Profiling coursework patterns in mathematics: Grades 8 to 12.

Interest in student coursework, especially in mathematics and science, has been rapidly increasing over the past decade, because the emerging global economy requires new generations to become more knowledgeable in mathematics and science and more skillful in mathematical and scientific thinking. It has become apparent that students who do not have adequate education in mathematics and science during their high school years can be disadvantaged in their career options. This escalating need to acquire more knowledge and skills in mathematics is consistent with the finding that mathematics coursework of high school students is a powerful indicator of educational aspiration and college performance in general and mathematics proficiency and achievement in particular (e.g., Bryk, Lee, & Smith, 1990; Medrich, 1996; National Center for Education Statistics, 1995; Rock, Owings, & Lee, 1994; Shakrani, 1996).

Traditionally, students in mathematics are classified into four categories: mathematics concentrators, four-year college bound mathematics students, general mathematics students, and non-participants (see West, Miller & Diodato, 1985). Students in the first two categories are considered college preparatory mathematics students who earn two or more credits from college preparatory mathematics courses in addition to credits in general and vocational mathematics courses. Students in the last two categories are considered non-college preparatory mathematics students who earn less than two credits from college preparatory mathematics courses. There is strong evidence that in recent years, high school students, especially college bound students, who take more advanced mathematics courses perform significantly better in the mathematics tests of the American College Testing (ACT) and the Scholastic Aptitude Test (SAT) (College Entrance Examination Board, 2000; National Center for Education Statistics, 1994; Rock et al., 1994; Shakrani, 1996).

A number of studies have examined mathematics coursework as a function of student (individual) and school (institutional) characteristics. The Longitudinal Study of American Youth (LSAY) is so far the best national education database to address this functional relationship, covering mathematics coursework in the entire secondary school years (Grades 7 to 12). Although the LSAY contains measures of both student and school characteristics, the current study focused on the relationship between mathematics coursework and student characteristics, given the lack of significant school effects on mathematics coursework in the LSAY (Ma & Willms, 1999) and the lack of sufficient measures on mathematics curriculum and instruction (in particular course-offering) in the LSAY.

Students' gender and socioeconomic status (SES) are often the focus of research in the examination of mathematics coursework. A decade ago, differences between males and females in mathematics achievement were found to be negligible during the elementary grades, noticeable during the intermediate grades, and pronounced during the high school grades (e.g., Crosswhite, Dossey, Swafford, McKnight, & Cooney, 1985; Ethington & Wolfle, 1984; Fennema, 1984; Leder, 1985; Peterson & Fennema, 1985). However, during the last decade, gender differences in mathematics have undergone dramatic changes. The gap in mathematics achievement between males and females has been decreasing dramatically and even reversed in favor of females (e.g., Beller & Gafni, 1996; Manger, 1995; National Assessment of Educational Progress, 1997; Tartre & Fennema, 1995). Recent meta-analytic reviews show that gender differences in mathematics achievement are either small (Friedman, 1996; Frost, Hyde, & Fennema, 1994) or declining over time (Hyde, Fennema, & Lamon, 1990). The decline in the gender gap in mathematics achievement appears not only in mathematics as a whole but also in various mathematical areas (see Battista, 1990; Ethington, 1990).

A similar phenomenon has also been observed in mathematics coursework. Gender differences in mathematics coursework have been decreasing gradually to the extent that they bear little practical importance. In the past, differences in mathematics coursework between males and females became evident during the high school years when females were less prepared mathematically than males (e.g., Kaufman, 1990; Marion & Coladarci, 1993; Noble & McNabb, 1989). For example, Lee and Ware (1986) found that females took fewer mathematics courses, were less persistent in transition from course to course, and were more likely to leave college preparatory mathematics sequences. In general, males spent more semesters in mathematics coursework than females, and more males than females engaged in advanced or accelerated mathematics courses (Doolittle, 1985). These differences occur even when males and females share equal achievement scores and classroom grades (Friedman, 1989).

Findings from more recent years, however, indicate a changing pattern. Males and females differ significantly in neither the number nor the type of mathematics courses they complete (Hoffer, Raksinski, & Moore, 1995). In fact, females have made greater gains in mathematics coursework than their male peers between 1987 and 1996 (McLure, Boatwright, McClanahan, & McLure, 1998). The College Entrance Examination Board (1996, 1997, 1998, 1999, 2000) has consistently reported that among students taking SAT, a higher percentage of females than males complete such courses as algebra, geometry, trigonometry, and pre-calculus (whereas males outnumber females in computer-related mathematics courses). In addition, McLure (1998) found that while females increase the number of mathematics courses they take, their ACT scores increase as well (more than do males).

