V. WHO TAKES COLLEGE-PREP? FINDINGS FROM
STUDENT TRANSCRIPTS

• THE BIG PICTURE: A SIMILAR OVERALL PATTERN OF ENGLISH AND MATH COURSETAKING
• TRACKING STUDENTS: WHERE DO THEY FALL?
• THE COLLEGE-PREP TRACK: WHO GAINS ACCESS?
• WHICH CHARACTERISTICS PREDICT COLLEGE-PREP PARTICIPATION?
• CONCLUSIONS

In this section, we describe the participation of Coolidge, Washington, and McKinley students in academic courses that prepare them for college. Here we focus on mathematics and English, since these courses signal whether a student is college-bound. As in the previous section, we find patterns of placement and coursetaking that differ across the three schools and for different groups of students within them. Here, too, we find a general pattern--one of less than perfect matches among students' prior academic performance and their placement in college-bound or non-college-bound classes. Some, but not all, of this variation relates to race and social class.

THE BIG PICTURE: A SIMILAR OVERALL PATTERN OF ENGLISH AND MATH COURSETAKING

The combined course offerings in English, mathematics, social studies, and science represented the same fraction (about 58 percent) of the total course offerings at each of the three schools in the Fall of 1988.[54] The three schools offer a similar array of mathematics courses, ranging from basic math to calculus.[55]

In contrast, the English course offerings vary substantially between McKinley, which has no English courses beyond the general, integrated English courses at each grade level, and Coolidge and Washington, which each have a variety of more specialized English electives. Despite these differences in the course offerings, all three schools require four years of English, one year beyond the state requirements. However, Coolidge and Washington require only two years of mathematics, the state requirement, and McKinley requires three.

The average number of mathematics courses taken by the students at the three schools was quite similar. Table 5.1 shows the average number of mathematics and English credits taken by students at each school, and the average share of students' total credits that were taken in mathematics and English.[56] Despite the different math requirements at each school, students took an average of 33 credits in mathematics, representing about 14 percent of their total credits. Thus, even though students at Coolidge and Washington were required to take only two years of math (the equivalent of 20 credits), the average student took over three years of math by the time he or she completed high school.

Although the three schools had the same English requirements, there are significant differences in the total amount of English credits taken and the share of total credits in English. Students at McKinley took an average of 37 English credits, slightly less than four years (40 credits), representing 16 percent of their total credits.

In contrast, students at Coolidge and Washington took an average of five to seven more credits, representing a larger fraction of their total credits (about 18 percent). Thus, a number of students at these two schools were taking more than the required four years. Despite the strong emphasis on academic coursetaking at McKinley reported during our interviews at the school, students there took fewer English courses than their counterparts at Coolidge and Washington.

TRACKING STUDENTS: WHERE DO THEY FALL?

Even when the overall amount of English and mathematics coursetaking is fairly similar among schools, there are potential differences in students' experiences in terms of the "ability level" or "track" that they are placed in (see, for example, Oakes, 1985; Oakes et al., 1990). Despite differences in the number of levels of courses in various subjects at the three schools, each school grouped students by ability, for example, by classifying courses generally as college-prep and non-college-prep, and more specifically as honors or AP courses within the college-prep category.[57]

To examine students' track placements in mathematics and English, we classified each school's courses into five track or level designations for English: ESL, low, mixed, high, and honors; and four track designations for math: low, medium, high, and honors.[58] Individual English courses were classified on the basis of the "track" or level explicit or implicit in the schools' printed course descriptions and student handbooks, and additional information provided by counselors and teachers in our interviews with them. These track or level classifications, based upon the specific system used in each school, allow comparisons across schools in the structure of the course offerings. However, because of differences in the degree to which students are separated by ability across the three schools, these classifications proved most useful for comparing the lower and higher tracks.[59]

The track designations for math are based on responses from school personnel to our questions concerning the ability levels of students who take various courses and their likely postsecondary destinations. These tracks or levels are also based on the sequencing and timing of courses, rather than simply on the requisite level of ability within a particular course. Thus, the academic or high mathematics track entails taking algebra 1 in 9th grade, geometry in 10th grade, algebra 2 in 11th grade, and trigonometry/math analysis in 12th grade. Students classified in the more advanced or honors math track take the same sequence starting with algebra 1 in 8th grade, and finishing with calculus in 12th grade.[60] Alternatively, students in the "average" or medium track begin with pre-algebra courses in 9th grade, follow with algebra 1 in 10th grade or later, and take algebra 2 in 12th grade at the earliest, if at all. Students in the low track initially take basic or remedial math courses and do not advance beyond pre-algebra courses in later years.

