High-school math courses and completion of the bachelor's degree.

Using a national longitudinal sample of 5,257 young people who were pursuing the bachelor's degree, we studied how credits in intensive high school mathematics courses affected their completion versus noncompletion of the degree. Finishing one unit in any of four intensive math courses more than doubled the likelihood that participants would later complete the bachelor's degree. Effects were present above and beyond the effects of background variables, including early math ability. Implications of findings are presented.

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Recent trends related to college enrollment and bachelor's degree completion have important implications for professional school counselors. Over the past two decades, the percentage of young people in the United States who expect to earn college degrees has increased (Wirt et al., 2000). The percentage of students who expect to later engage in professional occupations has likewise increased (Rasinski, Ingels, Rock, Pollack, & Wu, 1993). Over the past three decades, college enrollment in the United States has been steadily climbing (Wirt et al., 2002). There has also been a change in the advice that adults give students regarding college. In a 1980 to 1990 comparison (Rasinski et al.), fathers, mothers, teachers, and school counselors were more likely in 1990 to advise high school students to attend college. This increase was evident across socioeconomic classes, racial-ethnic groups, regions of the country, and achievement test score levels. For example, in the lowest fourth of test-scorers, 26% of sophomores in 1980 indicated that school counselors advised them to attend college after high school; whereas 56% in 1990 indicated that counselors advised them to attend college. One factor driving the increase in the number of students being advised to attend college may be economics. That is, Wirt et al. (2002) reported that the earnings gap between young people who have 4-year college degrees and those who do not widened through the 1970s, 1980s, and 1990s.

Bachelor's degree attainment has also increased in importance on social and political levels. Adelman (1999) maintained that bachelor's degree attainment has become the accountability standard for higher education institutions. Bachelor's degree completion rates in the United States have risen over the past three decades. Wirt and colleagues (2002) reported increases in percentages of Latinos, African Americans, and Whites in the 25 to 29 age range who have completed the bachelor's degree. Completion rates for women have increased faster than rates for men. The bachelor's degree is a common criterion used by employers in hiring; when people earn a bachelor's degree they expand the range of occupational options open to them. Thus, it seems that the psychological benefits of degree completion (e.g., increased self-worth, increased sense of hopefulness) would also be high.

RESEARCH ON STUDENTS' LONG-TERM EDUCATIONAL DEVELOPMENT

Some researchers have studied the long-term educational development of young people, using longitudinal data that spanned from middle school and high school to beyond high school. Hanson (1994) and Trusty and Harris (1999) examined students' expectations for post-secondary education, and how these expectations changed over time. Because these researchers studied students who were initially higher achievers in school, reduced (lowered) expectations over time were labeled "lost talent." That is, if a student showed early signs of academic talent and had an initial expectation to earn a bachelor's degree, and if the student's expectation for a bachelor's degree was reduced after high school graduation, the student's early talent was lost. In both of these studies, the strongest effect on lost talent was from socioeconomic status (SES), with lower levels of SES associated with more lost talent. Also, these researchers found, unexpectedly, that Whites were more likely than non-Whites to have reduced educational expectations and that young men had more lost talent than did young women.

Trusty (2000) studied reduced versus stable post-secondary expectations for students who had below-average academic ability. The strongest effects in this study were SES and scores on eighth grade math tests. Consistent with earlier studies (Hanson, 1994; Trusty & Harris, 1999), Whites were more likely than Asian Americans, Latino Americans, and African Americans to have reduced expectations over the period of adolescence. Asian Americans were least likely to have lowered expectations. Taking high school math courses was not examined in the three aforementioned studies.

Although the above studies of students' educational expectations have implications for long-term educational attainment, the true, explicit indicator of attainment is completion of degrees. Given that completion of the bachelor's degree is the barometer for educational success--and often economic and career success--in the United States, there are surprisingly few studies of degree completion (Adelman, 1999).

