Curricular Choice and Adolescents’ Interest in Math: The Roles of Network Diversity and Math Identity


by Brian V. Carolan & Jamaal S. Matthews - 2015

Background/Context: Over the last two decades, school districts in the United States have increasingly allowed students and their families to choose the schools they attend and, at the high school level, the courses they take. While the movement to provide more curricular choice for students and families has accelerated, so, too, has the policy emphasis on increasing students’ math achievement. The increased emphases on curricular choice and math achievement provide an opportunity to examine how students draw on their social capital when making curricular choices and whether the diversity of their relational resources is associated with math achievement.

Purpose: We build from a social capital framework to examine how students who are able to exercise curricular choice do so by drawing on their social networks and how the resources accessible through these networks, operationalized as network diversity, are associated with math achievement. We also examine how this relationship varies by students’ math interest; an important individual-level characteristic that we hypothesize moderates the influence of network diversity on math achievement.

Setting: Data for this study are from the restricted-use version of the High School Longitudinal Survey of 2009 (HSLS: 09), the fifth in a series of National Center for Education Statistics’ multisource, secondary longitudinal studies. For this study, we rely on cross-sectional base-year data (2009) when all students were in Grade 9.

Participants: Our analytic sample consists of those students who: (1) were enrolled in and able to select their fall 2009 math course; (2) have valid scores on the dependent variable; and (3) have no missing values on items that constitute the independent variable-of-interest, network diversity. This subsampling strategy resulted in a final weighted, analytic sample of 5,570 students in 920 schools.

Research Design: Secondary analysis of cross-sectional observational survey data.

Data Analysis: Multilevel models with random intercepts are used to estimate students’ math achievement and properly adjust for the nested nature of the data. The models include controls for the HSLS stratified sampling design and for the probability of selection for individuals.

Results: After controlling for student- and school-level covariates, results indicate that our operational measure of social capital, network diversity, is significantly associated with math achievement. We also find that math interest significantly moderates this relationship, indicating that the presumed returns of social capital vary by this important non-cognitive characteristic.

Conclusions: Social capital in the form of network diversity helps all students reach resource- or information-rich contacts, such as teachers and counselors. However, by examining how math interest moderates the relation between network diversity and math achievement, we directly locate our work within an underappreciated theoretical niche that explicitly links how the presumed returns of social capital vary by student-level non-cognitive characteristics (e.g., math interest). Network diversity helps all students reach resource- or information-rich contacts including teachers and counselors. However, this does not guarantee that all students will see comparable returns. Results are further discussed in relation to schools’ curricular choice policies.



Over the last two decades, school districts in the United States have increasingly allowed students and their families to choose the schools they attend and, at the high school level, the courses they take (Bielick & Chapman 2003; Tice, Chapman, Princiotta, & Bielick, 2006). The option to choose both schools and courses is based on the assumption that students and families will make informed choices that are congruent with their interests and abilities, and that under-selected options will be replaced by more attractive ones. Similar to the logic that drove the expansion of charter school legislation in the 1990s (Renzulli & Roscigno, 2005), these choice options are thought to lead to a more efficient system of schools attended by students whose interests and needs drive course offerings.    


While the movement to provide more curricular choice for students and families has accelerated (reviewed in Brickman, 2014), so, too, has the policy emphasis on increasing student participation and performance in mathematics. Driven by concerns about the ability of U.S. schools to produce post-secondary graduates prepared for STEM-related careers (Schneider, Judy, & Mazuca, 2012), states and their K–12 school districts have implemented a number of policies designed to better prepare students in these critical subject areas (National Academy of Sciences, 2005). Given the historic underperformance of American students on international tests in STEM (Aud et al., 2013), it is worth examining how the growth of choice policies intersects with students’ achievement in these critical subject areas, particularly mathematics.  


Explanations of how individuals make choices, in general, are varied (Elster, 2007).  These explanations range from rational choice theories that focus on individuals’ human capital and their motivation to minimize loss and maximize gain, to structural theories that emphasize the link between an individual’s action (e.g., choosing a course) and the social structure of which the individual is a part. Pertaining to the former, a rational choice explanation would posit that a student would choose a program of study that maximizes the student’s self-interest: If a student aspires to attend a select college, then he or she would select a course that would facilitate that trajectory (Becker & Hecken, 2009). Structural theories, however, focus attention on the relationships to which one has access and how an individual’s motivations and behaviors both shape, and are shaped by, the size and range of the social structure in which the individual is embedded (Bourdieu, 2005). Framed more generally around the concept of social capital (Coleman, 1990), this explanation gives primacy to students’ social networks and the resources that are accessible through this network.


PURPOSE


We build from this social capital framework to examine how students who are able to exercise curricular choice do so by drawing on their social networks and how the resources accessible through these networks are associated with their math achievement. First, we define and measure social capital in terms of network diversity (Lin, 1999; Lin & Erikson, 2008), arguing that students with more extensive networks are more likely to select math courses that result in higher math achievement, above and beyond the influence of other relevant student- and school-level characteristics. Next, we employ this measure in a multilevel framework on a nationally representative sample of Grade 9 students to examine whether and to what degree network diversity predicts students’ math achievement. Finally, we examine whether this relation is significantly moderated by students’ math interest, an important non-cognitive construct that is strongly associated with math-related outcomes and course selection (Fisher, Dobbs-Oates, Doctoroff, & Arnold, 2012; Waller, 2006).  