We used this classification scheme to examine English and math coursetaking behavior in two ways. Initially, we examined the distribution of students across the tracks at several points during their high school career. Tables 5.2 and 5.3 show student track placement by school and grade in math and English for the first semester in grades 10, 11, and 12.[61] As seen in Table 5.2, 90 to 95 percent of students in 10th grade at all three schools were taking some mathematics. Students at McKinley were concentrated in the low and medium tracks, whereas the majority of students at Coolidge and Washington were in the medium and high tracks. The highest participation in the honors tracks was at Washington with 18 percent, the lowest at McKinley with 6 percent.

Over time, participation in the honors track in math is relatively constant at Washington and McKinley, but it dropped precipitously at Coolidge by the 12th grade. At McKinley, there was movement throughout the three years out of the low track and into the medium track.

This probably represents efforts at McKinley to have all students take a college-prep curriculum, even if it takes longer for them to get there. Our data provide some evidence that these efforts pay off, as these students were more likely to be exposed to more advanced math classes. In contrast, the movement at the other two schools was out of all tracks and into non-participation. By 12th grade, almost half of the students at Coolidge and Washington were no longer taking a math course, whereas only one fourth of those at McKinley were in the same category.

Similarly, almost all students were taking an English course in 10th grade (93 to 97 percent). The four-year English requirement at the three schools meant that the overall participation rate remained relatively constant over time.

Yet there was a great deal of fluctuation across tracks and schools over time. Some of this fluctuation may reflect the idiosyncrasies of the tracking system at each school. For example, our Washington respondents told us that English classes at that school are largely untracked in 9th and 10th grade; most students not in ESL or honors English take English 1 and English 2 during those years. Consequently, in Table 5.3 we find that nearly 70 percent of Washington 10th graders are in the medium track. In the junior year, however, Washington students had more English alternatives. Non-college-bound students were gen-erally placed in English 3 or in one or two other "watered down" electives, whereas high achievers can select from a variety of faster-paced courses.[62]

Table 5.3 displays this increased stratification for 11th and 12th graders.[63]

THE COLLEGE-PREP TRACK: WHO GAINS ACCESS?

Given our interest in various groups of students' access to and participation in college-preparatory and vocational curriculum, we examined the characteristics of students who were in the high or honors English and math track at a particular point in time. In this way, we could more closely identify those factors associated with students' placements within a school and the differences in those factors across the three schools. For math, we defined the college-prep group as those students who took algebra 2 in their junior year or earlier.[64] Students in college-prep English were those taking a college-prep or honors/AP level English course in the 11th grade. Again, we have selected this point in the math and English curriculum to signal those students who were likely to be college-bound. Consequently, we refer to these students as taking "college-prep" math or English.

Tables 5.4 and 5.5 show the participation in college-prep math and English for all students and for different groups of students at each school. Participation in college-prep math in the 11th grade ranged from 22 percent of the students at McKinley to 45 percent of Washington students, more than a twofold difference. Coolidge lies between the two schools with 33 percent of the 11th grade students in our sample in college-prep math. These differences are consistent with the differences perceived by school personnel at the three schools about stu-dents' abilities and their post-high school aspirations. Thus, Washington may offer more college-prep math to meet the perceived needs and the demands of students and their parents for a more academic curriculum.

Participation in college-prep English was higher than in college-prep math at all three schools, with almost half of all students taking college-prep English in the 11th grade. This higher rate of participation was probably due to the higher English requirement. The comparable rate of participation in college-prep English across all three schools contrasts with the substantial differences observed for college-prep math.[65] When we disaggregate the data on these two tables by student characteristics, however, several interesting patterns emerge.