Adelman (1999), through the U.S. Department of Education, completed the most comprehensive study of college degree completion we could find in the literature. Adelman used data from a national longitudinal study that spanned from 1980 (when participants were high school sophomores) to 1993 (when they were around age 30). Two variables were most important to degree completion: (a) the intensity of students' high school curricula, and (b) the continuity of students' college enrollment (continuous versus intermittent enrollment). Of all courses within students' high school curricula, finishing intensive high school mathematics courses had the strongest effect on degree completion. Credits in intensive high school math courses were added together to create a math intensity variable. Adelman found that finishing one course beyond the Algebra 2 level (e.g., trigonometry, pre-calculus, calculus) more than doubled the likelihood that students who started their college education would complete their bachelor's degrees. The effect of high school math course-taking was stronger than the effects of high school test scores, grade point average (GPA), class rank, track, or background variables, including SES and race-ethnicity.

PURPOSE OF THE STUDY

The purpose of the present study was to examine the effects of background variables and students' high school math curricula on completion versus noncompletion of bachelor's degrees. Our data spanned 12 years from the eighth grade to 8 years after high school (National Education Longitudinal Study: 1988-2000 Data Files and Electronic Codebook System, 2002). We focused on the effects of intensive high school math course-taking, identified by Adelman (1999) as key variables. For our study, math course-taking variables were high school Carnegie units in Algebra 2, trigonometry, pre-calculus, and calculus. Background variables were gender, SES, racial-ethnic group membership, and eighth grade cognitive ability.

Our study differs from Adelman's (1999) study in three main ways. First, we included only participants who were attending college with the expectation of attaining the bachelor's degree. Adelman specified only that students had attended a 4-year college. Adelman's procedure likely excluded some students who were pursuing the bachelor's and included some who were not. Second, we included pre-high school cognitive ability variables, whereas Adelman did not. We were interested to see if the influences of math course-taking in high school extended beyond the influences of students' reading mad math ability in the eighth grade. Also, research (Maple & Stage, 1991; Trusty, 2002) suggests that early cognitive ability influences math course-taking in high school, and we were interested in these effects. Third, Adelman summed credits across three intensive math courses (trigonometry, pre-calculus, calculus) to create a math intensity variable. We were interested in the separate effects of these courses and the effects of Algebra 2, so we included credits in the four courses as separate variables.

Our purpose was more practical than theoretical. We sought to generate knowledge that could help school counselors, teachers, and parents in their counseling, advising, and individual planning with students. Individual planning is a major role for professional school counselors, and course selection is a major part of individual planning (Gysbers & Henderson, 2000). We found little research with implications for individual planning (e.g., see Whiston & Sexton, 1998). We also found little research on college degree completion. Although our purpose was more practical than theoretical, all theories of career development (e.g., Holland, 1997; Krumboltz, 1979; Super, 1990) attribute importance to young people's educational experiences, skills, and abilities. Although career theorists and all other reasonable people recognize that students' early educational experiences affect their later educational experiences, very little is known about the magnitude and character of these effects. For example, which math courses have the greatest influence on bachelor's degree completion? Does math ability make more of a difference than math course-taking? The knowledge base is sorely lacking regarding the effects of any high school variables on bachelor's degree completion, and this is surprising given the roles of professional school counselors in students' academic, career, and personal-social development.

Participants

Participants were 5,257 young people from the National Education Longitudinal Study: 1988-2000 Data Files and Electronic Codebook System (NELS:88, 2002). Data came from four waves of NELS:88 data collection: (a) 1988, when participants were in the eighth grade; (b) 1992, when they were high school seniors; (c) 1994, when participants were 2 years past high school; and (d) 2000, when they were 8 years past high school.

