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Chapter 1. Elementary and Secondary Mathematics and Science Education

Transition to Higher Education

One role of high school education in the United States is to prepare students for further education. This section presents indicators of how well prepared high school graduates are, especially in math and science, to engage in postsecondary education.

Although calculating accurate high school graduation rates has been a perennial challenge, existing data indicate that less than three-quarters of students graduate from high school in 4 years. On the other hand, a small but growing number of students earn college credit during high school by passing AP tests. For those students who complete high school, this section presents indicators of their movement into postsecondary education. It begins with data on the association of students' high school mathematics and science coursetaking and achievement with their postsecondary enrollment and remediation; then it examines long-term trend data on students' immediate enrollment in postsecondary education and presents current data in the context of international rates. Together, these indicators describe high school students' preparation for and transition into postsecondary education.

High School Completion

In 2006, the national on-time high school graduation rate—the percentage of entering ninth graders who graduated 4 years later—was 73% (Stillwell and Hoffman 2008). About three-quarters of students have completed high school on time since 2003. Differences in on-time graduation rates between students in various racial/ethnic groups remain large: the graduation rate for white students was approximately 20 percentage points higher than the rates for black, Hispanic, and American Indian/Alaska Native students in 2006 (figure 1-13 ). The Asian/Pacific Islander rate was higher than that of all other groups.[20]

Some students who fail to graduate from high school on time eventually earn a high school diploma or alternative award such as a General Educational Development (GED) credential. In 2006, 88% of 18- through 24-year-olds who were not enrolled in high school, institutionalized, or incarcerated had earned a high school diploma or other credential, continuing a rising trend that began in 1980 (Laird et al. 2008).[21]

Graduation Rate Standards
NCLB requires states to set both standards for graduation rates and annual improvement targets for schools or groups not meeting the standard, but the act provides no minimum for either measure, and states' targets for this measure vary considerably. (See sidebar "Measuring High School Graduation Rates.") Nearly half the states (23) and the District of Columbia set graduation rate goals for the class of 2007 at or below 75%, and more than half of states defined their improvement targets as "any progress," or even none, as long as their rates did not decline. Thirty-six states had annual improvement targets of 0.1% or less in 2008, or less than one additional graduate per year for an average-sized high school (Alliance for Excellent Education 2008).

Since 2002, states have reported graduation rates disaggregated by racial/ethnic group, family income, disability status, and English-language proficiency. Until 2008, however, the determination of whether schools and districts have made adequate yearly progress under NCLB rested only on overall graduation rates. Regulations issued in 2008 require that, beginning in 2011–12, schools and districts must meet graduation rate goals for all subgroups to achieve adequate yearly progress.[22]

Graduation Rates in the United States and in Other OECD Nations
Difficulties in establishing precise U.S. graduation rates notwithstanding, broad comparison can be made of the United States and other OECD member countries. Among the 23 OECD countries for which graduation data were available, the United States ranked 17th in secondary school graduation rates in 2006 (OECD 2008) (figure 1-14 ).

Participation and Performance in the Advanced Placement Program

A relatively small but increasing number of secondary students take AP courses, which are designed to be equivalent to some college courses. Students who complete an AP course may take the test offered in that subject, and those who earn a passing score can earn college credits. Growth in the number of students taking AP tests was faster than growth in the number of 11th and 12th grade students: 15% of the class of 2008 earned a score of 3 or higher on at least one AP test during high school, up from 12% in the class of 2003 (College Board 2009).

The number of students taking AP tests in mathematics and science subjects has increased steadily (table 1-14 ; appendix table 1-19 ). In most subjects, this increase has been substantial, rising by at least fivefold in many subjects since 1990. The AP statistics test stands out as experiencing especially rapid growth: in 1997 slightly fewer than 7,600 students took the test, rising to more than 106,000 students in 2008. In sum, proportionately more students are taking tests, but the AP program continues to involve a relatively small proportion of high school students.

