# Predictive factors in intensive math course-taking in high school.

This article presents a study that investigated factors that
distinguish high school students who completed at least one course
beyond Algebra 2 from those who completed a course in Algebra 2 or less.
The sample included a cohort of 11,909 high school seniors who
participated in the Educational Longitudinal Study 2002-2004. Data were
analyzed using a multinomial logistic regression and results indicated
that student expectations, parent aspirations, race, and socioeconomic
status were among the most significant predictors. Implications for
school counselors are discussed.

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Recent influences in the field of school counseling have all emphasized the advocate role of the school counselor. The National Standards of the American School Counselor Association (ASCA, 1997; Campbell & Dahir, 1997), the ASCA National Model (2005), and the Transforming School Counseling Initiative (Education Trust, 1997) have contributed to determining the role of the school counselor as more proactive in maximizing the academic, career, and personal/social development of students. A principal form of this advocacy is curriculum planning. The high school counselor is in a unique position to help students make informed choices about courses with important consequences for their postsecondary lives.

The intensity of the high school curriculum and its relationship to postsecondary life has been a topic of investigation with a long history. A crucial turning point in this history was the publication of A Nation at Risk (National Commission on Excellence in Education, 1983), which documented that America's schools were lagging behind those of other developed nations with falling scores in reading and math and issued a dire warning about the need to improve the quality of education in the United States. As a result, major changes took place in the high school graduation requirements (Stedman & Jordan, 1986). The 1980s also saw the second of the U.S. Department of Education's national grade-cohort study, High School and Beyond, which followed a national sample of 10th graders from 1980 to 1992 and permitted an analysis of the relationships between precollegiate educational history and postsecondary educational status (U.S. Department of Education, 1995). For example, Adelman (1999) found that curriculum intensity had the greatest influence not only upon college entrance but upon bachelor's degree completion when compared to academic performance based on grade point average (GPA) or class rank and senior-year test scores. Furthermore, the most significant contributor to the strength of the curriculum was the highest level of mathematics completed by the student and that completing one course beyond Algebra 2 more than doubled the odds that students would complete their baccalaureate degree (Adelman). These effects were even stronger for African American and Latino students when compared to White and Asian students and led to the suggestion that Algebra 2 should be considered a threshold course.

Analysis on the third longitudinal cohort study, "National Educational Longitudinal Study: 1988-2000" (U.S. Department of Education, 2002), reached similar conclusions. Using this data set, Trusty and Niles (2003) found strong effects for all intensive math courses: the more intensive math courses one takes, the greater the likelihood of completing a college degree. Adelman (2006) produced similar results but also showed that, in contrast to 1982 12 graders, 1992 12th graders' chance of completing a baccalaureate degree turned positive only after completing a course beyond Algebra 2 such as trigonometry, precalculus, or calculus (Adelman). It does appear, then, from the more recent data that Algebra 2 serves as a threshold course in regards to the completion of the baccalaureate degree.

PREVIOUS RESEARCH

Research has documented that African American and Latino high school students take fewer advanced level math courses than their White peers (Jones, Mullis, Raizen, Weiss, & Weston, 1992; Ladson-Billings, 1997; Lucas, 1999; Riegle-Crumb, 2006). While the gender gap has closed recently in regards to advanced math course-taking (see, for example, Bae, Choy, Geddes, Sable, & Snyder, 2000; Freeman, 2004; Xie & Shauman, 2003), the racial gap remains wide. Based on the 2004 High School Transcript Data File (U.S. Department of Education, 2006a), 21.7% of Indian, 69% of Asian, 41.7% of African American, 34.3% of Latino, and 54.3% of White students took a course beyond Algebra 2.

Another factor worthy of consideration is English as a second language. Fry (2007) found that students who are English language learners are among the farthest behind in reading and math based on national standardized test scores. To our knowledge, no study has investigated the relationship between being an English language learner and the math curriculum in high school.

If going beyond Algebra 2 is clearly linked to the successful attainment of the baccalaureate degree, it is also important to examine the relationship between student expectations and their curricular choices especially in light of the fact that more and more students say they expect not only to attend college but to earn at least a bachelor's degree. Adelman (2006) found that 12th graders who expected to earn at least a bachelor's degree increased from 22.5 percent in 1982 to 59.4 percent in 1992. In 2004, this percentage increased to 75.7% (U.S. Department of Education, 2006a).

Parental aspirations have long been considered an important variable in postsecondary educational attainment (Lippman et al., 2008; Osokoya, 2005). Children whose parents speak to them often about going to college stand a greater chance of doing so. Aspirations are a more active concept than expectations (Adelman, 2006) and for the purposes of this study refer to how far a parent wants his or her child to go in school. While studies have examined the relationship between parental aspirations and postsecondary outcome, less is known about their relationship to curricular choices in high school.

Socioeconomic status (SES) and its relationship to the high school curriculum has been a subject of much debate and investigations have produced confounding results. Adelman (2006), for example, found schools that served a predominantly low-SES population were less likely to offer courses beyond Algebra 2 while Riehl, Pallas, and Natriello (1999) reported that such schools go to great lengths to offer advanced courses even when enrollment is low. Other have argued that SES creates a developmental academic pathway early on that allows those from higher-SES strata entrance to more advanced courses while excluding those from a lower SES (Attewell & Domina, 2008; Crosnoe & Huston, 2007). In other words, students from a higher SES will begin high school at a more advanced course level because of a more privileged academic preparation than those from a lower SES. The latter group would be excluded from going beyond Algebra 2, for example, because of their math starting point in freshman year of high school.

Less investigation has been done on family composition (single- versus dual-parent families) and its effect upon curriculum intensity perhaps because of the often assumed high correlation between SES and family composition. Studies have examined the association between family composition and problems in school (see, for example, DeLeire & Kalil, 2003; Hill, Yeung, & Duncan, 2001; Schiller, Khmelkov, & Wang, 2002). While it is true that on average dual-parent families belong to a higher SES than single-parent families, it cannot be assumed that those from single-parent families will follow a less intense curriculum. What does seem more evident from previous research is that a cumulative effect of familial loss, where being in an alternate family is just one example of loss, can have negative effects upon a child's performance in school (Hill et al, 2001; Teachman, 2003).

PURPOSE OF THE PRESENT STUDY

In contrast to previous research, this study uses intensive math course-taking not as a predictor variable but as an outcome variable. If we can predict that certain factors have a greater or less influence in allowing students to pursue more intensive math course-taking, school counselors will be in a stronger position to advocate for those less likely to go beyond Algebra 2. They can encourage students to pursue an academic curriculum consistent with their postsecondary goals that, according to current data, increasingly include the completion of a baccalaureate degree. Understanding the significance of going beyond Algebra 2 and the contributing factors to this process can be an important articulation of the school counselor's contemporary role in promoting greater academic achievement/attainment for all students. Specific research questions include the following: Are there certain predictors that allow us to account for the variance in separating those who complete more intensive math from those who do not? What background variables account for the greatest significance? Is intensive math course-taking simply a function of cognitive ability (math standardized scores) and/or achievement (GPA)? What happens to the significance of demographic factors once academic factors are added to the equation?

METHOD

Our data came from the 2002-2004 Educational Longitudinal Study (ELS; U.S. Department of Education, 2004). The base year of ELS included 10th graders in 2002, and the first follow-up took place in 2004 along with the high school transcripts, a restricted use file that contained academic data on the participants for all 4 years of high school (U.S. Department of Education, 2006a, 2006b). ELS began in 2002 with a nationally representative probability sample of 15,362 10th graders and collected subsequently a second wave of data in 2004 from the same base-year participants who were in senior year. A total of 13,420 seniors participated in the second wave. Base-year data also were collected from 13,488 parents, 7,135 teachers, 743 principals, and 718 librarians.

Participants

Transcript data were not available for all who participated in the second wave of ELS 2002. As a result, 11,909 seniors scheduled to graduate in 2004 were eligible for the present study. The participants were divided equally according to gender: 50% were female and 50% were male. Their racial identification was 1% Native American, 4.1% Asian, 14.4% African American, 15.5% Latino, and 65% White. Table 1 shows the SES of participants in quartile percentages. In regards to location, 34% of the participants attended urban, 48% suburban, and 18% rural schools while 77% attended public, 13% Catholic, and 10% other private schools. Data were weighted to adjust for unequal probabilities in the selection of students and to adjust for the fact that not all selected students participated (see Ingels, Pratt, Rogers, Siegel, & Stutts, 2004). In addition, weighting was used to adjust for nonresponse bias. Data analysis using SPSS incorporated a relative weight derived by dividing the panel weight of the database by the average weight of the sample.

Variables

The study employed two categories of predictors: background and academic variables. For the independent/predictor variables, data came from the 2002 base year file while for the dependent variable, math course-taking, data came from the 2004 transcript file. Background variables included gender, SES (measured in quartiles), race (Native American, Asian, African American, Latino, and White), family composition (single vs. dual parent), student postsecondary school expectations (less than a baccalaureate degree vs. baccalaureate degree or higher), parent aspirations for student's postsecondary schooling (less than a baccalaureate degree vs. baccalaureate degree or higher), and whether or not the student was ever in an English as a Second Language (ESL) or bilingual class.