Although other researchers continued to report gender differences in mathematics coursework, they did indicate that gender differences appear mainly in the later grades of high school. Thus, gender differences are much less widespread than before. For example, using data from the LSAY, Ma (1997) reported that gender differences in mathematics coursework are significant only in Grade 12 in favor of males. Rates of course-taking in mathematics are equivalent between males and females in algebra I, algebra II, and trigonometry, and are in favor of males only in the most advanced mathematics courses such as calculus (Blank & Dalkilic, 1990; O'Sullivan, Weiss, & Askew, 1998).

Another important phenomenon regarding gender differences in mathematics coursework is that the variation in mathematics coursework is larger among males than females. More males take both the most advanced and the least advanced mathematics courses, while more females take the moderately advanced mathematics courses (Blank & Engler, 1992). Data from the High School Transcript Study (HSTS) and the National Education Longitudinal Study (NELS) both indicate a similar pattern (Davenport, Davison, Kuang, Ding, Kim, & Kwak, 1998; Rock & Pollack, 1995).

Mathematics coursework is also related to students' SES. This relationship emerges as early as Grades 6 or 7. West et al. (1985) reported that, among students in the mathematics concentrator category, 17% were from high SES class, and 2% were from low SES class. Among students in the four-year college bound category, 52% were high SES students, and 23% were low SES students. Conversely, low SES students dominated the general mathematics and non-participant category. In addition, low SES students were also underrepresented among the mathematics concentrator and four-year college bound categories, relative to their number in the student population. Middle SES students were slightly underrepresented in the mathematics concentrator category, but students from high SES class were significantly over-represented in the same category (West et al., 1985).

Ma (1997) found that SES is particularly influential on mathematics coursework in the early grades of high school. Useem (1990) reported a high correlation between parents' SES and students' placement in mathematics groups in Grades 6 and 7. Students in the lowest level group are more likely to come from single-parent and low-income families. Hoffer et al. (1995) provided evidence that there is considerable impact of SES on high school coursework, which subsequently results in significant differences between students coming from lower and higher income families in college completion and attendance (see also Pelavin & Kane, 1990). In general, low SES students are less likely to take advanced mathematics courses, attend college, and obtain a university degree. Although students from low SES families are making some gains recently in the number of advanced mathematics courses, their gains are not as much as gains of students coming from middle and high SES families (McLure et al., 1998).

In addition to gender and SES, prior mathematics achievement has been found to be another significant predictor of mathematics coursework. Rock et al. (1994) reported that students who are classified as being proficient in mathematics are more likely to take high-level mathematics courses (i.e., geometry, algebra II, trigonometry, and pre-calculus) than their peers who are classified as being low achieving. Ma (1997) found that prior mathematics achievement is the only variable that has significant effects on mathematics coursework in every grade level from 7 to 12. Lee, Burkam, Chow-Hoy, Smerdon, and Goverdt (1998) concluded that students' completing high level of mathematics courses is strongly associated with their prior mathematics achievement (see also Secada, 1992).

Although inadequate attention has been paid to the interaction between gender, SES, and aspects of mathematics learning (achievement and coursework),

some recent empirical work is relevant to the purpose of the current study. Supported with results from national data such as the NELS and the National Assessment of Educational Progress (NAEP), Tate (1997) described current gender trends as very small differences in mathematics achievement, and he attributed the slightly higher performance of males over females to differential coursework patterns. Meanwhile, Tate (1997) described current socioeconomic trends as strongly in favor of students from high SES. There is an urgent need to raise the mathematics achievement of students from low SES, and in line with Hoffer et al. (1995), Tate (1997) suggested that a potential mechanism for intervention is course-taking.

Some researchers do perceive the linkage between gender difference in mathematics achievement and the socioeconomic and cultural environment in which students live, either in school or at home, as being critical (e.g., Atweh & Cooper, 1995; Byrnes, Hong, & Xing, 1997; Carr, Jessup, & Fuller, 1999). As discussed above, the importance of the interaction between gender, SES, mathematics achievement, and mathematics coursework has been recognized. Tate (1997) concluded that

  One cannot predict differences in mathematics performance on the basis
of gender. Other factors must be considered, such as prior socialization
and expectations. (p. 667)

Tate (1997) did point out, however, that SES has been "rarely examined in relationship to gender achievement" (p. 667). In addition, the literature is sparse in longitudinal studies of mathematics coursework. Without longitudinal data, it is not possible to yield differential patterns of mathematics coursework (see Willett & Singer, 1991). The purpose of the current study was to use longitudinal data (which cover the entire secondary grades) to investigate mathematics coursework patterns of students classified based on gender and SES (which is an avenue to examine in detail interactive effects between gender and SES on mathematics coursework) with control over prior mathematics achievement.