BACKGROUND


STUDENT CURRICULAR CHOICE


The idea of allowing students to select their courses reflects a historical distinction between two educational philosophies regarding the core purposes of American schooling (Ready & Lee, 2008). On one side, according to Ready and Lee (2008), progressives argued that high school courses should be more tightly linked to students’ future professions (Ayres, 1909; Bobbit, 1924). This required that schools provide a broad curriculum that included a range of offerings. Ready and Lee (2008) go on to describe how, on the other side, there existed a custodial view that argued that students’ academic needs were more similar than different, and thus intellectually challenging coursework should prepare them equally well for college or work (National Education Association, 1893). Over the past 100 years, these opposite perspectives coalesced around the idea that student academic heterogeneity was best addressed through differentiated curricula—different courses and programs for different types of students (Powell, Farrar, & Cohen, 1985). What has changed in the past two decades, however, is the mechanism through which this differentiation occurs. Rather than sort students into predetermined courses of study through tracking, more high schools now provide students significant leeway to design their own academic programs (Finn, 1997; Lee & Ready, 2007).


Without a traditional tracking mechanism to rigidly guide students through the curriculum (Lucas, 2001), academic progress rests on the assumption that students make curricular choices based on logical appraisals of their needs, abilities, and aspirations. Ready and Lee (2008) describe how this implied “rational choice” model of behavior posits that individual actions are based on self-interested evaluations of available options that are most likely to maximize personal utility (Becker, 1993). When used in the context of schooling, rational choice arguments go hand-in-hand with human capital theory to claim that whether an individual decides to invest in schooling is based on a calculation that assesses if investment will result in a worthwhile “return” (Ready & Lee, 2008).


The intuitive appeal of both rational choice and human capital theories has contributed to an educational environment that increasingly relies on student-choice processes to replace either neighborhood school-based assignment or tracking as a means to better and more efficiently match students to academic programs and courses. For example, from 1993 to 2007, the percentage of children in the United States attending a “chosen” public school (a public school other than their assigned public school) increased from 11% to 16%, while the percentage of children attending an assigned public school decreased from 80% to 73% (Planty et al., 2009). While questions persist about whether school choice programs attain desired outcomes (Buckley & Schneider, 2007), within-school choice opportunities continue to expand; for example, states such as Louisiana, Arizona, Florida, and Georgia, among others, permit some degree of curricular choice, especially at the high school level, with the intention of expanding these opportunities (Brickman, 2014).


This increased ability of high school students to choose the courses they take is occurring within a federal policy context that is emphasizing greater participation and better performance in STEM subject areas. In fact, The Race to the Top Fund, part of the American Recovery and Reinvestment Act (2009) that provides competitive grants to encourage and reward states for innovative reforms, identified STEM instruction and preparation as one of six high-priority areas.  


One key to inducing higher student achievement in STEM is to develop greater student interest in mathematics, which has historically lagged when compared to other Organization for Economic Co-operation and Development nations (Aud et al., 2012, Chapter 26). The link between students’ interest in a subject area and achievement in that area is well established (Hidi, Renninger, & Krapp, 1992), especially in mathematics (Köller, Baumert, & Schnabel, 2001; Ma, 1997). Therefore, within this context of increased curricular choice, coupled with a greater emphasis on generating interest and ultimately achievement in mathematics, it is worth examining how the social context influences the curricular choices that students are able to make and the achievement outcomes associated with these choices.    


THE SOCIAL CONTEXT OF CURRICULAR CHOICE


While rational choice theory provides an intuitive explanation for how students make curricular choices, empirical observations suggest that a more complex and muddled calculus influences these selections (McFarland & Rodan, 2009). The context in which these choices are made is influenced by a number of individual-level characteristics, specifically students’ race/ethnicity, gender, and social class (see, e.g., Carter, 2006; Mickelson, 1990; Wells & Crain, 1997). For example, ethnic minority students may be less likely to select more advanced courses when they perceive that such classes enroll few minority students (Yonezawa, Wells, & Serna, 2002). Teachers and counselors may steer disadvantaged students away from more rigorous coursework, whereas more advantaged students might be encouraged to enroll in more challenging courses (Ready & Lee, 2008). Social background is also associated with access to information about curricular choices, with disadvantaged students being less likely to have access to important knowledge (Hassrick & Schneider, 2009).  


In addition to these socio-demographic characteristics, students’ subject-specific interest levels influence their curricular choices and their associated learning outcomes, including achievement. Generally, theory and previous research suggest that students’ academic interest is a significant factor in cognitive development and learning (see Hidi, Renninger, & Krapp, 1992).  Interest, in general, promotes skill development through (1) deeper levels of information processing (Hidi, 2001; Hidi, Renninger, & Krapp, 2004; Schiefele, 1998, 2001), (2) increased time spent on a task (Schiefele, 2001), and/or (3) increased effort and sustained practice (Ericsson, Krampe, & Tesch-Römer, 1993). The relation between math interest, in particular, and math achievement is well documented in older children and adults (see the meta-analysis of Schiefele, Krapp, & Winteler, 1992). In some studies, math interest predicted later achievement (Köller et al., 2001; Schiefele & Csikszentmihalyi, 1995; Singh, Granville, & Dika, 2002), and in others, early ability was related to later attitudes (Onatsu-Arvilommi & Nurmi, 2000; Stevenson & Newman, 1986), including a greater likelihood of enrolling in more, and even more advanced, math coursework.  