For the purposes of this study, student-participant and parent-participant formed the basic unit of analysis for the independent predictors. The two academic variables were 10th-grade GPA based on school-provided transcripts and standardized math achievement scores generated from the same test administered to participants by the National Center for Educational Statistics (NCES) and also recorded in 10th grade. NCES measured math achievement through the use of math standardized tests with item response theory (IRT) scores converted to T scores. IRT scores use a pattern of right, wrong, and omitted responses to account for the difficulty, discriminating ability, and guess-ability of each item (Ingels, Pratt, Rogers, & Siegel, 2005).

The ELS 2004 High School Transcript file created a math course-taking pipeline variable that consisted of six levels of math: Level 1 (no math), Level 2 (basic math), Level 3 (core secondary through Algebra 2), Level 4 (trigonometry, statistics), Level 5 (precalculus), and Level 6 (calculus). In order to create the dependent variable, the six levels of math were dichotomized into Algebra 2 or less (levels 1, 2, and 3) and more than Algebra 2 (Levels 4, 5, and 6).

Data Analysis

The dependent variable in this analysis was math course-taking in high school, a categorical variable with two levels: Algebra 2 or less, and more than Algebra 2. In order to model the relationship between a categorical dependent variable and a set of independent or predictor variables, a multinomial logistic regression was used (Norusis, 2004). Logistic regression models produce odds ratios for the independent variables. These odds reflect the increase or decrease in the likelihood of an outcome (e.g., level of math course-taking) for every one-unit increase in the independent variables. Since our dependent variable had two possible values, one nonredundant logit is formed. For each group of the dependent variable, the log of the ratio of the probability of being in that group is compared to being in the baseline group. For this analysis, the second category (more than Algebra 2) was the baseline or reference group to which the other group was compared based on the independent variables.

Two multinomial logistic regression models were created: Model 1, which used only demographic variables as predictors, and Model 2, which added the two academic variables, math achievement scores and 10th-grade GPA, to the eight background variables. This arrangement is consistent with previous research (Adelman, 1999, 2006; Trusty, 2002; Trusty & Niles, 2003) that has considered demographic factors separate and in conjunction with academic variables as predictors of baccalaureate degree completion. Rather than baccalaureate degree completion, this study uses completion or not of a course beyond Algebra 2 as the outcome variable. The use of both models allows us to answer two questions: First, if all we know about the participants were demographics, what would the various associations of demography look like in regards to taking a course beyond Algebra 2? Second, what happens to these associations when academic variables are added to the mix?

RESULTS

Likelihood ratio tests for Model 1 indicated that all eight background variables (gender, SES, student expectations, parent aspirations, race, ESL class, bilingual class, and family composition) were significant in the overall model. Likelihood ratio tests for Model 2 indicated that gender ([chi square] [1, 11,359] = 2.22, p = .09), ESL ([chi square] [1, 11,357] = .91, p = .341), and family composition ([chi square] [1, 11,359] = 2.60, p = .18) were not significant in the overall model and therefore were dropped from subsequent analyses. The revised Model 2 included the five remaining background variables (SES, student expectations, parent aspirations, race, and bilingual class) plus the two academic variables. Correlations for the variables used in the principal analysis are reported in Table 2.

For Model 1, the multinomial logistic regression examining the effects of the eight background-only/predictor variables produced the likelihood ratio test for the overall model and revealed that the overall model was significantly better than the intercept-only model ([chi square] [13, 1840.65] = 2669.37, p < .000). In other words, the null hypothesis (that the regression coefficients of the independent variables are zero) was rejected. In addition, the likelihood ratio test for individual effects reveals that all of the independent variables are significantly related to the categories of the dependent variable (gender: [chi square] [1] = 8.95, p < .01; SES: [chi square] [3] = 366.48, p < .001; student expectations: [chi square] [1] = 512.43, p < .001; parent aspirations: [chi square] [1] = 110.26, p < .001; race: [chi square] [4] = 214.37, p < .001; bilingual class: [chi square] [1] = 165.90, p < .001; ESL class: [chi square] [1] = 44.37, p < .001; family composition: [chi square] [1] = 16.14, p < .001).

In Model 2, which added the two academic variables (10th-grade math achievement scores and GPA) and removed gender, ESL, and family composition, the likelihood ratio test for the overall model again revealed that the overall model was significantly better than the intercept-only model ([chi square] [12, 11,537] = 5149.94, p < .001). The likelihood ratio test for individual effects in Model 2 reveals that all of the independent variables are significantly related to the categories of the dependent variable (math achievement: [chi square] [1] = 960.63, p < .001; GPA: [chi square] [1] = 679.60, p < .001; SES: [chi square] [3] = 83.63, p < .001; student expectations: [chi square] [1] = 98.25, p < .001; parent aspirations: [chi square]2 [1] = 21.10, p < .001; race: [chi square] [4] = 121.10, p < .001; bilingual class: [chi square] [1] = 27.44, p < .001).

Table 3 reports the parameter estimates from the logistic regression model examining the effects of the independent variables on math course-taking status. Estimates of the predictor variables are provided for the two different levels of math: Algebra 2 or less and more than Algebra 2. According to these results, the parameter estimates in Model 1 for all eight background variables (gender, SES, student expectations, parent aspirations, race, bilingual class, ESL class, and family composition) are significantly different from zero for the logit (Algebra 2 or less compared to more than Algebra 2). In other words, all these positively related to this distinction. For gender, men were coded the value 1 and women were coded the value 2. Therefore, because the logistic regression coefficient is positive, men were slightly less likely to complete a course beyond Algebra 2 than women.

For SES, the highest quartile is the comparison category. Therefore, those in the highest SES quartile were 3 times less likely (odds = 3.04) to complete a course in Algebra 2 or less than those in the lowest quartile and 2 1/2 times less likely (odds = 2.46) than those in the second SES quartile, and almost 2 times less likely (odds = 1.79) than those in the third SES quartile. This was true even when compared to those in the third SES quartile who were 79 times (in Model 1) more likely to not complete a course beyond Algebra 2 in comparison to those in the highest SES quartile. These odds increase even more dramatically when compared to those students in the second quartile, who were 146 times more likely to not complete a course beyond Algebra 2 while those in the first quartile were 200 times more likely to not advance beyond Algebra 2.

As for student expectations, those students who expected to complete less than a baccalaureate degree were more than 4 times less likely (odds = 4.23) to complete a course beyond Algebra 2 than those who expected to complete a baccalaureate degree or higher. The same is true for parent aspirations though to a lesser degree. Students whose parents wanted them to complete less than a baccalaureate were a little over 2 times more likely (odds = 2.30) to complete a course in Algebra 2 or less than those whose parents wanted them to complete a 4-year college degree.

As for race, Native Americans were almost 4 times more likely (odds = 3.79), African Americans 1 1/2 times more likely (odds = 1.44) and Latinos twice as likely (odds = 1.97) to complete a course in Algebra 2 or less than Whites (the comparison category). Asians were slightly less likely than Whites to complete a course in Algebra 2 or less than a course in more than Algebra 2. In regards to bilingual class, those who were ever in a bilingual class were slightly less likely to complete a course in Algebra 2 or less while those who were ever in an ESL class were almost twice as likely (odds = 1.72) to complete a course in Algebra 2 or less than a course in more than Algebra 2. Finally, in regards to family composition, those students who came from dual-parent families were less likely (23% greater chance) to take a course in less than Algebra 2 than those from single-parent families. Regarding effect sizes, the Nagelkerke [R.sup.2] (Norusis, 2004) in the overall model was .27, considered to be a large effect size (Sink & Stroh, 2006). Therefore, the independent variables included in the model explained 27% of the variability between those who completed Algebra 2 or less and those who completed courses beyond Algebra 2.

Table 3 also reports the results from the logistic regression for Model 2 where two academic variables, math achievement scores and 10th-grade GPA, have been added. The addition of these two variables reduced, to some degree, the significance of the background variables. Gender, ESL, and family composition were dropped from the original model. SES continues to be a significant contributor to math course-taking in Model 2 with those in the lowest quartile (odds = 1.74), the second quartile (odds = 1.71), and the third quartile (odds = 1.40) more likely to have course completion in Algebra 2 or less than those in the highest SES quartile.

The same is true for student expectations (odds = 2.08) and parent aspirations (odds = 1.50) with students who expected and parents who aspired to less than a baccalaureate were more likely to complete a course in Algebra 2 or less. Among our sample, 94.3% of the 45% who said they expected to attain a baccalaureate degree or higher completed a course beyond Algebra 2. On the other hand, of the 55% who did not complete a course beyond Algebra 2, 68.7% said they expected to attain a baccalaureate degree or higher.

In regards to race, the differences between Native Americans and Whites, and Asian Americans and Whites, are the same as in Model 1. Native Americans were much more likely (odds = 2.11) and Asian Americans slightly less likely to have terminated their math course-taking with Algebra 2 or less when compared with Whites. However, in contrast to Model 1, African Americans in Model 2 were less likely than Whites to have completed Algebra 2 or less, and the difference between Latinos and Whites in regards to math course-taking was not significant.

