (1991). Describing secondary curriculum in 

mathematics and science: Current conditions and future indicators 

(N-3406-NSF). A RAND note presented to the National Science 

Foundation, Arlington, VA; Blank, R.K. & Gruebel, D. (1993). State 

Indicators of Science and Mathematics Education 1993. Washington, 

DC: Council of Chief State School Officers.

FIGURE 5

Percent of states imposing 

graduation requirements 

in mathematics: 1974 to 1992
High schools also appear to be placing more emphasis on science and mathematics

education. Whereas 20 percent of states required high school students to complete 2

or more years of mathematics in 1974, 86 percent of states had that requirement in

1992. (See figure 5.) The indicators are similar for science.

Despite elevated graduation requirements by states, the requirements still fall short

of the standards recommended by reform advocates—4 years each of science and

math. By 1992, high school graduates earned about 3 years each in science and

mathematics. (See figure 6.)

Teachers and the Learning Environment

Overall, high school teachers are likely to be academically well prepared to teach

science and mathematics, but elementary teachers are likely to be unprepared. (See

figure 7.) This is an important matter, since teachers’ ability to implement science

and mathematics reform, such as early introduction of challenging concepts and

ideas, often depends on their own levels of competence and professionalism.

Only about two-thirds of teachers of grades 1 through 8 have completed at least one

college course in the biological, physical, or earth sciences. Indeed, less than 30 percent of elementary school teachers say they feel well qualified to teach life science,

while 60 percent feel well qualified to teach mathematics and close to 80 percent

feel well qualified to teach reading.

1 2 HIGHLIGHTS

1982 1987 1990 1992 1

1.5

2

2.5

3

3.5

4

4.5

English

Mathematics

Science

History or social studies

FIGURE 6

Mean number of credits 

earned by high school graduates 

in each subject field: 1982 to 1992

NOTE: Credits are measured as Carnegie Units.

SOURCES: Legum, S., et al. (1993). The 1990 high school transcript 

study tabulations: Comparative data on credits earned and 

demographics for 1990, 1987, and 1982 high school graduates 

(NCES 93-423). Washington, DC: National Center for Education 

Statistics; National Center for Education Statistics. (1992). National 

education longitudinal study of 1988: Second teacher follow-up study. 

Unpublished tabulations. Mean number of credits earned

1–4 5–8 9–12 0

10

20

30

40

50

60

70

80

Percent of teachers

Grade range

1 3

11

21

63

72

Science teachers

Mathematics teachers

FIGURE 7

Percent of science and mathematics

teachers with undergraduate or graduate 

majors in science or mathematics 

fields, by grade range: 1993

NOTE: "Field" includes any science 

or science education major for 

science teachers and any mathematics 

or mathematics education major for 

mathematics teachers.

SOURCE: Weiss, I.R., Matti, M.C., 

& Smith, P.S. (1994). Report of the 1993 

national survey of science and mathematics 

education. Chapel Hill, NC: Horizon 

Research, Inc. 

90

100
Academic preparation is only one element of teacher competence. Other elements

include continuing professional education, in-service training, and formal and informal contacts with colleagues and experts. In 1993, about one-third of all science and

mathematics teachers had taken college courses within the past 3 years, and most

had had at least some in-service education in their field. (See figure 8.) Elementary

science and mathematics teachers had the least amount of in-service training.

Overall, teachers are not yet following recommendations for reforming classroom

practice; for example, teachers have not implemented early introduction of algebraic

concepts or alternative assessments. Additionally, despite strong recommendations

for hands-on approaches in science and mathematics education, teachers still rely

heavily on lectures. Fewer than 40 percent of junior high or high school classes used

hands-on activities in their most recent lesson. (See figure 9.) Teachers may not be

following recommendations for reforming classroom practice because science and

mathematics classrooms tend to lack adequate facilities or supplies, such as up-todate textbooks or modern computers.

THE LEARNING CURVE 13

1–4 5–8 9–12 0

20

40

60

80

100

Percent of teachers

Grade range

None Less than 6 hours 6–35 hours More than 35 hours

1–4 5–8 9–12 0

20

40

60

80

100

Percent of teachers

Grade range

Science Mathematics

SOURCE: Weiss, I.R., Matti, M.C., & Smith, P.S. (1994). Report of the 1993 national survey of science and mathematics education. Chapel Hill, NC: 

Horizon Research, Inc. 