Few studies, however, have gone beyond this assortment of individual-level characteristics to examine the role that students’ broader social contexts play in influencing curricular choices, which requires that the most important contexts be identified and defined (Frank et al., 2008). For example, Frank et al. (2008) describe how there is the school itself, which is essentially a collection of students with varying degrees of familiarity. However, they continue, within-school variation in course selection and learning outcomes suggests that the most salient social contexts for adolescents are defined neither by schools nor individual-level characteristics. Instead, one of the most under-appreciated contexts exists between these two levels: a web of relations—a social network—that links students to others in roles such as teachers, counselors, and peers, providing a relational infrastructure through which choices about coursework are influenced.


We consider these networks to be the key mechanisms through which students generate social capital, which we define as an investment in relations through which access to resources is gained in order to enhance an expected return (Lin, 2001). In relation to the issue of students’ curricular choices, those with more social capital are more likely to be embedded in relationships that provide access to information that result in better, more informed choices. So, while individual- and school-level characteristics shape curricular choices to some extent, students whose social networks facilitate the accumulation of social capital are generally at an advantage when it comes to exercising these choices (Lauen, 2007). According to this logic, the calculus through which students exercise curricular choice is influenced by a combination of individual characteristics, the larger school context, and students’ social networks. Ignoring this latter intermediate level may result in missing an important contextual piece in which these important curricular choices are exercised.


NETWORK DIVERSITY


Key is the idea that social capital is generated through and by networks (Kadushin, 2011).  Individuals’ social ties to one another allow for the exchange of valuable social resources. This social capital perspective has led to a number of related network-based measures that have been used in educational research, including network bridges (Mangino, 2009), density (Maroulis & Gomez, 2008), betweenness (Spillane, Healey, & Kim, 2010), and centrality (Moolenaar, Daly, & Sleegers, 2011). An alternative conceptualization and measure, network diversity (Son & Lin, 2012), focuses less on the structural properties of an individual’s network—the pattern of relations between an individual and a set of others—and more so on the diversity of assets available to an individual through his or her network. Here, network diversity enhances the likelihood of obtaining novel information and diverse resources, largely due to the fact that contacts reached through such ties occupy a range of positions (Baum & Oliver, 1991; Gulati, 1998). A variety of studies have examined the favorable correlates of network diversity (for an overview, see Lin & Erikson, 2008). Erikson has elaborated network diversity’s payoff by stating,  “Variety is the key. Knowing many kinds of people in many social contexts improves one’s chances of getting a good job, developing a range of cultural interests, feeling in control of one’s life and being healthy” (2003, p. 25).   


Operational measures of network diversity are varied, including heterophily (Benediktsson, 2012) and heterogeneity (Moody, 2001), which have been used to examine phenomena such as high school friendship formation. Other measures, for example, the index of qualitative variation (IQV), have been used to study student friendship ties on social media sites (Lewis, Kaufman, Gonzalez, Wimmer, & Christakis, 2008). Network diversity has also been operationalized to measure an individual’s network extensity across an array of empirical contexts to examine phenomena such as status attainment among job seekers (Son & Lin, 2012), the productivity of corporate research and development teams (Reagans & Zuckerman, 2001), and inequalities in workplace performance and pay (Joshi, Liao, & Jackson, 2006). While these empirical examples are varied, they share the commonality that network diversity is, in general, favorably associated with outcomes ranging from decreases in delinquency among African American adolescents (Mangino, 2009) to the increased production of creative works (Lingo & O’Mahony, 2010).  


CONTRIBUTIONS OF THE PRESENT STUDY


In this study we build on the important foundation provided by Burt (1992), Lin (2001), and Erikson (2003) to examine whether social capital in the form of network diversity is associated with math achievement in students’ selected math courses. In addressing this issue, our study makes three contributions to the extant literature on students’ curricular choices, and, more generally, on the social capital associated with network diversity. First, we define and measure social capital in terms of network diversity, using information on the extent to which students consult individuals in different roles when making a curricular choice. Second, we employ this measure in multilevel models in order to determine whether and to what degree it predicts students’ Grade 9 math achievement. This provides a direct test of the network diversity argument while simultaneously adjusting for individual-level characteristics and other salient characteristics of the social context in which curricular choices are made. Because the association between math course selection and achievement is likely influenced by students’ subject-specific interest levels, our final contribution is that we examine whether the relation between our observed measure of network diversity and achievement in math is significantly moderated by students’ math interest.    


