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Science and Engineering Indicators 2004
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Chapter 1:
Student Performance in Mathematics and Science
Mathematics and Science Coursework and Student Achievement
Curriculum Standards and Statewide Assessments
Curriculum and Instruction
Teacher Quality
Teacher Induction, Professional Development, and Working Conditions
Information Technology in Schools
Transition to Higher Education
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Figure 1-9

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Figure 1-10

Elementary and Secondary Education

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Mathematics and Science Coursework and Student Achievement

Advanced Mathematics and Science Courses Offered in High Schools
Advanced Mathematics and Science Coursetaking in High School

A Nation At Risk attributed the disappointing performance of U.S. students, in part, to "extensive student choice" in high school coursetaking (National Commission on Excellence in Education 1983). The report called for strengthened curricular requirements and graduation standards. In subsequent years, many states and school systems increased their graduation requirements (Blank and Engler 1992 and Clune and White 1992), including requirements for mathematics and science (figure 1-9 figure). In addition to specifying the number of courses students must complete to graduate, some states also introduced requirements for particular courses, most commonly algebra, biology, and physical sciences (CCSSO 2002).

Increases in student coursetaking in mathematics and science followed. (See sidebar "Requirements and Coursetaking.") High school graduates now earn more mathematics and science credits overall and take more advanced courses.[6] When students complete challenging courses, their overall achievement improves. (See sidebar "Coursetaking and Achievement.")

This section looks at overall coursetaking patterns with a specific look at early enrollment in algebra. It then examines patterns in advanced course offerings and in students' advanced coursetaking behavior.

Coursetaking top of page

In 1982, high school graduates earned an average of 2.6 mathematics credits and 2.2 science credits (1 credit equals 1 year of a daily 1-hour course). By 1998, those numbers grew to 3.5 and 3.2 credits, respectively (NCES 2001a). This expansion of academic coursetaking included all racial/ethnic groups and both male and female students.

The proportion of high school graduates completing advanced mathematics and science coursework also increased over this period. From 1982 to 1998, the percentage of students completing at least one advanced mathematics course (defined as more challenging than algebra II or geometry) grew from 26 to 41 percent. In science, the proportion completing at least one advanced course (defined as more challenging than general biology) increased from 35 to 62 percent.

Algebra is considered a gatekeeper course for the more advanced mathematics and science courses (Oakes et al. 1990; and Schneider, Swanson, and Riegle-Crumb 1998). Compared with their peers who do not take algebra in grade 8, students who begin studying algebra during that year are more likely to complete algebra III, trigonometry, and calculus (Atanda 1999).

NAEP data indicate that the proportion of students who take algebra early increased between 1986 and 1999 (figure 1-10 figure). In 1986, 16 percent of 13-year-olds enrolled in algebra and an additional 19 percent enrolled in prealgebra; by 1999, these figures had risen to 22 and 34 percent, respectively.

Nevertheless, a study using TIMSS data showed that about 20 percent of 1995 U.S. eighth graders attended schools that offered none of the more challenging eighth grade mathematics courses: enriched mathematics, prealgebra, algebra, or geometry (Cogan, Schmidt, and Wiley 2001). One in three eighth graders in the United States attended schools that did not offer them an algebra class. Lack of access to rigorous coursework likely has negative effects on achievement. Two measures of the difficulty of a mathematics class (time spent on various topics and combining the challenges posed by course content and textbook content) were both positively related to students’ average TIMSS assessment score in this study (Cogan, Schmidt, and Wiley 2001).

In the nation as a whole, enrollment size and concentration of minority students were both related to students' access to challenging mathematics content: more eighth graders had access to three of the more difficult mathematics courses (enriched mathematics, prealgebra, and algebra) as the size of eighth grade enrollment increased and as the percentage of minorities in the school decreased.

Advanced Mathematics and Science Courses Offered in High Schools top of page

Student coursetaking is constrained by the courses schools offer. Advanced courses are not equally available in all schools. Oakes et al. (1990) reported that as the proportion of low-income and minority students increased, the relative proportion of college preparatory and advanced courses decreased. For example, schools serving students from primarily high-income families offered approximately four times the number of sections of calculus per student as schools serving large proportions of students from low-income families.

The 1990, 1994, and 1998 NAEP assessments collected information on the courses high schools offered (appendix tables 1-8 Microsoft Excel icon and 1-9 Microsoft Excel icon). Much larger percentages of graduates attended schools that offered advanced courses compared with the proportion of graduates who actually completed these courses. For example, although 86 percent of 1998 graduates attended schools that offered calculus, only 12 percent of graduates completed it (appendix tables 1-8 Microsoft Excel icon and 1-10 Microsoft Excel icon). Compared with 1990, greater percentages of graduates in 1998 attended schools that offered precalculus/analysis, statistics/probability, and calculus.[7] Schools did not widely offer International Baccalaureate (IB) precalculus or AP statistics courses, but the majority (64 percent) of students could take AP/IB calculus courses. (The AP and IB programs provide students in participating high schools with advanced coursework across a variety of subjects, allowing them to potentially earn college credit while in high school. Starting in 1998, AP and IB coursetaking were reported separately by the National Center for Education Statistics.)