Participants had to meet several criteria to be included in our study. First, they had to belong to the high school transcript panel sample; data were weighted accordingly (see Curtin, Ingels, Wu, & Heuer, 2002). Second, we selected only participants who indicated in 1994 that they planned to complete at least a bachelor's degree. Third, participants had to have started their post-secondary education by June of 1994. In our sample, 91% of participants had completed at least one full academic year at a post-secondary institution by August of 1994. Therefore, most participants had 7 to 8 years to complete the bachelor's degree, and 9% had 6 to 7 years to complete the degree.

Of our 5,257 participants, 22% attended high school in the Northeast, 25% in the Midwest, 33% in the South, and 19% in the West (1% were missing data for this variable). With regard to race-ethnicity, 5% were Asian American, 9% were Latino, 11% were African American, 74% were White, and 1% were Native American Indians or Alaska Natives. Regarding post-secondary institutions, 42% started (from 1992 to 1994) at public 4-year institutions, 32% at public 2-year schools, and 22% at private 4-year schools. The remaining 4% started at various other institution types.

Variables

Bachelor's degree completion. The dependent variable in our study was whether students had or had not completed a bachelor's degree by the year 2000. Because all participants started their post-secondary education expecting to earn the bachelor's degree, completion of the degree indicates realized educational expectations, and noncompletion indicates--at least in our 8-year time frame--unrealized educational expectations.

Background variables. Background variables were SES, race-ethnicity, and scores on eighth grade cognitive ability tests. Cognitive ability test scores were formulated by the National Center for Education Statistics and were item response theory (IRT) scores. IRT scores take into account item difficulty, the ability of items to discriminate among students' ability levels, and students' guessing at answers. We used IRT scores on eighth grade reading and mathematics tests as indicators of pre-high school ability.

High school mathematics course-taking. Data on course-taking variables came from students' high school transcripts. Algebra 2, trigonometry, pre-calculus, and calculus are the most common intensive math courses offered in U.S. schools. Geometry was not included because nationally, the intensiveness of geometry courses is variable across high schools. Typically, Algebra 2, trigonometry, pre-calculus, and calculus are less variable in their intensiveness (R. M. Zbiek, personal communication, September 12, 2002). Across the math courses, from Algebra 2 to trigonometry to pre-calculus to calculus, there was a steady decrease in the number of participants receiving some credit (from 65% to 15%).

Data Analysis

Preliminary analysis. Before creating models examining the effects of the independent variables on degree completion, we examined the correlations between various curricular variables (units in high school courses) and degree completion. That is, we wanted to use our sample to verify Adelman's (1999) earlier findings that intensive math courses were the curricular variables most highly related to degree completion.

Logistic regression models. The dependent variable in our analysis, completion or noncompletion of the bachelor's degree, was a dichotomous (two-category) variable. Logistic regression is the appropriate form of analysis when a multivariate analysis involves a dichotomous dependent variable and continuous independent variables (Agresti, 1990; Menard, 1995). According to Adelman (1999), logistic regression is the most appropriate form of analysis for studying bachelor's degree completion. Logistic regression models produce odds ratios for independent variables; these odds reflect the increase or decrease in the likelihood of the outcome (i.e., degree completion) for every one-unit increase in the independent variable. SES and cognitive ability variables were expressed in z scores, with the unit of measurement therefore being the standard deviation. The course-taking variables were expressed in high school Carnegie units.

For our logistic regression analyses, variables were entered in two blocks (hierarchical logistic regression). The first model included background variables--gender, SES, race-ethnicity, eighth grade reading ability, and math cognitive ability. The second model included the aforementioned variables and math course-taking variables. This arrangement is consistent with previous research investigating the effects of course-taking (i.e., Adelman, 1999; Maple & Stage, 1991; Trusty, 2002; Ware & Lee, 1988), and it allows for gauging indirect effects in the models. That is, it is likely that background variables have effects on course-taking variables, which in turn have effects on degree completion.