Method

Data

The Longitudinal Study of American Youth (LSAY) is a national, six-year (Grades 7 through 12) panel study of mathematics and science education in public middle and high schools in the United States (see Miller & Hoffer, 1994). Two groups of public schools participated in the LSAY. One was a national probability sample of 52 schools, and the other was a special sample of 8 schools in school districts with outstanding elementary science programs. The LSAY started in the fall of 1987 with samples of about 60 seventh graders (referred to as cohort 2), and 60 tenth graders (referred to as cohort 1), from each of sixty localities across the United States. The 7th and 10th graders were both followed for six years. The current study employed the cohort 2 data which cover Grades 7 to 12. The sample contained a total of 3,116 students.

Variables

The current study attempted to profile mathematics coursework for each group of students classified according to their major background characteristics, gender and SES. Student gender was based on students' reports, and the LSAY staff checked this variable against the students' first names with miscodings being corrected. Parental SES was a composite variable based on parents' reports of their education and occupation, and students' reports of household possessions. The 30th and 70th percentiles were used as the "cutoff" points to categorize SES into three levels. Students with SES below the 30th percentile were defined as coming from low SES families; students with SES from the 30th to 70th percentile (inclusive) were defined as coming from middle SES families; and students with SES above the 70th percentile were defined as coming from high SES families. Students, therefore, were classified into 6 groups on the basis of gender (male and female) and SES (low, middle, and high).

Prior mathematics achievements was used as a major control variable. Prior mathematics achievement referred to student mathematics achievement one year before the year of interest. For example, when examining mathematics coursework in Grade 10, one takes mathematics achievement in Grade 9 as prior mathematics achievement. Note that measures of mathematics achievement described three skill dimensions with 60 items: simple recall and recognition, routine problem-solving, and complex problem-solving. The reliabilities of mathematics achievement tests were 0.86, 0.91, 0.92, 0.94, 0.95, and 0.95 from Grades 7 to 12 respectively. Test scores are actually formula scores that have been adjusted for difficulty, reliability, and guessing, on the basis of item response theory (IRT). As a result, test scores can be compared across test forms and grade levels.

Measures of mathematics coursework were derived from the LSAY composite variable measuring the highest mathematics course that each student took in each grade. Each composite variable included all the possible courses that students could take as their most advanced course in that grade. These courses (covering Grades 8 to 12) included low Grade 8 mathematics, average Grade 8 mathematics, basic mathematics, vocational mathematics, consumer mathematics, NEC mathematics, geometry (including honors), prealgebra, algebra I (including honors), algebra II (including honors), trigonometry (including honors), analytic geometry (pre-calculus), and calculus. Following Hoffer (1997), a number of dummy variables were created from the composite variable with the category "no course" as the reference.

Statistical Procedures

Logistic regression analysis was used to estimate the probability that students in a particular group would take a certain mathematics course in a particular grade. A series of logistic regressions were performed for each group in each grade, one for each mathematics course. In each logistic regression, participation in a mathematics course was the dependent variable, and gender, SES, and prior mathematics achievement were the independent variables. For example, in the 8th grade, one equation regressed a coursework variable, say, pre-algebra, on gender, SES, and prior (Grade 7) mathematics achievement. The purpose was to estimate the probability of students in a particular group taking pre-algebra conditional on gender, SES, and prior mathematics achievement.

Prior mathematics achievement was used as the major control variable. With this variable in the equation, the probability of taking a certain mathematics course was adjusted for prior mathematics achievement. Such a probability became the "adjusted" measure of mathematics coursework. This study also presented the "absolute" measure of mathematics coursework obtained without prior mathematics achievement in the logistic regression. The difference between these two measures might indicate the potential increase in probability associated with changes in student mathematics achievement. This difference was also an indicator of the importance of prior mathematics achievement in taking each mathematics course.

Statistical comparisons were not carried out in a systematic way in the current study, because it contained a large number of pairs of measures that could be contrasted. In cases where comparisons (e.g., gender differences and socioeconomic differences) can lead to important theoretical and practical implications, tests of statistical significance were performed. Pairs of probabilities contrasted between adjusted and absolute measures of mathematics coursework, between male and female measures of mathematics coursework, and between measures of mathematics coursework of students in different socioeconomic groups were compared for statistical significance at the alpha level of 0.05, using statistical procedure for testing difference between proportions (see Glass & Hopkins, 1996).

Results

The current study classified students into 6 groups based on two categories on gender (male and female) and three categories on SES (low, middle, and high). Figures 1 to 6 contain data that show mathematics coursework patterns for the 6 groups of students. Numbers in each figure indicate the probability that a student would take a certain mathematics course. Bold numbers are adjusted measures, whereas regular numbers are absolute measures. Probabilities less than 0.10 (both adjusted and absolute) are considered trivial and not presented in the figures.