As the number of students taking AP tests has increased, so has the number passing each exam (i.e., receiving a score of 3, 4, or 5 on a scale of 1–5). Almost 250,000 students passed a mathematics AP exam in 2008, compared with a little more than 50,000 in 1990. More than 200,000 passed a science AP exam in 2008, compared with about 100,000 in 1997 and fewer than 50,000 in 1990.

While increasing numbers of students are taking and passing AP exams, passing rates have declined or remained steady in most subjects. The percentage of students passing the calculus AB, biology, and chemistry tests dropped by at least 9 points between 1990 and 2008, and in only one subject, computer science A, did the passing rate increase by more than 2 percentage points.

Generally, more students of both sexes and all racial/ethnic groups took AP tests in these subjects in 2008 than in 1997 (appendix table 1-19 ). Passing rates did not change by more than about 3 percentage points for most of these groups in most subjects.

Relationship of High School Courses Taken to Postsecondary Success

The rigor of states' academic standards and graduation requirements and student enrollment in advanced mathematics and science courses other than AP courses continue to increase.[23] The number of students taking advanced math and science courses increased on average between 1990 and 2005, although most of the gains in science leveled off after 2000 (NSB 2008). At 29%, precalculus/analysis had the highest completion rate among advanced mathematics courses; chemistry was the most commonly completed science course at 54%. Overall, state policies have shifted to increase the rigor of high school standards and improve preparation for college. Twenty states have published definitions of college readiness, and 11 more are working on such definitions (Editorial Projects in Education Research Center 2009b). In 2009, 23 states had aligned K–12 standards with college and employer expectations, up from only four in 2006, according to benchmarks established by the American Diploma Project, an initiative that promotes high expectations for high school graduates to prepare them for college (Achieve, Inc. 2009). Twenty states and the District of Columbia have raised course-taking requirements to meet standards consistent with that initiative. Nearly half of states required the class of 2008 to pass exit exams, 23 of which included math and 12 of which included science, to earn a diploma (Editorial Projects in Education Research Center 2009b). The most recent available data on courses required for high school graduation indicate that the majority of states require 3–4 math courses (36 states) and 3–4 science courses (30 states) to graduate. In addition, 26 states require specific math courses and 21 states require specific science courses. The most commonly required courses are algebra and biology. However, only a few states require advanced courses, for example, nine require algebra II (CCSSO 2009).

Taking certain high school courses, particularly advanced mathematics, is linked to postsecondary enrollment and outcomes, as many studies have shown (Adelman, Daniel, and Berkovits 2003; Horn 1997; Horn and Kojaku 2001; Horn and Nuñez 2000; Laird, Chen, and Levesque 2006; Sadler and Tai 2007). Although they do not imply causality, data from the high school class of 2004 show that the highest course students completed in mathematics and science and whether they earned advanced credits in these subjects were closely related to whether students had enrolled in a postsecondary institution by 2006 (appendix table 1-20 ). These indicators of better preparation in high school were also associated with a greater likelihood of enrolling in a 4-year program. For example, among students whose highest mathematics course was below algebra II (the lowest level, which also includes students with no high school mathematics course), 9% had enrolled in a 4-year program by 2006, compared with 83% of those who studied calculus. Among students with more than two advanced mathematics or science credits, 88% and 90%, respectively, had enrolled in a 4-year college (figure 1-15 ). High mathematics achievement was also associated with enrollment in a 4-year institution: 76% of those with scores in the highest mathematics quartile enrolled in a 4-year college, compared with 13% of students who scored in the lowest quartile.

Conversely, taking lower-level mathematics courses was associated with enrolling in a 2-year college. Among students with no advanced mathematics credits, 33% had enrolled in a 2-year college by 2006, compared with 6% of students with two or more advanced mathematics credits.

