Chapter 2:

Precollege Education

Science and Mathematics Coursetaking and Achievement

The number of courses taken in mathematics and science is an important indicator of preparation for undergraduate majors in science and engineering as well as of general scientific literacy and is, as we have seen, an important influence on mathematics and science achievement.

Women top

Mathematics Course Taking top

Female and male students are similar in completion of high school mathematics courses. More than half of both male and female high school graduates in 1994 had taken algebra II and geometry, but far fewer had taken trigonometry and calculus in high school. Nevertheless, the same percentages of male and female students had taken these advanced courses: 17 percent of male and 18 percent of female students had taken trigonometry, 9 percent of both had taken calculus, and 7 percent of both had taken advanced placement calculus. (See appendix table 2-5.)

Science Course Taking top

Male and female high school students differed only slightly in science course taking in 1994. Female students were slightly more likely than males to have taken biology and chemistry, and males were slightly more likely than females to have taken physics: 92 percent of males and 95 percent of females had taken biology, 53 percent of males and 59 percent of females had taken chemistry, and 27 percent of males and 22 percent of females had taken physics. (See appendix table 2-5.) The increases in physics course taking from 1982 to 1994 were greater for females than for males. During that period, the proportion of male high school graduates who had taken physics increased 8 percentage points (from 19 percent to 27 percent) and the proportion of females who had taken physics increased 12 percentage points (from 10 percent to 22 percent).

Mathematics and Science Achievement top

The National Assessment of Educational Progress (NAEP), funded by the National Center for Education Statistics in the U.S. Department of Education, is designed to determine the achievement levels of precollege students in a number of areas, including mathematics and science and to measure changes in achievement over time. Both mathematics and science assessments are administered periodically to students in the 4th, 8th, and 12th grades. National results are reported by NAEP for each grade level and within various subgroups (for example, males and females, racial/ethnic groups).

Mathematics top

The 1996 NAEP mathematics assessment measured mathematics performance in five content areas: number sense, properties, and operations; measurement; geometry and spatial sense; data analysis, statistics, and probability; and algebra and functions as well as mathematical abilities (conceptual understanding, procedural knowledge, and problem solving) and mathematical power (reasoning, connections, and communication). Achievement was measured on a scale ranging from 0 to 500.

Results of the 1996 mathematics assessment showed that the gender gap in mathematics achievement is narrowing. (See appendix table 2-6.) Previous NAEP mathematics assessments showed that males scored higher than females in grade 12, but in 1996, average mathematics scores for males and females in 8th and 12th grade were not significantly different. (See figure 2-3.) In 4th grade, the average mathematics assessment score for males (226) was higher than that for females (222). (See appendix table 2-7.) Although the difference is small, it is statistically significant.

Differences remain, however, in the percentages performing at the proficient and advanced levels of achievement. NAEP developed three achievement levelsóbasic, proficient, and advancedóto measure level of knowledge and skills. (See sidebar, this page.) Among 8th graders, the differences in the percentages of male and female students at each achievement level were not statistically significant. (See appendix table 2-8.) Among 4th and 12th grade students, however, higher percentages of males than females scored at the advanced level and at or above the proficient level. (See figure 2-4.)

Science top

The 1996 NAEP science assessment measured achievement on knowledge of facts, concepts, and analytical reasoning skills; abilities to explain, integrate, apply, reason about, plan, design, evaluate, and communicate scientific information; and abilities to use materials to make observations, perform investigations, evaluate experimental results, and apply problem-solving skills. Science achievement was measured on a scale ranging from 0 to 300.

Among 12th graders, female students scored lower than male students on the 1996 science assessment. (See figure 2-3.) Although the average science scores (152 for males and 148 for females) did not differ greatly, the difference is statistically significant. The differences in malesí and femalesí science scores at grades 4 and 8 are not statistically significant.

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Diversity Among Asian American High School Students top

Although Asian Americans are often treated as a single group for statistical analysis, a recent report (Kim, 1997) found many differences in educational and family background among Asian American high school seniors depending on whether they were Chinese, Filipinos, Koreans, Japanese, Southeast Asians, or South Asians.[2]  Differences were also found between native-born and foreign-born Asian Americans. Data for the report were drawn from the Second Follow-up Survey of the 1988 National Education Longitudinal Study (NELS:88).[3] 

The author of the report, Heather Kim, argues that even though stereotypes of Asian Americans may be largely favorable, they still can be harmful. For example, because there is a widespread belief that Asian Americans are strong academically, there may not be sufficient effort to provide help for those groups of Asian Americans that are less highly educated. She states, "The myth of them all being educational high achievers has kept many from needed student services and support."

