The non-cognitive returns to vocational school tracking: South Korean evidence

International Journal of Educational Research 98 (2019) 379–394

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The non-cognitive returns to vocational school tracking: South Korean evidence

T

Baeksan Yu*, Sean Kelly University of Pittsburgh, United States

ARTICLE INFO

ABSTRACT

Keywords: Career and technical education Vocational education School tracking School sorting Curriculum organization Non-cognitive skill development

This study investigates whether attending career and technical (or vocational) high schools (vs. general high schools) leads to different non-cognitive skill developmental trajectories. Using the Seoul Educational Longitudinal Study data (SELS: 2010), we apply quasi-experimental methods including matching and growth mixture models. Contrary to much of the evidence from studies of both within- and between-school vocational tracking, we found significant positive impacts of career and technical schools on non-cognitive skills. However, the mediating role of school curriculum (e.g., number of hours spent on extra curriculum or career development) was found to be trivial.

1. Introduction Educational researchers have long-debated the role of technical/vocational (or career and technical) tracking in exacerbating or ameliorating differences in school success among high and low-achieving secondary school students. As high-achieving students are tracked into academic courses and schools, a variety of mechanisms are likely to create greater opportunity to learn compared to lower-achieving students tracked into career and technical education (CTE) schools, from peer effects (Duflo, Dupas, & Kremer, 2011; Fruehwirth, 2013), to differences in teacher quality (Clotfelter, Ladd, & Vigdor, 2006; Kalogrides, Loeb, & Beteille, 2013; Kelly, 2004), to more compelling incentives for academic achievement for college-bound students (Rosenbaum & Jones, 2000).1 Yet, proponents of CTE argue that such factors may be offset by positive instructional and social processes, including more favorable social comparisons and changes in academic self-concept (e.g., Kelly & Price, 2009). However, to date, research has generally not documented substantially positive effects, either in cognitive or non-cognitive outcomes of vocational tracking (Dougherty, 2018; Kelly & Price, 2009). As noted by Heckman and Rubinstein (2001), non-cognitive skills are significant determinants of labor-market outcomes, and they are also interrelated with the development of cognitive skills (Borghans, Meijers, & Ter Weel, 2008). Non-cognitive skills refer to a set of attitudes, beliefs, and behaviors such as perseverance and self-concept. Differences in such skills and approaches to learning emerge early in schooling, setting the stage for different academic growth trajectories throughout elementary and middle school (Gutman & Schoon, 2013; Lubotsky & Kaestner, 2016). Non-cognitive schooling outcomes widen further in the transition to high school (Kelly & Price, 2014). We build on existing cross-sectional studies of the relationship between vocational school tracking and non-cognitive skills (e.g., Van Houtte, 2005; Van Houtte & Van Maele, 2012) with longitudinal data from Korea.

Corresponding author at: #806 Learning Research & Development Center (LRDC), 3939 O’Hara Street, Pittsburgh, PA 15260, United States. E-mail address: [email protected] (B. Yu). 1 When we refer to tracking, we primarily employ the term “technical/vocational tracking” or “vocational tracking” instead of “CTE tracking”, following Van Houtte et al.’s terminology for consistency with international research in tracking studies. ⁎

https://doi.org/10.1016/j.ijer.2019.09.008 Received 21 January 2019; Received in revised form 22 July 2019; Accepted 24 September 2019 0883-0355/ © 2019 Elsevier Ltd. All rights reserved.

International Journal of Educational Research 98 (2019) 379–394

B. Yu and S. Kelly

To provide longitudinal empirical evidence on whether attending technical/vocational track high schools leads to different noncognitive skill development trajectories we examine the Seoul Educational Longitudinal Study (SELS). The SELS data is unique in that it provides a rich set of covariates prior to entering high school in addition to providing measures of important non-cognitive skills such as creativity and resilience. Previous studies on vocational school tracking and student non-cognitive traits have focused on students’ sense of belonging, self-esteem, self-control, or academic engagement (e.g., Malmberg & Trempała, 1997; Van Houtte, 2005, 2006a; Van Houtte & Van Maele, 2012; Van Houtte & Stevens, 2016). In this study, we analyze between-school vocational track effects on an elaborated set of non-cognitive skills including: creativity, resilience, self-concept, and self-control. As such, despite the high volume of research regarding CTE schools, this study makes an important contribution by investigating the potential causal effects of attending CTE schools on multiple dimensions of non-cognitive skill development with large scale data. Beyond estimating the total effects of school type, this study attempts to account for the mediating role of school curriculum. Given the different educational purposes and curriculum (e.g., college preparatory vs. career and technical training) between CTE and general high schools (Jung & Kang, 2013), we expect that school curriculum (e.g., number of hours spent on core subjects, career development emphasis, etc.) may play a significant mediating role in shaping students’ non-cognitive traits. Tracking logically entails a certain amount of curricular adaptation, including an effort to match the challenge of materials and assignments to students’ academic readiness (Gamoran, 1993; Northrop & Kelly, 2019). We focus, in an exploratory fashion, on over-arching curricular dimensions that may stem from the institutional logic of tracking (time spent on core subjects, career development emphasis), but also dimensions that may be less intentionally related to tracking but nevertheless differ and affect the student experience (e.g., time spent on extracurricular activities). Additionally, after first examining results based on matching methods, we utilize methods that allow us to explicitly model and explore heterogeneity in student growth trajectories. Formally, conventional growth models assume that all student growth trajectories can be adequately modeled using a single growth parameter (or specified piecewise growth) and students come from a single homogenous population (Collins & Lanza, 2010). There might be, however, various identifiable subpopulations in the growth of student non-cognitive traits (e.g., Luyckx, Teppers, Klimstra, & Rassart, 2014). The prediction of membership in different classes of growth offers an alternative analytic lens to study the school experience. Consequently, our research questions are as follows: (1) Are there any significantly different developmental trajectories in noncognitive skills between CTE and general high school students, even after accounting for initial differences in student, family, and school characteristics? (2) If so, to what extent are differences in growth attributable to basic features of the school curriculum? 2. Literature review 2.1. Career and technical education and non-cognitive skill development Career and technical education (CTE) or vocational education is provided both in separate CTE schools and within comprehensive schools that have CTE programs of study. In the US and UK, secondary school tracking is primarily between-class grouping or streaming within a comprehensive school. However, in continental Europe school tracking tends to take the form of programs in separate schools specializing in general and career and technical education (Brunello & Checchi, 2007; Van Houtte, Demanet, & Stevens, 2012). East Asian nations such as South Korea, the focus of this study, also provide a between-school tracking system (general vs. CTE high schools) after compulsory education. Generally speaking, relative to academic course taking, CTE is undervalued in advanced economies, and there are poor future expectations (e.g., lower income and lower educational attainment) for CTE students (OECD, 2016; Van Houtte & Stevens, 2010). Although there are numerous studies theorizing and documenting the positive impacts of CTE on students’ career efficacy and other educational outcomes (e.g., Dougherty, 2018; Kemple & Willner, 2008; McWhirter, Rasheed, & Crothers, 2000; Stern, Dayton, & Raby, 2010), previous empirical studies also suggest adverse effects of CTE, especially to the extent that it overlaps with overall curricular tracking in academic courses. Previous studies on curricular tracking consistently report that it is likely to negatively influence student educational outcomes, especially for lower-achieving or lower-SES students due to the stigmatization associated with lower academic tracks (Van Houtte et al., 2012). Kelly and Carbonaro (2012) further argued that teachers in low track classes tend to have lower college expectations for students than those teachers in high track classes. Within-school vocational tracking in particular may have negative associations with students’ cognitive and non-cognitive educational outcomes. Since within-school vocational track tends to increase the exposure to students in other tracks (e.g., the academic track), compared to the experience of between-school tracking where the school context is more homogeneous, researchers hypothesize that within-school tracking is especially likely to result in feelings of relative deprivation. Tracking related academic achievement gaps are well-documented (Gamoran, 2009). Concerning non-cognitive outcomes, vocational track students in the same schools report lower levels of belonging (Smerdon, 2002), self-esteem (Van Houtte et al., 2012), and study involvement (Van Houtte & Stevens, 2009). Yet, empirical findings on the effect of the technical/vocational school track on other non-cognitive outcomes are not clearly positive or negative. For instance, Kelly and Price (2009) could not find compelling evidence of within-school vocational track effects on several measures of engagement. Turning to systems that use between-school tracking, a set of positive mechanisms may be present that make anticipated effects less clear (see subsequent discussion of Fig. 1). However, as with within-school tracking, available studies report negative