DATA AND METHOD


SAMPLE


Data for this study are from the restricted-use version of the High School Longitudinal Survey of 2009 (HSLS: 09), the fifth in a series of National Center for Education Statistics’ multisource, secondary longitudinal studies (Ingels et al., 2011). For this study, we rely on cross-sectional base-year data (2009) when all students were in Grade 9. The HSLS: 09 used a two-stage random stratified sampling design to yield a nationally representative base-year design of approximately 21,000 students nested in 940 schools. Our analytic sample consists of those students who: (1) were enrolled in and able to select their fall 2009 math course; (2) have valid scores on the dependent variable (math achievement); and (3) have no missing values on items that constitute the independent variable-of-interest (network diversity). This subsampling strategy resulted in a final weighted, analytic sample of 5,570 students in 920 schools.  


VARIABLES


Dependent Variable


Our dependent variable is students’ math achievement, a standardized score based on student’s performance on an HSLS-administered assessment of algebraic reasoning. Covering six domains of algebraic content and four algebraic processes, the assessments were administered by computer using a two-stage design and scored through item response procedures (Hambleton & Swaminathan, [1985] 2010). Several types of scores were generated to describe students’ performance, all derived from the IRT model, which uses patterns of correct, incorrect, and omitted responses to obtain ability estimates that are comparable across the low-, moderate-, and high-difficulty test forms. We use standardized scores, which provide a norm-referenced measurement of achievement; that is, an estimate of achievement relative to the HSLS: 09 student population (i.e., fall 2009 Grade 9 students) as a whole (M = 50, SD = 10). All test items were field tested and evaluated in terms of reliability and validity (Ingels et al., 2011, Section 2.3.4).


We focus on achievement in math for three reasons. First, this is a subject area identified as a priority by the No Child Left Behind Act of 2002 and the Race to the Top Program, a competitive federally funded grant initiative started in 2009. Second, it is particularly sensitive to school-based influences (Burris, Heubert, & Levin, 2006). Finally, math is a subject area that is widely considered to be a critical “gateway” to secondary and post-secondary success (Matthews & Farmer, 2008).  


Independent Variable


Lin’s (2001) definition of social capital provides the conceptual backdrop for the operationalization and measurement of our independent variable, network diversity. For Lin, social capital consists of “resources embedded in a social structure that are accessed and/or mobilized in purposive actions” (Lin, 2001, p. 58). Dissatisfied with the popular “name-generator” strategy (Laumann, 1973) used to measure access to social capital, Lin and Dumin (1986) developed the “position-generator” method (Lin, 2001; Lin & Erickson, 2008; Lin, Fu, & Hsung, 2001), which requires respondents to indicate contact, if any, with a sample of ordered hierarchical positions (e.g., lawyer, high school teacher, carpenter, etc.). The major strength of this technique over the name-generator strategy is that it better reflects access individuals have to structurally embedded resources (Lin, 2001; Lin & Erickson, 2008).


The modified position-generator on the HSLS student questionnaire asked, “Since the beginning of the last school year (2008–2009), which of the following people have you talked with about which math courses to take?” Respondents could then select from people in the following non-hierarchical positions: mother (or female guardian), father (or male guardian), favorite teacher, friends, or school counselor. We then calculated the number of ties to the five possible positions that constitute each respondent’s network. Thus, network diversity scores range from 0 (social isolate) to 5 (full diversity); for example, if a respondent indicated that she or he talked with their mother and friends about which math course to take, then her or his network diversity score equals 2.


Moderator Variable


Our models also include an interaction term between network diversity and a scale measure of students’ math interest, a composite measure provided by the HSLS: 09 that was derived from six items on the student questionnaire (e.g., enjoying math, math is a waste of time, math is boring) that reflects a student’s interest in her or his fall 2009 math course. This generated measure was created through principal component analysis and standardized with higher scores reflecting higher interest (M = 0, SD = 1, a = .75). This measure’s items are similar to those used in other studies (e.g., Marsh, Trautwein, Ludtke, Köller, & Baumert, 2005) and other scale measures of math interest based on similar items that have been shown to have convergent and discriminant validity in relation to classroom-based performance (Köller et al., 2001). The procedures used to field test this scale and its items are reported in Ingels et al. (2010).  


Covariates


Because the hypothesized associations are examined using cross-sectional observational data, it is necessary to adjust for a number of student- and school-level variables that potentially confound the relationships that are being investigated. Specifically, because students’ curricular choices and achievement are influenced by individual- and school-level characteristics, we include a number of covariates related to both of these levels. Demographic controls at the student-level include: a composite measure for socio-economic status (SES), and indicators for race/ethnicity, female, and native English-speaker status. Other student-level controls are related to students’ prior and current academic experiences, including: indicators for Grades 8 and 9 math courses, Grade 8 math course grade, whether they currently have an individualized educational plan (IEP), and continuous scale measures for sense of school belonging (five items, a  = .72) and school engagement (four items, a  = .67). Controls at the school-level include indicators for regular school, grade span, region, and locale, and continuous measures for school climate (14 items, a  = .65), average number of instructional hours per day, and percent of students that receive free lunch. Table 1 presents the descriptive statistics for all variables used in the analysis.