RESULTS

For the preliminary analysis, we created several curriculum-intensity variables by summing high school credits in various areas. Preliminary analyses revealed that of all high school curricular areas and courses, credits in intensive math courses were most strongly related to degree completion. For example, the math-intensity variable was correlated more highly to degree completion than the science-intensity variable, the total number of units in math, total units in science, and total units in foreign languages. However, the relationships of chemistry credits and physics credits to degree completion were relatively strong.

See Table for results of the logistic regression models examining the effects of background variables and math credits on degree completion. Gender had a strong effect on bachelor's degree completion. Men were coded the value 1 and women were coded the value 2. Therefore, because the logistic regression coefficient was positive, women were more likely to complete the bachelor's degree than men. Interpreting the odds in the full model (Model 2), women were 70% more likely than men (odds = 1.70) to complete the bachelor's degree, while controlling for all other variables in the model. SES had a strong positive effect on whether young people completed the bachelor's degree or not. The SES effect became only slightly weaker in Model 2 (see Table), revealing that the SES effect was largely direct. That is, the effect was largely independent of math course-taking. With all other variables controlled (Model 2), a one-standard deviation increase in SES increased the odds of degree completion by 70%.

The effect of the racial-ethnic group variable as a whole was significant in both models, and Asian Americans and Whites were significantly more likely than young people from other racial-ethnic groups to complete the bachelor's degree. The number of Native Americans in the analysis was small; therefore, results for this group should be interpreted tentatively. When math courses were added to the equation (Model 2), the effect of race-ethnicity became slightly weaker, indicating that taking math courses somewhat equalized differences among racial-ethnic groups.

The effect of eighth grade reading ability was significant and positive. This effect did not change as the math course-taking variables were added to the equation; that is, the reading ability effect was unchanged across Models 1 and 2 (see Table). The effect of math ability was stronger, but this effect decreased dramatically when math course-taking variables were added to the equation. That is, eighth grade math ability affected math course-taking in high school, which in turn affected bachelor's degree completion. Stated differently, early math ability had an indirect effect on degree completion via math course-taking in high school.

The effects of course-taking variables were very strong (see Table). Finishing one high school unit in Algebra 2 more than doubled the odds of receiving a bachelor's by 8 years after high school (a 140% increase); finishing one-unit in trigonometry more than doubled the odds (a 137% increase). Getting credit for one unit of pre-calculus more than doubled the odds of degree completion (a 155% increase), and finishing one unit of calculus more than doubled the odds of degree completion (a 112% increase). These effects were independent of the effects of all other variables, including pre-high school math ability.

Regarding effect sizes, the Nagelkerke [R.sup.2] in Model 1 was .241, and the [R.sup.2] in Model 2 was .338. Therefore, background variables alone explained 24% of the variability in bachelor's degree completion; math course-taking explained an additional 10% of variability in degree completion above and beyond the variability in degree completion explained by background variables. Of the 5,257 young people in the analysis, 53% had completed their bachelor's by 2000, and 47% had not. The full logistic regression equation (Model 2) correctly classified 70% of the noncompleters and 76% of the completers. The overall percentage of correctly classified participants was 73%.

DISCUSSION AND IMPLICATIONS

We used a nationally representative sample to investigate the effects of background variables and math course-taking on completion of the bachelor's degree. All participants in our sample had attended college, and all indicated early in their college careers that they planned to receive at least a bachelor's degree. In the results section of this article and elsewhere, we used the terminology bachelor's degree completion in describing the dependent variable. Because all participants in our study expected to complete the bachelor's degree, degree completion signifies realized educational expectations in the 8-year, post-high school time frame. Inversely, noncompletion of the bachelor's degree in the 8-year time frame signifies unrealized expectations.

Preliminary analyses revealed that intensive math courses had the strongest effects of all curricular areas on degree completion. This finding is consistent with Adelman's (1999) results, which are based on data from an earlier longitudinal study. This is not to say that curricular areas or courses other than math are unimportant to degree completion; rather, the main focus of our study was on intensive math courses.