Table 5.4 shows that there is no statistically significant difference in participation in college-prep math by girls and boys within each school. However, significant differences exist at both Coolidge and Washington in participation rates by race or ethnicity. Most notably, the participation rate for Asian students was over 70 percent at the two schools; Latino students participated at a much lower rate than average. In contrast, African American and Latino students at McKinley participated at the same rate in college-prep math. The existence of differences by race or ethnicity at Coolidge and Washington, but not at McKinley, is consistent with the data presented in Sec. II showing significantly higher mathematics test scores for Asian students at Coolidge and Washington, but no differences for African American and Latino students at McKinley. Thus, differences in group rates of participation may be related to differences in mathematics interest and academic achievement. This relationship will be explored below.

Girls at all three schools participated at a higher rate than boys in college-prep English. The differences displayed in Table 5.5 are striking; more than 10 percentage points separate participation rates for girls and boys at each school. There are also clear differences in the participation of students from different racial and ethnic groups in college-prep English. At Coolidge, the pattern is similar to that for math participation; Asians participated at the highest rate and Latinos at the lowest. The same pattern holds for Washington and McKinley, although the differences in participation rates by race or ethnicity are not significant at these two schools (despite the fact that reading scores at the two schools do differ by race or ethnicity, as discussed in Sec. II).

Tables 5.4 and 5.5 also demonstrate a dichotomy at the three schools between students taking college-prep math and English and those taking a large number of vocational courses (six or more). At each school students who were classified as vocational concentrators were far less likely than non-concentrators to be enrolled in college-prep math and English. For example, only 4 percent of vocational concentrators at Coolidge took college-prep math, whereas non-concentrators were more than ten times as likely to be in the college-bound track. A similar sharp difference exists as well for college-prep English. This division is consistent with the perception by teachers at Coolidge that students taking vocational courses are less likely to be in the "fast" track academic courses. Because of Washington's practical arts requirement, the contrast between participation in college-prep courses is not as stark there as at Coolidge, yet a large and statistically significant higher rate of participation still exists between vocational non-concentrators and concentrators. This same differential pattern of participation characterizes students at McKinley as well. However, although the difference between concentrators and non-concentrators at McKinley is nonetheless significant, the size of the difference in the participation rates of these groups is smaller than at Coolidge, perhaps reflecting the high overall rate of vocational coursetaking by McKinley students.[66]

Figures 5.1 and 5.2 show the relationship between student academic achievement as measured by 10th grade scores and placement in college-prep math and English.[67] For takers and nontakers of college-prep math, Fig. 5.1 shows the mean 10th grade math achievement score and the range of scores as measured by the 5th and 95th percentiles. The distribution of 10th grade reading scores is shown in Fig. 5.2 for college-prep English takers and nontakers. The pattern is similar for all three schools: students who participated in college-prep English or math had significantly higher average test scores than students who did not take those college-prep courses.[68]

Yet, these figures also indicate that access to college-prep math was more restricted at Coolidge and Washington than at McKinley. Figure 5.1 shows that the scores of students taking college-prep math at Coolidge and Washington were concentrated within a narrow range compared with the scores of nontakers. College-prep math students at McKinley displayed a broader range of scores.

Fig. 5.1--Distribution of Math Scores for Takers and
Nontakers of College-Prep Math, by School

Fig. 5.2--Distribution of Reading Scores for Takers and Nontakers of
College-Prep English, by School

In contrast, access to college-prep English appeared to be more open to students with a wider range of achievement scores at all three schools. Test scores in the 5th percentile for students in college-prep English were in the 20-30 national percentile range.

These tables reveal that, as with vocational coursetaking, college-prep coursetaking did not correspond neatly with achievement. Perhaps most significant, some students at all three schools who had scores high enough to participate in college-prep math and English failed to do so. Figures 5.1 and 5.2 indicate that Coolidge and Washington students who did not take college-prep math or college-prep English had a wide range of scores, with test scores in the 95th percentile reaching the 80-90 national percentile range. The scores of some McKinley college-prep students overlapped with those of non-college-prep students in the middle range of scores. In general, these figures indicate that students in and out of the college-bound track may have been divided according to criteria that extend beyond achievement alone.

