Chapter 1: Introduction

A major focus of education policy in the United States is improving both the quality and rigor of core courses taught in schools and ensuring that all students have access to these courses. Mathematics in particular has received extensive attention, both because of its importance in an increasingly technical and global economy and because of the performance of American youth when compared with their international peers. Recent research shows that U.S. 15-year-olds continue to lag behind their international peers in mathematics—ranking 24th of 29 nations in problem solving and mathematics literacy on the 2003 Program for International Student Assessment (Lemke et al. 2004). As a means to improve proficiency in this area, many states have increased their course 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). Accordingly, contemporary students are receiving more mathematics training than their predecessors. In 2004, high school seniors left high school with an average of 3.6 credits in mathematics, up from 2.7 in 1982 (Dalton et al. 2007). Further, contemporary students are more likely to take advanced mathematics courses. For example, 6 percent of high school seniors were taking calculus in 1982. By 2004, 14 percent of high school seniors were doing so (Dalton et al. 2007).

If students are enrolling in more mathematics courses and more high-level courses, are they necessarily developing an advanced comprehension of mathematics? The existing research indicates that mathematics achievement is associated with advanced mathematics coursetaking (Leow et al. 2004; Rock, Owings, and Lee 1994; Rock and Pollack 1995a; Scott et al. 1995; Wang and Goldschmidt 2003). However, the bulk of existing research on the topic is limited in two respects: first, possibly dissimilar courses are placed into broad categories for analytic convenience; and second, the scores used to assess achievement growth preclude the identification of specific concepts and skills students are developing and/or lacking. The implications these methodological setbacks have for understanding the relationship between curricular structures and learning are discussed in turn.

First, most studies bundle courses into broad categories to make comparisons.¹ Two common methods used to assess achievement growth for those in different curricular tracks, such as an honors track, a general track, or a vocational track (Carbonaro 2005; Hallinan 1994) or to assess achievement growth for those reaching different levels of mathematics, such as calculus, algebra II, or geometry (Lee et al. 1998; Rock, Owings, and Lee 1994; Rock and Pollack 1995a; Scott et al. 1995). For example, Rock and Pollack's (1995b) analysis of the National Education Longitudinal Study of 1988 (NELS:88) found that those whose highest mathematics course was calculus gained 5.61 points between the 10th and 12th grade on the mathematics assessment. What is obscured here are the other mathematics courses the student had taken prior to calculus. While mathematics is largely hierarchical and sequential, some students may have taken precalculus prior to calculus, others may have jumped directly into calculus from algebra II, and others may have taken another advanced course (e.g., statistics, trigonometry). These different pathways may provide students with different foundational skills for learning more advanced concepts. As a consequence, the gains attributed to the highest course—in this instance, calculus—may be under- or overstated.

Second, most use an aggregate measure of mathematics achievement and consequently, overlook the content of the learning involved. For example, Rock and Pollack's finding that students who reach calculus gain 5.61 points on the NELS:88 mathematics assessment reveals little about the content of that learning. That is, are students who take calculus developing fluency in operations with real numbers, vectors, and matrices, or are they augmenting their base understanding of algebra and geometry? As most research relies on aggregated outcomes—for example, standardized composite scores or the number of correct answers on an assessment—the depth and breadth of learning and its relationship to curricular pathways is unclear. There may be differential advantages and disadvantages associated with taking a certain set of courses, and/or differential gains in learning certain mathematics skills and concepts. In most of the research, these contingencies are obscured.

This study, which uses data from the Education Longitudinal Study of 2002 (ELS:2002), improves upon past research by using information from high school transcripts to identify the exact course sequences students take and links them with achievement test scores that have been scaled to indicate different levels of mathematics proficiency. This linkage provides a more detailed understanding of the curricular pathways students travel and the types of proficiencies they acquire along the way. This chapter provides a brief background description of the pattern of mathematics coursetaking in the United States and lists the research questions. Chapter 2 describes the ELS:2002 data and the measures used in the analysis. Chapter 3 provides the results of the analysis. Chapter 4 concludes with a discussion of the findings and their limitations.

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¹ This classification approach is useful in documenting aggregate trends in coursetaking, as is in done in Dalton et al. (2007). However, it is less useful in assessing the relationship between coursetaking and achievement gains, the focus of this study.