FIGURE 8

Percent of science and mathematics teachers with various amounts 

of in-service education in these fields during the past 3 years: 1993

0

20

40

60

80

Percent of classes

Grades 1–3

Science

Mathematics

1977* 1986 1993 1977 1986 1993 1977 1986 1993 1977 1986 1993

Grades 4–6 Grades 7–9 Grades 10–12

* 1977 data include kindergarten.

SOURCES: Weiss, I.R. (1987). Report of the 1985–86 national survey of science and mathematics education. 

Research Triangle Park, NC: Research Triangle Institute; Weiss, I.R. (1994). 1993 National survey of science 

and mathematics education. Unpublished tabulations. 

FIGURE 9

Percent of classes using hands-on activities 

in most recent lesson, by subject and grade range: 1977 to 1993

100
Equity

Although proficiency gains are evident across both sexes and all racial and ethnic

groups, these gains have not eliminated the gaps among different population groups

or between males and females. For example, in 1977, the largest gap between the

percentage of males and the percentage of females scoring at selected NAEP anchor

points was in science at age 17. The gap between the achievement of males and

females remained in 1992, although it had decreased from 14 percentage points in

1977 to 9 percentage points in 1992. (See figure 10.)

1 4 HIGHLIGHTS

1977 1982 1986 1990 1992 0

20

40

60

80

100

Percent

Age 17 at or above 300

Male

Female

 Science

1978 1982 1986 1990 1992 0

20

40

60

80

100

Percent

Age 17 at or above 300

 Mathematics

Female

Male

FIGURE 10

Science and mathematics proficiency—percent of students 

at or above selected anchor points, by age and sex: 1977 to 1992

1977 1982 1986 1990 1992 0

20

40

60

80

100

Percent

Age 13 at or above 250

Male

Female

1978 1982 1986 1990 1992 0

20

40

60

80

100

Percent

Age 13 at or above 250

Female

Male

1977 1982 1986 1990 1992 0

20

40

60

80

100

Percent

Age 9 at or above 200 

Male

Female

1978 1982 1986 1990 1992 0

20

40

60

80

100

Percent

Female

Male

SOURCE: Mullis, I.V.S., et al. (1994). NAEP [National Assessment of Educational Progress} 1992 trends in academic progress (Report No. 23-TR01). 

Washington, DC: National Center for Education Statistics.

Age 9 at or above 200 
Furthermore, the amount of change in achievement for students in all racial and

ethnic groups has been somewhat mixed, depending on test subject matter and age

of students. NAEP science and mathematics tests, which were first administered in

1977, suggest that the gap between the percentage of white, black, and Hispanic students scoring at selected anchor points decreased for mathematics and, to a lesser

degree, for science until 1990. Since 1990, however, science score differences have

increased. (See figure 11.)

Between 1982 and 1992, female and male high school graduates earned credit in all

science and mathematics courses at about the same rate, except in physics, where

males significantly exceeded females. (See figure 12.) However, substantial differences

in course taking existed among students in various racial and ethnic groups. (See figure 13.) For example, while about the same proportion of white, black, and Hispanic

high school graduates had earned credits in biology and introductory algebra in 1992,

a significantly higher proportion of white graduates had completed courses in chemistry, physics, geometry, advanced algebra, and trigonometry.

THE LEARNING CURVE 15

1977 1982 1986 1990 1992

0

20

40

60

80

100

Percent

Age 17 at or above 300

White

Black

Hispanic

Science

1977 1982 1986 1990 1992

0

20

40

60

80

100

Percent

Age 13 at or above 250

White

Black

Hispanic

1978 1982 1986 1990 1992

0

20

40

60

80

100

Percent

Age 17 at or above 300

Mathematics

Black

Hispanic

White

1978 1982 1986 1990 1992

0

20

40

60

80

100

Percent

Age 13 at or above 250 

Black

Hispanic

White

SOURCE: Mullis, I.V.S., et al. (1994). NAEP [National Assessment of Educational Progress] 1992 trends in academic progress (Report No. 23-TR01). 

Washington, DC: National Center for Education Statistics.