Finally, both academic variables (math achievement scores from sophomore year and 10th-grade GPA) contributed significantly to whether or not a student went beyond Algebra 2. Because both these variables are continuous, for every one-unit decrease in math standardized scores and GPA, the more likely a student would remain at Algebra 2 or less. Regarding effect sizes, the Nagelkerke [R.sup.2] (Norusis, 2004) in the overall model was .462, considered to be a large effect size (Sink & Stroh, 2006). Therefore, the independent variables included in the second model explained 46% of the variability between those who completed a course in Algebra 2 or less and those who completed courses beyond Algebra 2.

DISCUSSION

Both models significantly predicted course-taking beyond Algebra 2. Background variables alone accounted for 27% of the variability, and this increased to 46% when two academic variables are added. Math achievement scores and GPAs from sophomore year, when added as predictors to the equation, reduced or eliminated some of the significance of the background variables. This is consistent with previous research on baccalaureate degree completion (Adelman, 1999; Alexander, Riordan, Fennessey, & Pallas, 1982) in which academic background, a composite variable of curriculum and GPA/class rank, was far more important than demographic variables. Adelman (2006) added senior test scores (the equivalent of a mini-SAT) to the composite academic variable and produced the same result in regards to demography. The present study is taking a step backward in the path toward baccalaureate degree completion by using Algebra 2 as a threshold course along the path and examining the variables that contribute most strongly to going beyond Algebra 2. This study reveals the same pattern as other studies that have examined degree completion: academics (GPA and math achievement), while not eliminating the importance of demographics, certainly reduce their significance.

Gender was a significant predictor in Model 1 with women, in general, more likely than men to go beyond Algebra 2, but it was not significant in Model 2. Today, with more women than men going to college, these results, while distinct from those in the past, are not all that surprising. If, in general, more women than men are going to college, than it stands to reason that more women than men are following a curriculum designed to have greater success in college. But when GPA and math achievement are controlled for, gender ceases to be a significant factor, a result consistent with other research (Riegle-Crumb, 2006). The idea advanced for so long and so often that men are better at math than women and could have easily led to women pursuing a less intense math curriculum in high school appears unsupportable. If anything, the opposite is true. With equal or greater numbers of women than men pursuing courses beyond Algebra 2, concerns about women being less prepared for success in college are no longer valid. On the contrary, the results of this study indicate a greater concern about men not being adequately prepared for postsecondary education.

SES was a strong, significant predictor in both models. This finding is of little surprise with those in the highest-SES quartile more likely to complete math courses beyond Algebra 2 when compared to students in lower-SES quartiles. Having resources makes a difference when it comes to curriculum intensity in math. Nevertheless, when math achievement scores and GPA are added to the mix, the predictive effect of SES is noticeably diminished. For those in the lowest-SES quartile, their chances of completing a course beyond Algebra 2 increase by almost 50% when they were performing well academically but are still less likely to do so when compared to those who are wealthy. It may be, as previous research has suggested (see, for example, Adelman, 2006), that schools with low-SES students were less likely to offer mathematics courses beyond Algebra 2. Another possibility is the intersection of race and SES. Among the participants of this study, more African American and Latino students came from the two lowest-SES quartiles compared to other racial groups, and failure rates in math are significantly higher among African American and Latino students compared to their Asian and White peers. Riegle-Crumb (2006) found that approximately 20% of all male African American and Latino students fail their freshman year math course with female counterparts exhibiting a slightly less percentage. Students who fail their freshman year math course will have greater difficulty reaching higher level math courses as they will most likely find themselves repeating freshman year math in sophomore year.

Student expectations along with parent aspirations are a powerful predictor in regards to math course-taking. Students who expected to complete a baccalaureate degree or higher were more than 4 times more likely in Model 1, and 2 times more likely in Model 2, to complete a course beyond Algebra 2. However, there were still a large number of students who indicated in sophomore year that they expected to complete a baccalaureate degree who followed a math curriculum (completing Algebra 2 or less) that research shows does not adequately prepare them for success in college. Only among Whites and Asian Americans did more students than not go beyond Algebra 2 who said they wanted to attain a baccalaureate degree. In other words, among Native Americans, African Americans, and Latinos, the number of students who said they expected to attain a baccalaureate degree or higher and did not complete a course in Algebra 2 was higher than the number of students who said they expected to attain a baccalaureate degree or higher and did complete a course beyond Algebra 2.

The data indicate that a large number of students of color are not following a curriculum designed to successfully meet their expectations of postsecondary life. One explanation for this discrepancy may be that the expectation for completing a baccalaureate degree was student reported at a particular point in time--sophomore year. As such, the measure of expectations lacks consistency. Students may very well say they want to go to college without revealing the seriousness of the intent, the self-efficacy behind the expectation, or accurate knowledge about what is needed to get into a 4-year college. This may be especially true for first-generation college-bound students who may be more limited in accessing and understanding accurate information about the college process information (Pascarella, Pierson, Wolniak, & Terenzini, 2004). School counselors need to evaluate a student's expectation for college in terms of anticipation, a construct that describes both the consistency and level of a student's expectation (Adelman, 2006). For example, students who in sophomore year say they expect to graduate from a 4-year college should be asked the same question in junior year to test the consistency of the expectation. If the expectation is consistent, the school counselor can plan the senior-year math course, often voluntary, according to the student's future plans.

When examining parent aspirations, the same pattern emerges as with student expectations. Overall, in both models, whether or not parents wanted their child to attain a baccalaureate degree is a significant predictor of math course-taking. Yet, except for Asian Americans and Whites, more students whose parents aspired for them to attain a college degree failed to complete a course beyond Algebra 2 when compared to the number of students who actually did. Put another way, for many Native American, African American, and Latino students, parent aspirations for their children's postsecondary life are not consistent with their children's curriculum, at least in terms of math course-taking. What appears to be emerging from the results of this study is that, while overall expectations and aspirations are significant predictors for math course-taking in high school, differences do exist across racial groups in regards to how well those expectations and aspirations are consistent with what students are actually doing. Research has documented that racial minorities have equal or greater educational aspirations than Whites (see, for example, Jodl, Michael, Malanchuk, Eccles, & Sameroff, 2001; Qian & Blair, 1999). Emerging from this study is that among African American, Latino, and Native American high school students, their course-taking in math is not consistent with either their expectations or their parents' aspirations for postsecondary educational achievement. The results of this study indicate that school counselors need to focus their attention on those racial minority students who expect to earn a baccalaureate degree and do not follow a high school curriculum, especially in math, that would increase the probability of meeting their expectations.

Race as an overall predictor resulted in some interesting comparisons especially across the two models. Whites were the comparison category in both models and when only background factors were considered, Native Americans, African Americans, and Latinos were more likely than Whites to not complete a course beyond Algebra 2. Only Asian Americans were slightly more likely than Whites to complete a course beyond Algebra 2. When the two academic variables were added, however, the results changed somewhat dramatically in that not only Asian Americans and but also African Americans were slightly more likely than Whites to complete a course beyond Algebra 2 while Native Americans were less likely to do so with no significant difference between Latinos and Whites. Achievement seems to moderate racial differences when it comes to math course-taking. Simply put, if students do well academically, their math course curriculum, regardless of race, will appear more similar than different. It is very possible, then, that prior achievement levels determine math course-taking. However, when African American, Latino, and White students follow the same rigorous math curriculum, their math scores improve equally well (National Assessment of Educational Progress, 1994). One argument is the need for early intervention to minimize the achievement gap among racial groups so that by the time students reach high school, intensive course-taking will be more similar than different. On the other hand, do school counselors take the chance of putting students in a more challenging course, regardless of prior achievement, with the understanding that a more rigorous curriculum will eventually lead to higher achievement levels in math?

Two other background variables with significant predictive ability were bilingual class and ESL class. There are some interesting distinctions between the two. In both models, being in a bilingual class increased the odds of completing a course beyond Algebra 2, but the opposite was true for participation in an ESL class (at least in Model 1 as ESL was not a significant predictor in Model 2). It may be somewhat surprising at first that bilingual class and ESL would have different effects upon math course-taking in high school. One possible explanation is that participation in bilingual class is voluntary and not so in ESL class. In most states, ESL learners are required to take a language proficiency exam. If they score below a certain threshold, the students are then required to participate in ESL, thereby making ESL a very heterogeneous group in regards to levels of achievement and ability in other subject areas. Students and parents, on the other hand, can opt for a bilingual program if it exists in their school system. It is possible that those who opt for such a program receive more support and may have more motivation to achieve, evidenced by opting for such a program. Those in bilingual programs are generally separated from the mainstream student body for most of their classes where they receive special attention.

Thompson (2009) examined both sides of the issue through a school in Prince William County, Virginia--Cecil B. Hylton High School in Woodbridge. The report confirmed that those immigrant students who were in special programs did have higher achievement levels, albeit at the price of being segregated from the mainstream population. The political aspects of such programs cannot be minimized. In recent years, Arizona, California, and Massachusetts have had policies that either limited or eradicated bilingual programs, and how best to deal with recent immigrants to our school systems continues to be a hotly debated topic. This study appears to confirm in some small way that segregated programs in the form of bilingual classes do predict better outcomes, at least in the area of intensive math course-taking.