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associations between student non-cognitive traits and between-school vocational tracking. Specifically, students in CTE schools have lower levels of academic culture (Van Houtte & Stevens, 2016; Van Houtte, 2006b), sense of belonging (Van Houtte & Van Maele, 2012), self-esteem (Van Houtte, 2005), self-control (Malmberg & Trempała, 1997), and teacher trust (Van Maele & Van Houtte, 2011) than academic school students. The observed detrimental effects of between-school vocational tracking are also often reported for student cognitive outcomes (e.g., Horn, 2013; Kim, 2014). Yet, Salmela-Aro, Kiuru, and Nurmi (2008) showed that students in an academic track report higher levels of school exhaustion and tiredness compared to vocational track students. Furthermore, some empirical studies highlight both positive and negative cognitive returns to between-school vocational tracking (e.g., Brunello & Checchi, 2007; Holm, Jæger, Karlson, & Reimer, 2013). When gaps are found in studies of between-school vocational tracking, researchers hypothesize that because low-SES and lowachieving students are concentrated in CTE schools (Levesque et al., 2008; OECD, 2016), these disparities may be accounted for by reduced access to a variety of educational resources, including social resources and a high quality teaching workforce (Van Houtte et al., 2012). For example, in addition to basic differences in teacher qualifications in CTE schools (Brunello & Checchi, 2007), the concentration of low-achieving students in CTE schools makes teachers less satisfied with their current jobs compared to those in academic schools (Van Houtte, 2006a). In the following section, we discuss limitations of the previous studies and provide a theoretical rationale that suggests the potential for positive non-cognitive returns to vocational tracking. 2.2. Limitations of previous studies Unfortunately, however, from previous studies, it is somewhat unclear whether the observed negative impacts of between- and within-school tracking are causal or reflect the unobserved characteristics of low-SES students. In CTE school studies, omitted confounders likely lead to downwardly biased estimates (i.e. CTE school effects are negatively overestimated). As an example, since unobserved parental academic support tends to be negatively (−) associated with the probability of attending CTE school, and it tends also to be positively associated (+) with student educational achievement, the effect of vocational school track on student educational outcomes is likely to be negatively overestimated (see similar examples in Pearl, 2009). In addition to confounding selection effects, there are several reasons to hypothesize that CTE may provide benefits for noncognitive skill development, even if overall effects on achievement are negative. In particular, Kelly and Price (2009), focusing on curriculum, argued that CTE can provide disengaged students with an educational “clean slate” that leads to a recovery of engagement for students at risk. Put another way, core elements of CTE (i.e. choice, career education, experiential learning, teacherstudent mentoring relationships, and multidimensional performance criteria) may enhance students’ social psychological adjustment to school. Building on Kelly and Price (2009) and the international literature on between-school tracking (e.g., Van Houtte & Stevens, 2009; Trautwein, Lüdtke, Marsh, Köller, & Baumert, 2006), we interrogate the possibilities of the CTE experience. Why might positive effects on non-cognitive outcomes accrue even in the context of lower overall status or resources? First, career education is a central component of many CTE programs of study and may promote students’ career self-efficacy. Within-school vocational tracking in the US has been described as a weak-form of career and technical education, where students still take the vast majority of courses in traditional academic subjects, and only in rare instances participate in job-embedded training (Müller & Shavit, 2000). In contrast, in other nations where upper-secondary vocational education is common and more highly developed (e.g., Finland or Singapore) career and technical education and/or workplace training can be quite extensive (Jackson & Hasak, 2014). Career self-efficacy refers to an individual’s confidence in pursuing career related tasks (Hackett & Betz, 1995) and is significantly associated with students’ motivation (Komarraju, Swanson, & Nadler, 2014), global self-esteem (Betz & Klein, 1996), and labor market outcomes (Abele & Spurk, 2009). Second, teaching students of homogenous academic interests and achievement, by allowing for narrowly tailored programs of study, might be more efficient and effective (Trautwein et al., 2006). Third, students in CTE schools may be less likely to make social comparisons with high-achieving (and often high-SES) students compared to those students in academic schools, and thus be shielded from developing a sense of inferiority or relative deprivation (Crocker & Major, 1989). As an example, in a study of a lottery-based system of school attendance, West et al. (2016) found significant negative impacts of over-subscribed charter schools on students’ non-cognitive skills traits (e.g., self-control, grit). In particular, the characteristics of academically and behaviorally demanding charter schools may encourage students to rate their non-cognitive skills more critically (West et al., 2016). Several studies indeed have reported that being in the vocational track or program has a positive relationship with student educational or labor market outcomes (e.g., Dougherty, 2018; McWhirter et al., 2000; Kemple & Willner, 2008; Neumark & Rothstein, 2006). To date, however, scant evidence demonstrating the positive returns to between-school vocational track placement for student non-cognitive skills has been provided. Fig. 1 depicts our overall conceptual framework illustrating both positive and negative mechanisms associated with CTE schools. In Fig. 1, we do not make any assumptions about institutional context; variation in educational systems between states and nations (e.g., social recognition of career and technical education or curriculum) may create a different mixture of exacerbating and positive mechanisms in a given context. Yet, from prior research, it is clear that career and technical schooling is likely to have detrimental effects on students’ overall academic/cognitive outcomes in many systems. Then again, some educators might argue that career and technical schooling should not be primarily designed to develop students’ academic skills (Jung & Kang, 2013). In other words, one conception of career and technical schooling is that the educational purposes of CTE high schools and college-preparatory academic

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high schools are functionally different. On a more practical level, differences in curricular content (e.g., college preparatory vs. career and technical training), and thus test content and assessment criteria (e.g., emphasis on test-taking and study skills) between CTE and general high schools, may make a fair comparison of learning difficult. Under this view, in order to fully evaluate the role of CTE schools in exacerbating or ameliorating differences in student success, researchers need to consider more diverse educational outcomes other than academic test scores.

Fig. 1. Conceptual framework illustrating positive and negative mechanisms of career and technical schools.

2.3. South Korean context While primary and middle school attendance is compulsory in S. Korea, high school attendance is not compulsory. Generally speaking, there are two types of high school in S. Korea: 1) general (i.e. academic) high schools, attended by about 70% of all high school students, provide a college preparatory education. 2) career and technical (or vocational) high schools provide vocational education and skills for those students who plan to enter the job market or a 2-year college right after graduation. Whereas CTE schools primarily serve low-achieving and low-SES students in S. Korea, general high schools serve high-achieving and upper-middleclass students (Byun & Park, 2017). This disparity cannot be explained by the relatively small tuition gap between school types, but rather, is due to substantial differences in middle school academic performance, which is a strong determinant of general/academic high school attendance. Previous studies revealed that CTE school students tend to have lower scores on college entrance exams (Kim, 2014) and lower occupational aspirations (Lee, Choi, & Oh, 2012) compared to general high school students even after controlling for family SES or basic school characteristics. Byun and Park (2017) further showed that while disadvantaged students in academic high schools tend to go to a 4-year college, those similarly disadvantaged in CTE high schools typically move to a 2-year college. It is also important to note other unique characteristics of the Korean educational system. First, Korean educational curriculum is highly standardized, and schools are governed by a uniform set of educational policies (Park, 2013). Second, due to the early influence of Confucianism and economic development-oriented policies, Koreans compete intensely for educational credentials; Korean parents have been characterized as having an “educational fever” (Lee, Lee, & Jang, 2010). As a result, a “cramming” approach to education or rote learning style is generally preferred among both parents and teachers to foster student academic achievement (Kim, Im, Nahm, & Hong, 2012). Although South Korean students are generally high-achieving on most international comparisons (Waldow, Takayama, & Sung, 2014), critics worry that the highly standardized characteristics of Korean education may undermine the development of student non-cognitive skills such as critical thinking, creativity, or decision-making skills (See discussion in Park, 2013). From this perspective, those students who attend academically-oriented high schools may have lower levels of creativity or critical thinking compared to those in other developed countries. Yet, Park (2013) argued that such criticism is based on insufficient empirical evidence and amounts to conjecture, demonstrating that Korean students have the highest average levels of PISA problem-solving skills (which draw on critical thinking skills) among all OCED nations, except for Finland.