FIGURE 11

Science and mathematics proficiency—percent of students 

at or above selected anchor points, by age, and race or 

ethnic origin: 1977 to 1992
1 6 HIGHLIGHTS

NOTE: Credits are measured in Carnegie Units

SOURCES: Legum, S., et al. (1993). The 1990 high school transcript study tabulations: Comparative data on credits earned and demographics 

for 1990, 1987, and 1982 high school graduates (NCES 93-423). Washington, DC: National Center for Education Statistics; National Center for 

Education Statistics. (1992). National education longitudinal study transcripts. Washington, DC: Author.

1982 1987 1990 1992

0

20

40

60

80

100

 Male

 Female

Geometry

Algebra II

Trigonometry

Calculus

Percent

Mathematics

FIGURE 12

Percent of high school graduates earning credits in science 

and mathematics courses, by subject and sex: 1982 to 1992

1982 1987 1990 1992

 Male

 Female

Biology

Chemistry

Physics

Science

0

20

40

60

80

100

Percent 0

20

40

60

80

100

Percent of graduates

FIGURE 13

Percent of high school graduates earning credits in science 

and mathematics courses, by race or ethnic origin: 1982 to 1992

Any science Biology

Chemistry

Physics

82 87 90 92 82 87 90 92 82 87 90 92 82 87 90 92

0

20

40

60

80

100

Percent of graduates

Algebra I

Geometry

Algebra II

Trigonometry

White

Black

Hispanic

NOTE: Credits are measured in Carnegie Units.

SOURCES: Legum, S., et al. (1993). The 1990 high school transcript study tabulations: Comparative data on credits earned and 

demographics for 1990, 1987, and 1982 high school graduates (NCES 93-423). Washington, DC: National Center for Education 

Statistics; Smith, T.M., et al. (1994). The condition of education, 1994 (NCES 94-149). Washington, DC: National Center for 

Education Statistics. 

 

82 87 90 92 82 87 90 92 82 87 90 92 82 87 90 92
FIGURE 14

Ability composition of high school science and mathematics classes: 

1986 and 1993

NOTE: High school includes grades 10–12.

SOURCES: Weiss, I.R. (1987). Report of the 1985–1986 national survey of science and mathematics education. Research Triangle Park, NC: Research 

Triangle Institute; Weiss, I.R. (1994). 1993 National survey of science and mathematics education. Unpublished tabulations. 

Science

Mathematics

Science

Mathematics

Science Science Mathematics

0

5

10

15

20

25

30

35

40

45

50

Low ability

86

Average ability High ability

Heterogeneous classes

Percent of classes

 

 Homogeneous classes

93 86 93 86 93 86 93 86 93 86 93 86 93 86 93

Mathematics

During this same period, ability grouping—assigning students to specific classes such

as honors or remedial courses—in secondary science and mathematics classrooms

declined, creating a more heterogeneous environment. (See figure 14.) Whatever

may have stimulated this change, it is a move toward greater classroom equity, since

homogeneous classrooms may deprive low-achieving students of exposure to

demanding coursework and the stimulation and encouragement to achieve.

Demographic Changes 

During the past two decades, the demographic context of the U.S. educational system has evolved in ways that directly influence averages of student performance. For

example, students were more likely to be living below the poverty level in 1993 than

in 1970; the proportion of students between 6 and 17 years old living in poverty rose

from 14 percent to 20 percent during that period.

At the same time, the proportion of all parents who had received at least some college education increased from 25 percent in 1970 to 49 percent in 1993. The trend

held for white, black, and Hispanic parents, although in 1993, parents of Hispanic

students still had less education than parents of white or black students.

Additionally, the proportion of families with children younger than age 18 living

with only one parent increased from only 13 percent in 1970 to 30 percent by 1993.

Postsecondary Education

In the past, the primary purpose of secondary science and engineering education was

seen as to provide credentials to students seeking to enter the workforce in science and

engineering. Recently, this task has been augmented by the need to prepare users—

THE LEARNING CURVE 17

FIGURE 14

Ability composition of high school science and mathematics classes: 

1986 and 1993

NOTE: High school includes grades 10–12.

SOURCES: Weiss, I.R. (1987). Report of the 1985–1986 national survey of science and mathematics education. Research Triangle Park, NC: Research 

Triangle Institute; Weiss, I.R. (1994). 1993 National survey of science and mathematics education. Unpublished tabulations. 