In the logistic regression models, we found that background variables and earned credits in intensive high school math courses had strong influences on realized and unrealized expectations. These effects are especially noteworthy considering their strength across time and considering that we did not include any post-high school variables. For example, events such as marriage and having children would seem to have potential to influence degree completion. The effects of pre-high school and high school variables that we found were strong despite any post-high school influences.

Effects of Math Course-Taking

Units in intensive high school mathematics courses showed the strongest effects in the logistic regression models. These findings are consistent with earlier findings of Adelman (1999)--that completing these courses is salient to participants' completion of the bachelor's degree. We found strong effects for all intensive math courses--Algebra 2, trigonometry, pre-calculus, and calculus. Taking one high school unit in any of these courses more than doubled the likelihood of young people completing the bachelor's degree versus not completing the bachelor's. These strong effects of credits in intensive math courses were independent of the influences of eighth grade reading and math ability, gender, SES, and racial-ethnic group membership. Early math ability did have an influence on math course-taking in high school. That is, students with higher ability tended to finish more intensive math courses. However, the positive effects of math course-taking on bachelor's degree completion extended well beyond the influences of early math ability; this finding adds to earlier findings of Adelman.

It is clear from our analyses that all the intensive high school math courses are important to young people in realizing their expectations of a bachelor's degree. That is, there is no threshold course, no key course, and no point of diminishing return. All have positive effects on degree completion: the greater the number of intensive math courses taken, the greater is the likelihood of degree completion.

Implications for Individual Planning

Slightly over half of the participants in our sample completed the bachelor's degree in our 8-year rime frame; slightly under half did not. In our sample, there were many students who were attending college and expected to earn a bachelor's degree, yet they had not taken more than one credit in intensive math courses. These observations show that students' behavior (high school course-taking) is not consistent with their goals (degree completion). Therefore, students would benefit from better individual planning and advising. Specifically, professional school counselors can use the results of this study to inform students and their parents and guardians of the important role that high school math courses play with regard to subsequent bachelor's degree completion. Moreover, because counselors, teachers, and parents are increasingly advising students to attend college (Rasinski et al., 1993), it is prudent for these adults to also advise students to progress as far as possible in an intensive high school math curriculum; this advice will help increase the likelihood that students will be academically successful in college.

It appears that students' high expectations for post-secondary education are not enough. Rosenbaum (2003)--basing conclusions on extensive research--asserts that the college-for-all policy now prevalent in U.S. high schools has unintended, negative results. That is, supporting high school students' high expectations when students show little effort leads students to erroneously believe that their high school achievement is unimportant to their college success. Rosenbaum stressed the importance of (a) providing students with realistic estimates of their likelihood of success and (b) presenting a variety of post-secondary options to students. Almost half of students in our sample--all of whom had high expectations--did not realize their goal of the bachelor's degree. Therefore, many students need options other than the bachelor's degree (e.g., technical degrees, certificates, other post-secondary training, work options).

In light of our results and Rosenbaum's (2003) work, it is critical that school counselors inform and advise students and parents effectively. Students who maintain expectations for completing the bachelor's degree but opt out of intensive math courses are placing themselves at risk for achieving their educational aspirations and expectations. Counselors may find it useful to explore with these students the factors driving the students' career decision making and education planning. Obviously, counselors should have student data from multiple sources--achievement test scores, aptitude test scores, performance samples, teacher observations, products from guidance activities--for aiding students in scheduling decisions and individual education-career planning.

It seems particularly important that both achievement and aptitude data are available to help counselors make valid assessments of whether students are achieving their potential or not. Without these data, the most negative consequences would be for underachieving students. If these students' performance in prior math courses are the only basis for counselors', teachers', or parents' judgments regarding course-scheduling and planning, then capable students would likely be continually placed in lower-level math courses, leading them to further wasting of their talent.

