Chapter 1: Elementary and Secondary Education

Student Coursetaking in Mathematics and Science

Responding to calls for higher educational standards in the 1980s, many states began to increase the number of courses required for high school graduation, particularly in the core academic subjects of mathematics, science, English, and social studies, as well as in foreign language. These policies reflect widespread concern that too few U.S. students were adequately preparing for college study or self-supporting employment and that the nation's global competitive edge was threatened (National Commission on Excellence in Education 1983). Many high school graduates were also thought to lack the numeracy and literacy skills needed to make informed decisions in their adult roles as parents, citizens, and consumers (Barth 2003).

Policies requiring students to spend more time in academic courses are largely intended to push more students to complete advanced courses, which can substantially boost achievement (Adelman 1999; Campbell, Hombo, and Mazzeo 2000; Meyer 1998; Schmidt et al. 2001). Since 1987, many states have increased the number of years that students must study mathematics and science to graduate from high school (table 1-7 table.). In 1987, most states required 2 or fewer years of high school mathematics and science, whereas in 2002, 29 states required 3 or more years of mathematics and 23 states required 3 or more years of science. The remaining states either required fewer than 3 years or allowed school districts to set these policies. In states with requirements, school districts may also require students to take additional courses as well as to complete specific courses.

Curriculum reform efforts in the past 15–20 years have gone beyond time-based course requirements to setting standards for the skills and content that students need to learn. Organizations such as the National Council of Teachers of Mathematics, the American Association for the Advancement of Science, and the National Research Council began to develop content standards in the 1980s and 1990s. State education agencies have used these standards to develop their own standards and curriculum guides, and in some cases model lesson plans specific to subject and grade level. Along with aligned instructional, teacher training materials and assessments to test students' mastery of course material, curriculum standards are primary building blocks for accountability-based reform. Efforts to set curriculum standards have sought to make clear what students need to learn (and thus to make course content more consistent) and to raise the bar so that all high school graduates meet standards comparable to those in other industrialized nations (Achieve, Inc. 2004; Carnoy, Elmore, and Siskin 2003).

Standards documents vary greatly in their specificity and clarity as well as their level of rigor (Achieve, Inc. 2002; Cross et al. 2004). In addition, alignment between content standards and tests used for accountability is lacking in many states (AFT 2001; Barton 2004; Cross et al. 2004). In academic year 2004, 49 states and the District of Columbia had content standards for mathematics and science, as well as for English/language arts and social studies (Editorial Projects in Education 2005, p. 86). Many states continue to revise their standards, curriculum frameworks, and instructional materials as they gain information about their classroom use. By 2004, 31 states had set a regular timeline for reviewing and modifying their standards.

Despite these initiatives, most states do not specify the courses students must complete in all academic subjects to graduate. In mathematics, for example, 22 states do not require specific courses, and only 3 states require algebra I, geometry, and algebra II,[26] which some standards advocates consider less than the minimum needed to prepare adequately for college (Achieve, Inc. 2004). Furthermore, for most students, a significant gap currently separates high school graduation requirements from the skill levels that students need to succeed in college and to prepare for jobs that can support a family (Achieve, Inc. 2004; American Diploma Project 2004; Barth 2003).

Even some students who meet college admission requirements (which are often higher than those for high school graduation) must take remedial courses before they can earn college credits (remedial coursetaking is discussed in the "Transition to Higher Education" section). To better prepare students for postsecondary study, educators are striving to increase the rigor of high school courses and encouraging more high school students to take higher-level courses. For some students, a higher level of rigor means taking college preparatory, honors, or other advanced courses, whereas others earn college credits during high school through AP or dual-enrollment courses.

This section examines the degree to which high schools offered advanced mathematics and science courses, and the proportions of graduates who completed such courses, including trends and differences by student characteristics.[27] The section concludes with a look at recent growth in the AP program of courses and exams.

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Advanced Coursetaking in High School

Trends in Course Offerings

Curriculum and the degree of course difficulty influence both the content students learn and their level of skill development (Barth 2003; Cogan, Schmidt, and Wiley 2001). Not only has rigorous high school study been identified as the best predictor of making progress in college (Horn and Kojaku 2001) and completing a bachelor's degree, advanced mathematics study may be particularly useful in preparing students for college (Adelman 1999). Adelman found, for example, that although college degree completion rates differ substantially by racial/ethnic group, the gaps narrow considerably for college entrants who have completed advanced high school courses and are therefore well prepared.