Finally, family composition (single- versus dual-parent) was a significant predictor of math course-taking in Model 1 but not in Model 2. While some may argue that family composition and SES are highly correlated, the data from this study indicate that, while significant, the correlation between the two is relatively modest and warrants a discussion of family composition separate from SES. Previous research has indicated that family structure does have an effect upon the intensity of math course-taking in high school. For example, Cavanagh, Schiller, and Riegle-Crumb (2006) found that adolescents in less stable families were less likely to complete Algebra 1 in the ninth grade. No one is suggesting that single-parent families are less stable than dual-parent families, but one explanation for why students from dual-parent families have a greater chance of going beyond algebra may be a parent involvement issue. Single parents may have more difficulty finding the time to provide the necessary academic support for their children in the form of monitoring and helping with their child's schoolwork. This also may explain why family composition was not significant in Model 2. If students are doing well academically early on in high school, they may be able to function more independently and rely less on parental support to intensify their academic curriculum.

Implications for School Counselors

The results of this study have some practical implications for school counselors in their role of curriculum planning with high school students. Results showed that student expectations overall were a very strong predictor for math course completion beyond Algebra 2. Furthermore, among the Native American, African American, and Latino populations, the number of students who said they expected to go to college and did not complete a course beyond Algebra 2 was greater than the number who did go beyond Algebra 2. School counselors who work with these racial subgroups can be more proactive in aligning students' curricular choices with their expectations. If students say they expect to go to college, then it becomes incumbent upon the school counselor to challenge students, evaluate the seriousness of the expectation, and facilitate an intensification of the math curriculum, if indeed the expectation is judged as consistently serious. "I'm not good at math," "I don't like math," or "I'm done with math" are simply not acceptable positions for those who wish to proceed to and succeed in higher education. Because many curricular decisions are based upon past performance, what happens to an average student in math who tells the school counselor his or her expectations of going to and succeeding in a 4-year college? Situations like these truly define the role of the school counselor. On the one hand, the school counselor does not want to place students in courses in which they will have difficulty passing; on the other hand, the school counselor's job is to challenge students and support their expectations with good curricular decisions.

Because math course-taking becomes largely voluntary over time (Crosnoe & Huston, 2007), school counselors might consider using "choice theory" (Glasser, 1998, 2002, 2005) in working with students around course selection. If students say they want to succeed in a 4-year college but indicate reluctance in pursuing more than the required math for graduation, the school counselor can emphasize that the students' current choices are not consistent with what they want in the future. This study has found that the lack of appropriate classes consistent with expectations was especially true for African American, Latino, and Native American students. One of the reasons for this lack of consistency is that state diploma requirements do not specify courses in math but simply the number of math credits needed (ACT, 2007). School counselors who work with racial minority groups have to be proactive in educating students and parents that simply having enough math credits to graduate is not adequate preparation for success in college.

In addition, counselors who work with immigrant children ought to consider, if the possibility exists, a bilingual program versus simply being in ESL class. While bilingual education may not exist in all school systems or may not be in the student's language, it does appear that bilingual class was a significant predictor of more intensive math course-taking. If there are a large number of bilingual students and no bilingual education, school counselors, in their advocate role, might consider lobbying for such a program in their schools.

This study also raises the awareness of gender equity in regards to math course-taking in line with other research that has shown the same in terms of math achievement. Today, more women attend college than men and it is reasonable to expect that women would intensify their math course-taking to increase their chances of success in college. School counselors are urged to use the results of this study to encourage those women who may refrain from taking voluntary, intensive math courses because they think that courses like precalculus and calculus are a man's domain. Current data defy this belief, enabling school counselors to challenge, dispute, and effectuate a cognitive restructuring for those women who suffer from such an irrational belief. This would be especially true for women who plan to attend and graduate from a 4-year institution.

Limitations and Future Research

The present study suffers from a number of limitations. First, the data came from a national database of a longitudinal study published by the U.S. Department of Education's National Center for Educational Statistics. In examining the factors related to math course-taking, the investigator is limited to variables in the database. Other variables, such as self-efficacy, were not available and could play an important role in determining math course-taking. Math achievement was measured by a standardized test and raises issues of reliability. The use of a math GPA instead of an overall GPA would have helped but was not available. Another limitation is a statistical one. With very large samples, small differences can achieve levels of significance and may not represent a real difference. The discussion section highlighted what variables had greater odds ratios and could be considered real differences. Having said that, both models did have high effect sizes, meaning that overall the two models explained a high amount of the variance in distinguishing those who completed a course beyond Algebra 2 from those who did not. Therefore, counselors are urged to consider the totality of the models when understanding the implications of this study. Rather than look at one variable in particular, it is more important to look at the variables as a whole in terms of getting a profile of students who are less likely to intensify their math course-taking, to determine their postsecondary plans, and to counsel them to make more appropriate curricular choices.

Because ELS 2002 is a longitudinal study with a second wave of data from 2006 (2 years after scheduled high school graduation) already published and a fourth in the preparation stage, future studies can continue to confirm the predictive validity of math course-taking and success in college. This study built upon previous studies that supported the importance of intensive math course-taking. Future studies can examine other course-taking variables and their relationship to attaining a baccalaureate degree. Using more sophisticated designs such as path analysis, future studies might examine the pathways toward more intensive course-taking. For example, this study did not analyze the ninth-grade starting point in math of the participants, and it would be very difficult for a student to go beyond Algebra 2 if his or her ninth-grade math course was less than Algebra 1. Studies using structural equation modeling, for example, might examine more carefully the pathway to intensive math course-taking by examining variables prior to starting high school such as math achievement in middle school and ninth-grade math placement.

Finally, math course-taking among Native Americans, African Americans, and Latinos needs further investigation. Future research can investigate the reason(s) why more students from these groups who said they expected to attain a baccalaureate degree did not go beyond Algebra 2 compared to the number who did. Expectations do not necessarily equate to self-efficacy. One may self-report they expect to achieve without truly believing they are capable of meeting their expectations. The same might be true for those who work with these students. Do those responsible for their education (e.g., parents, teacher, and school counselors) believe the students can meet their expectations? If future studies could include self-efficacy variables and examine the relationship between expectation, self-efficacy, and intensive course-taking in high school, it would help to understand further the determination of curricular decisions in regards to intensive courses that are largely voluntary.

Conclusion

This study has sought to examine factors that distinguish high school students whose math curriculum includes the completion of at least one course beyond Algebra 2 from those students who do not go beyond Algebra 2. Based on previous studies that strongly supported the relationship between intensive math course-taking and the attainment of the baccalaureate degree, the present study investigated background factors alone (Model 1) and together with academic variables (Model 2) to test their predictive significance in completing a course beyond Algebra 2. The background factors with the strongest predictive odds ratios were SES, student expectations, parent aspirations, and race. Bilingual class, ESL, family composition, and gender also were significant but with weaker odds ratios. The significance of all background factors was diminished or eliminated with the addition of two academic variables, math achievement and 10th-grade GPA.

Achieving success in college has never been more important than in today's society. Without it, economic stability, while not impossible, is harder to achieve as college graduates earn, on average, about 70% more than high school graduates (Markow & Bagnaschi, 2005). Given that certain subgroups are more likely to follow a more intensive math curriculum in high school, school counselors can play a critical role in diminishing the achievement gap that exists among racial groups by being more proactive in intensifying a student's curriculum, especially in math. Because prior academic achievement diminishes some of these differences, it is also imperative that school counselors encourage and support even lower-achieving students to complete more intensive courses especially if they plan to attend and succeed in a 4-year college.

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Daniel T. Sciarra, Ph.D., is a professor of counselor education at Hofstra University, Hempstead, NY. E-mail: cprdts@hofstra.edu

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Recent influences in the field of school counseling have all emphasized the advocate role of the school counselor. The National Standards of the American School Counselor Association (ASCA, 1997; Campbell & Dahir, 1997), the ASCA National Model (2005), and the Transforming School Counseling Initiative (Education Trust, 1997) have contributed to determining the role of the school counselor as more proactive in maximizing the academic, career, and personal/social development of students. A principal form of this advocacy is curriculum planning. The high school counselor is in a unique position to help students make informed choices about courses with important consequences for their postsecondary lives.

The intensity of the high school curriculum and its relationship to postsecondary life has been a topic of investigation with a long history. A crucial turning point in this history was the publication of A Nation at Risk (National Commission on Excellence in Education, 1983), which documented that America's schools were lagging behind those of other developed nations with falling scores in reading and math and issued a dire warning about the need to improve the quality of education in the United States. As a result, major changes took place in the high school graduation requirements (Stedman & Jordan, 1986). The 1980s also saw the second of the U.S. Department of Education's national grade-cohort study, High School and Beyond, which followed a national sample of 10th graders from 1980 to 1992 and permitted an analysis of the relationships between precollegiate educational history and postsecondary educational status (U.S. Department of Education, 1995). For example, Adelman (1999) found that curriculum intensity had the greatest influence not only upon college entrance but upon bachelor's degree completion when compared to academic performance based on grade point average (GPA) or class rank and senior-year test scores. Furthermore, the most significant contributor to the strength of the curriculum was the highest level of mathematics completed by the student and that completing one course beyond Algebra 2 more than doubled the odds that students would complete their baccalaureate degree (Adelman). These effects were even stronger for African American and Latino students when compared to White and Asian students and led to the suggestion that Algebra 2 should be considered a threshold course.