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3. Methodology 3.1. Data and sample To investigate the effects of attending career and technical (or vocational) high schools, we employ nationally representative data from the Seoul Educational Longitudinal Study (SELS). The SELS data collection began with a panel of students attending the first year of middle school (i.e. 6th or 7th graders) in Seoul in 2010, who were followed in six yearly waves. The analytic sample consists of 2,507 students who participated in waves 3–6 (from the last year of middle school to the last year of high school).2 Since the original data and questionnaires were separate for general and CTE schools, we first identified variables with identical content and measurement scale, and then merged the data. Our final models compare outcomes among 724 students from 191 schools (362 who attended CTE schools for three consecutive years and 362 who attended general high schools), who were identified from a sparse optimal matching process. 3.2. Measures 3.2.1. Dependent variable To capture the non-cognitive effects of attending CTE schools, this study employs four composite dependent variables, student reports of: creativity, resilience, self-concept, and self-control. Appendix A provides descriptive statistics for the dependent and independent variables. Cronbach alphas ranged from .76 to .91. 3.2.2. School track The synthetic treatment group (=1) is defined as those students who attended CTE schools (versus students who attended general high schools), from the first year to the third year of high school. 3.2.3. Mediators We utilize a set of variables measuring school curriculum as possible mediating variables that might explain the relationship between school type and student’s non-cognitive skills. It includes the number of hours spent on core subjects, career development, extra-curricular activities at schools (activities per week), and whether the school has autonomy in curriculum selection (see Appendix A). 3.2.4. Covariates In order to model the selection process of attending CTE schools, this study identifies potential confounding variables from the year prior to entering high school for use as student and family-level covariates. Previous studies showed that lower-achieving, as well as poorly motivated, and low-SES students are more likely to enroll in CTE high schools (e.g., Byun & Park, 2017). We thus carefully selected students’ family backgrounds (e.g., income or single parent) and their relationships with parents (including parent academic support) as well as prior cognitive and non-cognitive skills as potential confounders. We also controlled for the measures of peer relationship (Wentzel, 2005) and health condition (Shaw, Gomes, Polotskaia, & Jankowska, 2015), which are strong predictors of educational achievements or aspirations. By doing so, we can create a quasi-experimental situation that both vocational and general school track students have very similar baseline characteristics before entering high schools. The selection of variables was also guided by data available in the SELS. The original measurement scale and descriptive statistics of all variables are presented in Appendix A. School-level covariates such as an indicator for private school type, school district (i.e. school district fixed-effects), and school SES are included in the models after the matching to disentangle the vocational school track effect from other school characteristics identified in the school effects literature (Byun & Kim, 2012; Yu, Lim, & Kelly, 2019). 3.3. Analytic strategy To address the selection mechanism of attending CTE high schools at the student level, we first employ a sparse optimal matching method using the rcbalance module in R. While results from matching methods are often similar to more traditional covariate adjustment techniques (and they generally use the same set of available covariates), they differ in an important way; matching seeks to control not only for the cumulative effect of a set of covariates, but for the joint effect of multiple covariates. In other words, matching models function under the logic that when multiple covariates are jointly similar, cases are more comparable. Pimentel, Kelz, Silber, and Rosenbaum (2015) provide further discussion of sparse optimal matching, while Lee (2016) provides a more general overview of the advantages of matching techniques. After extracting a well-balanced sample with similar values of observed 2

Transfer (89), gifted and talented or special education students (32) and those who attended special types of high schools such as special purpose (81), Innovation (118), and Meister (81) high schools are dropped. These schools are distinct from other schools in that they have special educational purposes and there are only a few of them. Specifically, Innovation and Meister high schools are newly developed (pilot) public schools designed to replace traditional general and CTE high schools. Meister schools, for instance, provide industry-customized training to meet rapidly changing industry needs. The final sample consists of 77% of all general high school students, and the final CTE high school sample consists of 93% of all CTE school students. 383

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covariates, we apply a three-level growth curve model to investigate the longitudinal consequence of attending CTE schools (time points are nested within students, which are then nested within schools). Our key independent variable, vocational track, is introduced at level 3. Note that there is no within-school variation in the treatment variable. We also control for student’s previous academic achievement as well as family SES in our matched sample to remove any remaining heterogeneity between groups. We provide the statistical notation for our model specification in Appendix B. Additionally, to explore heterogeneity in student growth trajectories, we apply a growth mixture model (GMM). While this can also be used to study moderation (i.e. students on a different growth trajectory are affected differently by intervention/context X), we use it here as an additional test of the school effect itself. That is, we investigate whether attending different types of schools causes individuals to display different types of trajectories (see also Appendix C). Since we have relatively small sample sizes with many covariates, we fix the variance of the intercept and slope parameters (as in a latent class growth model) but freely estimate the covariances between time-specific residuals (see similar hybrid approach in Lutz, Stulz, & Köck, 2009). As suggested by Nylund, Asparouhov, and Muthén (2007), we select the appropriate number of latent growth patterns based on the Bayesian Information Criterion (BIC) and Bootstrap Likelihood Ratio Test (BLRT). After classifying the distinctive classes, we investigate the effects of CTE schools on the odds of belonging to a specific trajectory class relative to a reference class using a multinomial logit model (Wickrama, Lee, O’Neal, & Lorenz, 2016). We apply the 3-step approach suggested by Asparouhov and Muthén (2014) to account for measurement error. To address missing data, given the nested structure of the SELS data, we performed multi-level multiple imputation with Mplus, generating five data sets. Sample sizes prior to imputation are reported in Appendix A. The three-level growth curve models are estimated in HLM using a full information maximum likelihood estimator, and the GMM is implemented in Mplus with a robust maximum likelihood estimator. 4. Results 4.1. Balancing test Table 1 illustrates the results of the sparse optimal matching step. As can be seen from Table 1, before matching, the students who attended CTE schools for three consecutive years tended to come from disadvantaged family backgrounds in addition to having lower cognitive, and non-cognitive educational outcomes prior to entering high school. After the matching process, however, the observed differences on covariates (including our focal DVs) between treatment and control groups are substantially reduced at the outset. Specifically, matching did result in a notable compression of the effect-size differences (< .10), particularly the extreme differences in family background and prior achievement (see Fig. 2). Since our analytic sample now represents students at the lower-end of the family SES and educational achievement distributions in Seoul, subsequent results pertain only to that part of the student population. Table 1 Mean differences before and after sparse optimal matching: Measures from the last year of middle school. Variables

Creativity Self–control Self–concept Resilience Male GPA_overall GPA_Korean GPA_Math GPA_English Free lunch status Single parent Dual income family Ln_income Parent educational level Parent academic support Ln_private education Parent-student relationship Cultural activities Peer relationship Health condition

Before matching

After matching

Control (2,042)

Treated (457)

Mean difference

Control (362)

Treated (362)

Mean difference

3.65 3.37 3.65 3.37 .52 557.05 550.64 549.43 571.09 .11 .11 .51 7.08 14.16 3.48 5.18 3.75 4.35 4.22 .91

3.55 3.13 3.50 3.28 .44 544.01 541.56 534.36 556.10 .25 .21 .49 6.92 12.62 3.21 5.10 3.57 3.63 4.09 .97

–.10*** –.24*** –.15*** –.09** –.09*** –13.05*** –9.08*** –15.07*** –14.98*** .15*** .10*** –.02 –.16*** –1.54*** –.27*** –.07*** –.17*** –.72*** –.13*** .06

3.54 3.17 3.51 3.27 .42 544.08 542.95 534.54 554.77 .27 .20 .47 6.92 12.75 3.32 5.09 3.63 3.75 4.15 .93

3.56 3.20 3.55 3.29 .45 543.92 542.28 534.73 554.76 .25 .19 .50 6.94 12.75 3.30 5.08 3.65 3.69 4.12 .93

.02 .03 .04 .03 .03 –.17 –.67 .19 –.02 –.02 –.01 .04 .02 .00 –.02 –.01 .02 –.06 –.03 .01

*P < .05 **P < .01 ***P < .001 Note: results are very similar between imputed data sets.

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Fig. 2. The differences in variance ratio and effect size for covariates before and after matching.