In some respects, the six groups of Asian Americans were fairly similar to one another. Nearly all believed that getting a good education was important in their lives. Three-fourths or more of the parents expected their child to earn a college degree or higher.

Parents of South Asian students had the highest occupational status and educational expectations for their children of any of the groups. The South Asian students themselves tended to have the highest educational aspirations, to be more involved in extracurricular activities, and to perform the best on the National Assessment of Educational Progress (NAEP) standardized tests in reading and (to a lesser degree) mathematics. By contrast, the parents of Southeast Asians were the least likely to have a college education and had the lowest occupational status on average. The Southeast Asian students tended to have the lowest educational aspirations, to be least likely to participate in extracurricular activities, and to receive the lowest scores on the NAEP standardized tests.

Native-born seniors tended to have greater educational advantages than foreign-born seniors. Their parents generally had achieved higher educational levels and higher status occupations. Native-born seniors on average spent more time on extracurricular activities than foreign-born seniors but less time on homework. Native-born seniors did better on the NAEP standardized test on reading, but about the same as their foreign-born peers on mathematics.

The ethnicity of Asian Americans and their likelihood of being native born are interrelated. Chinese immigration started earliest (about 1840), followed by the Japanese (between 1890 and 1920), and Korean (about 1903). Thus, among these groups one can expect to find substantial groups of native-born students. By contrast, Southeast Asians are more likely than other groups to be foreign born.

Aside from her use of the NELS data, Kim also cites other statistics concerning the disadvantages facing some Asian ethnic groups. These include high school dropout rates around 50 percent for schools with high concentrations of Southeast Asians and high dropout rates for Filipinos (46 percent) and Samoans (60 percent) in 1992. The median family income in 1990 for all Asian Americans was $41,241 but only $14,327 for Hmongs, $18,126 for Cambodians, and $23,101 for Laotians.

The NELS data are subject to relatively high standard errors because of the small sample sizes for these groups (for example, the total number of Asian Americans was 961, with only 70 Japanese and 97 South Asians in the sample) and clustering can be expected to increase the size of the standard errors further. (For example, many of the Japanese students may attend just a small number of the sampled schools.) Thus, the data are illuminating, but should not be considered definitive estimates. The groups of native-born and foreign-born Asian Americans were roughly equal in size, so the sample size is less of an issue for that portion of the analysis (though clustering remains an issue).

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NAEP Achievement Levels top

Basic levelódenotes partial mastery of the knowledge and skills that are fundamental for proficient work at a given grade.

Proficient levelórepresents solid academic performance. Students reaching this level demonstrate competency with a range of challenging subject matter.

Advanced levelósignifies superior performance at a given grade.

These performance levels are cumulativeóstudents performing at the advanced or proficient levels also perform at the immediately preceding levels.

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The International Gender Gap in
Mathematics and Science Achievement top

The United States is one of many nations worldwide in which the gender gap in mathematics and science achievement has virtually disappeared (Peak, 1997). No statistically significant difference was found between the mathematics scores of 8th grade boys and girls in 33 nations, including the United States, that participated in the Third International Mathematics and Science Study (TIMSS).[4]  Further, no statistically significant difference was found between the science scores of 8th grade boys and girls in 11 nations, including the United States, that participated in TIMSS. The 11 nations with no statistically significant gender differences in 8th grade mathematics and science scores were Australia, Columbia, Cyprus, Flemish Belgium, Ireland, Romania, the Russian Federation, Singapore, South Africa, and the United States.

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Gender Differences in Attitudes Toward Science and Mathematics top

Attitudes toward science and mathematics both reflect and reinforce achievement in these subjects. Those who do well tend to like science and mathematics, and those who like these subjects tend to have higher levels of achievement in them. It is not that surprising then that femalesí and malesí attitudes toward science and mathematics are similar given that their achievement levels are becoming more similar. Results from the 1995 TIMSS study show that for the most part, female and male students in 4th grade and in 8th grade were similar in their attitudes toward science and mathematics.