Table 1. Descriptive Statistics


 

HSLS: 09 Source Variable(s)

M (SD) or %

Math score

X1TXMTSCOR

53.22 (10.46)

Network diversity score

S1MOMTALKM, S1DADTALKM, S1FRNDTALKM, S1TCHTALKM, S1CNSLTALKM, S1NOTALKM

1.99 (1.41)

Math interest (z)

X1MTHINT

SES (z)

X1SES

Race

X1RACE

 

  Whitea

 

.58

  Black

 

.10

  Hispanic

 

.15

  Asian

 

.09

  Other

 

.10

Female

X1SEX

.44

English native language

ENGNATIVELANG

.83

Student has IEP

X1IEPFLAG

.20

At or above pre-Algebra Grade 8

S1M8

.80

Grade 8 Math course grade

S1M8GRADE

 

  A

 

.43

  B

 

.36

  C

 

.15

  D

 

.04

  Less than Da

 

.02

At or above Algebra I Grade 9

S1MFALL09

.86

School belonging (z)

X1SCHOOLBEL

School engagement (z)

X1SCHOOLENG

Region

X1REGION

 

  Southa

 

.36

  Midwest

 

.30

  West

 

.18

  Northeast

 

.15

Locale

X1LOCALE

 

  Suburba

 

.36

  Town

 

.12

  Rural

 

.24

  City

 

.29

School climate (z)

X1SCHOOLCLI

Average instruction hours/day (z)

A1CLASSHRS

Grade span

X1GRADESPAN

 

  Pre-K, 1, 2, 3, 4, or 5 through 12

 

.07

  6, 7, 8 through 11, or 12

 

.06

  9 through 11, or 12a

 

.88

Percent free lunch (z)

X1FREELUNCH

Regular school

A1SCHTYPE

.95

 

Note. N = 5,570 students in 920 schools. Descriptives are unweighted. SD reported for continuous variables only. z-scores: M = 0, SD = 1.  

aReference category in subsequent models.  


ANALYTIC PLAN


Multilevel models with random intercepts are used to estimate students’ math achievement and properly adjust for the nested nature of the data. The models include controls for the HSLS stratified sampling design and for the probability of selection for individuals. Therefore, clustered robust standard errors are used to obtain the most unbiased estimates of statistical significance. In addition, the models take advantage of the design of the HSLS study by controlling for respondents’ prior math experiences, which not only allows more precise specification of the relation between network diversity and achievement, but also adjusts for any relationships that might have resulted from previous school experiences. A small proportion of observations were missing for different control variables. To preserve these cases, we used multiple imputation based on multivariate imputation by chained equations (White, Royston, & Wood, 2011) to create five distinct data sets with imputed values, each of which was analyzed separately. The parameter estimates reported from one of these imputations were consistent across the other four. All variables with no missing values were used in predicting missing values. This procedure allowed us to retain all observations that met our subsampling criteria. Model fit was assessed using the BIC and AIC indices, with lower values indicating a better fit. Finally, likelihood-ratio tests were performed to compare nested models fitted with maximum likelihood estimation.


RESULTS


Table 2 presents the results from a series of multilevel models that predict math achievement. Model 1 is an unconditional model with no predictors at either the student- or school-level. The average student in the average school has an estimated math achievement score of 52.05. The derived intraclass correlation (ICC) based on a model without robust standard errors is .23, which reflects the proportion of change in math achievement attributable to schools (not reported in Table 2). This is consistent with typical estimates that range from 10%-25% in studies of educational performance, in general, in U.S. schools (Hedges & Hedberg, 2007). This unconditional ICC, therefore, further justifies our use of multilevel models (Snijders & Bosker, 2012).


Models 2 and 3 incorporate student- and school-level controls. The coefficient for at or above pre-Algebra Grade 8 is especially noteworthy in Model 2, predicting a 3.77-point increase in math achievement (b = 3.76, z = 9.05, p < .001), an estimate that is substantively consistent across subsequent models. In addition, students whose math course is at or above Algebra I Grade 9 are associated with a 3.80-point increase in math achievement (b = 3.80, z = 6.92, p < .001). Both results speak to the importance of earlier exposure to algebra (Stein, Kaufman, Sherman, & Hillen, 2011). The inclusion of school-level covariates in Model 3 results in a model that has a statistically significant better fit than Model 2, which includes only student-level covariates, LR[39_18114.htm_g/00001.wmf] (12, N = 5,570) = 2089.89, p < .001.


Model 4 directly addresses our first research question and includes student- and school-level controls. The results show that including network diversity as a predictor (Model 4) produces a model that has a statistically significant better fit than the previous one containing student- and school-level controls (Model 3), LR[39_18114.htm_g/00002.wmf] (1, N = 5,570) = 17,799.76, p < .001.  Specifically, a one-point increase in network diversity is associated with a 0.77-point increase in math achievement (b = 0.77, z = 6.99, p < .001), which translates into an 8% standard deviation increase (.77/10.46, where 10.46 is one standard deviation of math achievement). While this point estimate may seem small, it is only slightly smaller than what one may expect from raising teacher effectiveness by one whole standard deviation (Rivkin, Hanushek, & Kain, 2005). The results from this model, therefore, speak directly to the achievement benefits associated with social capital in the form of network diversity.