4.2. Effects of technical/vocational track on non-cognitive outcomes Using the well-balanced matched sample, we next examine the effect of attending CTE high schools on various student noncognitive outcomes in a multi-level regression framework. Table 2 reports the results of the three-level growth curve model for students’ creativity and resilience, with the time indicator centered such that initial status (i.e. time = 0) represents the first year of high school. M1 in Table 2 depicts the unconditional linear growth model. The average creativity in year one across all schools is 3.69. Student creativity growth across the three time points is negatively significant, averaging a .04 point decline per year. The expected decrease of creativity for 2 years is about 13% of a SD of creativity ((−.04*2)/.62), which is small. As we discussed, the “cramming” approach to education in academic schools might undermine the development of students’ creativity. The decline in creativity might also be due to the characteristics of our matched sample. However, we find a similar pattern (−.03***) in the whole sample. There is Table 2 Three-level growth curve model for creativity and resilience. Creativity

Resilience

M1

M2

M3

M1

M2

M3

b(SE)

b(SE)

b(SE)

b(SE)

b(SE)

b(SE)

3.69*** (.03)

3.16*** (.79) .01 (.13)

3.10*** (.79) .04 (.14) –.00 (.01) –.00 (.00) .00 (.00) .11 (.10)

3.39*** (.04)

3.09** (1.03) –.05 (.18)

3.00** (1.03) –.06 (.18) –.00 (.01) –.00 (.00) .01 (.01) –.06 (.13)

–.04** (.01)

.16 (.31) .11* (.05)

.18 (.31) .11* (.05) –.00 (.00) .00 (.00) –.00 (.00) –.02 (.04)

–.00 (.02)

–.21 (.39) .15* (.07)

–.21 (.39) .15* (.07) –.00 (.00) .00 (.00) –.00 (.00) .00 (.05)

Random effects

Variance components

Variance components

Variance components

Variance components

Variance components

Variance components

Level-1 error Student initial status Student growth rate School mean status

.15 .30*** .03*** .01*

.15 .27*** .02*** .00

.15 .27*** .02*** .00

.33 .44*** .01 .03**

.33 .39*** .00 .00*

.33 .39*** .00 .00*

Fixed effects Model for initial status Intercept Vocational track Core subjects Career development Extra curriculum School autonomy Model for growth rate Intercept Vocational track Core subjects Career development Extra curriculum School autonomy

* p < .05. ** p < .01. *** p < .001. 385

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Table 3 Three-level growth curve model for self-control and self-concept. Self-control

Self-concept

M1

M2

M3

M1

M2

M3

b(SE)

b(SE)

b(SE)

b(SE)

b(SE)

b(SE)

3.29*** (.04)

1.80* (.83) .12 (.15)

1.69* (.83) .14 (.15) –.00 (.01) –.00 (.00) .01 (.00) .09 (.10)

3.63*** (.04)

2.27* (.97) .12 (.17)

2.24* (.97) .11 (.17) .00 (.01) –.00 (.00) .00 (.01) –.04 (.12)

.06*** (.01)

.27 (.32) .11* (.05)

.31 (.32) .11 (.06) .00 (.00) .00* (.00) –.00 (.00) –.01 (.04)

–.00 (.01)

.43 (.37) .10 (.06)

.40 (.37) .10 (.06) –.00 (.00) –.00 (.00) .00 (.00) –.01 (.05)

Random effects

Variance components

Variance components

Variance components

Variance components

Variance components

Variance components

Level-1 error Student initial status Student growth rate School mean status

.21 .27*** .01 .03*

.21 .23*** .00 .00**

.21 .23*** .00 .00**

.23 .48*** .03*** .04***

.23 .45*** .03*** .01**

.23 .45*** .03*** .01**

Fixed effects Model for initial status Intercept Vocational track Core subjects Career development Extra curriculum School autonomy Model for growth rate Intercept Vocational track Core subjects Career development Extra curriculum School autonomy

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

significant variability among students in terms of estimated initial creativity score (.30), and in terms of estimated growth rate (.03). To gauge the variability in creativity growth, we calculated growth rates for students at about the 20th and 80th percentiles of estimated growth; over two years, students at the 20th percentile lost .10 points in creativity while students at the 80th percentile lost .06 points, a 6% standard deviation difference. There is also a small but significant variability between schools in terms of initial creativity score (.01). We found broadly similar patterns with respect to other non-cognitive traits. Since the unconditional model simply provides an average growth rate of creativity for both CTE and general high school students, we turn now to M2. We expect that students’ different school attendance patterns may explain some of the remaining variability across students. In M2 in Table 2, we introduce the school track indicator into the equation along with school-level covariates. Collectively, these measures explain about 10% of the variance in initial status at level 1, and virtually all of the school level variance in initial status. In this analytic sample of matched students, there is no significant effect of the technical/vocational track on students’ baseline, year one creativity. Yet, there is a significant effect of school type on creativity growth over time. When holding constant other factors, the technical/vocational track students gain an additional .11 points of creativity each year compared to their counterparts. At the end of high school, the effect of attending a CTE school is expected to be about 37% of a SD of creativity ((.01 + .11*2)/.62). In M3, we investigate whether the gap in creativity can be accounted for by the school curriculum measured here. We controlled school-level covariates in M3, since they are possible confounders in the mediation analysis. Yet, the results of M3 do not significantly differ with or without school-level controls. In this matched sample, while CTE schools tend to provide more career-oriented curriculum (a standardized difference = .20*), academic schools tend to have more autonomy in curriculum selection (a standardized difference = .30*). Yet, no significant differences are observed with respect to the number of hours spent on core subjects and extra curriculum between school types. Comparing the coefficient for CTE schools in M2 and M3 reveals that there is no mediating effect of the dimensions of school curriculum measured here. Yet, since the S. Korean educational system is highly centralized and provides a standardized curriculum (Park, 2013), the variation in school curriculum found here (an effect size of .2–.3) may be smaller than in other countries (OECD, 2014). We further discuss the limitations of our mediation analysis in the discussion section. To examine the effects of the technical/vocational track on a wider array of student educational outcomes, we also analyze student reports of resilience, self-concept, and self-control (see also Table 3). We do observe significant growth effects of attending a CTE school on resilience (.15) and self-control (.11). Regarding self-concept, no significant effect of vocational school track is found (p = .10). Yet, while the matching process we employed likely reduced bias, null effects in this analysis should be interpreted with caution due to low statistical power. Although the significant growth effects of CTE school attendance on self-control disappear at p < .05 after including school curriculum variables, the change in the coefficient itself is negligible. Finally, we re-estimated the models with an unstructured error covariance matrix and heteroskedastic level-1 residuals to check the robustness of the effects against autocorrelation and heteroscedasticity issues in a longitudinal study. Since a model with an unstructured error covariance matrix is the least efficient model (Singer & Willett, 2003), if the fixed effects of the proposed model are similar to this model, we may 386

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conclude that the results are robust to the autocorrelation issues. The results show very similar patterns, providing confidence in our findings. 4.3. Heterogeneity in change over Time The HLM specification identifies an individual growth trajectory for each student, and then models mean differences in growth as a function of school type and other covariates. In this section we use a growth mixture model (GMM), first identifing a set of discrete classes of growth displayed by students in these data, and then using those growth classes as dependent variables. Does attending a career and technical school, as opposed to an academic school, affect students’ growth trajectories (their membership in a specific class of growth)? The general process for conducting a GMM analysis is: (1) model specification (e.g., variance and covariance structure); (2) model estimation obtaining fit statistics; (3) final model selection (i.e. number of classes) based on the fit statistics and interpretation. The estimated number of latent classes in GMM can be used either as a dependent variable or a moderation variable. Ram and Grimm (2009) provide a general overview of GMM, and Jung and Wickrama (2008) provide more practical guideline for using a GMM analysis (for more information on GMM, see Appendix C). Based on the model specification provided in the analytic strategy, we begin by exploring how many growth classes are appropriate for each dependent variable. To do so, we illustrate the model fit comparison when different numbers of classes are specified in Table 4. We report several fit indices such as Akaike’s Information Criterion (AIC) or Entropy, yet, in selecting the preferred number of growth classes, we mainly rely on the Bayesian Information Criterion (BIC) and bootstrap likelihood ratio test (BLRT) as suggested by Nylund et al. (2007).3 The BLRT results show that a 3 class specification is favored for creativity and selfconcept (accepting the null model of 3 classes in favor of 4 classes at p < .05), and it also has the smallest values of BIC. Regarding student self-control, we selected a 4 class specification with the highest value of entropy and lowest value of BIC. We do not consider more than 5 classes due to our small sample sizes. For student resilience, the fit indices show that a homogenous single class is preferred. We thus conduct a class prediction model only for creativity, self-control, and self-concept. Fig. 3 shows the estimated means and observed growth pattern for each class. The graphs clearly demonstrate that there are heterogenous groups in the growth trajectories of student non-cognitive skills. Table 5 illustrates the result of a multinomial logit model controlling for both covariates and mediators.4 Those students who attended CTE schools tend to have significantly lower probabilities of belonging to a lower growth or declining class of growth. In particular, regarding student creativity and self-control, Table 4 Model fit comparison. Classes