WHICH CHARACTERISTICS PREDICT COLLEGE-PREP PARTICIPATION?

The preceding analysis of student placement demonstrates differences across and within schools in the characteristics of students found in the college-bound track. However, the previous comparisons, based on a single demographic or achievement measure, do not allow investigation of other factors that may simultaneously affect track placement. For example, we saw that Asian students were more likely to participate in college-prep math than were students from other ethnic groups. Is this pattern of participation a function of their higher achievement test scores relative to those of students from other ethnic backgrounds? Or did Asian students more frequently participate in college-prep math because they or their parents were more persistent than other groups about enrolling in those courses? Or did the
assumptions that school personnel make about the abilities of different groups of students
influence their decisions regarding student course placement? In other words, do racial or ethnic differences explain student placement once we control for student ability? And do differences in track placement across schools remain once we account for differences in student characteristics?

To examine the relationship between placement in college-prep courses and a number of individual characteristics, we performed separate logistic analyses to predict the probability that a student would be in college-prep math or English. These analyses are similar to those we presented in the previous section on vocational coursetaking. We estimated logistic models separately by school and with students pooled across all three schools. In both cases, we modeled student placement as a function of gender, race/ethnicity, and achievement scores.[69] In addition, for the models estimated separately by school, we included SES in the model for Coolidge and an indicator for foreign-born students in the model for Washington and McKinley.

The details and results of the logistic analysis are presented in Appendix D. The findings are summarized in Tables 5.6 through 5.11, which show the predicted probability that a student with various characteristics would be in the college-prep math track and college-prep English track.[70]

Table 5.6 shows the probability that a student from each of the three schools described by gender and race/ethnicity would take college-prep math. These estimated probabilities assume that the "representative student" had math and reading achievement scores equal to the average for his/her respective school.

Gender Matters in English Placement, But Not in Math

A comparison of the probabilities in Tables 5.6 and 5.7 confirms the results of Tables 5.4 and 5.5--that a student's gender did not play a role in mathematics placement but was important in English placement. Within each school, after controlling for differences among students in their achievement scores, there were no substantial differences in participation in college-prep math for boys and girls.

The reverse is true for college-prep English, where girls were significantly more likely to participate than boys.[71]

Race Matters in Math Placement, Less So in English

The results also show that, even after controlling for test scores, a student's race/ethnicity was often still important in determining the probability of participating in college-prep math and English. Again we find that Asian students at Coolidge and Washington had higher probabilities than white, African American, or Latino students with the same achievement scores of participating in college-prep math. For example, Asian girls and boys at Coolidge were more than ten times as likely as their Latino classmates with the same math and reading scores to be enrolled in college-prep math. In contrast, there is no difference in placement probabilities for African American and Latino students at all-minority McKinley High.

A student's race or ethnicity was a less important determinant of placement in college-prep English at Washington and McKinley. At these schools, the coefficient estimates on the indicators for race are not significant (Table D.5). Thus, even though the estimated probabilities in Table 5.7 are slightly lower for whites than for Asians and Latinos at Washington, and slightly lower for Latinos than for African Americans at McKinley, these differences are not statistically significant. However, a student's race/ethnicity was important for placement in college-prep English at Coolidge, our most racially diverse school. As in math, Asian students at Coolidge were most likely and Latino students were least likely to participate in college-prep English, even when their achievement levels were comparable. Falling in the middle, whites were less likely to participate than African Americans with the same scores.

In addition to highlighting important differences within schools in the placement probabilities for students with different status characteristics but similar achievement, Tables 5.6 and 5.7 show significant differences between the three schools, as well. The average Latino male and female, the only groups common to all three schools, had the lowest probability of placement in college-prep math or English at Coolidge. Asian students did best in terms of college-prep placement in both subjects at Coolidge. The average white student at Washington was more likely to secure a college-prep placement in math, but less likely in English, than his or her counterpart at Coolidge. The reverse was true for the average African American student at McKinley compared to Coolidge.[72] These comparisons show that, even after controlling for other student characteristics, including achievement scores, differences remain across the three schools for different racial and ethnic groups in the probability of being in the college-bound track, with traditionally disadvantaged minorities the least likely to occupy a slot in the college-prep track at the most diverse school.