Among 4th graders in the United States and in many countries, little difference was found in malesí and femalesí self-perceptions of doing well in mathematics (Mullis et al., 1997). Among 8th graders, females and males were about equally likely to like mathematics (Beaton et al., 1996b). In several countries, however, (Austria, France, Germany, Hong Kong, Japan, Norway, and Switzerland) males were more likely to like mathematics than were females. In Ireland, a greater percentage of females than males liked mathematics.

Similarly, among 4th and 8th graders, males and females in most countries that participated in the study (including the United States) did not differ significantly in self-perceptions of doing well in science or in liking science. In Austria, Japan, and Korea, however, a greater percentage of male than female 4th graders liked science, and in Iceland and Ireland a greater percentage of females than males liked science (Martin et al., 1997). Some differences were apparent by subject area, however. Eighth grade males and females differed little in liking of biological science or earth science, but male students in most countries were more likely to like physical science than were females (Beaton et al., 1996a).


Minorities top

Mathematics Course Taking top

Although substantial differences in course taking by racial/ethnic groups remain, the percentages of black, Hispanic, and American Indian students taking many basic and advanced mathematics courses have doubled between 1982 and 1994. For example, in 1982, 22 percent of black high school graduates had taken algebra II. By 1994, 44 percent had taken this course. (See figure 2-5.) Similarly, 29 percent of black high school graduates in 1982 had taken geometry, 6 percent had taken trigonometry, and 1 percent had taken calculus. By 1992, these percentages had increased to 58 percent, 14 percent, and 4 percent, respectively. (See appendix table 2-9.)

Despite the gains, racial/ethnic groups differ greatly in mathematics course taking. Black and Hispanic high school graduates in 1994 were more likely than white and Asian students to have taken remedial mathematics courses: 31 percent of black, 24 percent of Hispanic, and 35 percent of American Indian high school graduates, compared with about 15 percent of whites and Asians had taken remedial mathematics in high school. Black and Hispanic high school graduates in 1994 were less likely than white and Asian students to have taken advanced mathematics courses. Although more than 60 percent of both white and Asian students had taken algebra II, 44 percent of blacks, 51 percent of Hispanics, and 39 percent of American Indians had taken this course. Asians were the most likely of any racial/ethnic group to have taken advanced mathematics courses. Almost one-third of Asians had taken precalculus and 23 percent had taken calculus. By contrast, 18 percent of white, 10 percent of black, 14 percent of Hispanic, and 9 percent of American Indians had taken precalculus and less than 10 percent of any of these groups had taken calculus. (See appendix table 2-9.)

Science Course Taking top

As is the case with mathematics course taking, blacks, Hispanics, and American Indians are taking more science classes than they took in the past. The percentage of blacks and Hispanics taking chemistry and physics doubled between 1982 and 1994. In 1982, 22 percent of black, 16 percent of Hispanic, and 26 percent of American Indian high school graduates had taken chemistry. By 1994, this had increased to 44 percent, 46 percent, and 41 percent respectively. In 1982, approximately 7 percent each of blacks, Hispanics, and American Indians had taken physics; by 1994, 15 percent of blacks, 16 percent of Hispanics, and 10 percent of American Indians had taken physics. (See appendix table 2-9.)

Despite these gains, the percentage of black, Hispanic, and American Indian students taking chemistry and physics is below the percentage of white and Asian students taking these courses. Fifty-eight percent of white and 69 percent of Asian high school graduates in 1992 had taken chemistry, and 26 percent of white and 42 percent of Asian students had taken physics.

Mathematics and Science Achievement top

Mathematics top

Average mathematics scores have increased for all racial/ethnic groups since 1990, but differences between the scores of white students and black and Hispanic students have not significantly narrowed. For example, among 12th graders in 1990, the average difference between white studentsí mathematics scores and those of black students was 33 points. In 1996, it was 31 points. (See appendix table 2-7.) The average difference between 12th grade white studentsí mathematics scores and those of Hispanic students was 25 points in 1990; in 1996, it was 24 points. Differences are as great among 4th graders. In 1996, the average gap in mathematics scores between white and black 4th graders was 32 points, and the average gap between white and Hispanic 4th graders was 26 points.

Differences by race/ethnicity also existed in the percentages performing at proficient levels in mathematics. Among 4th, 8th, and 12th grade students, more than 20 percent of white students and less than 10 percent of black, Hispanic, and American Indian students scored at or above the proficient level. (See appendix table 2-8.) Half, or more than half, of black and Hispanic students at all three grade levels scored below the basic proficiency level in mathematics compared with about one-fourth of white students. (See figure 2-6.)