Table 2. Multilevel Models Predicting Students’ Grade 9 Math Scores from Network Diversity

 

Model 1

Model 2

Model 3

Model 4

Constant

52.05 (0.24)***

40.89 (1.26)***

42.17 (1.88)***

40.96 (1.87)***

Fixed Effects

    

  At or above pre-Algebra Grade 8

 

3.76 (0.42)***

3.76 (0.41)***

3.46 (0.41)***

  At or above Algebra I Grade 9

 

3.80 (0.55)***

3.79 (0.55)***

3.78 (0.54)***

  Network diversity

   

0.77 (0.11)***

  Student-level controlsa

No

Yes

Yes

Yes

  School-level controlsb

No

No

Yes

Yes

Random Effects

    

  Variance (level-2)

53.99 (2.96)

28.09 (1.58)

29.14 (1.57)

28.35 (1.52)

  Variance (level-1)

66.44 (2.49)

43.84 (1.50)

43.75 (1.49)

43.00 (1.46)

AIC

7,211,250

6,785,265

6,783,200

6,756,402

BIC

7,211,279

6,785,385

6,783,398

6,765,607

LR c2 (df)c

 

426,023.15 (15)***

2,089.89 (12)***

17,799.76 (1)***

Note. N = 5,570 students in 920 schools. Robust clustered standard errors are in parentheses. Models are weighted at the student-level (HSLS source variable: W1STUDENT).  

aStudent-level controls include indicators for race/ethnicity, female, native English-speaker status, Grade 8 math course grade, and IEP status, and continuous measures for SES, school belonging, and school engagement. bSchool-level controls include indicators for regular school, grade span, region, and locale, and continuous measures for school climate, average number of instructional hours per day, and percent of students that receive free lunch. cc2 value for the likelihood ratio (lr) test. Significant results indicate an improvement in fit from the previous model.  

* p < .05. ** p  < .01. *** p < .001. (two–tailed tests).


However, a more complicated and nuanced relation between network diversity and math achievement emerges when we include math interest in our models. Model 5, Table 3, reports the estimate for math interest in a model that includes all the student- and school-level covariates from the previous model, but excludes network diversity. This produces a model that has a statistically significant better fit than Model 3, LR[39_18114.htm_g/00003.wmf] (1, N = 5,570) = 11,226.75, p < .001, the model in which it is nested. This model continues to show the positive associations of prior and current coursework on math achievement, with at or above pre-Algebra Grade 8, for example, predicting a 3.74-point increase in math achievement (b = 3.74, z = 9.47, p < .001). The coefficient for math interest is especially noteworthy, showing that a one-unit increase is associated with a 0.88-point increase math achievement (b = 0.88, z = 5.23, p < .001). This result, in particular, points to the importance of math interest as a predictor of math achievement, above and beyond the influence of students’ prior coursework (at or above pre-Algebra Grade 8) and achievement (as measured by Grade 8 Math course grade).


Model 6 includes both network diversity and math interest and a full set of covariates as predictors of math achievement. This model tests whether there is an effect of network diversity, net the influence of math interest. The inclusion of network diversity produces a model that has a significantly better fit than Model 5, LR[39_18114.htm_g/00004.wmf] (1, N = 5,570) = 16,843.27, p < .001. The point estimate for math interest is still large and significant (b = 0.84, z = 6.77, p < .001), as is the estimate for network diversity (b = 0.75, z = 6.77, p < .001). The results from this model highlight the important and unique contributions of both variables on math achievement.   


Model 7 directly addresses our second research question by testing whether math interest moderates the association between network diversity and math achievement. That is, this model tests whether there are any return deficits of social capital experienced by those with lower levels of math interest. Alternatively, are there any return advantages of social capital for those with higher levels of math interest? This model shows that the point estimate for math interest is no longer significant (b = 0.42, z = 1.47, p = .141), whereas the point estimate for network diversity is still significant (b = 0.74, z = 6.73, p < .001). However, the interaction between these two continuous measures is significant (b = 0.22, z = 2.22, p = .026), suggesting that the achievement advantages associated with network diversity significantly vary by math interest. To ease interpretation, Figure 1 shows that as network diversity increases from 0 to 5, the achievement gaps between those with lower, average, and higher math interest become larger. In fact, those students with a network diversity score of 5 who are one standard deviation above the mean on math interest (Figure 1, top line) are predicted to score about three points higher than those with the same network diversity score, but who are one standard deviation below the mean on math interest (Figure 1, bottom line). This difference translates into slightly less than 30% of one standard deviation unit of math achievement (3/10.46, where 10.46 equals one standard deviation).  