Figure 1 contains information that shows the mathematics coursework pattern for male students from low SES. In Grade 8, students were 15% likely to take low Grade 8 mathematics. In contrast to this adjusted probability, the absolute probability was 26%. That is, if the effect of prior mathematics achievement was controlled, students were 26% likely to take low Grade 8 mathematics. Prior mathematics achievement had a significant effect on taking low Grade 8 mathematics. In addition, students were 19% likely to take average Grade 8 mathematics and 41% likely to take pre-algebra. The effects of prior mathematics achievement were insignificant on these courses (5% and 1% difference in probability respectively). Students were 41% likely to take algebra I in Grade 9. Similar to Grade 8, the effects of prior mathematics achievement were significant on relatively low mathematics courses.

In Grade 10, the priority courses were algebra I and geometry (53% in total probability). Again, significant effects of prior mathematics achievement were on relatively low mathematics courses (11% vs. 5% difference in probability for basic mathematics vs. algebra I). The priority courses were algebra II and geometry in Grade 11 (41% in total probability). Once more, prior mathematics achievement was significant for relatively low mathematics courses (6% vs. 1% difference in probability for algebra I vs. algebra II). Some students concentrated on analytic geometry and algebra II in Grade 12 (roughly 10% in probability on each), but prior mathematics achievement was not a significant consideration among these students when they took these courses.

Figure 2 contains information that shows the mathematics coursework pattern for female students from low SES families. The female pattern is quite similar to the male pattern (as shown in Figure 1) in Grades 8 to 11. Similar interpretation applies, therefore, including the effect of prior mathematics achievement. The difference is that female students from low SES never went beyond algebra II. Their participation in mathematics was quite inactive in Grade 12.

Figure 3 contains information that shows the mathematics coursework pattern for male students from middle SES families. The balance is certainly heavier on the side of advanced mathematics coursework. Students were not likely to engage in lowest mathematics courses in Grades 8 and 9, and students concentrated on no courses lower than geometry since Grade 10. Specifically, students were 46% likely to take pre-algebra in Grade 8 and 47% likely to take algebra I in Grade 9. In Grade 10, while students continued to catch up with algebra I (24% in probability), some were taking geometry (30% in probability). The priority courses were algebra II and geometry (44% in total probability) in Grade 11 and analytic geometry and algebra II (24% in total probability) in Grade 12. The effect of prior mathematics achievement was insignificant in Grades 8 to 10 (no more than 4% difference in probability). Prior mathematics achievement was significant in effect, however, on most advanced mathematics courses in Grades 11 and 12 (6% difference in probability for analytic geometry in Grade 11 and 8% difference in probability for calculus in Grade 12).

Figure 4 contains information that depicts the mathematics coursework pattern for female students from middle SES families. In comparison to Figure 3, female students were less likely to take both low (i.e., low Grade 8 mathematics) and advanced (i.e., algebra I) mathematics courses in Grade 8. The female pattern is similar to the male pattern (see Figure 3) in Grades 9 to 11. Female students did not show any potential to take calculus in Grade 12. Prior mathematics achievement did not seem to be a significant consideration when female students from middle SES made their decision on mathematics courses (no more than 5% difference in probability).

Figure 5 contains information that describes the mathematics coursework pattern for male students from high SES families. In terms of low mathematics courses, students were 12% likely to take average Grade 8 mathematics in Grade 8. Students had concentrated on no courses lower than geometry since Grade 9. In terms of advanced mathematics courses, students were 49% likely to take pre-algebra in Grade 8, and the absolute measures of advanced mathematics coursework add up to 70% in probability in Grade 8. Students were 53% likely to take algebra I in Grade 9. In Grade 10, students were 25% likely to take algebra II (including honors). The absolute measures of advanced mathematics coursework add up to 52% in probability in Grade 11 and 43% in probability in Grade 12. Figure 5 also contains data that illustrates well the significant effect of prior mathematics achievement on advanced mathematics courses: 12% difference in probability for algebra I in the 8th grade; 7% difference in probability for both algebra II honors and algebra II in the 10th grade; 7% difference in probability for both algebra II honors and algebra II in the 10th grade; 7% difference in probability for analytic geometry in the 11th grade; and 17% difference in probability for calculus in the 12th grade. Therefore, prior performance in mathematics seems to be decisive for male students from high SES to take advanced mathematics courses.