Among 2004 high school graduates who had enrolled in postsecondary education by 2006, 30% reported that they had taken a remedial course in mathematics at the postsecondary level. Students who completed advanced mathematics and science courses were less likely to undertake postsecondary remediation in mathematics.[24] More than 40% of students whose highest high school mathematics course was less advanced than algebra II reported taking remedial mathematics at the postsecondary level, compared with 17% of students who took calculus in high school. Achievement on mathematics assessments was also related to postsecondary remediation rates: 45% of those who scored in the bottom quartile of the twelfth grade mathematics test took a remedial mathematics course in college, compared with 18% of those who scored in the top quartile.[25]

Immediate Enrollment in Postsecondary Education

Most secondary students expect to attain a postsecondary degree. In 2007, 95% of eighth graders expected to attain a postsecondary education, and 70% planned to complete at least a bachelor's degree (Walston and Rathburn 2008). Not all meet these expectations, however: in 2008, 69% of students who completed high school (already a subset of all high school students) had enrolled in a postsecondary institution by the October following high school completion (appendix table 1-21 ). Wide differences in enrollment rates by family income, race/ethnicity, and parents' education persisted. In 2008, females outpaced men in immediate college enrollment 72% to 66%; most of this difference in immediate enrollment rates was accounted for by enrollment in 2-year colleges, where 31% of recently-graduated women and 25% of their male counterparts were enrolled in 2008 (figure 1-16 ).

Postsecondary Enrollment in an International Context
Only broad comparisons of postsecondary enrollment rates in the United States and other OECD countries are possible. By one measure, immediate entry rates, U.S. students ranked ninth, above the OECD average (table 1-15 ) (OECD 2009). In most OECD countries, including the United States, female enrollment rates were higher than those of males. These comparisons are complicated by differences among education systems, types of degrees awarded, and methodological issues with the measure itself.[26]


[20] There are several other widely accepted estimates of on-time graduation rates. Using the Cumulative Promotion Index, the annual Diploma's Count report reported a nationwide rate of 69.2% (Editorial Projects in Education Research Center 2009b).
[21] This measure of high school completion has its critics, however. Some believe that those who earn General Educational Development credentials should not be included with high school graduates in measures of graduation rates and also object to the base for the calculation. Because the base typically excludes incarcerated or institutionalized dropouts, critics believe this measure overestimates the high school completion rate for young people overall (Heckman and La-Fontaine 2008; Pinkus 2006; Greene 2002).
[22] Cited in Title I—Improving the Academic Achievement of the Disadvantaged, Final Rule (73 Fed. Reg. 64435 [2008]).
[23] Advanced courses referenced in this section are defined as courses that not all students complete and that are not, as a rule, required for graduation. They include trigonometry or algebra III, precalculus or analysis, statistics or probability, any calculus, AP/IB calculus, advanced biology, chemistry, physics, environmental science, engineering, and engineering or science technologies.
[24] Postsecondary transcript data are not yet available, and so information about taking remedial courses comes from student reports, which may be less accurate.
[25] While rates of remediation are lower for students who achieve on tests and take courses at the highest levels, almost one in five of those students still reports taking remedial math. In part, this may be due to a lack of alignment in academic expectations between secondary and postsecondary institutions. The Education Commission of the States (ECS) tracks states' efforts to resolve these discrepancies by means of P-16 or P-20 councils, which involve stakeholders from early childhood education through college or graduate school and work to align expectations and provide seamless transitions between levels of education (ECS 2008). As of May 2008, 38 states had established a P-16 or P-20 council, and 5 more had consolidated agencies or boards that perform essentially the same function. The scope and mission of these councils vary widely, however, and there is no nationwide indicator of their accomplishments.
[26] OECD measures of enrollment rates shown in table 1-15 are imperfect and have been criticized by some researchers in the United States and Europe (Wellman 2007; Adelman 2008; Kaiser and O'Heron 2005), who argue that the OECD methodology—dividing total tertiary enrollment by the population at the most common age of entry—penalizes countries, such as the United States, whose population is growing. They also contend that the differences between education systems and types of degrees awarded across countries make international comparisons problematic.

Science and Engineering Indicators 2010   Arlington, VA (NSB 10-01) | January 2010