Science top

As with mathematics scores, differences in science scores persist across racial/ethnic groups. Scores for white, Asian, and American Indian students are substantially higher than those for black and Hispanic students in grades 4, 8, and 12.[5]  (See figure 2-7.) Among 12th graders in 1996, average science scores were 159 for whites, 149 for Asians, 145 for American Indians, 130 for Hispanics, and 124 for blacks.

Students With Disabilities top

Variations in Estimates of the Number of Students With Disabilities top

Determining the number of students with disabilities is challenging given variations in age ranges of the population, in definitions, in data collection procedures, and in the individual reporting the disability (for example, student, parent, teacher, school official) (Rossi, Herting, and Wolman, 1997). For differences in prevalence and classification from various sources, see text table 2-1.

According to the Department of Educationís Office of Special Education and Rehabilitative Services, the percentage of children enrolled in school and between the ages of 6 and 17 who were served in Federally supported special education programs was 10 percent in 1994–1995.[6]  [7]  [8]  Eight percent of all children ages 6 through 21 were served in these programs. Fifty-one percent of the children age 6 through 21 with disabilities had specific learning disabilities, and another 21 percent had speech or language impairments. (See appendix table 2-10.) About 12 percent were mentally retarded, 9 percent had a serious emotional disturbance, 2 percent had "other" health impairments, and 1 percent each had mobility or hearing impairments. Visual impairments, autism, deaf-blindness, and traumatic brain injury each accounted for less than 1 percent of the students with disabilities.

Students participating in Federal programs for children with disabilities have been increasing both in number and as a fraction of total public school enrollment. Between 1977 and 1995, the number of students who participated in Federal programs for children with disabilities increased 47 percent, from 3.7 million to 5.4 million students. Part of this growth is due to an increase in the number of students identified with specific learning disabilities. Students with specific learning disabilities increased from approximately 800,000 students or 2 percent of total public K–12 enrollment in 1977 to 2.5 million students or 6 percent of total public K–12 enrollment in 1995. The number of students with other types of disabilities (with the exception of students with serious emotional disturbance) went down during that time period (U.S. Department of Education, 1997).

Students with disabilities made up 11 percent of students in grade 4, 9 percent of students in grade 8, and 5 percent of students in grade 12 in 1996 (Reese et al., 1997). These students take fewer science and mathematics courses, have lower grades, and have lower achievement scores than students without disabilities.

Mathematics and Science Course Taking top

Twelfth-grade students with disabilities[9]  earned fewer credits in mathematics in 1992 than did those without disabilities. (See appendix table 2-11.) Differences are not great by type of disability. Students with disabilities also earned fewer science credits than those without disabilities. (See appendix table 2-11.)

Mathematics and Science Achievement top

Students with disabilities have lower average high school grades in mathematics and in science than those without disabilities. (See appendix table 2-11.)

Twelfth grade students with disabilities scored lower than those without disabilities on standardized cognitive tests of mathematics proficiency[10]  and had less gain in scores from 1988 to 1992 than students without disabilities. Students with disabilities were more likely than those without disabilities to score in the lowest proficiency levels on these tests. (See appendix table 2-12.) Students with multiple disabilities and students with learning disabilities scored at the lowest performance levels. Students identified as having health problems had 1992 proficiency scores similar to students without disabilities and had gains in proficiency from 1988 to 1992 similar to those without disabilities.

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Federal Definitions of Special Education
Disability Categories top

Specific learning disability. A disorder in one or more of the basic psychological processes involved in understanding or using language, spoken or written, which may manifest itself in an imperfect ability to listen, think, speak, write, spell, or do mathematical calculations; this includes perceptual handicaps, brain injury, minimal brain dysfunction, dyslexia, and developmental aphasia, but does not include learning problems resulting from visual, hearing, or motor handicaps, or from mental retardation.

Seriously emotionally disturbed. Exhibition of behavior disorders over a long period of time that adversely affect educational performance; this includes an inability to learn that cannot be explained by intellectual, sensory, or health factors; an inability to build or maintain satisfactory interpersonal relationships with peers and teachers; inappropriate types of behaviors or feelings under normal circumstances; a general pervasive mood of unhappiness or depression; or a tendency to develop physical symptoms or fears associated with personal or school problems.

