Recent research shows that U.S. 15-year-olds are behind their international counterparts in problem solving and mathematics literacy, ranking 24th of 29 nations (Lemke et al. 2004). Therefore, a key concern among policy makers and educators is improving the quantitative and analytical skills of American youth, who face job prospects in an economy that increasingly values a strong foundation in mathematics and science. One policy response has been to raise mathematics coursetaking requirements for graduation. For example, between 1987 and 2004, the number of states requiring at least 2.5 credits in mathematics for graduation increased from 12 to 26 (Council of Chief State School Officers 2004). Despite the focus on overall credit requirements, less is known about particular types of courses and their relationship with learning different types of mathematics skills and concepts—a critical piece of information for those interested in preparing American students for postsecondary training and the labor market.

Using data from the Education Longitudinal Study of 2002 (ELS:2002) this report is one of the first to examine both the course sequences that students follow during the last 2 years of high school and the level of mathematics proficiency they acquire during that period. ELS:2002 is a nationally representative longitudinal study of American students who were in the 10th grade in 2002. Students, their parents, teachers, and school administrators were interviewed and mathematics assessments were administered to students in the spring of 2002. Students were reinterviewed and retested in mathematics in the spring of 2004. Their transcripts were collected in the 2004–05 school year.

In this analysis, high school transcript information and mathematics assessment scores are used to examine coursetaking patterns and learning gains across sociodemographic characteristics of students and the types of schools they attend. These coursetaking patterns are then linked with learning gains to identify the concepts and skills learned by students who follow a particular course sequence. Differences are only reported if the comparisons were statistically significant (using *t* statistics with an *alpha* criterion of .05) and met the effect size criteria (using effect sizes [standardized mean differences] that are greater than 0.20 standard deviations for continuous variables and 5 percentage points for categorical variables). Findings from regression analyses are only reported if the coefficients have a *p* value of .05 or less. The main findings are summarized below.

Over the last 2 years of high school, students improved their mathematics skills. At the end of their senior year, students gave an average of 51.2 correct answers (out of 81 possible correct answers) on the mathematics assessment, compared to an average of 46.7 correct answers during their sophomore year—a gain of about 5 correct answers (about a third of a standard deviation). Because most students (94 percent) entered the second half of high school with a mastery of basic mathematics skills such as simple arithmetic and operations, most of their learning during this time was in intermediate-level mathematics skills and concepts. Specifically, the percentage of students with an understanding of simple problem solving skills grew from 53 to 65 percentage points over the second half of high school. Students learned very little of the most advanced skills such as solving multistep word problems and applying analytic logic: 96 percent of the students in the sample left high school without proficiency at this advanced level. As with many educational outcomes, learning levels and learning gains were associated with the sociodemographic characteristics of students and the types of schools they attended. High socioeconomic status (SES) students, students who attended Catholic or other private schools, and students who expected to earn a bachelor's degree exhibited gains in the most advanced areas and showed levels of proficiency at the most advanced levels at the end of high school.

Next, student transcripts were examined to understand both the types of courses that students were taking and how they relate to learning mathematics. Course sequences were identified in terms of the types of courses taken during the 2002–03 and 2003–04 school years—the 2 academic years between the mathematics assessments. The most common mathematics sequences taken during this time period were algebra II–no mathematics, followed by 13 percent of students; geometry–geometry/no mathematics, followed by 8 percent of students; and algebra II–precalculus, followed by 7 percent of students. In accord with previous research on coursetaking patterns, the most advanced course sequences—precalculus–calculus and precalculus–Advanced Placement/International Baccalaureate calculus—were more likely to be followed by Asian and White students, high SES students, students who live with both parents in the family, students who attended Catholic schools, and students who expected to earn a bachelor's degree.

While past research has shown that more advanced courses or curricular tracks are associated with aggregate gains in learning, it has not identified the specific courses related to this growth. Toward this end, this analysis links course sequences with gains in mathematics proficiencies at different levels. The findings show that the largest overall gains are made by students who take precalculus paired with another course during the last 2 years of high school. In terms of learning in specific content areas, the largest gains in intermediate skills such as simple operations and problem solving were made by those who followed the geometry–algebra II sequence. The largest gains in advanced skills such as derivations and making inferences from algebraic expressions were made by students who took precalculus paired with another course. The smallest gains were made by students who took one mathematics course or no mathematics courses during their last 2 years.

While the findings reported here corroborate other research on the topic, readers should keep in mind that without an experimental design, establishing a causal link between coursetaking and learning is not possible. Also, ELS:2002 provides only observational data: students were not randomly assigned to schools, classrooms, course sequences, or teachers. As a consequence, establishing a causal link between coursetaking and achievement is not possible. Additionally, the analysis requires test scores at two different periods of time (sophomore and senior years), thereby excluding students who had dropped out, transferred schools, or started homeschooling.

The resulting analytic sample includes a higher proportion of students who are White, a higher proportion of students who expect to receive a bachelor's degree or higher, and a higher proportion of students living with both their father and their mother than the full sophomore panel. Thus, the findings may not generalize to all students, particularly those who are non-White, those who have educational expectations that do not include college completion, and those who are not living with their mother and father. Readers should keep these caveats in mind when interpreting the results.

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