Figure 6 contains information that illustrates the mathematics coursework pattern for female students from high SES families. The female pattern very much resembles the male pattern (see Figure 5). The probabilities for female participation in advanced mathematics courses are basically compatible to those from Figure 5, except that the female probability was 10% (significantly) higher on advanced mathematics courses in Grade 10 than the male one (25% for males and 35% for females) and 10% (significantly) lower on advanced mathematics courses in Grade 12 than the male one (43% for males and 33% females). Prior mathematics achievement did not seem as important for females as for males. But still, the effect of prior mathematics achievement was significant (11% difference in probability for algebra I in Grade 8, analytic geometry in Grade 11, and calculus in Grade 12; as well as 6% difference in probability for algebra II in Grade 10). Therefore, prior mathematics achievement seems also decisive for female students from high SES to participate in advanced mathematics.

Logistic regression models were examined for model-data-fit using overall percentage of correct prediction in the current study. The cut point was 0.50. Students with estimated probabilities larger than 0.50 for a particular course were classified as taking that course, whereas students with estimated probabilities smaller than 0.50 for a particular course were classified as not taking that course. Most logistic regression models had overall percentage of correct prediction above 70%. A common problem with these models was underestimation. These models displayed a general tendency to misclassify students who took a certain course as not taking that course. Therefore, estimated probabilities as shown in the above figures were somewhat conservative for mathematics participation.

Discussion

Summaries and Contributions

The current study profiled mathematics coursework patterns for students in 6 groups cross-classified by gender and SES (see Figures 1 to 6). In each figure, the upper boundary shows the highest possible courses students took. For students from low SES families, male and female lower boundaries are quite similar not only in shape but also in magnitude. The upper boundaries are also commensurate up to Grade 11. Gender differences appeared mainly in Grade 12 in favor of males. These students (both males and females) from low SES families seem to weight their prior performance in mathematics when making decisions about taking low mathematics courses such as low Grade 8 mathematics and basic mathematics. Overall, this socioeconomic group as a whole signals problems--students from low SES had mathematics preparation lower than the level of algebra II. The upward trend of the upper boundary is greatly downgraded by the sharply decreasing probabilities.

Students from middle SES families showed more evident gender differences than those from low SES families. The lower boundary is in favor of female students, indicating that males are more likely than females to engage in low mathematics coursework. On the other hand, the upper boundary is in favor of male students, indicating that males are also more likely than females to engage in advanced mathematics coursework. This is similar to the phenomenon that has been described in Davenport et al. (1988). The current study, however, suggests that this phenomenon depends on students SES. Only did students from middle SES demonstrate this phenomenon in the current study.

Gender differences appeared mainly in the first and last grades of high school for students from middle SES. In Grade 8, more males engaged in low Grade 8 mathematics, whereas most females taking low mathematics courses concentrated on average Grade 8 mathematics. In Grade 12, males from middle SES showed potential to take calculus, whereas females did not show any potential of taking calculus. Overall, prior mathematics achievement was not significantly associated with whether to take mathematics courses. The only exception is the significant effect of prior mathematics achievement on males taking calculus (8% difference in probability). This socioeconomic group as a whole also signals concerns. Students had mathematics preparation only up to the level of algebra II. Similar to students from low SES, the upward trend of the upper boundary is seriously compromised by the sharply decreasing probabilities.

For students from high SES families, male and female lower boundaries resemble each other closely both in shape and in magnitude. The upper boundaries are different between males and females. A potential to take algebra II honors in Grade 10 was observed for males but not females. Major gender differences, however, appeared in the last grade of high school, not in terms of shape but in terms of magnitude. The potential figures in advanced mathematics coursework are certainly in favor of males. For this socioeconomic group as a whole, the adjusted measures cannot be described as promising. Students had mathematics preparation up to the level of algebra II. But the absolute measures do signal hope. Potentially, males may have mathematics preparation up to pre-calculus and calculus, but the potential is lower for females. Prior mathematics achievement appeared to be quite significant for both males and females to take advanced mathematics courses.

The current study, therefore, has illustrated a very interesting phenomenon on gender differences in mathematics coursework. In each SES group, gender differences are actually small, if one considers the adjusted measures of mathematics coursework. This conclusion is in line with the current trend of trivial gender differences in mathematics coursework (e.g., College Entrance Examination Board, 1996,1997,1998,1999,2000; McLure, 1998; Tate, 1997). Males and females are quite different, however, in the absolute measures of mathematics coursework. Across SES groups, males consistently show higher potential than females to engage in advanced mathematics coursework. These findings, to some degree, also support the significance of gender differences in mathematics coursework (e.g., Bae & Smith, 1997; Kaufman, 1990; Marion & Coladarci, 1993). Therefore, the current study illustrates the complexity of gender differences that has not been fully discussed in the literature--gender differences are small in mathematics coursework, but the potentials are substantially different between males and females.