These concerns underscore the importance of counselor-teacher-parent communication. Often, math teachers will recognize underachievement through observing students in classes. Also, parents generally have knowledge of students' potential and levels of effort. All available data should be used in course selection and individual planning, and individual planning should be systematic and continual.

There are two formats for organizing and summarizing the data needed for helping students in decision making and education-career planning: (a) the written education-career plan, and (b) the career development portfolio. Education-career plans include courses taken and planned, strengths and obstacles, interests and values, educational and career goals, and data from teacher and parent contact. Plans provide a format for counselor-teacher-parent-student communication (see Brown & Trusty, in press; Schmidt, 2003). Trusty and Niles (in press) developed a practical framework for assembling career development portfolios. Portfolios are collections of formal and informal assessment data that follow students through elementary, middle, and high school. They contain data on broad areas of students' functioning, spanning competence in academic, career, and personal-social areas of development. In the Trusty and Niles framework, a large portion of the data in portfolios comes from classroom guidance activities; data from teachers and parents are included. Career development portfolios provide data that can be shared among counselors, teachers, parents, and students; the portfolios provide the information needed to develop appropriate education-career plans.

Our findings imply that the consequences of individual planning, or lack thereof; are extreme and long-term. If the earnings potential of those with post-secondary educational attainment versus those without is considered (see Wirt et al., 2002), the consequences are likely lifelong and even extend to subsequent generations.

Implications for the Math Curriculum

The current nationwide shortage of high school mathematics teachers is especially alarming in light of our findings. In U.S. public schools in the 1999-2000 school year, 69% of middle school students and 31% of high school students were taught by teachers who did not have both a major and a teacher-certification in math teaching. In the same year, 22% of middle school students and 9% of high school students had math teachers without a major, minor, or certification in math teaching (Seastrom, Gruber, Henke, McGrath, & Cohen, 2002). Additionally, many high schools do not offer calculus and other intensive math courses; these schools are likely to be in lower SES areas and have higher percentages of non-White students (Lee, Burkam, Chow-Hoy, Smerdon, & Geverdt, 1998).

If the math curriculum and math instruction are inadequate in middle school or high school, students are denied the opportunity to learn. Also, inadequate curricula and instruction compound difficulties in educational and career planning, and more students with high academic goals and potential are likely to follow a path toward wasted talent. The current trend toward moving high school math courses into middle schools has some rewards, but this practice forces individual planning into earlier grades, thereby complicating the planning process. This practice also sets students on inflexible tracks earlier in their educational careers. The insidious effects of these tracking processes are the basis for the constrained curriculum argument; a constrained math curriculum is one in which few math courses other than intensive math courses are offered in a school. Findings of Lee et al. (1998) and Lee, Croninger, and Smith (1997) imply that a constrained curriculum contributes to higher levels of math achievement for all students, including lower SES students. On the other hand, offering more choices rather than fewer may be helpful. For example, schools could offer pre-calculus in an extended, slower-paced format for students who do not progress as quickly as the highest-achieving students. In any case, an intensive math curriculum should not be an elitist curriculum, serving only the best-behaved, highest-achieving students.

Professional school counselors, in addition to helping students with individual planning and advising, can advocate for students on this broader level. Advocacy and leadership in curriculum development are important roles in the American School Counselor Association National Model (ASCA, 2003). All students need the opportunity to learn. Counselors should advocate for students' long-term educational development by supporting an intensive high school curriculum in their schools. Increasing the intensity of the curriculum requires two main conditions: (a) a willingness on the part of schools to provide the resources for making an intensive curriculum available, and (b) demand for an intensive curriculum by students and parents. The recent initiative of dual-enrollment (concurrently receiving high school and college credit for courses) is one possible solution for some schools. Collaborative arrangements among high schools may also be helpful in creating opportunity to learn. Counselors should advocate for such practices when appropriate for their students.