Opportunities for Access to the College-Prep Track Vary by School

In addition to comparing the probability of taking college-prep courses across students with different racial and ethnic characteristics, we also used the logistics model to compare the extent to which achievement test scores predict college-prep placement.

Tables 5.8 and 5.9 show the probabilities of taking college-prep math and English for students at the same relative points in the test score distribution at each school, specifically the 25th percentile, the 50th percentile (or median), and the 75th percentile. We made these comparisons for boys of different race/ethnicity groups.[73] This comparison indicates how a student's relative standing in his school affected his opportunities, compared to both his peers and his counterparts at one of the other schools.

As expected, within each school, a student's probability of taking college-prep math or college-prep English increased as his test scores increased from the 25th to the 75th percentile--the reverse of the pattern we observed with vocational coursetaking.[74] Again, the same differences within schools in placement for different race/ethnic groups are apparent. At every point in the test score distribution at Coolidge and Washington, Asian boys were most likely and Latino boys were least likely to be taking college-prep math and college-prep English. Yet at McKinley there is no significant difference for African American and Latino boys.

The findings we have presented in the preceding pages lend some support to the conclusions from our interviews and observations that the schools provided academic opportunities based on their perceptions of the abilities of their students. Moreover, data from our logistics analysis indicate that those perceptions were shaped not only by students' achievement test scores but also by race or ethnicity. Therefore, a student in the top fourth of his class was most likely to participate in college-prep math at Washington, the school with the highest average test scores, and least likely at McKinley, the school with the lowest average scores. Yet, within schools, students with the same test scores, but who were from different racial or ethnic groups, did not appear to have the same access to college-prep math. Asian students were more likely than were white, African American, or Latino students with the same test scores to be placed in college-prep math at Coolidge and Washington.

Another way to examine the effect of achievement scores on placement is to compare placement probabilities within and across schools for students with similar absolute test scores as measured by their national percentile ranking, as we did in Sec. III for vocational coursetaking. Tables 5.10 and 5.11 show the estimated probabilities of taking college-prep math and English for boys in different race or ethnic groups with national percentile scores equal to 30, 50, and 80. The within-school differences are similar to those reflected in Tables 5.6 through 5.9, as discussed above. The more interesting comparison is for students at the different schools.

A student with a given absolute achievement score had a different probability of being in the college-prep track depending upon whether he or she was at Coolidge, Washington, or McKinley.

For example, Tables 5.10 and 5.11 indicate that a Latino student at McKinley with achievement scores falling in the 80th percentile nationally had a probability of participating in college-prep math equal to 84 percent. A Latino student with the same scores at Coolidge or Washington had a 35 to 39 percent probability of participating. This distribution, with the highest probabilities of taking college-prep math at McKinley and the lowest at Washington, holds for all races at each test score level, as tabulated in Table 5.10. This pattern also applies to placement in college-prep English for all students except Latinos, who were more likely to be in those classes at Washington than at Coolidge. Again, the differences in teachers' and counselors' perceptions of Latinos at Washington and Coolidge provide a clue about this pattern. As noted in Secs. III and IV, Washington seemed to regard its Latino students as "just like whites," whereas the Coolidge staff reported their Latino group to have fewer home advantages, more academic deficiencies, and limited futures.

This pattern of between-school probabilities suggests several possible interpretations. If we form an imaginary queue of students from highest to lowest ability, our data indicate that a higher percentage of students at Washington than at McKinley would take college-prep math. However, a student with above-average ability (for example, with percentile scores equal to 80) would have had less than a 50-50 chance of entering the college-prep track at Washington but would almost certainly have been in the college-prep track at McKinley.

One interpretation is that this student would have been "crowded out" of the college-prep track at Washington by the large number of students with higher ability and "crowded into" the college-prep track at McKinley by virtue of the fact that he or she was one of the top students. Alternatively, the student at Washington with above-average ability may have been less motivated or encouraged than his or her counterpart at McKinley, perhaps because of a large cohort of high-achieving peers, to participate in the college-bound track. Finally, the interview data from McKinley indicate that because that school encourages students to at-tend college, its college-prep track may simply have been broader and substantively different from those at the other two schools.