Analysis on the third longitudinal cohort study, "National Educational Longitudinal Study: 1988-2000" (U.S. Department of Education, 2002), reached similar conclusions. Using this data set, Trusty and Niles (2003) found strong effects for all intensive math courses: the more intensive math courses one takes, the greater the likelihood of completing a college degree. Adelman (2006) produced similar results but also showed that, in contrast to 1982 12 graders, 1992 12th graders' chance of completing a baccalaureate degree turned positive only after completing a course beyond Algebra 2 such as trigonometry, precalculus, or calculus (Adelman). It does appear, then, from the more recent data that Algebra 2 serves as a threshold course in regards to the completion of the baccalaureate degree.

PREVIOUS RESEARCH

Research has documented that African American and Latino high school students take fewer advanced level math courses than their White peers (Jones, Mullis, Raizen, Weiss, & Weston, 1992; Ladson-Billings, 1997; Lucas, 1999; Riegle-Crumb, 2006). While the gender gap has closed recently in regards to advanced math course-taking (see, for example, Bae, Choy, Geddes, Sable, & Snyder, 2000; Freeman, 2004; Xie & Shauman, 2003), the racial gap remains wide. Based on the 2004 High School Transcript Data File (U.S. Department of Education, 2006a), 21.7% of Indian, 69% of Asian, 41.7% of African American, 34.3% of Latino, and 54.3% of White students took a course beyond Algebra 2.

Another factor worthy of consideration is English as a second language. Fry (2007) found that students who are English language learners are among the farthest behind in reading and math based on national standardized test scores. To our knowledge, no study has investigated the relationship between being an English language learner and the math curriculum in high school.

If going beyond Algebra 2 is clearly linked to the successful attainment of the baccalaureate degree, it is also important to examine the relationship between student expectations and their curricular choices especially in light of the fact that more and more students say they expect not only to attend college but to earn at least a bachelor's degree. Adelman (2006) found that 12th graders who expected to earn at least a bachelor's degree increased from 22.5 percent in 1982 to 59.4 percent in 1992. In 2004, this percentage increased to 75.7% (U.S. Department of Education, 2006a).

Parental aspirations have long been considered an important variable in postsecondary educational attainment (Lippman et al., 2008; Osokoya, 2005). Children whose parents speak to them often about going to college stand a greater chance of doing so. Aspirations are a more active concept than expectations (Adelman, 2006) and for the purposes of this study refer to how far a parent wants his or her child to go in school. While studies have examined the relationship between parental aspirations and postsecondary outcome, less is known about their relationship to curricular choices in high school.

Socioeconomic status (SES) and its relationship to the high school curriculum has been a subject of much debate and investigations have produced confounding results. Adelman (2006), for example, found schools that served a predominantly low-SES population were less likely to offer courses beyond Algebra 2 while Riehl, Pallas, and Natriello (1999) reported that such schools go to great lengths to offer advanced courses even when enrollment is low. Other have argued that SES creates a developmental academic pathway early on that allows those from higher-SES strata entrance to more advanced courses while excluding those from a lower SES (Attewell & Domina, 2008; Crosnoe & Huston, 2007). In other words, students from a higher SES will begin high school at a more advanced course level because of a more privileged academic preparation than those from a lower SES. The latter group would be excluded from going beyond Algebra 2, for example, because of their math starting point in freshman year of high school.

Less investigation has been done on family composition (single- versus dual-parent families) and its effect upon curriculum intensity perhaps because of the often assumed high correlation between SES and family composition. Studies have examined the association between family composition and problems in school (see, for example, DeLeire & Kalil, 2003; Hill, Yeung, & Duncan, 2001; Schiller, Khmelkov, & Wang, 2002). While it is true that on average dual-parent families belong to a higher SES than single-parent families, it cannot be assumed that those from single-parent families will follow a less intense curriculum. What does seem more evident from previous research is that a cumulative effect of familial loss, where being in an alternate family is just one example of loss, can have negative effects upon a child's performance in school (Hill et al, 2001; Teachman, 2003).

PURPOSE OF THE PRESENT STUDY

In contrast to previous research, this study uses intensive math course-taking not as a predictor variable but as an outcome variable. If we can predict that certain factors have a greater or less influence in allowing students to pursue more intensive math course-taking, school counselors will be in a stronger position to advocate for those less likely to go beyond Algebra 2. They can encourage students to pursue an academic curriculum consistent with their postsecondary goals that, according to current data, increasingly include the completion of a baccalaureate degree. Understanding the significance of going beyond Algebra 2 and the contributing factors to this process can be an important articulation of the school counselor's contemporary role in promoting greater academic achievement/attainment for all students. Specific research questions include the following: Are there certain predictors that allow us to account for the variance in separating those who complete more intensive math from those who do not? What background variables account for the greatest significance? Is intensive math course-taking simply a function of cognitive ability (math standardized scores) and/or achievement (GPA)? What happens to the significance of demographic factors once academic factors are added to the equation?

METHOD

Our data came from the 2002-2004 Educational Longitudinal Study (ELS; U.S. Department of Education, 2004). The base year of ELS included 10th graders in 2002, and the first follow-up took place in 2004 along with the high school transcripts, a restricted use file that contained academic data on the participants for all 4 years of high school (U.S. Department of Education, 2006a, 2006b). ELS began in 2002 with a nationally representative probability sample of 15,362 10th graders and collected subsequently a second wave of data in 2004 from the same base-year participants who were in senior year. A total of 13,420 seniors participated in the second wave. Base-year data also were collected from 13,488 parents, 7,135 teachers, 743 principals, and 718 librarians.

Participants

Transcript data were not available for all who participated in the second wave of ELS 2002. As a result, 11,909 seniors scheduled to graduate in 2004 were eligible for the present study. The participants were divided equally according to gender: 50% were female and 50% were male. Their racial identification was 1% Native American, 4.1% Asian, 14.4% African American, 15.5% Latino, and 65% White. Table 1 shows the SES of participants in quartile percentages. In regards to location, 34% of the participants attended urban, 48% suburban, and 18% rural schools while 77% attended public, 13% Catholic, and 10% other private schools. Data were weighted to adjust for unequal probabilities in the selection of students and to adjust for the fact that not all selected students participated (see Ingels, Pratt, Rogers, Siegel, & Stutts, 2004). In addition, weighting was used to adjust for nonresponse bias. Data analysis using SPSS incorporated a relative weight derived by dividing the panel weight of the database by the average weight of the sample.

Variables

The study employed two categories of predictors: background and academic variables. For the independent/predictor variables, data came from the 2002 base year file while for the dependent variable, math course-taking, data came from the 2004 transcript file. Background variables included gender, SES (measured in quartiles), race (Native American, Asian, African American, Latino, and White), family composition (single vs. dual parent), student postsecondary school expectations (less than a baccalaureate degree vs. baccalaureate degree or higher), parent aspirations for student's postsecondary schooling (less than a baccalaureate degree vs. baccalaureate degree or higher), and whether or not the student was ever in an English as a Second Language (ESL) or bilingual class.

For the purposes of this study, student-participant and parent-participant formed the basic unit of analysis for the independent predictors. The two academic variables were 10th-grade GPA based on school-provided transcripts and standardized math achievement scores generated from the same test administered to participants by the National Center for Educational Statistics (NCES) and also recorded in 10th grade. NCES measured math achievement through the use of math standardized tests with item response theory (IRT) scores converted to T scores. IRT scores use a pattern of right, wrong, and omitted responses to account for the difficulty, discriminating ability, and guess-ability of each item (Ingels, Pratt, Rogers, & Siegel, 2005).

The ELS 2004 High School Transcript file created a math course-taking pipeline variable that consisted of six levels of math: Level 1 (no math), Level 2 (basic math), Level 3 (core secondary through Algebra 2), Level 4 (trigonometry, statistics), Level 5 (precalculus), and Level 6 (calculus). In order to create the dependent variable, the six levels of math were dichotomized into Algebra 2 or less (levels 1, 2, and 3) and more than Algebra 2 (Levels 4, 5, and 6).

Data Analysis

The dependent variable in this analysis was math course-taking in high school, a categorical variable with two levels: Algebra 2 or less, and more than Algebra 2. In order to model the relationship between a categorical dependent variable and a set of independent or predictor variables, a multinomial logistic regression was used (Norusis, 2004). Logistic regression models produce odds ratios for the independent variables. These odds reflect the increase or decrease in the likelihood of an outcome (e.g., level of math course-taking) for every one-unit increase in the independent variables. Since our dependent variable had two possible values, one nonredundant logit is formed. For each group of the dependent variable, the log of the ratio of the probability of being in that group is compared to being in the baseline group. For this analysis, the second category (more than Algebra 2) was the baseline or reference group to which the other group was compared based on the independent variables.