Effects of Background Variables

In our sample, women were 70% more likely than men to have completed the bachelor's degree than not. This finding is consistent with the trend of higher completion rates for young women in the general U.S. population (see Wirt et al., 2002). This higher completion rate may be related to the observation reported by Wirt et al. that the economic rewards associated with the bachelor's degree are greater for women than men. That is, when contrasting earnings of bachelor's degree recipients with earnings of those with a high school diploma only, the contrast is greater for women. Men who hold a bachelor's or higher degree still earn more--22% more in median earnings in 2000 for the 25 to 34 age bracket (see Wirt et al.)--than women with a bachelor's or higher degree. We found that SES had a relatively strong effect on degree completion; this effect was largely independent of the effects of course-taking and other variables. A one standard deviation increase in SES resulted in a 70% increase in the odds of degree completion, net of the effects of all other variables. This result portrays sizeable obstacles for lower SES individuals. The social mobility process is difficult, and in this country, education has traditionally been viewed as a viable and important route to social and economic advancement. The SES effects we found are consistent with findings from earlier studies (e.g., Adelman, 1999; Hanson, 1994; Trusty, 2000; Trusty & Harris, 1999). Although economic resources for post-secondary education are available for lower SES individuals (e.g., student grants and loans), completing the bachelor's degree taxes family economic resources more than other types of educational achievement (e.g., test scores, completing high school).

With regard to effects of racial-ethnic group membership, Asian Americans had the highest frequencies of degree completion, Whites were next highest, and Latinos and African Americans were comparatively lower. Native Americans were comparatively low in degree completion, but the number of Native Americans ha the sample was too small to make solid inferences. The effects of race-ethnicity were somewhat weaker in the full model (Model 2), indicating that math course-taking somewhat eroded racial-ethnic differences.

Our findings for racial-ethnic groups are inconsistent with findings from earlier studies of the stability of young people's educational expectations (Hanson, 1994; Trusty, 2000; Trusty & Harris, 1999). These research studies suggested that Whites were more likely to falter along the way in their long-term educational development. Our results are more valid than the implications from these earlier studies because we had data quantifying bachelor's degree completion. Our results indicate that, comparatively, Latinos and African Americans have more unrealized educational expectations than Asian Americans or Whites. This result is consistent with national statistics on degree completion. That is, in the 25 to 29 age bracket, the college degree completion rate is lower for Latinos and African Americans than for Whites (Wirt et al., 2002). Therefore, students and families of lower SES and from Latino and African American groups will need higher levels of resilience in overcoming barriers to degree completion. We did observe that several participants from these groups did complete the bachelor's degree.

The effect of eighth grade reading ability was statistically significant in both models. This effect, however, was modest compared with the effects of other variables. The effect of eighth grade math ability was indirect. When math course-taking variables were entered into the equation, the positive effect of math ability disappeared. This finding indicates that the effect of early math ability on degree completion is almost completely mediated and dominated by math course-taking. In plain terms, what students do (finishing courses) is more important than what they are capable of doing (early ability).

CONCLUSION

Earlier in this article, we related that our purpose was more practical than theoretical. We wanted to generate knowledge on how school personnel--particularly middle and high school counselors--could help students in their long-term educational and career development. The following are our main findings and their implications:

1. Students who earn credits in intensive high school math courses have a much greater likelihood of realizing their goals of completing bachelor's degrees than students who do not finish these courses. Further, taking intensive math courses in high school has positive effects that extend well beyond the influence of pre-high school math ability.

2. Each of the common intensive math courses--Algebra 2, trigonometry, pre-calculus, calculus--is important. The benefit is cumulative.

3. Effective individual planning and advising are critical to students' long-term educational development.

a. If counselors advise students to pursue the bachelor's degree, or if students have goals of completing the bachelor's, students should be advised to be well-prepared in mathematics.

b. Individual planning should be systematic and continual, and data from multiple sources should be used.

c. Knowing students' math achievement and aptitude--not just prior performance--is important for individual planning and advising.

d. Communication among counselors, teachers, parents, and students is needed for effective individual planning and advising.

e. Because a high percentage of students do not realize their expectations, students need knowledge of a variety of educational and career options.