Science

Mathematics

Science

Mathematics

Science Science Mathematics

0

5

10

15

20

25

30

35

40

45

50

Low ability

86

Average ability High ability

Heterogeneous classes

Percent of classes

 Homogeneous classes

93 86 93 86 93 86 93 86 93 86 93 86 93 86 93

Mathematics
future professionals and managers—for a

workplace transformed by scientific and

technological innovations.

As the value of postsecondary education has increased across all sectors of

the economy, the percentage of high

school students aspiring to obtain a

bachelor’s, or higher, degree has

increased dramatically, regardless of sex,

race, or ethnic origin. (See figure 15.)

During the 1980s, despite decreases in

the population of college-age youth,

the number of bachelor’s degree recipients increased markedly. The number

of science and engineering bachelor’s

degree recipients also increased,

although not as notably. However,

compared with nations such as Japan,

South Korea, and Germany, the United

1 8 HIGHLIGHTS

Mathematical sciences

Computer sciences

Physical sciences

Biological sciences

NATURAL SCIENCES

AND ENGINEERING

Business

ENGINEERING

History or political science

Education

Fine arts

SOCIAL AND

BEHAVIORAL SCIENCES

English

0 10 20 30 40 50 60 70 80 90 100

Percent of students

63

54

51

51

44

41

38

35

32

30

28

15

37

46

49

49

56

60

62

65

68

70

72

85

Moved to other group of majors Remained in same or like major

FIGURE 16

Percent of 1987 first-year undergraduate students in 4-year institutions 

who stayed in or switched to other (declared or intended) majors by 1991, 

by field of major: 1991

NOTE: Totals may not add to 100 percent as a result of rounding.

SOURCE: Seymour, E., & Hewitt, N.M. (1994). Talking about leaving: Factors contributing to high attrition rates among science, mathematics & engineering 

undergraduate majors. Final report to the Alfred P. Sloan Foundation on an ethnographic inquiry at seven institutions. Boulder, CO: University of Colorado.

 

1980 0

20

40

60

80

100

Percent of students

Graduate degree

College graduate

Two years or less of college 

or vocational

High school diploma or less

1990 1980 1990 1980 1990

White Black Hispanic

FIGURE 15

Percent of high school sophomores

 aspiring to various levels of 

postsecondary education, by race 

or ethnic origin: 1980 and 1990

SOURCES: National Center for Education Statistics. (1992). High 

school and beyond, 1980 to 1992.Washington, DC: Author; 

National Center for Education Statistics. (1992). National educational

longitudinal study of 1988: Second teacher follow-up study. 

Washington, DC: Author.

 
States graduates significantly fewer persons with first degrees in natural sciences and

engineering.

The slow growth in science and engineering degrees conferred in the United States

may be partially attributed to “major switching,” which is more prevalent for science

and engineering majors than for any other major. (See figure 16.) While 28 percent

of male and 10 percent of female high school seniors planned to major in one of the

science or engineering fields, by the time they were college seniors, only 11 percent of

males and 4 percent of females actually completed the major.

Another explanation for the slow rate of growth in science and engineering fields

may be the lack of female and minority participation. Females constituted 54 percent of all bachelor’s degree recipients in 1991, yet they earned only 44 percent of

all bachelor’s degrees in science and engineering. (See figure 17.)

Between 1971 and 1991, graduate degrees in science and engineering increased at a

faster rate than at the bachelor’s level. By 1991, doctorates in science and engineering constituted almost two-thirds of all doctorates granted in the United States.

Universities awarded about 22,000, or 39 percent, more science and engineering

master’s degrees in 1991 than in 1971 and about 4,500, or 23 percent, more science

and engineering doctoral degrees. (See figure 18.)

THE LEARNING CURVE 19

77 79 81 83 85 87 89 91

0

100,000

200,000

300,000

400,000

500,000

600,000

Number of bachelor's degrees

All bachelor's degrees

Male

Female

Male

Female

Science and engineering

bachelor's degrees

SOURCE: National Science Foundation. (1994). Science and

engineering degrees: 1966-91 (NSF 94-305). Arlington, VA: Author.

FIGURE 17

Number of bachelor's degrees 

awarded, by sex and major field 

group: 1977 to 1991

1971 1975 1979 1983 1987 1991

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

Associate

Bachelor's

Master's

Doctoral

FIGURE 18

Science and engineering degrees 

awarded, by degree level: 1971 to 1991

NOTE: Associate degree data available beginning in 1983.