In this section, students are described as having access to courses if the school from which they graduated offers the courses, but in practice, students usually have access only to those courses for which they can demonstrate preparation. Decision-making about which students may enroll in specific courses, particularly in mathematics, differs across schools, but in many high schools guidance counselors play a gate-keeping role and are influenced to varying extents by students, their parents, and teachers. By the time students reach high school, some courses are already closed to them, or are at least difficult to reach, because of earlier decisions and students' previous performance in courses and on tests. Sorting of students into curricular groups, or tracks, that differ in speed and depth of curriculum coverage is often done by teachers and counselors in consultation with parents starting as early as elementary school grades; these decisions and their repercussions are often difficult to change after the middle grades.

Students' access to advanced mathematics courses at their high school—specifically, to precalculus, statistics, and calculus—has increased since 1990 (figure 1-9 figure.; appendix table1-15 Excel table.) (see sidebar "Advanced Mathematics and Science Courses"). The percentage of students attending high schools that provided a statistics/probability course has more than doubled, from 24% in 1990 to 51% in 2000. On the other hand, fewer 2000 graduates attended schools offering trigonometry or algebra III courses than graduates of a decade earlier. This decrease does not necessarily mean that fewer schools taught these topics; some schools may have reconfigured courses so that rather than providing a full semester of trigonometry, they may include that material in a precalculus or other course. Overall in 2000, 93% of graduates attended schools offering at least one calculus course and 87% were offered a precalculus or analysis course.[28]

Science course offerings showed little or no trend changes over the decade, largely because the availability of these courses was already widespread. The percentage of students who were offered advanced biology courses fluctuated between 93% and 96% over the decade, and nearly all students had access to chemistry and physics courses in every year examined. Schools have increased their offerings of AP or International Baccalaureate (IB) courses in calculus, biology, chemistry, and physics since 1998, when NAEP began coding these courses separately from other advanced courses. Almost all 2000 graduates attended schools offering courses in chemistry, physics, and advanced biology; AP and IB courses were less common but still widely available. The percentage of graduates with access to AP/IB classes was 67% for biology, 57% for chemistry, and 47% for physics. About 10% of students could take a relatively new offering, AP/IB environmental science (appendix table1-16 Excel table.).

Access to Courses by School and Student Characteristics

Access to some mathematics classes differed by community type and school size. Students graduating in 2000 from urban or suburban schools, which tend to be relatively large, generally were more likely to have access to statistics/probability and calculus courses than those attending rural schools (figure 1-10 figure.). Urban and suburban schools were more than twice as likely as rural schools to offer statistics courses. Likewise, students attending small schools had less access to these mathematics courses than those attending medium or large schools, except for trigonometry and algebra III classes. Although most rural students were offered some kind of calculus (82%), an AP/IB course in calculus was far less common (45%).

No overall pattern of differential access to mathematics courses occurred by race/ethnicity (appendix table1-15 Excel table.). White students, however, were less likely than their Asian/Pacific Islander counterparts to have a statistics or AP/IB calculus course offered by their school. In addition, 47% of Hispanic students had access to a statistics course in high school, compared with 68% of their Asian/Pacific Islander peers.

Chemistry, physics, and advanced biology courses were offered nearly universally by high schools; student access to these did not differ by community type (figure 1-11 figure.). However, for AP/IB courses in those three sciences, rural students were at a disadvantage (appendix table1-16 Excel table.). For chemistry and physics, rural students were less than half as likely as those in other types of communities to have access to AP/IB courses. Small schools exhibited the same patterns for AP/IB biology, chemistry, and physics, and medium-sized schools were less likely than large schools to offer these courses. White students were less likely than Asian/Pacific Islander students to attend schools that offered AP/IB chemistry or physics.

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Courses Completed by High School Graduates

Trends in Coursetaking

High school students increased their course loads during the 1990s, both overall and in core academic courses (Perkins et al. 2004). In both mathematics and science, the highest level of coursework completed tended to correlate with students' NAEP scores in the respective subjects, which is consistent with earlier research demonstrating that most students gain proficiency by completing more high-level courses (Madigan 1997; Meyer 1998).