4. Professional school counselors, teachers, parents, and school administrators should work to provide opportunity for students to receive effective instruction in intensive mathematics courses.

5. School counselors should provide particular support for students who desire to complete the bachelor's degree if they are of lower SES or belong to Latino or African American groups.

Our study leaves many remaining questions regarding the influences on bachelor's degree completion. There is a need for researchers to examine the effects of high school variables on degree completion for disaggregated groups. For example, separate analyses for genders, SES groups, and racial-ethnic groups could reveal differing processes of degree completion or noncompletion. Also, high school variables other than curricular variables (e.g., school behavior, parenting variables) may affect course-taking and degree completion differently for young people from these various groups. Researchers should investigate degree completion for particular college majors. It is likely that high school curricular experiences will differentially affect degree completion depending on students' particular college majors.

Perhaps most importantly to school counselors and students, researchers should focus on individual planning and advising processes. Through our study and Adelman's (1999) study, we now have strong indication that intensive high school math coursework is salient to bachelor's degree completion. Researchers need to focus on developing and validating effective individual planning models (e.g., Trusty & Niles, in press) that lead students to setting appropriate goals, using their talents, and realizing their goals. An outcome in such studies could be the percentage of students in the high school who achieve (complete courses) to the level of their potential, or the number of students who complete courses and gain knowledge consistent with their interests and educational goals. Our findings and Adelman's findings suggest that the most important high school academic achievement outcome for researchers and practitioners to focus on is courses completed--as opposed to GPA, class rank, scores on college entrance examinations, or scores on other aptitude or achievement tests. After all, completing courses is the main activity of students in schools.

The greatest strengths of our study were the nationally representative sample and the longitudinal nature of the data. The NELS:88 study offered us a chance to do what is rarely seen in the literature--namely, study the effects of students' high school learning experiences on completion of the bachelor's degree. With so few existing studies on such an important outcome, this study supplies much-needed knowledge for professional school counselors, teachers, parents, students, and schools.

Logistic Regression Models of Effects on Bachelor's Degree Completion
(N = 5,257)

                                      Model 1             Model 2

Variable                             B        Odds       B        Odds

Background Variables
  Gender                           .53 ***    1.69     .53 ***    1.70
  SES                              .58 ***    1.79     .53 ***    1.70
Race-Ethnicity (a)
  Asian American                   .50 ***    1.64     .35 *      1.42
  Latino                          -.11         .90    -.11         .90
  African American                -.06         .94    -.13         .88
  White                            .26 *      1.29     .25 *      1.29
  Native American                 -.59         .56    -.36         .70
Eighth Grade Cognitive Ability
  Reading                          .19 **     1.21     .20 **     1.23
  Math                             .46 ***    1.58     .06        1.07
High School Math Course-Taking
  Algebra 2                                            .88 ***    2.40
  Trigonometry                                         .86 ***    2.37
  Pre-Calculus                                         .94 ***    2.55
  Calculus                                             .75 ***    2.12

Note. Standard errors for sampling design effects calculated with the
use of AM software (American Institutes for Research, 2003) were
adjusted. Logistic regression coefficients (Bs) for continuous
variables are standardized coefficients except those for courses taken,
which are expressed in high-school units. Nagelkerke [R.sup.2] = .241
in Model 1, and .338 in Model 2.

* p < .05; ** p < .01; *** p < .001.

(a) Race-ethnicity was deviation coded. The Native American group was
the comparison category; the B coefficient was calculated as the
negative sum of the other categories; and the odds ratio was calculated
from the B coefficient.

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Jerry Trusty, Ph.D., and Spencer G. Niles, D.Ed., are professors in the Department of Counselor Education, Counseling Psychology and Rehabilitation Services, The Pennsylvania State University, University Park. Email: [e-mail].