Two multinomial logistic regression models were created: Model 1, which used only demographic variables as predictors, and Model 2, which added the two academic variables, math achievement scores and 10th-grade GPA, to the eight background variables. This arrangement is consistent with previous research (Adelman, 1999, 2006; Trusty, 2002; Trusty & Niles, 2003) that has considered demographic factors separate and in conjunction with academic variables as predictors of baccalaureate degree completion. Rather than baccalaureate degree completion, this study uses completion or not of a course beyond Algebra 2 as the outcome variable. The use of both models allows us to answer two questions: First, if all we know about the participants were demographics, what would the various associations of demography look like in regards to taking a course beyond Algebra 2? Second, what happens to these associations when academic variables are added to the mix?

RESULTS

Likelihood ratio tests for Model 1 indicated that all eight background variables (gender, SES, student expectations, parent aspirations, race, ESL class, bilingual class, and family composition) were significant in the overall model. Likelihood ratio tests for Model 2 indicated that gender ([chi square] [1, 11,359] = 2.22, p = .09), ESL ([chi square] [1, 11,357] = .91, p = .341), and family composition ([chi square] [1, 11,359] = 2.60, p = .18) were not significant in the overall model and therefore were dropped from subsequent analyses. The revised Model 2 included the five remaining background variables (SES, student expectations, parent aspirations, race, and bilingual class) plus the two academic variables. Correlations for the variables used in the principal analysis are reported in Table 2.

For Model 1, the multinomial logistic regression examining the effects of the eight background-only/predictor variables produced the likelihood ratio test for the overall model and revealed that the overall model was significantly better than the intercept-only model ([chi square] [13, 1840.65] = 2669.37, p < .000). In other words, the null hypothesis (that the regression coefficients of the independent variables are zero) was rejected. In addition, the likelihood ratio test for individual effects reveals that all of the independent variables are significantly related to the categories of the dependent variable (gender: [chi square] [1] = 8.95, p < .01; SES: [chi square] [3] = 366.48, p < .001; student expectations: [chi square] [1] = 512.43, p < .001; parent aspirations: [chi square] [1] = 110.26, p < .001; race: [chi square] [4] = 214.37, p < .001; bilingual class: [chi square] [1] = 165.90, p < .001; ESL class: [chi square] [1] = 44.37, p < .001; family composition: [chi square] [1] = 16.14, p < .001).

In Model 2, which added the two academic variables (10th-grade math achievement scores and GPA) and removed gender, ESL, and family composition, the likelihood ratio test for the overall model again revealed that the overall model was significantly better than the intercept-only model ([chi square] [12, 11,537] = 5149.94, p < .001). The likelihood ratio test for individual effects in Model 2 reveals that all of the independent variables are significantly related to the categories of the dependent variable (math achievement: [chi square] [1] = 960.63, p < .001; GPA: [chi square] [1] = 679.60, p < .001; SES: [chi square] [3] = 83.63, p < .001; student expectations: [chi square] [1] = 98.25, p < .001; parent aspirations: [chi square]2 [1] = 21.10, p < .001; race: [chi square] [4] = 121.10, p < .001; bilingual class: [chi square] [1] = 27.44, p < .001).

Table 3 reports the parameter estimates from the logistic regression model examining the effects of the independent variables on math course-taking status. Estimates of the predictor variables are provided for the two different levels of math: Algebra 2 or less and more than Algebra 2. According to these results, the parameter estimates in Model 1 for all eight background variables (gender, SES, student expectations, parent aspirations, race, bilingual class, ESL class, and family composition) are significantly different from zero for the logit (Algebra 2 or less compared to more than Algebra 2). In other words, all these positively related to this distinction. For gender, men were coded the value 1 and women were coded the value 2. Therefore, because the logistic regression coefficient is positive, men were slightly less likely to complete a course beyond Algebra 2 than women.

For SES, the highest quartile is the comparison category. Therefore, those in the highest SES quartile were 3 times less likely (odds = 3.04) to complete a course in Algebra 2 or less than those in the lowest quartile and 2 1/2 times less likely (odds = 2.46) than those in the second SES quartile, and almost 2 times less likely (odds = 1.79) than those in the third SES quartile. This was true even when compared to those in the third SES quartile who were 79 times (in Model 1) more likely to not complete a course beyond Algebra 2 in comparison to those in the highest SES quartile. These odds increase even more dramatically when compared to those students in the second quartile, who were 146 times more likely to not complete a course beyond Algebra 2 while those in the first quartile were 200 times more likely to not advance beyond Algebra 2.

As for student expectations, those students who expected to complete less than a baccalaureate degree were more than 4 times less likely (odds = 4.23) to complete a course beyond Algebra 2 than those who expected to complete a baccalaureate degree or higher. The same is true for parent aspirations though to a lesser degree. Students whose parents wanted them to complete less than a baccalaureate were a little over 2 times more likely (odds = 2.30) to complete a course in Algebra 2 or less than those whose parents wanted them to complete a 4-year college degree.

As for race, Native Americans were almost 4 times more likely (odds = 3.79), African Americans 1 1/2 times more likely (odds = 1.44) and Latinos twice as likely (odds = 1.97) to complete a course in Algebra 2 or less than Whites (the comparison category). Asians were slightly less likely than Whites to complete a course in Algebra 2 or less than a course in more than Algebra 2. In regards to bilingual class, those who were ever in a bilingual class were slightly less likely to complete a course in Algebra 2 or less while those who were ever in an ESL class were almost twice as likely (odds = 1.72) to complete a course in Algebra 2 or less than a course in more than Algebra 2. Finally, in regards to family composition, those students who came from dual-parent families were less likely (23% greater chance) to take a course in less than Algebra 2 than those from single-parent families. Regarding effect sizes, the Nagelkerke [R.sup.2] (Norusis, 2004) in the overall model was .27, considered to be a large effect size (Sink & Stroh, 2006). Therefore, the independent variables included in the model explained 27% of the variability between those who completed Algebra 2 or less and those who completed courses beyond Algebra 2.

Table 3 also reports the results from the logistic regression for Model 2 where two academic variables, math achievement scores and 10th-grade GPA, have been added. The addition of these two variables reduced, to some degree, the significance of the background variables. Gender, ESL, and family composition were dropped from the original model. SES continues to be a significant contributor to math course-taking in Model 2 with those in the lowest quartile (odds = 1.74), the second quartile (odds = 1.71), and the third quartile (odds = 1.40) more likely to have course completion in Algebra 2 or less than those in the highest SES quartile.

The same is true for student expectations (odds = 2.08) and parent aspirations (odds = 1.50) with students who expected and parents who aspired to less than a baccalaureate were more likely to complete a course in Algebra 2 or less. Among our sample, 94.3% of the 45% who said they expected to attain a baccalaureate degree or higher completed a course beyond Algebra 2. On the other hand, of the 55% who did not complete a course beyond Algebra 2, 68.7% said they expected to attain a baccalaureate degree or higher.

In regards to race, the differences between Native Americans and Whites, and Asian Americans and Whites, are the same as in Model 1. Native Americans were much more likely (odds = 2.11) and Asian Americans slightly less likely to have terminated their math course-taking with Algebra 2 or less when compared with Whites. However, in contrast to Model 1, African Americans in Model 2 were less likely than Whites to have completed Algebra 2 or less, and the difference between Latinos and Whites in regards to math course-taking was not significant.

Finally, both academic variables (math achievement scores from sophomore year and 10th-grade GPA) contributed significantly to whether or not a student went beyond Algebra 2. Because both these variables are continuous, for every one-unit decrease in math standardized scores and GPA, the more likely a student would remain at Algebra 2 or less. Regarding effect sizes, the Nagelkerke [R.sup.2] (Norusis, 2004) in the overall model was .462, considered to be a large effect size (Sink & Stroh, 2006). Therefore, the independent variables included in the second model explained 46% of the variability between those who completed a course in Algebra 2 or less and those who completed courses beyond Algebra 2.

DISCUSSION

Both models significantly predicted course-taking beyond Algebra 2. Background variables alone accounted for 27% of the variability, and this increased to 46% when two academic variables are added. Math achievement scores and GPAs from sophomore year, when added as predictors to the equation, reduced or eliminated some of the significance of the background variables. This is consistent with previous research on baccalaureate degree completion (Adelman, 1999; Alexander, Riordan, Fennessey, & Pallas, 1982) in which academic background, a composite variable of curriculum and GPA/class rank, was far more important than demographic variables. Adelman (2006) added senior test scores (the equivalent of a mini-SAT) to the composite academic variable and produced the same result in regards to demography. The present study is taking a step backward in the path toward baccalaureate degree completion by using Algebra 2 as a threshold course along the path and examining the variables that contribute most strongly to going beyond Algebra 2. This study reveals the same pattern as other studies that have examined degree completion: academics (GPA and math achievement), while not eliminating the importance of demographics, certainly reduce their significance.

Gender was a significant predictor in Model 1 with women, in general, more likely than men to go beyond Algebra 2, but it was not significant in Model 2. Today, with more women than men going to college, these results, while distinct from those in the past, are not all that surprising. If, in general, more women than men are going to college, than it stands to reason that more women than men are following a curriculum designed to have greater success in college. But when GPA and math achievement are controlled for, gender ceases to be a significant factor, a result consistent with other research (Riegle-Crumb, 2006). The idea advanced for so long and so often that men are better at math than women and could have easily led to women pursuing a less intense math curriculum in high school appears unsupportable. If anything, the opposite is true. With equal or greater numbers of women than men pursuing courses beyond Algebra 2, concerns about women being less prepared for success in college are no longer valid. On the contrary, the results of this study indicate a greater concern about men not being adequately prepared for postsecondary education.