The Role of SES and Country of Birth

Student demographic characteristics such as race, sex, and achievement measures are not the only possible candidates to explain placement in college-prep math. However, as noted in Sec. IV, our data were not complete enough to allow us to estimate the effect of student characteristics such as SES and country of birth on track placement for all three schools. However, when we estimate the logistic model separately by school, it is possible to include SES as a predictor in the model for Coolidge, and an indicator for foreign-born students in the models for Washington and McKinley. The results, tabulated in Table D.4, show that, holding student gender, race, and achievement scores constant, low-SES and middle-SES students were less likely to be placed in college-prep math than high-SES students. This negative relationship is strongest for the low-SES students. Thus, students from poorer families at Coolidge faced a disadvantage relative to equally talented students from more prosperous families.

A student born abroad may face language difficulties that preclude placement in the high track. However, although foreign-born students were less likely than native-born students
with comparable achievement levels to be enrolled in high-track English, at Washington there was no significant effect upon mathematics placement of being born outside of the United States. In contrast, foreign-born students at McKinley were more likely than U.S.-born students to be found in the college-prep mathematics track.

CONCLUSIONS

The analyses of our student transcript data for patterns and probabilities of academic track placement that we presented in this section largely conform to the complex picture we drew of the curriculum decisionmaking process from our field work. Differences in access to college-preparatory coursework appear to have been driven by a number of factors both between and within schools. In our analysis of academic coursetaking patterns in this section, we again find a pattern of race- and social-class-related differences that are not entirely explained by achievement. Individuals' enrollment in college or non-college courses--as in vocational education--appears to have been influenced by judgments made about the race and social class groups to which they belong. These judgments also seem to affect the overall number of positions that schools provided in various tracks--with the fewest positions available at schools serving substantial numbers of low-income and African American and Latino students. They also seem to have affected the relative chances to enroll in college preparatory courses of students from different groups within the same school. However, these patterns are complicated by the uneven distribution of achievement among schools. Lower-achieving schools provided fewer opportunities to take college-preparatory classes overall, a circumstance that decreased students' opportunities overall. At the same time, these schools' achievement criteria for entry into these classes were lower than at other schools, a circumstance that had the effect of increasing minority students' opportunities.

Perhaps because schools with lower average levels of achievement want to offer a full range of academic programs--from remedial to honors--these schools give lower-achieving students greater opportunities to participate in higher-level courses than they would have at schools where the average achievement levels are higher. What results is a complex structure of differentiated opportunities both between and within schools. Moreover, the overlap in achievement among students in college-prep and non-college-prep programs is so great that factors other than prior achievement, race, and social class clearly play a role in student coursetaking.

In the section that follows we place our findings about vocational and academic coursetaking in the context of our earlier findings from our interviews and observations and suggest a conceptual framework for better understanding the culture of curriculum differentiation at comprehensive high schools--the dynamics of curriculum decisions, student placements, and the role of vocational education.

[54]For a more complete description of the course offerings at each school, see Selvin et al. (1990).

[55]An important caution here, and throughout this and the next section, is that although academic course titles may make the curriculum at the schools appear to be similar, they may mask considerable variation in the actual content and rigor of the courses themselves. For further explication of this issue, see McDonnell et al. (1990).

[56]The results shown in Table 5.1 are similar when the calculations are made for the 9th through 12th grade cohort.

[57]Coolidge, with the most formal "tracking" system of the three schools, contrasts with McKinley, which "detracked" all classes in the Fall of 1988. Washington, with a less-formal tracking system, fell somewhere in between. Note, however, that the "detracking" at McKinley does not affect the cohort of students that we are studying, as they graduated in the Spring of 1988. See Selvin et al. (1990) for descriptions of variations in the tracking systems at the three schools during the 1988-1989 school year.

[58]A detailed description of the track or level designations is found in Appendix B.