Table 3. Multilevel Models Predicting Students’ Grade 9 Math Scores from Network Diversity and Math Interest


 

Model 5

Model 6

Model 7

Constant

42.22 (1.86)

41.04 (1.85)

40.98 (1.85)

Fixed Effects

   

  At or above pre-Algebra Grade 8

3.74 (0.39)***

3.45 (0.39)***

3.50 (0.40)***

  At or above Algebra I Grade 9

3.69 (0.54)***

3.67 (0.54)***

3.70 (0.54)***

  Network diversity

 

0.75 (0.11)***

0.74 (0.11)***

  Math interest

0.88 (0.17)***

0.84 (0.17)***

0.42 (0.28)

  Network diversity * math interest

  

0.22 (0.10)*

  Student-level controlsa

Yes

Yes

Yes

  School-level controlsb

Yes

Yes

Yes

Random Effects

   

 Variance (level-2)

28.50 (1.54)

27.79 (1.49)

27.72 (1.49)

 Variance (level-1)

43.27 (1.50)

42.57 (1.48)

42.49 (1.47)

AIC

6,771,975

6,755,134

6,753,228

BIC

6,722,180

6,755,346

6,753,446

LR c2 (df) c

11,226.75 (1)***

16,843.27 (1)***

1,907.89 (1)***


Note. N = 5,570 students in 920 schools. Robust clustered standard errors are in parentheses. Models are weighted at the student-level (HSLS source variable: W1STUDENT).  

aStudent-level controls include indicators for race/ethnicity, female, native English-speaker status, Grade 8 math course grade and IEP status, and continuous measures for SES, school belonging, and school engagement. bSchool-level controls include indicators for regular school, grade span, region, and locale, and continuous measures for school climate, average number of instructional hours per day, and percent of students that receive free lunch. c c2 value for the likelihood ratio (lr) test. Model 3 is nested in Model 5. Model 5 nested in Model 6, and Model 6 nested in Model 7.

* p < .05. ** p < .01. *** p < .001. (two–tailed tests)



Figure 1. Predictive margins of network diversity and math interest on Grade 9 math scores.


[39_18114.htm_g/00006.jpg]

Note. This figure illustrates how the effect of network diversity on math scores gets stronger as math interest increases.


DISCUSSION


Choices made in high school establish a foundation for adult life, but adolescents rarely have such a long view when deciding what courses to take (Frank et al., 2008). Because course selection, especially in math, triggers a whole set of subsequent curricular outcomes that extend past high school, we draw important attention to how choices about math course selection are made and whether the relational resources upon which students draw on are associated with higher achievement. Specifically, we used a nationally representative dataset of U.S. students in Grade 9 who are able to exercise curricular choice to quantitatively test whether and to what degree network diversity is associated with their math achievement. Drawing from the literature on network diversity serving as a form of social capital, we hypothesized that as students’ use of their social networks to inform math course selection increased, so, too, would their math achievement. We conceptualized and operationalized social capital (Lin, 1999) through a modified position-generator that served as our measure of network diversity. Operationalizing social capital in this manner allowed us to precisely measure social capital and align this measurement with more current theorizing in this area (e.g., Lin & Erikson, 2008).  


Results from models that employ this measure extend and challenge extant research literature on the benefits of network diversity and draw much needed attention to the issues confronting students as they make curricular choices that potentially have long-term consequences. Our results provide evidence of an empirical association between students’ social capital in the form of network diversity and math achievement, which supports our primary theoretical claim that the more extensive a student’s network, the better the social resources to be accessed and mobilized. Our empirical context focused on the informational resources accessible to students as they consider which Grade 9 math course to take. Our argument is that students with diverse networks will have greater access to information from varied sources, encouraging them to weigh and consider this information as they make a choice about which math course to take. This deliberative process is then associated with higher achievement, above and beyond the influence of the prior or even current math experiences. Even after adjusting for a large number of covariates, results from Model 4 support this argument.  


In addition, this argument moves beyond the rational choice idea that students make curricular choices based on a calculated appraisal of their needs and aspirations, and shifts the focus onto the relational resources that are accessed and mobilized while deliberating which course to take. In this respect, our work parallels a small number of notable efforts that have examined the ways in which features of social networks intersect with the increased number of educational choices confronting students, their families, and school leaders (e.g., Frank et al., 2008; Jennings, 2010; Neild, 2005).  


While our results confirm an association between network diversity and an important educational outcome (i.e., Grade 9 math achievement), we extend this focus on students’ networks by incorporating a measure of math interest into our analysis. The more common approach to studying social capital in the context of educational research has been to treat network-based measures as an independent variable and achievement or attitudes as the dependent variable (e.g., Carolan, 2012). Our second set of analyses move beyond this by how students’ subject-specific interest moderates the association between social capital in the form of network diversity and achievement. In the first step of this second set of analyses we use a standardized composite measure of math interest that combines information from six items and find that math interest has a strong, unique association with math achievement. This result confirms those from other recent studies that have found an empirical correlation between students’ subject-specific interest and achievement in that subject area (Köller et al., 2001; Schiefele & Csikszentmihalyi, 1995; Viljaranta, Lerkkanen, Poikkeus, Aunola, & Nurmi, 2009).  


However, by examining how math interest moderates the relation between network diversity and math achievement, we directly locate our work within an underappreciated theoretical niche that explicitly links how the presumed returns of social capital vary by student-level non-cognitive characteristics (e.g., math interest). Network diversity helps all students reach resource- or information-rich contacts including teachers and counselors. However, this does not guarantee that all students will see comparable returns. For example, students with high math interest will likely put the resources in their diverse network to better use than those who have fewer resources.