The gender equity in mathematics coursework as shown in the current study is positive. Tate (1997) insisted that "course taking was a powerful variable, often resulting in similar achievement gains across diverse groups" (p. 652). The potential gender differences can be overcome by increasing graduation requirements on mathematics (see Ma, 1997). The gender equity in mathematics coursework is likely to create a good foundation for the gender equity in mathematics achievement (Hoffer et al., 1995; Rock & Pollack, 1995; Tate, 1997).

In comparison to gender differences in mathematics coursework, socioeconomic differences are far more evident. The lower boundaries are different across SES groups (for both males and females) in favor of students from high SES. The upper boundaries are also different with that for students from low SES standing out more evidently. These conclusions extend the current trend of socioeconomic differences in mathematics achievement (Tate, 1997)--there are also socioeconomic differences in mathematics coursework. Such a socioeconomic gap in mathematics coursework is negative to the effort of raising the mathematics achievement of low SES students through intervention on their mathematics course-taking (Hoffer et al., 1995; Tate, 1997).

Compared with the small gender gap and the gradually narrowing racial-ethnic gap, the socioeconomic gap appears much more enduring in both mathematics achievement (see Tate, 1997) and mathematics coursework. As advocated in Hoffer et al. (1995) and Tate (1997), special attentions need to be paid to the mathematics coursework of low SES students which is very negative in the current study. Again, increasing graduation requirements on mathematics may channel low SES students into more mathematics coursework. A word of caution is that increasing graduation requirements on mathematics has to be done properly to have positive effects on mathematics achievement (see Hoffer, 1997).

Prior mathematics achievement does not seem to be able to narrow down either gender differences or socioeconomic differences in mathematics coursework, particularly in advanced mathematics coursework. This limited function of mathematics achievement in promoting gender and socioeconomic equities in mathematics coursework has rarely been discussed in the literature. It also signals a need to examine other essential factors, such as student affective characteristics (e.g., attitude toward mathematics, anxiety toward mathematics, and mathematics self-concept) and school characteristics (e.g., discipline climate, academic expectation, and parental involvement) that may help promote gender and socioeconomic equities in mathematics coursework.

Limitations and Remedies

Given that the last data collection in the LSAY was in 1992, the current study may be more of historical than contemporary interest to mathematics educators. Still, the LSAY is the best and most comprehensive database so far available to study mathematics education with sufficient information covering the entire secondary school years. The mathematics coursework patterns provide some useful working knowledge to current mathematics educators. Furthermore, to overcome the difficulty in using a relatively dated database, we also attempted to link our results with the contemporary trends of gender and socioeconomic differences in mathematics coursework.

SES was categorized into groups in the current study for the purpose of creating profiles in mathematics coursework. There is, of course, the loss of information when a continuous variable is turned into a categorical one. We are less concerned about this in our particular case, because there are abundant research studies using SES as a continuous variable. The significant socioeconomic gap in mathematics achievement and mathematics coursework is well known in other words (see, for example, Tate, 1997 for a review). What lacks in the literature is sufficient analyses of mathematics coursework within specific SES categories (low, middle, and high).

The other methodological concern is the lack of prior mathematics coursework in the model. The use of indicators of prior mathematics courses tends to create a clumsy model where gender differences are often pushed aside in the presence of a large number of coursework indicators. Given the high correlation between prior mathematics achievement and prior mathematics coursework, we used prior mathematics achievement as the control variable (which is also an important explanatory variable in itself). However, with efficient research designs, future researchers may explore this idea of including indicators of prior mathematics courses.

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Ma, X. (1997). A national assessment of mathematics participation in the United States: A survival analysis model describing students' academic careers. Lewiston, NY: Edwin Mellen.

Max, X., & Willms, J.D. (1999). Dropping out of advanced mathematics: How much do students and schools contribute to the problem? Educational Evaluation and Policy Analysis, 21, 365-383.

Manger, T. (1995). Gender differences in mathematical achievement at the Norwegian elementary-school level. Scandinavian Journal of Educational Research, 39, 257-269.

Marion, S.F., & Coladarci, T. (1993, April). Gender differences in science course-taking patterns among college undergraduates. Paper presented at the annual meeting of the American Educational Research Association. Atlanta.

McLure, G.T. (1998). High school mathematics course taking and achievement among college-bound students: 1987-1996. NASSP Bulletin, 82, 110-118.

McLure, G.T., Boatwright, M., McClanahan, R., & McLure, J.W. (1998, April). Trends in high school Mathematics course taking and achievement by gender, race/ethnicity, and class, 1987-1997. Paper presented at the annual meeting of the American Educational Research Association. San Diego.

Medrich, E. (1996). Preparation for work. (Rep. No. NCES-97-373). Washington, DC: U.S. Department of Education.