NAEP transcript data indicate increasing course completion in many advanced mathematics and science subjects during the 1990s[29] (figure 1-12 figure.). For example, students exhibited steady growth over the decade in studying precalculus, statistics or probability, and calculus (appendix table1-17 Excel table.). In addition, 2000 graduates were more likely than graduates in 1998 to take an AP/IB calculus course. However, participation in trigonometry or algebra III showed no notable change. Despite gains during the 1990s, the proportions of students taking these mathematics courses remained relatively modest: thirteen percent of the 2000 graduates earned credits for calculus, 20% for trigonometry and algebra III, 27% for precalculus, and 6% for statistics and probability.

In science, the proportions of graduates completing chemistry and physics courses increased over the decade, from 45% to 63% for chemistry and from 21% to 33% for physics (figure 1-12 figure.). Study in advanced biology increased over part of the decade, then leveled off (appendix table1-18 Excel table.). For the small proportion of students completing at least one course in each of three science subjects (chemistry, physics, and advanced biology), the trend climbed through 1998 to 12% and then leveled off. Few students took AP/IB courses in any of the three science subjects in either 1998 or 2000; there is insufficient evidence to conclude that their completion rates are increasing.

Coursetaking Differences by Student Characteristics

Students with different characteristics completed courses in advanced mathematics at different rates, reflecting in part their access to such courses.[30] For example, students who graduated from rural schools in 2000 were significantly less likely than others to have studied precalculus, statistics, any calculus, or AP/IB calculus. About 18% of rural graduates studied precalculus, compared with 29%–30% of urban and suburban graduates (appendix table1-17 Excel table.). Similarly, students from small schools were about half as likely as those from medium or large schools to complete an AP/IB calculus course. Students at schools with very low poverty rates (those where 5% or less of students were eligible for the free or reduced-price lunch program) were generally more likely to complete courses in precalculus, calculus, and AP/IB calculus than Students at other schools (figure 1-13 figure.). In part these differences are related to differing access; for example, very low school poverty rates were associated with a higher likelihood that students were offered AP/IB biology and chemistry courses.

Generally, although black and Hispanic students were at least as likely as students from other groups to have advanced mathematics study offered at their school, they were less likely than others to complete these courses. Hispanic graduates were less likely than white or Asian/Pacific Islander graduates to complete any of the mathematics courses shown in figure 1-13 figure., and Asian/Pacific Islander graduates were the most likely to complete each of these mathematics courses, except possibly for statistics and probability.[31] Black graduates were also less likely than their white or Asian/Pacific Islander peers to complete courses in precalculus and analysis, calculus, or AP/IB calculus, and less likely than Asian/Pacific Islanders to study statistics and probability. Except for trigonometry and algebra III, which black students studied at higher rates, black and Hispanic graduates did not differ from each other in their likelihood of taking these mathematics courses.

Males and females graduating in 2000 did not differ significantly in the percentage completing advanced mathematics courses (appendix table1-17 Excel table.) but did differ in science coursetaking (see sidebar "Mathematics and Science Coursetaking: How Do the Sexes Differ?").

Coursetaking in science also differed by some school and student characteristics. Graduates who studied chemistry, physics, or all three science subjects (chemistry, physics, and advanced biology) were less common in rural than in urban high schools. About 52% of students at rural schools completed a chemistry course, compared with 68% at urban schools, for example. Students at schools with very low poverty rates were in general the most likely to complete courses in chemistry, physics, AP/IB chemistry, AP/IB physics, or the combination of all three science subjects; appendix table1-18 Excel table.). However, advanced biology does not fit this pattern; 44% of students at schools with an intermediate poverty rate studied this subject, more than the 31–33% at schools with low or high poverty rates.

Except for advanced biology, chemistry, and AP/IB environmental science, Asian/Pacific Islander students were consistently more likely than their peers in each other group to complete science courses included in appendix table1-18 Excel table.. Hispanic students were less likely than white students to study advanced biology, physics, AP/IB physics, or the array of three subjects. In none of these science categories did Hispanic and black students differ significantly in course completion rates.