N

# of free parameters

LL

Entropy

Criteria AIC

BIC

CAIC

ssBIC

BLRT

Creativity 1 2 3 4

724 724 724 724

8 11 14 17

–1740.857 –1725.151 –1710.676 –1709.982

NA .958 .788 .830

3497.71 3472.30 3449.35 3453.96

3534.39 3522.73 3513.54 3531.91

3542.39 3533.73 3527.54 3548.91

3508.99 3487.81 3469.08 3477.93

1 vs.2 *** 2 vs.3 *** 3 vs.4

Resilience 1 2 3 4

724 724 724 724

8 11 14 17

–2423.523 –2420.634 –2413.627 –2412.356

NA .937 .784 .769

4863.05 4863.27 4855.25 4858.71

4899.72 4913.70 4919.44 4936.65

4907.72 4924.70 4933.44 4953.65

4874.32 4878.77 4874.99 4882.67

1 vs.2 2 vs.3 *** 3 vs.4 ***

Self-control 1 2 3 4 5

724 724 724 724 724

8 11 14 17 20

–1949.952 –1940.655 –1928.556 –1885.316 –1881.837

NA .719 .801 .914 .913

3915.90 3903.31 3885.11 3804.63 3803.67

3952.58 3953.74 3949.30 3882.57 3895.37

3960.58 3964.74 3963.30 3899.57 3915.37

3927.18 3918.81 3904.84 3828.59 3831.86

1 2 3 4

Self-concept 1 2 3 4

724 724 724 724

8 11 14 17

–2191.685 –2167.038 –2152.833 –2148.656

NA .998 .944 .942

4399.37 4356.08 4333.67 4331.31

4436.05 4406.51 4397.85 4409.25

4444.05 4417.51 4411.85 4426.25

4410.65 4371.58 4353.40 4355.27

1 vs.2 *** 2 vs.3 *** 3 vs.4

vs.2 vs.3 vs.4 vs.5

*** *** *** ***

Note: AIC is Akaike’s Information Criterion; BIC is Bayes’ information Criterion; CAIC is consistent AIC; ssBIC is sample size adjusted BIC; BLRT is bootstrapped likelihood ratio test.

3

The model with smaller values of ICs is preferred. A higher value of Entropy indicates that there are fewer errors in classification. The least squares dummy variable (LSDV) approach for school district fixed effects was not feasible in the class prediction model with the 3-step approach. Thus, we re-estimated the model with a group-mean centering approach. 4

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Fig. 3. Estimated means and observed growth trajectories of each class for creativity, self-control, and self-concept (bottom). Table 5 Multinomial logistic model using the 3-step approach. Creativity (C3 solution)

Class classification

CTE schools (growth pattern)

C1 b(SE)

C2 b(SE)

C3 b(SE)

C4 b(SE)

Estimates (Ref = C1: upward) Estimates (Ref = C2: downward) Estimates (Ref = C3: stagnant)

– 1.40* (.63) 2.40 (2.00)

–1.40* (.63) – 1.00 (1.94)

–2.40 (2.00) –1.00 (1.94) –

– – –

Self-control (C4 solution)

Class classification

CTE schools (growth pattern)

C1 b(SE)

C2 b(SE)

C3 b(SE)

C4 b(SE)

Estimates Estimates Estimates Estimates

– –.56 (.94) –1.60*** (.41) –2.15** (.78)

.56 (.94) – –1.04 (.94) –1.60 (1.16)

1.60*** (.41) 1.04 (.94) – –.55 (.78)

2.15** (.78) 1.60 (1.16) .55 (.78) –

(Ref = C1: (Ref = C2: (Ref = C3: (Ref = C4:

stagnant / some decline) downward) upper stagnant) upward)

Self-concept (C3 solution)

Class classification

CTE schools (growth pattern)

C1 b(SE)

C2 b(SE)

C3 b(SE)

C4 b(SE)

Estimates (Ref = C1: downward) Estimates (Ref = C2: upward) Estimates (Ref = C3: stagnant)

– 2.95 (4.30) 4.01 (2.64)

–2.95 (4.30) – 1.06 (3.41)

–4.01 (2.64) –1.06 (3.41) –

– – –

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

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CTE school reduces the odds of belonging to a downward growth class (C1 vs. C2 in creativity) by approximately 75% (1-exp(−1.40)) and to stagnant/some decline class (C4 vs. C1 in self-control) by approximately 88% (1-exp(−2.15)). Yet, we did not observe any significant effects of CTE school attendance on student self-concept as in the HLM specification. Since the model has small sample sizes in class 1 (.6%) and 2 (3.8%), however, we do not place much emphasis on this result. 5. Discussion This study contributes to previous vocational tracking studies by investigating different developmental trajectories of multiple non-cognitive traits (creativity, self-control, self-concept, and resilience) between career and technical and academic high school students with a robust longitudinal design. In the present study, we found that career and technical schooling does play a role in promoting students’ non-cognitive skills. In particular, over three years, the returns from attending CTE high schools versus general high schools are expected to be about 37% and 30% of SDs of creativity and resilience respectively (in M3), which are not trivial. Although the measures of students’ non-cognitive skills in this study are based on student self-reports, how students themselves perceive their own abilities is crucial in that it affects their identities and behaviors (Voelkl, 1997; Wang & Holcombe, 2010). What mechanisms might account for the positive CTE school effect on non-cognitive skills? A few studies have had success explaining educational gaps between academic and CTE schools by measuring teacher trust (Van Houtte & Van Maele, 2012), teachers’ perceptions of students’ teachability (Van Maele & Van Houtte, 2011), and student’s sense of futility (Van Houtte & Stevens, 2008). In the present study, we explored whether differences in a few generic features of the school curriculum might account for the positive effect of CTE school attendance on non-cognitive skills, but we did not find any effect of school curriculum. Yet, since the Korean educational system is highly centralized under the Ministry of Education, providing a standardized curriculum, the variation of school curriculum measured here was limited (ranging from D = .2–.3). Moreover, our measures of curriculum did not fully capture important differences in the quality of instruction and learning investigated elsewhere (e.g., Swanson, Valiente, Bradley, Lemery-Chalfant, & Abry, 2016). Future studies still need to consider features of the school curriculum as potential mediating variables between CTE school attendance and educational outcomes. We also used a growth mixture model to more explicitly explore the heterogeneity in student non-cognitive skill development and found different growth trajectories for creativity, self-control, and self-concept. We did find that career and technical schooling contributes to a reduced risk of belonging to a low or declining growth class. Again, overall, these results provide empirical evidence that CTE school attendance does help promote student non-cognitive skill development. We offer several hypothetical explanations for the observed positive impacts of CTE schools. First, as we discussed, the core elements of career and technical education and training (e.g., experiential learning or teacher-student mentoring relationship) may contribute to the development of students’ non-cognitive traits such as creativity and resilience. Second, in S. Korea the so-called “cramming education” in academic schools may undermine the development of students’ non-cognitive skills, especially for creativity. Yet, given that the number of hours spent on core subjects (one basic measure of curriculum related to academic press) failed to account for the significant gaps in student non-cognitive skills, the underdevelopment of non-cognitive skills among academic high school students may not necessarily be attributable to the academic-oriented curriculum measured here. Third, there is also a possibility that the characteristics of academically and behaviorally demanding academic high schools may encourage students to rate their non-cognitive skills more critically (West et al., 2016) compared to CTE school students. Perhaps, another compelling explanation is that the observed higher levels of non-cognitive skills among vocational track students might be due to over reporting (or overconfidence). S. Korea is well known for a culture of “education fever” among middle class parents, with an especially strong emphasis on pursuing educational credentials (Lee et al., 2010). Given that CTE schools are undervalued and there are poor future expectations for those students, they may develop self-protective coping strategies to maintain their positive social identities (Kelly, 2009; Warikoo & Carter, 2009). A certain degree of confidence in one’s creativity may provide psychological compensation for lower academic status. An overconfidence among low performers might also be due to metacognitive processing deficits (Miller & Geraci, 2011). Since low-achieving and low-SES students are segregated in CTE schools, they may also develop more myopic perspectives compared to those students in academic schools. In a similar vein, the segregated characteristics of CTE schools may further provide a shield from developing a sense of deprivation compared to the matched students in academic schools. Thus, uncertainty about the mechanism for positive non-cognitive returns to CTE school in S. Korea remains. Our findings, however, add significantly to our previous understanding of between-school vocational track effects, which are based on correlational, cross-sectional analyses and to date have primarily emphasized negative non-cognitive outcomes of career and technical education. Considering the overall role of CTE schools in S. Korea and beyond: Can CTE schools help reduce educational inequality? CTE schools may have a basic role to play in bolstering students’ efficacy as learners and belonging in school. Inaccurate and unnecessarily low self-evaluations of skills may undermine students’ learning, and such evaluations may be more common in academic schools (West et al., 2016). Our findings are consistent with the hypothesis that all else equal, students’ resilience and other non-cognitive domains may improve in CTE schools. From a policy-standpoint then, our findings highlight the risk of focusing too narrowly on academic course taking and achievement growth in evaluating school performance and curricular offerings. Our findings may also encourage practitioners in academic high schools to focus greater attention on evaluating opportunity to learn in non-cognitive domains in their curriculum. Yet, in order to fully evaluate the role of CTE schools in exacerbating or ameliorating gaps in educational outcomes researchers will need to consider even more diverse educational outcomes than we have here, and strive to reveal the mechanism of observed vocational track effects (e.g., Van Houtte & Van Maele, 2012). Finally, it is worthwhile to reiterate the importance of the societal context of the data. In particular, we investigated CTE school 389