SES was a strong, significant predictor in both models. This finding is of little surprise with those in the highest-SES quartile more likely to complete math courses beyond Algebra 2 when compared to students in lower-SES quartiles. Having resources makes a difference when it comes to curriculum intensity in math. Nevertheless, when math achievement scores and GPA are added to the mix, the predictive effect of SES is noticeably diminished. For those in the lowest-SES quartile, their chances of completing a course beyond Algebra 2 increase by almost 50% when they were performing well academically but are still less likely to do so when compared to those who are wealthy. It may be, as previous research has suggested (see, for example, Adelman, 2006), that schools with low-SES students were less likely to offer mathematics courses beyond Algebra 2. Another possibility is the intersection of race and SES. Among the participants of this study, more African American and Latino students came from the two lowest-SES quartiles compared to other racial groups, and failure rates in math are significantly higher among African American and Latino students compared to their Asian and White peers. Riegle-Crumb (2006) found that approximately 20% of all male African American and Latino students fail their freshman year math course with female counterparts exhibiting a slightly less percentage. Students who fail their freshman year math course will have greater difficulty reaching higher level math courses as they will most likely find themselves repeating freshman year math in sophomore year.

Student expectations along with parent aspirations are a powerful predictor in regards to math course-taking. Students who expected to complete a baccalaureate degree or higher were more than 4 times more likely in Model 1, and 2 times more likely in Model 2, to complete a course beyond Algebra 2. However, there were still a large number of students who indicated in sophomore year that they expected to complete a baccalaureate degree who followed a math curriculum (completing Algebra 2 or less) that research shows does not adequately prepare them for success in college. Only among Whites and Asian Americans did more students than not go beyond Algebra 2 who said they wanted to attain a baccalaureate degree. In other words, among Native Americans, African Americans, and Latinos, the number of students who said they expected to attain a baccalaureate degree or higher and did not complete a course in Algebra 2 was higher than the number of students who said they expected to attain a baccalaureate degree or higher and did complete a course beyond Algebra 2.

The data indicate that a large number of students of color are not following a curriculum designed to successfully meet their expectations of postsecondary life. One explanation for this discrepancy may be that the expectation for completing a baccalaureate degree was student reported at a particular point in time--sophomore year. As such, the measure of expectations lacks consistency. Students may very well say they want to go to college without revealing the seriousness of the intent, the self-efficacy behind the expectation, or accurate knowledge about what is needed to get into a 4-year college. This may be especially true for first-generation college-bound students who may be more limited in accessing and understanding accurate information about the college process information (Pascarella, Pierson, Wolniak, & Terenzini, 2004). School counselors need to evaluate a student's expectation for college in terms of anticipation, a construct that describes both the consistency and level of a student's expectation (Adelman, 2006). For example, students who in sophomore year say they expect to graduate from a 4-year college should be asked the same question in junior year to test the consistency of the expectation. If the expectation is consistent, the school counselor can plan the senior-year math course, often voluntary, according to the student's future plans.

When examining parent aspirations, the same pattern emerges as with student expectations. Overall, in both models, whether or not parents wanted their child to attain a baccalaureate degree is a significant predictor of math course-taking. Yet, except for Asian Americans and Whites, more students whose parents aspired for them to attain a college degree failed to complete a course beyond Algebra 2 when compared to the number of students who actually did. Put another way, for many Native American, African American, and Latino students, parent aspirations for their children's postsecondary life are not consistent with their children's curriculum, at least in terms of math course-taking. What appears to be emerging from the results of this study is that, while overall expectations and aspirations are significant predictors for math course-taking in high school, differences do exist across racial groups in regards to how well those expectations and aspirations are consistent with what students are actually doing. Research has documented that racial minorities have equal or greater educational aspirations than Whites (see, for example, Jodl, Michael, Malanchuk, Eccles, & Sameroff, 2001; Qian & Blair, 1999). Emerging from this study is that among African American, Latino, and Native American high school students, their course-taking in math is not consistent with either their expectations or their parents' aspirations for postsecondary educational achievement. The results of this study indicate that school counselors need to focus their attention on those racial minority students who expect to earn a baccalaureate degree and do not follow a high school curriculum, especially in math, that would increase the probability of meeting their expectations.

Race as an overall predictor resulted in some interesting comparisons especially across the two models. Whites were the comparison category in both models and when only background factors were considered, Native Americans, African Americans, and Latinos were more likely than Whites to not complete a course beyond Algebra 2. Only Asian Americans were slightly more likely than Whites to complete a course beyond Algebra 2. When the two academic variables were added, however, the results changed somewhat dramatically in that not only Asian Americans and but also African Americans were slightly more likely than Whites to complete a course beyond Algebra 2 while Native Americans were less likely to do so with no significant difference between Latinos and Whites. Achievement seems to moderate racial differences when it comes to math course-taking. Simply put, if students do well academically, their math course curriculum, regardless of race, will appear more similar than different. It is very possible, then, that prior achievement levels determine math course-taking. However, when African American, Latino, and White students follow the same rigorous math curriculum, their math scores improve equally well (National Assessment of Educational Progress, 1994). One argument is the need for early intervention to minimize the achievement gap among racial groups so that by the time students reach high school, intensive course-taking will be more similar than different. On the other hand, do school counselors take the chance of putting students in a more challenging course, regardless of prior achievement, with the understanding that a more rigorous curriculum will eventually lead to higher achievement levels in math?

Two other background variables with significant predictive ability were bilingual class and ESL class. There are some interesting distinctions between the two. In both models, being in a bilingual class increased the odds of completing a course beyond Algebra 2, but the opposite was true for participation in an ESL class (at least in Model 1 as ESL was not a significant predictor in Model 2). It may be somewhat surprising at first that bilingual class and ESL would have different effects upon math course-taking in high school. One possible explanation is that participation in bilingual class is voluntary and not so in ESL class. In most states, ESL learners are required to take a language proficiency exam. If they score below a certain threshold, the students are then required to participate in ESL, thereby making ESL a very heterogeneous group in regards to levels of achievement and ability in other subject areas. Students and parents, on the other hand, can opt for a bilingual program if it exists in their school system. It is possible that those who opt for such a program receive more support and may have more motivation to achieve, evidenced by opting for such a program. Those in bilingual programs are generally separated from the mainstream student body for most of their classes where they receive special attention.

Thompson (2009) examined both sides of the issue through a school in Prince William County, Virginia--Cecil B. Hylton High School in Woodbridge. The report confirmed that those immigrant students who were in special programs did have higher achievement levels, albeit at the price of being segregated from the mainstream population. The political aspects of such programs cannot be minimized. In recent years, Arizona, California, and Massachusetts have had policies that either limited or eradicated bilingual programs, and how best to deal with recent immigrants to our school systems continues to be a hotly debated topic. This study appears to confirm in some small way that segregated programs in the form of bilingual classes do predict better outcomes, at least in the area of intensive math course-taking.

Finally, family composition (single- versus dual-parent) was a significant predictor of math course-taking in Model 1 but not in Model 2. While some may argue that family composition and SES are highly correlated, the data from this study indicate that, while significant, the correlation between the two is relatively modest and warrants a discussion of family composition separate from SES. Previous research has indicated that family structure does have an effect upon the intensity of math course-taking in high school. For example, Cavanagh, Schiller, and Riegle-Crumb (2006) found that adolescents in less stable families were less likely to complete Algebra 1 in the ninth grade. No one is suggesting that single-parent families are less stable than dual-parent families, but one explanation for why students from dual-parent families have a greater chance of going beyond algebra may be a parent involvement issue. Single parents may have more difficulty finding the time to provide the necessary academic support for their children in the form of monitoring and helping with their child's schoolwork. This also may explain why family composition was not significant in Model 2. If students are doing well academically early on in high school, they may be able to function more independently and rely less on parental support to intensify their academic curriculum.

Implications for School Counselors

The results of this study have some practical implications for school counselors in their role of curriculum planning with high school students. Results showed that student expectations overall were a very strong predictor for math course completion beyond Algebra 2. Furthermore, among the Native American, African American, and Latino populations, the number of students who said they expected to go to college and did not complete a course beyond Algebra 2 was greater than the number who did go beyond Algebra 2. School counselors who work with these racial subgroups can be more proactive in aligning students' curricular choices with their expectations. If students say they expect to go to college, then it becomes incumbent upon the school counselor to challenge students, evaluate the seriousness of the expectation, and facilitate an intensification of the math curriculum, if indeed the expectation is judged as consistently serious. "I'm not good at math," "I don't like math," or "I'm done with math" are simply not acceptable positions for those who wish to proceed to and succeed in higher education. Because many curricular decisions are based upon past performance, what happens to an average student in math who tells the school counselor his or her expectations of going to and succeeding in a 4-year college? Situations like these truly define the role of the school counselor. On the one hand, the school counselor does not want to place students in courses in which they will have difficulty passing; on the other hand, the school counselor's job is to challenge students and support their expectations with good curricular decisions.

