1.1 The Correlates of Mathematics Coursetaking
Courses are the building blocks of schooling and the larger system of education. Linked together across school years, courses teach students knowledge and skills unique to a particular subject area and how concepts relate to other areas of the curriculum. While courses, particularly in mathematics, are the primary means through which students learn advanced subject material, not all students take the same courses and/or course sequences.
As with many indicators of educational success, coursetaking in the United States has differed with socioeconomic status. In broad terms, students from more affluent backgrounds—families with high incomes and more highly educated parents—tend to take more advanced courses than their peers (Lee et al. 1998; Stevenson, Schiller, and Schneider 1994). For example, using transcript data in NELS:88, Hoffer, Rasinski, and Moore (1995) found that students from the highest socioeconomic quartile earned an average of 3.5 Carnegie units in mathematics during high school.2 In contrast, those in the lowest socioeconomic quartile earned an average of 2.1 Carnegie units in mathematics during high school. Other analyses of NELS:88 have revealed that students from wealthy families and students with college-educated parents are most likely to enroll in an advanced mathematics course like calculus or trigonometry (Schneider, Swanson, and Riegle-Crumb 1998). Though these studies do not identify the specific mechanism linking socioeconomic status with coursework, they provide firm evidence that, on average, affluence and higher parental education translate into a curricular advantage in high school mathematics.
In addition to differences according to socioeconomic status, racial/ethnic and sex differences in education are well documented. With respect to race/ethnicity, Hispanic and Black students on average tend to lag behind their White and Asian peers in school (Kao and Thompson 2003). These broad patterns are evident in the mathematics coursetaking patterns of high school students. For example, a recent analysis of ELS:2002, the data used in this paper, showed that 87 percent of Asian and 79 percent of White high school seniors reached algebra II in high school, compared to 75 percent of Black and 67 percent of Hispanic high school seniors (Dalton et al. 2007). These disparities in coursetaking have implications for learning—a substantial portion of racial/ethnic differences in student achievement has been linked to differences in coursetaking patterns. For example, differences between Black and White students on standardized tests are minimized when comparing students who have taken advanced courses at comparable rates (Berends, Lucas, and Briggs 2002; Gamoran 1987).
While the largest differences in coursetaking are along socioeconomic and racial/ethnic lines, sex differences in mathematics are also apparent. Historically, girls have trailed behind boys in mathematics coursetaking (U.S. Department of Education 1997), and some researchers maintain that this difference explains sex differences in academic achievement among elementary and high school-aged boys and girls (Oakes 1990; Pallas and Alexander 1983). However, there is evidence that the sex gap has been closing in recent years: recent research shows that rates of mathematics coursetaking and mathematics achievement performance among high school aged boys and girls is reaching parity (Dalton et al. 2007; Perkins et al. 2004). As young women make strides in this traditionally male dominated subject area, assessing how the distribution of learning opportunities varies between the sexes is currently of interest.
Though sociodemographic characteristics have been shown to be associated with coursetaking patterns and curricular experiences, different school structures affect this relationship. Most schools in the United States follow the comprehensive high school model, wherein the curriculum remains flexible and diversified to accommodate the needs of a wide range of students with different interests, skills, and aptitudes (Oakes 1985). Not all schools follow this model. Catholic high schools, for example, tend to adhere to a constrained curriculum, offering higher level academic courses, such as intermediate and advanced mathematics, to all their students (Lee et al. 1998). Additionally, when compared with their public school peers, students who enroll in Catholic schools tend to have families who are better educated and more involved in their children's education (Coleman and Hoffer 1987; Morgan and Sorenson 1999).
Taken together, these research findings show that both background characteristics of students and the types of schools they attend are associated with their curricular experiences. Accordingly, the present analysis will explore how mathematics course sequences are distributed along these dimensions in contemporary American high schools.
2 A Carnegie unit is a standard of measurement used for secondary education that represents the completion of a course that meets one period per day for 1 year.