Precalculus/analysis and AP/IB calculus courses were more commonly available to students in urban and suburban than in rural schools. Course offerings in precalculus/analysis, calculus, and AP/IB calculus tended to increase as student enrollment increased. Significant differences in course offerings by school poverty level occurred only for precalculus and statistics/probability.

Advanced science courses were more widely available than advanced mathematics courses (appendix tables 1-8 Microsoft Excel icon and 1-9 Microsoft Excel icon). In 1990, 1994, and 1998, more than 90 percent of high school graduates attended schools that offered advanced biology, chemistry, and physics, or all three. High schools attended by 27 percent of 1998 graduates offered AP/IB physics, schools attended by 39 percent offered AP/IB chemistry, and schools attended by 46 percent offered AP advanced biology.

Despite an overall prevalence of advanced science offerings, availability varied by school characteristics. Students attending urban and suburban schools were more likely to be offered advanced science courses, particularly AP/IB courses compared with students in rural schools. However, there was no statistically significant difference in chemistry offerings by location or in physics offerings for students in rural schools compared with suburban ones. School size was related to offerings for all seven advanced science categories, with the likelihood of attending a school offering advanced courses rising with school size. A particularly pronounced association occurred in the AP/IB categories. In AP/IB chemistry and AP/IB physics, a link existed with school poverty, with students in low-poverty schools more likely to be offered these courses.

Advanced Mathematics and Science Coursetaking in High School top of page

In the 1990s, as more high schools offered more courses, students increased their advanced coursetaking in mathematics. (Mathematics courses considered "advanced" include trigonometry/algebra III, precalculus/analysis, statistics/probability, and calculus.) In conjunction with the 12th grade NAEP assessments, the National Center for Education Statistics collected information on courses completed by 1990, 1994, and 1998 high school graduates. In 1998 (compared with 1990), larger proportions of students completed precalculus/analysis (23 versus 14 percent), statistics/probability (4 versus 1 percent), and calculus (12 versus 7 percent) (appendix table 1-10 Microsoft Excel icon).

Only a few students completed AP/IB courses. For example, in 1998, only 6 percent of high school graduates completed an AP/IB calculus course. Male and female graduates were equally likely to have taken advanced mathematics courses in high school, including AP/IB courses. However, considerable racial/ethnic differences existed in advanced mathematics course participation. In general, Asians/Pacific Islanders were most likely to take advanced courses, followed by whites, then blacks and Hispanics; the latter two groups exhibited similar advanced coursetaking patterns (appendix table 1-10 Microsoft Excel icon).

Advanced course participation also varied by type of school attended. High school graduates from urban and suburban schools were more likely to complete precalculus and AP/IB calculus than students from rural schools, but no significant differences existed by school location for the remaining categories of advanced mathematics courses. Course participation in AP/IB calculus was higher in medium and large schools than small ones, but participation in other course categories did not differ significantly by school size. The completion of advanced mathematics courses decreased as school poverty increased for precalculus, statistics/probability, calculus, and AP/IB calculus but not for trigonometry/algebra III.

For science, increased advanced coursetaking also occurred from the beginning of the 1990s to the end of the decade (appendix table 1-11 Microsoft Excel icon). (Science courses considered "advanced" include advanced or AP/IB biology, any chemistry, and any physics.) Compared with 1990, larger proportions of 1998 high school graduates completed courses in advanced biology, chemistry, and physics. Relatively low participation in AP/IB science courses occurred in 1998, with 5 percent of graduates completing an AP/IB course in biology; 3 percent, one in chemistry; and 2 percent, one in physics.

In contrast to mathematics, sex differences existed in advanced science coursetaking. In 1998, female high school graduates were more likely than males to take advanced biology, AP/IB biology, and chemistry, although males were more likely to have completed a physics course (including an AP/IB course). For racial/ethnic groups, a pattern of participation existed similar to that for mathematics. Smaller proportions of blacks and Hispanics tended to complete advanced science courses compared with whites and Asians/Pacific Islanders.

Consistent with mathematics findings, high school graduates from urban and suburban schools were generally more likely than their counterparts from rural schools to have completed advanced science courses. A significant relationship with school size existed for AP/IB biology and AP/IB chemistry, with participation rising with enrollment. As school poverty increased, fewer students completed courses in chemistry and physics.


[6]  In drawing conclusions from transcript data, one must keep in mind the fact that courses with the same titles may vary considerably from school to school in terms of content and demand on the student.

[7]  Statistical weights are not available to generate national school estimates from the sample of high schools. Instead, student weights can be used to estimate what students were offered at their schools. This means, for example, that rather than report that urban schools offered more advanced mathematics courses, it would be reported that students attending urban schools were offered more advanced courses.

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