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Participation in AP Testing

The AP program provides students with an opportunity to demonstrate a high level of proficiency in a subject by passing a rigorous AP Exam. About two-thirds of public high schools offer one or more AP courses, reflecting steady growth over the years. The number of students taking AP tests also has grown rapidly, both overall and in mathematics and science subjects. (The AP test-taking data discussed in this section are actual counts collected by the College Board; they should not be confused with AP/IB course data discussed in the previous section. The latter are data estimated in the NAEP study of high school students' transcripts.) Between 1990 and 2004, for example, the number of students taking the Calculus AB exam (see sidebar "Multiple AP Courses/Tests in One Subject") nearly tripled, and the number taking Calculus BC increased almost fourfold (table 1-9 table.). The number of students taking AP science exams increased sharply as well, more than tripling for Physics C and Biology and increasing nearly fivefold for Physics B. To put this growth in perspective, the high school student population increased from 1990 to 2004 by about 24% (NCES 2004b).

Students earning a passing score on an AP Exam generally receive college credit for an introductory course in that subject, allowing them to begin at a higher level of college study, and in some cases, reducing the time needed to earn a bachelor's degree. Overall, a majority of students who take AP Exams receive a passing score, but passing rates vary by subject. The 2004 passing rates for AP mathematics and science tests ranged from 56% for chemistry to 80% for Calculus BC (table 1-9 table.). Nationally, about 13% of students graduating from high school in 2004 had passed one or more AP tests, up from 10% in 2000 (The College Board 2005). Passing rates for 2004 increased for every state and the District of Columbia over 2003.

Although the number of students taking these AP tests has increased greatly since 1990, the percentages earning passing scores have declined slightly (table 1-9 table.). For most subjects, the drop in the overall passing rate was relatively small, with the exceptions of Calculus AB and Chemistry.

Increases in the numbers of students taking AP tests from 1997 to 2004 occurred for both males and females and for all racial/ethnic groups. Gaps in the percentage of those passing the tests by sex and race/ethnicity were consistent across mathematics and sciences in 1997 and 2004: male test takers were more likely than females to pass the tests (with the single exception of Computer Science AB in 1997), as were whites and Asians/Pacific Islanders compared with blacks and Hispanics (appendix table1-19 Excel table.). Although passing rates of white and Asian/Pacific Islander students were mostly far above 50%, those for blacks and Hispanics generally ranged from 23% to 48% in 2004. The single exception was Calculus BC; 58% of blacks and 62% of Hispanics passed in 2004.

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The preceding discussion shows that high schools have increased their offerings of advanced mathematics and science courses since 1990. Students in smaller and rural schools were less likely than others to have certain courses taught at their school. High school students have responded to tighter high school graduation requirements by taking more academic courses overall; more students also completed courses in advanced mathematics and science subjects as the 1990s progressed. Nevertheless, relatively modest proportions complete any of these courses except for chemistry.

Very small proportions of students complete advanced mathematics or science courses that provide college credit (such as AP/IB courses). The most popular category among these is AP/IB calculus; even there, only 8% of 2000 graduates completed such a course. More females than males completed courses in advanced biology, AP/IB biology, and any chemistry, although males had the edge in AP/IB physics. Participation in AP test taking has grown rapidly since 1990 in all mathematics and science subjects, whereas the percentage of test takers who earn passing scores has dropped slightly in most subjects. Males were more likely than females to earn passing scores, as were Asians/Pacific Islanders and whites compared with their black and Hispanic peers.

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[26] Even in these three states, students and parents may choose a less rigorous program, but these requirements are the default. These requirements were in effect in Texas for the class of 2008 and were scheduled to begin in the near future in Arkansas and Indiana.

[27] The data on courses offered and completed are from the NAEP High School Transcript Study from 1990 to 2000. A caveat: courses are classified based on titles and content descriptions. However, material studied, methods used, and overall difficulty can differ widely across schools for courses with similar titles or in the same category.

[28] It may seem odd that the calculus courses percentage is larger than the precalculus percentage. However, although most students would be required to study precalculus or similar content to prepare for calculus, in some schools such material may be taught in a course such as trigonometry or algebra III, or even, in rare cases, in a course not included in the categories shown in the table.

[29] Coursetaking and course completion are used interchangeably in this section. The NAEP data show credits for specific courses; students earn credits by completing a course and earning a passing grade.

[30] Percentages taking courses are percentages of all graduates who had complete transcripts rather than of the subset who had access to each type of course.

[31] A single exception qualifies this statement: Asian/Pacific Islander graduates did not differ from graduates in the group classified as "other" in the likelihood of completing a statistics course.

National Science Board.