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effects in a highly standardized educational system and racially homogenous society. It might be difficult to generalize the results of the Korean experience to different educational contexts. Relatedly, although we explored the heterogeneity in students’ non-cognitive trait development, we could not apply more complex interaction models due to the small sizes of the matched sample and few cases in the latent classes. Yet, it may be that the observed returns also vary by educational contexts. For instance, given that students’ evaluations of their non-cognitive traits are affected by school climate (West et al., 2016), school contexts such as the racial composition of students might also matter (as a reference group). In Flanders, Van Houtte (2005) found that while male students in general schools tended to have higher self-esteem than male students in CTE schools, no significant difference was observed for female students. Future studies will also need to consider the heterogeneity in returns to CTE schools. Acknowledgement An earlier version of this paper was presented at the 2019 annual meeting of American Educational Research Association (AERA), Toronto in Canada. Appendix A. Description of original variables Variables Dependent variable Creativity

Resilience

Self-concept

Self-control

Covariates Before Matching (wave 3) Male Average GPA Free lunch students Single parent Dual income family

Description

N

2,475 (W3) 2,446 (W4) 2,431 (W5) 2,420 (W6) A standardized composite (mean) of students’ responses (on five-point scales of agreement-disagreement): I 2,473 recover quickly after a hard time; I endure external stress effectively; I have always tried to be positive. (W3) 2,442 (W4) 2,432 (W5) 2,420 (W6)

3.63 3.66 3.60 3.60

(.64) (.63) (.61) (.61)

3.35 3.43 3.40 3.42

(.87) (.86) (.81) (.82)

A standardized composite (mean) of students’ responses (on five-point scales of agreement-disagreement): I 2,473 personally think I have a good temperament; I am a person with ability; I see myself as valuable; I talk (W3) positive to myself; I am satisfied with myself. 2,444 (W4) 2,431 (W5) 2,420 (W6) A standardized composite (mean) of students’ responses (on five-point scales of agreement-disagreement): I 2,473 can exercise authority over myself without supervision; I do not give up easily even if a given task is hard; I (W3) first make a plan before I start. 2,440 (W4) 2,431 (W5) 2,419 (W6)

3.62 3.68 3.64 3.67

(.80) (.77) (.76) (.77)

3.32 3.43 3.45 3.48

(.73) (.69) (.66) (.65)

Dummy; female ( = 0) Average academic achievement (Korean, English, and Math, which are measured with standardized vertical scales). Dummy: student who received school free lunch ( = 1) Dummy: students with a single parent ( = 1) Dummy: two parents working full-time ( = 1)

.51 (.50) 554.72 (31.05) .13 (.34) .13 (.34) .51 (.50)

A standardized composite (mean) of students’ responses (on five-point scales of agreement-disagreement): I know well about what I am interested in; I have experience in searching for what I am interested in; I try to find out and solve the problems in various ways; I cannot pass if I face something new; I like to know the cause of if something occurs; I question the things people consider natural; I would like to make mine with anything I do; I would like to work in my own special way; I prefer individuality over intelligence.

Monthly household income Parent’s reported monthly household income is transformed by natural logarithms after plus 1. (Korean won) Parent educational level Average educational level of parent for the highest level of education. Parent academic support

Mean (SD)

2,461 2,474 2,480 2,446 2,435 2,328 2,420

A standardized composite (mean) of students’ responses (on five-point scales of agreement-disagreement): 2,469 My parents advise me on my study. My parents check my homework; My parents have interests in my school life; My parents encourage me to study hard.

390

460.71 (504.27) 13.88 (2.13) 3.43 (.77)

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Sum of parent’s reported monthly household expenditures on private education in Korean, Math, and English is transformed by natural logarithms after plus 1.

1,772

50.11 (75.87)

Parent–student relationship

A standardized composite (mean) of students’ responses (on five-point scales of agreement-disagreement): My parents try to spend lots of time with me; My parents show me love and affection; My parents understand me well; I talk with my parents first when I face difficulties. Sum of following experienced cultural activities at home: dining out; traveling; sports participation with parents; visiting museum/art gallery/concert; attending sports events. A standardized composite (mean) of students’ responses (on five-point scales of agreement-disagreement): I have a friend whom I can trust; I spend most of my break and lunch hours with friends; I make up with my friends right away even after we fight; I help friends who need my help. Sum of following experiences at schools: absence due to disease; early leave due to disease; infirmary use; un–submission of assignment due to disease.

2,468

3.71 (.86)

2,443

4.22 (1.56)

2,477

4.19 (.61)

2,466

.92 (1.17)

After matching Single-sex school Private school School free lunch School size

Dummy; coeducational school ( = 0) Dummy; public school ( = 0) Percentage of free lunch students at school Total number of students

2,507 2,438 2,467 2,467

School locale School SES

School districts in Seoul (nominal scale) Family SES is aggregated by school levels.

2,490 2,502

.61 (.49) .67 (.47) .23 (.14) 1221.49 (374.31) –– 451.61 (169.28) .40 (.14)

Cultural activities at home Peer relationship Health condition

Percentage of teachers with Proportion of licensed teachers with MA or PhD degrees in school MA/PhD Teacher years of experiA standardized composite (mean) of teachers’ years of experience in teaching at school ence Percentage of part–time t- Percentage of part–time teacher at school eacher Mediation variables # of hours for core subjects # of hours for career development # of hours for extra curriculum School autonomy

2,397 2,349 2,440

Number of hours spent on Korean, Math, and English at schools by weekly Number of hours spent on students’ career developments at schools by weekly

2,457 2,432

Number of hours spent on extra curriculum at schools by weekly

2,398

Dummy: school with autonomy in curriculum selection (=1)

2,467

20.15 (3.87) .20 (.11)

5.30 (5.25) 6.05 (14.83) 5.87 (12.52) .19 (.39)

Appendix B. Model specification for HLM After extracting a well-balanced sample with similar values of observed covariates, we apply a three-level growth curve model (time points are nested within students, which are then nested within schools) to investigate the longitudinal consequence of attending CTE schools. In addition to the matching process, we include family characteristics in the models to adjust for any remaining covariate imbalance. The Level 1 (time points) thus is

Ytij =

0ij

+

1ij (Time )

+ etij , etij

2 ),

(0,

where Ytij is the student-reported dependent variable for time t in school j; 0ij is the intercept for time = 0 for student i in school j; etij is a Level 1 random effect, assuming that etij ’ s are independently normally distributed with a mean of zero and constant variance. The Time variable is coded 0, 1, and 2, so that the intercept (when time = 0) represents the year 1 (first year of high school). The Level 2 (students) is n 0ij

=

+

00j

0qj X qij

+ r0ij

1qj Xqij

+ r1ij,

q=1 n 1ij

=

10j

+ q= 1

r0ij r1ij

N

0 , 0

00 01

11

.