[59]For all three schools, differentiating the ESL and the highest-level English classes was straightforward: ESL classes were placed in the ESL category, "college-prep" classes were assigned to the high category, and "honors/AP" classes were designated as honors courses. However, the practice of placing students of low and average ability in mixed-ability courses made it more difficult to identify the two remaining tracks, low and mixed. At Coolidge, with the most extensive tracking system, we classified three levels of courses--"low/regular non-college-prep," "regular non-college-prep," and "non-college-prep/college-prep"--as the mixed/medium track. In contrast, the mixed/medium track at Washington contains only those classes where the schools combined "non-college-prep" and "college-prep" students, and there are no mixed/medium track English courses at McKinley, since all the English classes there were considered either "high" or "low." Finally, the low category includes "special education" and "low/remedial" courses at all three schools, and combined "low/regular non-college-prep" courses at Washington and McKinley only.

[60]In addition, students at Washington and McKinley who take an advanced placement computer science class are also classified as being in the honors track.

[61]The findings are similar when examining the second semester in 10th and 11th grades. For 12th grade at each school, there is an approximate increase of 10 percentage points in the percentage of students not taking a math course in the second semester compared to the first semester. For English, there is a 3 to 10 point increase in non-participation from the first to second semesters. If a student was taking more than one English or math course in a semester where the track level was different, the highest track level was assigned for that semester.

[62]Selvin et al. (1990).

[63]In a similar manner, English track placement distributions at McKinley reflect school-specific curriculum offerings as much as perceptions of student ability. McKinley did not appear to offer medium-level courses; English courses at that school appeared either to be high or low track.

[64]Using this definition, we classified students in the high math track (i.e., taking algebra 2) and honors math track (i.e., taking geometry) as "college-prep" students.

[65]There are no significant differences in participation in college-prep English across the three schools.

[66]See Sec. IV.

[67]The data for Figs. 5.1 and 5.2 are found in Tables C.5 and C.6. The tables also show the mean, 5th, and 95th percentiles for 8th grade achievement scores as well as 10th grade achievement scores. The pattern is similar to that shown in the figures.

[68]Tables C.5 and C.6 document that the means are always significantly different for both math and reading scores (8th and 10th grade) between takers and nontakers of college-prep math and English.

[69]Since 8th grade achievement scores were not available for McKinley, we used 10th grade achievement scores in math and reading so that we could make comparisons across the three schools. Yet the results are similar for Washington and Coolidge when we compare 8th grade achievement scores. Therefore, although 8th grade scores may be a better measure of prior achievement as they are uncontaminated by initial track placement in high school, our use of 10th grade scores does not bias the results.

[70]The results in Tables 5.6 through 5.11 are based on separate logistic models for each school. This method of analysis allows for differential effects of student characteristics within schools and therefore is appropriate for within-school comparisons. These results can also be used to make between-school comparisons. Alternatively, a pooled model with dummy variables can be used for between-school comparisons. The estimated probabilities from the pooled model lead to similar conclusions in most cases; exceptions will be noted in the discussion.

[71]This finding follows from the coefficient estimates reported in Appendix D which show that the coefficient on the variable measuring gender is never significantly different from zero in both the school-specific and pooled logistic models predicting the probability of being in college-prep math. In contrast, the coefficient on gender is always significant in the models predicting the probability of being in college-prep English.

[72]When the pooled model is used to calculate the probabilities, there is a constant ranking across the three schools for each race/ethnicity group. This occurs because the pooled model, as estimated, restricts the effect of race/ethnicity to be the same across the three schools. For college-prep math, the probabilities are highest for the average student at Washington and lowest for the average McKinley student. However, the estimated coefficients on the school-specific indicators are not significant. For placement in college-prep English, there is a positive and significantly higher probability for the average McKinley student than one at Coolidge or Washington. The pooled model was also estimated with interaction terms for race and school (see the discussion in Appendix D for details).

[73]Comparison of the same analysis for girls with our findings for boys of the same race/ethnic groups produces the same pattern exhibited in Tables 5.6 and 5.7. At each point in the within-school test score distribution, there is no difference in placement probabilities for college-prep math, but girls have higher probabilities of being in college-prep English.

[74]This finding follows from the coefficient estimates in Tables D.4 and D.5, which show a positive and significant relationship between the probability of being in college-prep math or English and math and reading achievement scores.