Miller, J.C., & Hoffer, T.B. (1994). Longitudinal Study of American Youth: Overview of study design and data resources. DeKalb, IL: Social Science Research Institute, Northern Illinois University.

National Assessment of Educational Progress. (1997). NAEP 1996 mathematics report card for the nation and the states. Washington, DC: National Center for Education Statistics.

National Center for Education Statistics. (1995). High school students ten years after "A nation at risk". (Rep. No. NCES-95-764). Washington, DC: U.S. Department of Education.

National Center for Education Statistics. (1994). Mathematics and Science course taking patterns. Indicator of the month. (Rep. No. NCES-94-672). Washington, DC: U.S. Department of Education.

Noble, J.P., & McNabb, T. (1989). Differential coursework and grades in high school: Implications for performance on the ACT assessment. Iowa City, IA: American College Testing Program.

O'Sullivan, C.Y., Weiss, A.R., & Askew, J.M. (1998). Students learning science: A report on policies and practices in U.S. schools. (Rep. No. NCES-98-493). Washington, DC: U.S. Department of Education.

Pelavin, S.H., & Kane, M. (1990). Changing the odds: Factors increasing access to college. New York: College Board Publications.

Peterson, P., & Fennema, E. (1985). Effective teaching, student engagement in classroom activities, and gender-related differences in learning mathematics. American Educational Research Journal, 22, 309-335.

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Xin Mia

Joanna T. Tomkowicz

University of Alberta

                             Grade 8     Grade 9     Grade 10

Calculus
Analytic geometry
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II
Algebra I honors
Algebra I                                0.41  0.38  0.28  0.33
Pre-algebra                  0.41  0.42  0.16  0.20
Honors geometry
Geometry                                             0.25  0.22
Mathematics (NEC)
Consumer mathematics                                 0.06  0.10
Vocational mathematics
Basic mathematics                        0.18  0.31  0.04  0.15
Average Grade 8 mathematics  0.19  0.24
Low Grade 8 mathematics      0.15  0.26

                             Grade 11    Grade 12

Calculus
Analytic geometry                        0.10  0.10
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                   0.22  0.21  0.11  0.13
Algebra I honors
Algebra I                    0.11  0.17
Pre-algebra
Honors geometry
Geometry                     0.19  0.20
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics
Average Grade 8 mathematics
Low Grade 8 mathematics

Figure 1. Mathematics coursework pattern for male students from low
socioeconomic status (group size is 436). Numbers indicate the
probability of a student taking a certain mathematics course, or the
proportion of students in this particular group who take a certain
mathematics course. The bold numbers have been adjusted for prior
mathematics achievement, whereas the regular numbers have not.
Probabilities or proportions that are less than 0.10 in both situations
(adjusted and unadjusted) are deemed as trivial and not presented in the
figure.

                             Grade 8     Grade 9     Grade 10

Calculus
Analytic geometry
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II
Algebra I honors
Algebra I                                0.43  0.41  0.28  0.32
Pre-algebra                  0.44  0.44  0.19  0.20
Honors geometry
Geometry                                             0.29  0.26
Mathematics (NEC)
Consumer mathematics                                 0.06  0.10
Vocational mathematics
Basic mathematics                        0.18  0.26  0.05  0.11
Average Grade 8 mathematics  0.23  0.26
Low Grade 8 mathematics      0.11  0.17

                             Grade 11    Grade 12

Calculus
Analytic geometry
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                   0.23  0.22  0.09  0.10
Algebra I honors
Algebra I                    0.10  0.13
Pre-algebra
Honors geometry
Geometry
Mathematics (NEC)            0.20  0.21
Consumer mathematics
Vocational mathematics
Basic mathematics
Average Grade 8 mathematics
Low Grade 8 mathematics

Figure 2. Mathematics coursework pattem for female students from low
socioeconomic status (group size is 351). Numbers indicate the
probability of a student taking a certain mathematics course, or the
proportion of students in this particular group who take a certain
mathematics course. The bold numbers have been adjusted for prior
mathematics achievement, whereas the regular numbers have not.
Probabilities or proportions that are less than 0.10 in both situations
(adjusted and unadjusted) are deemed as trivial and not presented in the
figure.