Speech impaired. Communication disorders, such as stuttering, impaired articulation, and language or voice impairments, that adversely affect educational performance.

Mentally retarded. Significantly subaverage general intellectual functioning with concurrent deficits in adaptive behavior that were manifested in the development period and that adversely affect educational performance.

Visually impaired. A visual impairment that, even with correction, adversely affects educational performance, including students who are partially sighted or completely blinded.

Hard of hearing. A hearing impairment, permanent or fluctuating, that adversely affects educational performance but that is not included in the deaf category.

Deaf. A hearing impairment that is so severe that the child is impaired in processing linguistic information through hearing, with or without amplification, which adversely affects educational performance.

Orthopedically impaired. A severe orthopedic impairment that adversely affects educational performance, including those caused by congenital anomaly, disease, or other causes.

Other health impaired. Limited strength, vitality, or alertness due to chronic or acute health problems that adversely affect educational performance (includes autistic students).

Multiply handicapped. Concomitant impairments, the combination of which causes such severe educational problems that they cannot be accommodated in special education programs solely for one of the impairments (does not include deaf/blind).

Deaf/blind. Concomitant hearing and visual impairments, the combination of which causes such severe communication and other developmental and educational problems that they cannot be accommodated in special education programs solely for deaf or blind students.

SOURCE: U.S. Department of Education, Office of Special Education Programs. 1991. Youth With Disabilities: How Are They Doing? The First Comprehensive Report from the National Longitudinal Transition Study of Special Educational Students. Menlo Park, CA: SRI International, pp. 2–3.

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Increasing the Inclusion of Students With Disabilities
in Science and Mathematics Assessments top

Students with disabilities were often excluded from the National Assessment of Educational Progress (NAEP) in the past because State and local policies often excluded them from testing, school staff may have believed they were unable to participate fully, and no accommodations were available that met the needs of their legally required Individualized Education Plans. Half or more than half of students with disabilities were excluded from NAEP assessments before 1995.

The 1996 NAEP science and mathematics assessment explored the effects of various mechanisms to increase the participation of students with disabilities in the national assessments. Exclusion or inclusion rules were changed to be clearer, rules were more inclusive and more likely to be applied consistently, and accommodations were provided, including "provision of large-print booklets and large-face calculators, provision of Braille booklets and talking calculators, and accommodations in administration procedures (e.g., unlimited testing time, individual or small-group administrations, allowing a facilitator to read directions, allowing students to give answers orally, allowing students to give answers using a special mechanical apparatus)" (Olson and Goldstein, 1996, p. 5).

Before these modifications can be implemented as official policy, several statistical and measurement issues need to be addressed. One of the issues to be addressed is the effect of accommodations or adaptations on measurement of trends in achievement. Inclusion of additional students and improved testing of students with disabilities who have in the past been assessed under standard conditions complicates the interpretation of trend results. Another issue is the comparability of results of students included and assessed with accommodations to those from other students. The special sample design developed for the 1996 NAEP assessment will allow these issues to be examined.


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[2] Southeast Asians include Vietnamese, Laotian, Cambodian/Kampuchean, and Thai. South Asians include Asian Indian, Pakistani, Bangladeshi, and Sri Lankan.

[3] The Second Follow-Up Survey of the 1988 National Education Longitudinal Study of 1988 (NELS:88) was conducted in 1992 by the National Opinion Research Center (NORC) at the University of Chicago for the National Center for Education Statistics, U.S. Department of Education.

[4] TIMSS was a study of science and mathematics knowledge in 41 nations during the 1995 school year.

[5] An accurate determination of the standard error associated with the average scale score for 12th grade American Indian students was not possible; therefore differences between this group and other groups at grade 12 should be interpreted with caution.

[6] It should be noted that not all children with impairments require special education.

[7] The data collected by the Office of Special Education and Rehabilitative Services are the only data collected specifically to provide counts of students eligible to receive services.

[8] The Individuals with Disabilities Education Act (IDEA), Part B, requires that "all children and youth with disabilities have access to a free appropriate public education that is determined on an individual basis and designed to meet their unique needs" (Barbett and Korb, 1997).

[9] Students were identified by their parents as being disabled. The source of these data is the National Center for Education Statistics, National Education Longitudinal Study, 1988.

[10] These tests were administered to all NELS:88 student participants in 1992. The most severely disabled students were excluded from this survey.

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