Because math course-taking becomes largely voluntary over time (Crosnoe & Huston, 2007), school counselors might consider using "choice theory" (Glasser, 1998, 2002, 2005) in working with students around course selection. If students say they want to succeed in a 4-year college but indicate reluctance in pursuing more than the required math for graduation, the school counselor can emphasize that the students' current choices are not consistent with what they want in the future. This study has found that the lack of appropriate classes consistent with expectations was especially true for African American, Latino, and Native American students. One of the reasons for this lack of consistency is that state diploma requirements do not specify courses in math but simply the number of math credits needed (ACT, 2007). School counselors who work with racial minority groups have to be proactive in educating students and parents that simply having enough math credits to graduate is not adequate preparation for success in college.

In addition, counselors who work with immigrant children ought to consider, if the possibility exists, a bilingual program versus simply being in ESL class. While bilingual education may not exist in all school systems or may not be in the student's language, it does appear that bilingual class was a significant predictor of more intensive math course-taking. If there are a large number of bilingual students and no bilingual education, school counselors, in their advocate role, might consider lobbying for such a program in their schools.

This study also raises the awareness of gender equity in regards to math course-taking in line with other research that has shown the same in terms of math achievement. Today, more women attend college than men and it is reasonable to expect that women would intensify their math course-taking to increase their chances of success in college. School counselors are urged to use the results of this study to encourage those women who may refrain from taking voluntary, intensive math courses because they think that courses like precalculus and calculus are a man's domain. Current data defy this belief, enabling school counselors to challenge, dispute, and effectuate a cognitive restructuring for those women who suffer from such an irrational belief. This would be especially true for women who plan to attend and graduate from a 4-year institution.

Limitations and Future Research

The present study suffers from a number of limitations. First, the data came from a national database of a longitudinal study published by the U.S. Department of Education's National Center for Educational Statistics. In examining the factors related to math course-taking, the investigator is limited to variables in the database. Other variables, such as self-efficacy, were not available and could play an important role in determining math course-taking. Math achievement was measured by a standardized test and raises issues of reliability. The use of a math GPA instead of an overall GPA would have helped but was not available. Another limitation is a statistical one. With very large samples, small differences can achieve levels of significance and may not represent a real difference. The discussion section highlighted what variables had greater odds ratios and could be considered real differences. Having said that, both models did have high effect sizes, meaning that overall the two models explained a high amount of the variance in distinguishing those who completed a course beyond Algebra 2 from those who did not. Therefore, counselors are urged to consider the totality of the models when understanding the implications of this study. Rather than look at one variable in particular, it is more important to look at the variables as a whole in terms of getting a profile of students who are less likely to intensify their math course-taking, to determine their postsecondary plans, and to counsel them to make more appropriate curricular choices.

Because ELS 2002 is a longitudinal study with a second wave of data from 2006 (2 years after scheduled high school graduation) already published and a fourth in the preparation stage, future studies can continue to confirm the predictive validity of math course-taking and success in college. This study built upon previous studies that supported the importance of intensive math course-taking. Future studies can examine other course-taking variables and their relationship to attaining a baccalaureate degree. Using more sophisticated designs such as path analysis, future studies might examine the pathways toward more intensive course-taking. For example, this study did not analyze the ninth-grade starting point in math of the participants, and it would be very difficult for a student to go beyond Algebra 2 if his or her ninth-grade math course was less than Algebra 1. Studies using structural equation modeling, for example, might examine more carefully the pathway to intensive math course-taking by examining variables prior to starting high school such as math achievement in middle school and ninth-grade math placement.

Finally, math course-taking among Native Americans, African Americans, and Latinos needs further investigation. Future research can investigate the reason(s) why more students from these groups who said they expected to attain a baccalaureate degree did not go beyond Algebra 2 compared to the number who did. Expectations do not necessarily equate to self-efficacy. One may self-report they expect to achieve without truly believing they are capable of meeting their expectations. The same might be true for those who work with these students. Do those responsible for their education (e.g., parents, teacher, and school counselors) believe the students can meet their expectations? If future studies could include self-efficacy variables and examine the relationship between expectation, self-efficacy, and intensive course-taking in high school, it would help to understand further the determination of curricular decisions in regards to intensive courses that are largely voluntary.

Conclusion

This study has sought to examine factors that distinguish high school students whose math curriculum includes the completion of at least one course beyond Algebra 2 from those students who do not go beyond Algebra 2. Based on previous studies that strongly supported the relationship between intensive math course-taking and the attainment of the baccalaureate degree, the present study investigated background factors alone (Model 1) and together with academic variables (Model 2) to test their predictive significance in completing a course beyond Algebra 2. The background factors with the strongest predictive odds ratios were SES, student expectations, parent aspirations, and race. Bilingual class, ESL, family composition, and gender also were significant but with weaker odds ratios. The significance of all background factors was diminished or eliminated with the addition of two academic variables, math achievement and 10th-grade GPA.

Achieving success in college has never been more important than in today's society. Without it, economic stability, while not impossible, is harder to achieve as college graduates earn, on average, about 70% more than high school graduates (Markow & Bagnaschi, 2005). Given that certain subgroups are more likely to follow a more intensive math curriculum in high school, school counselors can play a critical role in diminishing the achievement gap that exists among racial groups by being more proactive in intensifying a student's curriculum, especially in math. Because prior academic achievement diminishes some of these differences, it is also imperative that school counselors encourage and support even lower-achieving students to complete more intensive courses especially if they plan to attend and succeed in a 4-year college.

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Daniel T. Sciarra, Ph.D., is a professor of counselor education at Hofstra University, Hempstead, NY. E-mail: cprdts@hofstra.edu

Table 1. Participant Socioeconomic Status by Racial Group and Quartile Percentages Lowest Second Third Fourth Racial Group Quartile Quartile Quartile Quartile % % % % M M M Native American 25.3 31.2 27.3 16.2 Asian 27.8 20.3 21.7 30.1 African American 32.4 31.1 22.2 14.3 Latino 49.9 24.4 15.8 10 White 15.6 25.1 28.1 31.2 Note. SES quartiles derived from five equally weighted components: father's education, mother's education, family income, father's income, and mother's income. Table 2. Correlations for Gender, SES, Student Expectations, Parent Aspirations, Race, Bilingual Class, ESL, Family Composition, Math Ability, and GPA Student Gender SES Expectations Gender 1.00 SES -.16 * 1.00 Student expectations .133 ** .245 ** 1.00 Parent aspirations .08 ** .20 ** .38 ** Race .01 .19 ** .03 * Bilingual class -.03 ** -.14 ** -.14 ** ESL class .00 .11 ** .06 ** Single/dual parent -.O1 .17 ** .07 ** GPA .12 ** .19 ** .26 ** Math ability -.05 ** .39 ** .35 ** Parent Bilingual ESL Aspirations Race Class Class Gender SES Student expectations Parent aspirations 1.00 Race -.04 ** 1.00 Bilingual class -.13 ** -.08 ** 1.00 ESL class .02 * .01 ** .03 ** 1.00 Single/dual parent .03 ** .16 ** -.04 ** .02 * GPA .15 ** .14 ** -.12 ** .05 ** Math ability .25 ** .25 ** -.24 ** .18 ** Single/ Dual Math Parent GPA Ability Gender SES Student expectations Parent aspirations Race Bilingual class ESL class Single/dual parent 1.00 GPA .09 ** 1.00 Math ability .15 ** .36 ** 1.00 Note. n = 11,909. * p < .05. ** p <.01. Table 3. Logistic Regression Models of Effects of Predictor Variables Upon Course-Taking Beyond Algebra 2 Model 1 Model 2 Variable B Odds B Odds Gender .12 * 1.13 SES quartile 1st 1.11 ** 3.04 .56 ** 1.74 2nd .90 ** 2.46 .53 ** 1.71 3rd .58 ** 1.79 .34 ** 1.40 4th (comparison category) Student expectations 1.44 ** 4.23 .73 ** 2.08 Parent aspirations .83 ** 2.30 .41 ** 1.50 Race/ethnicity Native American 1.33 ** 3.79 .74 * 2.11 Asian American -.63 ** 0.53 -.55 ** 0.58 African American .37 ** 1.44 -.67 ** 0.51 Latino .68 ** 1.97 .07 1.05 White (comparison category) Bilingual class -.58 ** 0.56 -.27 ** .77 ESL class .54 ** 1.72 Family composition .21 ** 1.23 Math achievement -.10 ** .91 10th-grade GPA -.73 ** .48 Note. N = 11,293. The reference category is more than Algebra 2. Gender: males = 1, females = 2. Fourth SES quartile Nvas the comparison category. Student expectations and parent aspirations: less than baccalaureate = 1, more than baccalaureate = 2. Bilingual and ESL class: 1 = yes, 2 = no. Family composition: 1 = single parent, 2 = dual parent. Math ability measured by 10th-grade standardized test score. Nagelkerke [R.sup.2] = .269 for Model 1; [R.sup.2] = .462 for Model 2. * p < .05. ** p < .001.

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Author: | Sciarra, Daniel T. |
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Publication: | Professional School Counseling |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Feb 1, 2010 |

Words: | 8927 |

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