In the Level 2, the value of the dependent variable when time = 0 ( 0ij ), as well as the linear growth parameter ( 1ij ) are specified as a function of the student-level covariates ( Xqij ) . The Level 2 random effects (r0ij and r1ij ) are assumed to have a multivariate normal distribution with a mean vector of zero and a covariance matrix . Finally, the Level 3 (schools) is n 00j

=

000

+

001 (Tech /Voca Sch )

+

00q Wqj

+ u00j

q=2

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=

100

+

101 (Tech / Voca Sch )

+

10q Wqj

+ u1oj ,

q=2

u 00j u1oj

N 0 , 0

00 10

11

.

In the Level 3, the average values of the dependent variable for students in school j when time = 0 ( 00j ) and the average linear growth slope for students in school j ( 10j ) are predicated by the treatment indicator and school-level covariates (Wqj ) . By doing so, we can capture whether there is a significant time-varying treatment effect controlling for other time-varying and invariant school-level covariates in addition to student-level covariates at level 2. Yet, the random slopes for schools in this matched sample are negligible (.00). In the subsequent analyses, we thus drop the random slope for schools.5 Appendix C. A brief introduction to growth mixture model The conventional growth model assumes that all of student growth trajectories can be modeled using a single growth parameter and students come from a single homogenous population (Collins & Lanza, 2010). However, this is an unrealistic assumption in many educational settings. There might be, for instance, various subpopulations in the growth of students’ cognitive and non-cognitive skills. The growth mixture model (GMM) can track differences in growth parameters across unobserved subpopulations in a post-hoc manner. The GMM can be written as follows (Ram & Grimm, 2009):

Y [t ]n =

C c=1

0

(

nc (g0nc nc

* A0c [t ] + g1nc * A1c [t ] + e [t ]nc ))

1 and

C c=1

nc

= 1,

where dependent variable Y is repeatedly measured at times t (e.g., t = 0–3); g0nc and g1nc represent two latent variables (i.e. intercept and slope); A0c and A1c are basis vectors representing factor loadings (i.e. stability over time and occasion-to-occasion changes); e [t ]nc is a time-specific residual. The differences among groups are described by c subscripts which represent the latent (or unobserved) group to which individual n belongs, and nc indicates the probability that individual n belongs to class c. That is, GMM explores how the classes differ in terms of means, variances, and covariance of g0nc and g1nc , and the general patterns of change in A0c and A1c . A latent class growth analysis (LCGA) is a special type of GMM fixing the variance of latent slope and intercept to zero within class. This approach is particularly useful with smaller sample size (Jung & Wickrama, 2008).

References Abele, A. E., & Spurk, D. (2009). The longitudinal impact of self-efficacy and career goals on objective and subjective career success. Journal of Vocational Behavior, 74(1), 53–62. Asparouhov, T., & Muthén, B. (2014). Auxiliary variables in mixture modeling: three–step approaches using M plus. Structural Equation Modeling A Multidisciplinary Journal, 21(3), 329–341. Betz, N., & Klein, K. (1996). Relationships among measures of career self-efficacy, generalized self-efficacy, and global self-esteem. Journal of Career Assessment, 4, 285–298. Borghans, L., Meijers, H., & Ter Weel, B. (2008). The role of noncognitive skills in explaining cognitive test scores. Economic Inquiry, 46(1), 2–12. Brunello, G., & Checchi, D. (2007). Does school tracking affect equality of opportunity? New international evidence. Economic Policy, 22(52), 782–861. Byun, S. Y., & Kim, K. K. (2012). Determinants of college attendance among vocational high school graduates. The Journal of Korean Education, 39(2), 79–107 (in Korean). Byun, S., & Park, H. (2017). When different types of education matter: Effectively maintained inequality of educational opportunity in Korea. The American Behavioral Scientist, 61(1), 94–113. Clotfelter, C. T., Ladd, H. F., & Vigdor, J. L. (2006). Teacher-student matching and the assessment of teacher effectiveness. The Journal of Human Resources, 41, 778–820. Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences, Vol. 718. John Wiley & Sons. Crocker, J., & Major, B. (1989). Social stigma and self-esteem: The self-protective properties of stigma. Psychological Review, 96(4), 608–630. Dougherty, S. M. (2018). The effect of career and technical education on human capital accumulation: Causal evidence from Massachusetts. Education Finance and Policy, 13(2), 119–148. Duflo, E., Dupas, P., & Kremer, M. (2011). Peer effects, teacher incentives, and the impact of tracking: Evidence from a randomized evaluation in Kenya. The American Economic Review, 101(5), 1739–1774. Fruehwirth, J. C. (2013). Identifying peer achievement spillovers: Implications for desegregation and the achievement gap. Quantitative Economics, 4, 85–124. Gamoran, A. (1993). Alternative uses of ability grouping in secondary schools: Can we bring high-quality instruction to low-ability classes? American Journal of Education, 102, 1–22. Gamoran, A. (2009). Tracking and inequality: New directions for research and practice. The Routledge international handbook of the sociology of education. Routledge231–246. Gutman, L. M., & Schoon, I. (2013). The impact of non-cognitive skills on outcomes for young people: Literature review. London: University of London, Institute of Education. Hackett, G., & Betz, N. E. (1995). Self-efficacy and career choice and development. In J. E. Maddux (Ed.). Self-efficacy, adaptation, and adjustment: Theory, research, and application (pp. 249–280). New York: Plenum Press. Heckman, J. J., & Rubinstein, Y. (2001). The importance of noncognitive skills: Lessons from the GED testing program. The American Economic Review, 91(2), 145–149. Holm, A., Jæger, M. M., Karlson, K. B., & Reimer, D. (2013). Incomplete equalization: The effect of tracking in secondary education on educational inequality. Social Science Research, 42(6), 1431–1442.

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The results with or without random slopes for schools are almost identical. 392