                             Grade 8     Grade 9     Grade 10

Calculus
Analytic geometry
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                                           0.08  0.10
Algebra I honors
Algebra I                    0.06  0.10  0.47  0.46  0.24  0.27
Pre-algebra                  0.46  0.45  0.11  0.13
Honors geometry
Geometry                                             0.30  0.29
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics                        0.12  0.17
Average Grade 8 mathematics  0.15  0.17
Low Grade 8 mathematics      0.10  0.14

                             Grade 11    Grade 12

Calculus                                 0.03  0.11
Analytic geometry            0.04  0.10  0.13  0.14
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                   0.27  0.27  0.11  0.13
Algebra I honors
Algebra I                    0.09  0.12
Pre-algebra
Honors geometry
Geometry                     0.17  0.17
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics
Average Grade 8 mathematics
Low Grade 8 mathematics

Figure 3. Mathematics coursework pattern for male students from middle
socioeconomic status (group size is 741). Numbers indicate the
probability of a student taking a certain mathematics course, or the
proportion of students in this particular group who take a certain
mathematics course. The bold numbers have been adjusted for prior
mathematics achievement, whereas the regular numbers have not.
Probabilities or proportions that are less than 0.10 in both situations
(adjusted and unadjusted) are deemed as trivial and not presented in the
figure.

                             Grade 8     Grade 9     Grade 10

Calculus
Analytic geometry
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                                           0.08  0.11
Algebra I honors
Algebra I                                0.49  0.48  0.23  0.26
Pre-algebra                  0.48  0.48  0.13  0.13
Honors geometry
Geometry                                             0.34  0.33
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics                        0.12  0.14
Average Grade 8 mathematics  0.18  0.18
Low Grade 8 mathematics

                             Grade 11    Grade 12

Calculus
Analytic geometry            0.05  0.10  0.12  0.12
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                   0.28  0.28  0.09  0.10
Algebra I honors
Algebra I
Pre-algebra
Honors geometry
Geometry                     0.17  0.18
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics
Average Grade 8 mathematics
Low Grade 8 mathematics

Figure 4. Mathematics coursework pattern for female students from middle
socioeconomic status (group size is 746). Numbers indicate the
probability of a student taking a certain mathematics course, or the
proportion of students in this particular group who take a certain
mathematics course. The bold numbers have been adjusted for prior
mathematics achievement, whereas the regular numbers have not.
Probabilities or proportions that are less than 0.10 in both situations
(adjusted and unadjusted) are deemed as trivial and not presented in the
figure.

                             Grade 8     Grade 9     Grade 10

Calculus
Analytic geometry
Trigonometry honors
Trigonometry
Algebra II honors                                    0.03  0.10
Algebra II                                           0.08  0.15
Algebra I honors
Algebra I                    0.08  0.20  0.53  0.54  0.19  0.20
Pre-algebra                  0.49  0.50
Honors geometry
Geometry                                 0.04  0.13  0.36  0.37
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics
Average Grade 8 mathematics  0.12  0.11
Low Grade 8 mathematics

                             Grade 11    Grade 12

Calculus                                 0.05  0.23
Analytic geometry            0.05  0.18  0.16  0.20
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                   0.32  0.34  0.11  0.13
Algebra I honors
Algebra I
Pre-algebra
Honors geometry
Geometry                     0.15  0.14
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics
Average Grade 8 mathematics
Low Grade 8 mathematics

Figure 5. Mathematics coursework pattern for male students from high
socioeconomic starus (group size is 436). Numbers indicate the
probability of a student taking a certain mathematics course, or the
proportion of students in this particular group who take a certain
mathematics course. The bold numbers have been adjusted for prior
mathematics achievement. whereas the regular numbers have not
Probabilities or proportions that are less than 0.10 in both situations
(adjusted and unadjusted) are deemed as trivial and not presented in the
figure.

                             Grade 8     Grade 9     Grade 10

Calculus
Analytic geometry
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                                           0.09  0.15
Algebra I honors
Algebra I                    0.08  0.19  0.56  0.57  0.19  0.20
Pre-algebra                  0.51  0.52
Honors geometry
Geometry                                 0.04  0.13  0.40  0.42
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics
Average Grade 8 mathematics  0.14  0.12
Low Grade 8 mathematics

                             Grade 11    Grade 12

Calculus                                 0.05  0.16
Analytic geometry            0.06  0.17  0.15  0.17
Trigonometry honors
Trigonometry
Algebra II honors
Algebra II                   0.34  0.36  0.09  0.10
Algebra I honors
Algebra I
Pre-algebra
Honors geometry
Geometry                     0.15  0.14
Mathematics (NEC)
Consumer mathematics
Vocational mathematics
Basic mathematics
Average Grade 8 mathematics
Low Grade 8 mathematics

Figure 6. Mathematics coursework pattern for female students from high
socioeconomic status (group size is 386). Numbers indicate the
probability of a student taking a certain mathematics course, or the
proportion of students in this particular group who take a certain
mathematics course. The bold numbers have been adjusted for prior
mathematics achievement, whereas the regular numbers have not.
Probabilities or proportions that are less than 0.10 in both situations
(adjusted and unadjusted) are deemed as trivial and not presented in the
figure.