In the context of our study, a student with strong math interest is considered one who has developed a certain attitudinal profile that is reinforced and rewarded by his or her network ties. According to this logic, the results reported in Model 7 may not be surprising, but are important nonetheless. They indicate that students who are interested in math likely make better use of the resources within their social network, which ultimately predicts their choice of and achievement in future math courses. Our primary contribution in this respect is to shift the conversation away from a narrow focus on networks and incorporate how an individual’s non-cognitive characteristics may influence the association between various measures of social capital and an array of educational outcomes.        


This dual focus on network diversity and interest also extends our understanding of the interplay among the many different factors that shape students’ school-related decisions. As the menu of choice options for students expands, complemented by an increased emphasis on participation and performance in STEM subject areas such as math, it is essential for researchers and policymakers to move beyond the typical assortment of student- and school-level characteristics. Like others (Crosnoe, Riegle-Crumb, Field, Frank, & Muller, 2008; Riegle-Crumb, Farkas, & Muller, 2006), our results point toward placing greater emphasis on how students draw upon their social networks when making school-related choices. But our results also emphasize how the effects of these resources depend on non-cognitive traits, which are undoubtedly important, but are neither explicitly taught nor appreciated by schools when implementing choice policies. To say, however, that networks and interest contribute to subject-specific outcomes such as math achievement is not to diminish the role of individual- and school-level characteristics. On the contrary, our models show that, for example, individual-level covariates such as at or above pre-Algebra Grade 8 or at or above Algebra I Grade 9 are consistently significant predictors of students’ Grade 9 math achievement. These results highlight the myriad of malleable factors that policymakers must consider when trying to increase achievement in critical subject areas.  


These conclusions should be considered in light of three limitations. First, students are not randomly assigned in the HSLS, and so these data have the same potential selection bias as all other observational studies. To limit the magnitude of this bias, we employ the standard strategy of using control variables that have been associated with students’ outcomes in previous research (Schneider, Carnoy, Kilpatrick, Schmidt, & Shavelson, 2007). As with all analyses based on observational data (and even for some studies based on randomized experimental data), caution must be exercised in interpreting any significant relationships as causal; it is through the accumulation of similar estimates from studies with varying data and alternative methodologies that causal conclusions become substantiated. Second, the position-generator used to construct our measure of network diversity had a small number of positions (five) from which students could select. This limited the possible range of resources that students draw on when making curricular decisions. In fact, position-generators list anywhere from 5–40 positions (reviewed in Lin & Erikson, 2008) and there remain unresolved issues to consider when developing these instruments (Lin et al., 2001; Van der Gaag &Webber, 2007). While we are confident that the HSLS position-generator produces network diversity scores that reflect adolescents’ access to a valuable instrumental resource (i.e., information about course selection), alternative conceptualizations and measures of social capital should also be considered. Third, our models exclude measures related to students’ Grade 9 math classrooms, including instructional rigor and quality and teacher characteristics. This point is noteworthy, as others have reported that achievement varies by these characteristics (e.g., Linver & Davis-Kean, 2005). We encourage subsequent research efforts to move in these directions.   


In spite of these limitations, what can high schools that permit curricular choice do in order to boost students’ math achievement? Our findings point to two possibilities. First, providing students with access to school counselors and teachers and encouraging them to discuss course selection with parents and peers are essential parts of diversifying students’ networks toward a positive end (Woolley, Kol, & Bowen, 2009). Unfortunately, this is often overlooked, as relatively few students access all these resources. Second, the strong association between math interest and math achievement suggests that schools should invest in the development of communities that promote attitudinal norms that are more tightly aligned with their academic mission. For example, years ago Coleman (1961) suggested enhancing the status of music, in relation to athletics, through school-sponsored, student-led activities such as music contests. By doing so, schools can make some activities more attractive and socially desirable (Frank et al., 2008) and thus encourage students to view themselves in relation to more academically oriented pursuits rather than the other non-academic interests that adolescents use to sort themselves within high schools (Ekert, 1989). An important component of such initiatives (reviewed in Faircloth, 2012), however, is that they need to be structured in a manner that values students’ roles in constructing math knowledge (Ernest, 1991). Simply devising competitions around math may increase anxiety and further discourage adolescents as seeing themselves as capable of and interested in math. These two possibilities focus greater attention on developing the social capital of students and the larger communities of which they are part.


In this study we operationalized social capital in terms of network diversity to empirically assess whether and to what degree it predicts math achievement for Grade 9 students who are able to exercise curricular choice. We also accounted for the moderating role of math interest. We found that network diversity—a continuous measure that captures the diversity of others that students draw on when considering which math course to select—predicts math achievement when conditioned on student- and school-level covariates, including measures related to previous math experiences. What is most noteworthy from our models is that the interaction between network diversity and math interest is significant. This interaction indicates that the effect of network diversity on math achievement is intensified for those with the higher levels of math interest. Not only does this result speak to the importance of social networks as an aspect of the social context, but it also suggests how the interaction may contribute to the stratification of students’ outcomes in relation to an important content area.  



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Cite This Article as: Teachers College Record Volume 117 Number 11, 2015, p. 1-28
https://www.tcrecord.org ID Number: 18114, Date Accessed: 10/26/2021 1:40:57 AM

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