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Horn, D. (2013). Diverging performances: The detrimental effects of early educational selection on equality of opportunity in Hungary. Research in Social Stratification and Mobility, 32, 25–43. Jackson, J. H., & Hasak, J. (2014). Look beyond the label: Reframing, reimagining, and reinvesting in CTE. American Educator, 38(3), 34–39. Jung, E., & Kang, H. (2013). Analysis of the vocational high school curriculum. Journal of Education and Research, 34(1), 1–40 (in Korean). Jung, T., & Wickrama, K. A. S. (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2(1), 302–317. Kalogrides, D., Loeb, S., & Beteille, T. (2013). Systematic sorting: Teacher characteristics and class assignments. Sociology of Education, 86, 103–123. Kim, E., Im, H., Nahm, E., & Hong, S. (2012). Korean American parents’ reconstruction of immigrant parenting in the United States. Journal of Cultural Diversity, 19(4), 124–132. Kim, Y. (2014). What determines the admission to university?: An evaluation on the degree of influences by socioeconomic status, residential area and educational environments. Korean Journal of Public Finance, 7(3), 127–171 (in Korean). Kelly, S. (2004). Are teachers tracked? On what basis and with what consequences. Social Psychology of Education, 7, 55–72. Kelly, S. (2009). Social identity theories and educational engagement. British Journal of Sociology of Education, 30(4), 449–462. Kelly, S., & Carbonaro, W. (2012). Curriculum tracking and teacher expectations: Evidence from discrepant course taking models. Social Psychology of Education, 15(3), 271–294. Kelly, S., & Price, H. (2009). Vocational education: A clean slate for disengaged students? Social Science Research, 38(4), 810–825. Kelly, S., & Price, H. (2014). Changing patterns of engagement in the transition to high school. Teachers College Record, 116, 15–36. Kemple, J., & Willner, C. J. (2008). Career academies: Long–term impacts on labor market outcomes, educational attainment, and transitions to adulthood. New York, NY: MDRC. Komarraju, M., Swanson, J., & Nadler, D. (2014). Increased career self-efficacy predicts college students’ motivation, and course and major satisfaction. Journal of Career Assessment, 22(3), 420–432. Lee, C. J., Lee, H., & Jang, H. (2010). The history of policy responses to shadow education in South Korea: Implications for the next cycle of policy responses. Asia Pacific Education Review, 11(1), 97–108. Lee, J., Choi, D., & Oh, C. (2012). Determinants of occupational aspirations of high school students. The Korean Society for Agricultural Education and Human Resource Development, 44(4), 25–43 (in Korean). Lee, M. J. (2016). Matching, regression discontinuity, difference in differences, and beyond. Oxford University Press. Levesque, K., Laird, J., Hensley, E., Choy, S. P., Cataldi, E. F., & Hudson, L. (2008). Career and technical education in the United States: 1990 to 2005. Statistical analysis report. NCES 2008-035. National Center for Education Statistics. Lubotsky, D., & Kaestner, R. (2016). Do `Skills beget skills’? Evidence on the effect of kindergarten entrance age on the evolution of cognitive and non-cognitive skill gaps in childhood. Economics of Education Review, 53, 194–206. Lutz, W., Stulz, N., & Köck, K. (2009). Patterns of early change and their `relationship to outcome and follow-up among patients with major depressive disorders. Journal of Affective Disorders, 118(1–3), 60–68. Luyckx, K., Teppers, E., Klimstra, T. A., & Rassart, J. (2014). Identity processes and personality traits and types in adolescence: Directionality of effects and developmental trajectories. Developmental Psychology, 50(8), 2144–2153. Malmberg, L. E., & Trempała, J. (1997). Anticipated transition to adulthood: The effect of educational track, gender, and self-evaluation on Finnish and Polish adolescents’ future orientation. Journal of Youth and Adolescence, 26(5), 517–537. McWhirter, E., Rasheed, S., & Crothers, M. (2000). The effects of high school career education on social-cognitive variables. Journal of Counseling Psychology, 47(3), 330–341. Miller, T. M., & Geraci, L. (2011). Unskilled but aware: Reinterpreting overconfidence in low-performing students. Journal of Experimental Psychology: Learning, Memory, and Cognition, 37(2), 502–506. Müller, W., & Shavit, M. (2000). Vocational secondary education. Where diversion and where safety net? European Societies, 2(1), 29–50. Neumark, D., & Rothstein, D. (2006). School-to-career programs and transitions to employment and higher education. Economics of Education Review, 25(4), 374–393. Northrop, L., & Kelly, S. (2019). Who gets to read what? Tracking, instructional practices, and text complexity for middle school struggling readers. Reading Research Quarterly, 54, 339–361. Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14(4), 535–569. OECD (2014). Lessons from PISA for Korea, strong performers and successful reformers in education. OECD Publishing. OECD (2016). PISA 2015 results in focus. OECD Publishing. Park, H. (2013). Re-evaluating education in Japan and Korea: De-mystifying stereotypes. Routledge. Pearl, J. (2009). Causality. Cambridge university press. Pimentel, S. D., Kelz, R. R., Silber, J. H., & Rosenbaum, P. R. (2015). Large, sparse optimal matching with refined covariate balance in an observational study of the health outcomes produced by new surgeons. Journal of the American Statistical Association, 110(510), 515–527. Ram, N., & Grimm, K. J. (2009). Methods and measures: Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups. International Journal of Behavioral Development, 33(6), 565–576. Rosenbaum, J. E., & Jones, S. A. (2000). Interactions between high schools and labor markets. In M. Hallinan (Ed.). Handbook of the sociology of education (pp. 411– 436). Boston, MA: Springer. Salmela-Aro, K., Kiuru, N., & Nurmi, J. E. (2008). The role of educational track in adolescents’ school burnout: A longitudinal study. The British Journal of Educational Psychology, 78(4), 663–689. Shaw, S. R., Gomes, P., Polotskaia, A., & Jankowska, A. M. (2015). The relationship between student health and academic performance: Implications for school psychologists. School Psychology International, 36(2), 115–134. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford. Smerdon, B. A. (2002). Students’ perceptions of membership in their high schools. Sociology of Education, 75(4), 287–305. Stern, D., Dayton, C., & Raby, M. (2010). Career academies: A proven strategy to prepare high school students for college and careers. Career Academy Support Network. Berkeley, CA: Career Academy Support Network. Swanson, J., Valiente, C., Bradley, R. H., Lemery-Chalfant, K., & Abry, T. (2016). Teachers’ effortful control and student functioning: Mediating and moderating processes. Social Development, 25(3), 623–645. Trautwein, U., Lüdtke, O., Marsh, H. W., Köller, O., & Baumert, J. (2006). Tracking, grading, and student motivation: Using group composition and status to predict self-concept and interest in ninth-grade mathematics. Journal of Educational Psychology, 98(4), 788–806. Van Houtte, M. (2005). Global self-esteem in technical/vocational versus general secondary school tracks: A matter of gender? Sex Roles, 53(9/10), 753–761. Van Houtte, M. (2006b). School type and academic culture: Quantitative evidence for the differentiation-polarisation theory. Journal of Curriculum Studies, 38, 273–292. Van Houtte, M. (2006a). Tracking and teacher satisfaction: The role of study culture and trust. The Journal of Educational Research, 99, 247–254. Van Houtte, M., Demanet, J., & Stevens, P. A. (2012). Self-esteem of academic and vocational students: Does within–school tracking sharpen the difference? Acta Sociologica, 55(1), 73–89. Van Houtte, M., & Stevens, P. A. (2008). Sense of futility: The missing link between track position and self-reported school misconduct. Youth & Society, 40(2), 245–264. Van Houtte, M., & Stevens, P. A. (2009). Study involvement of academic and vocational students: Does between–school tracking sharpen the difference? American Educational Research Journal, 46(4), 943–973. Van Houtte, M., & Stevens, P. A. (2010). The culture of futility and its impact on study culture in technical/vocational schools in Belgium. Oxford Review of Education,

393

International Journal of Educational Research 98 (2019) 379–394

B. Yu and S. Kelly

36(1), 23–43. Van Houtte, M., & Stevens, P. A. J. (2016). Track position, futility culture, and involvement with paid work: Investigating the correlates of lower-track students’ involvement with part-time employment in Flanders. Sociological Inquiry, 86(3), 372–399. Van Houtte, M., & Van Maele, D. (2012). Students’ sense of belonging in technical/vocational schools versus academic schools: The mediating role of faculty trust in students. Teachers College Record, 114(7), 1–36. Van Maele, D., & Van Houtte, M. (2011). Teacher trust in students in technical/vocational schools versus academic schools and the role of teacher perception of students’ teachability. In B. Curtis (Ed.). Psychology of trust (pp. 117–135). Nova Science Publishers. Voelkl, K. E. (1997). Identification with school. American Journal of Education, 105(3), 294–318. Waldow, F., Takayama, K., & Sung, Y. K. (2014). Rethinking the pattern of external policy referencing: Media discourses over the ‘Asian Tigers’’ PISA success in Australia, Germany and South Korea. Comparative Education, 50(3), 302–321. Wang, M. T., & Holcombe, R. (2010). Adolescents’ perceptions of school environment, engagement, and academic achievement in middle school. American Educational Research Journal, 47(3), 633–662. Warikoo, N., & Carter, P. (2009). Cultural explanations for racial and ethnic stratification in academic achievement: A call for a new and improved theory. Review of Educational Research, 79(1), 366–394. Wentzel, K. R. (2005). Peer relationships, motivation, and academic performance at school. In A. J. Elliot, & C. S. Dweck (Eds.). Handbook of competence and motivation (pp. 279–296). New York: Guilford Press. West, M. R., Kraft, M. A., Finn, A. S., Martin, R. E., Duckworth, A. L., Gabrieli, C. F. O., et al. (2016). Promise and paradox: Measuring students’ non-cognitive skills and the impact of schooling. Educational Evaluation and Policy Analysis, 38(1), 148–170. Wickrama, K. K., Lee, T. K., O’Neal, C. W., & Lorenz, F. O. (2016). Higher-order growth curves and mixture modeling with Mplus: A practical guide. Routledge. Yu, B., Lim, H., & Kelly, S. (2019). Does receiving a school free lunch lead to a stigma effect? Evidence from a longitudinal analysis in South Korea. Social Psychology of Education, 22(2), 291–319.

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