SOURCE: National Science Foundation. (1994). Science and 

engineering degrees: 1966-91 (NSF 94-305). Arlington, VA: Author.

Number of degrees
Recent data reveal that equity problems prevail in the postsecondary environment as

they do in elementary and secondary education. While there has been an increase in

the number of blacks, Hispanics, and Native Americans earning bachelor’s degrees

in science and engineering, all three ethnic groups remained significantly underrepresented when compared with their presence in the total U.S. college-age population. (See figure 19.)

2 0 HIGHLIGHTS

Black

Hispanic

Native American

1977 1979 1981 1985 1987 1989 1990 1991 0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

Number of bachelor's degrees

NOTE: Persons of Hispanic origin may be of any race.

SOURCE: National Science Foundation. (1994). Science and engineering degrees, 

by race/ethnicity of recipients: 1977-91 (NSF 94-306). Arlington, VA: Author.

 

FIGURE 19

Science and engineering bachelor’s degrees awarded, 

by selected racial and ethnic groups: 1977 to 1991 

Engineering Science and 

engineering

Natural 

sciences, total

Social and

 behavioral sciences

Non-science and

-engineering, total

0

5

10

15

20

25

30

35

40

Percent

2.5

5.9

16.6 17.0 16.7 15.4

22.8 24.8

29.1

36.5

1987 1992

FIGURE 20

Percent of full-time instructional faculty who are female, 

by field: Fall 1987 and Fall 1992

SOURCE: National Center for Education Statistics. (1994b). [Special tabulations from 

the 1993 national study of postsecondary faculty]. Unpublished data.
increased markedly. Still, females

account for only about 15 percent of

faculty in the natural sciences and

only about 6 percent of engineering

faculty (see figure 20); they make up

about one-third of all higher education faculty. Black faculty members

within science and engineering fields

are similarly underrepresented. (See

figure 21.) In 1992, blacks made up

about 5 percent of all higher education faculty, but they made up only 3

percent of natural sciences faculty and

less than 3 percent in engineering.

1987 1992

Engineering

Natural sciences

Non-science and -engineering

Social and behavioral sciences

SOURCE: National Center for Education Statistics (1994). [Special 

tabulations from the 1993 national study of postsecondary faculty]. 

Unpublished data.

0

1

2

3

4

5

6

Percent

0.5

1.2

3.6

4.8

2.8

3.3

5.2 5.3
Toward The Future

Although the syntheses of available statistics presented above, along with the

abundance of additional data published in the full report, provide significant insights into the evolution of U.S. science and mathematics education

over the past two decades, many elusive questions remain. It is becoming increasingly

clear that both additional data and new types of data are needed to describe reform

and its impact. For example:

◆ While available indicators reveal encouraging trends toward greater participation in science and mathematics by elementary school students and increased

course completion and achievement by high school students, many states have

yet to match their requirements to recommended standards. What are the

obstacles, and what incentives might be needed?

◆ Since 1978, advances in performance have been observable for students of all

ages and races; yet the pace is slow and uneven. Why is this so? What practices toward achieving full equity are proving most effective? Where are they

being implemented? Why do they succeed or fail?

◆ Why do science and mathematics students in some regions of the United

States consistently perform better than students in other areas? Is there solid

empirical support for the notion that demographic factors such as family

income and level of parental education have a profound impact on student

motivation and performance?

Review of available data also shows that critical gaps in information exist with

regard to 

◆ state-level indicators measuring trends in student achievement, course taking,

and teaching methods; 

◆ data on science and mathematics course taking and content in higher education institutions; and

◆ the relationship between the planned and implemented classroom curricula.

Finally, comprehensive reports from bodies such as the National Academy of

Sciences and the RAND Corporation suggest additional areas that indicator systems

need to address, including adult literacy, resources committed by governmental and

nongovernmental bodies, and teachers’ knowledge.

NSF is taking steps to address these concerns and fill these gaps by supporting the

development of measures of adult literacy and by considering studies to collect

information on resources committed to science and mathematics education.

However, few measures of teachers’ knowledge exist in surveys of teachers. 

22 TOWARD THE FUTURE

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