Trajectories of implicit theories and their relations to scholastic aptitude: A mediational role of achievement goals

Contemporary Educational Psychology 59 (2019) 101800

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Trajectories of implicit theories and their relations to scholastic aptitude: A mediational role of achievement goals☆

T

You-kyung Leea, Eunjin Seob,

⁎

a b

Division of Education, Sookmyung Women’s University, Republic of Korea School of Family and Consumer Sciences, Texas State University, USA

ARTICLE INFO

ABSTRACT

Keywords: Implicit theories Mindset Scholastic aptitude Academic achievement Achievement goals Parallel process models

Implicit theories of intelligence play an important role in students’ academic motivation and achievement. This longitudinal study examined how the trajectories of implicit theories of intelligence from Grade 8 to Grade 10 were related to Grade 12 SAT achievement via Grade 11 achievement goals. We employed parallel process models to examine changing patterns of Korean students’ (N = 6491) entity and incremental theories over three years. Results showed that both entity and incremental theories increased over time. The intercept and the slope of entity theory were negatively related with the intercept and the slope of incremental theory, respectively. In line with Dweck’s theoretical framework, increases in incremental theory were found to predict SAT achievement via mastery-approach goals, whereas increases in entity theory predicted SAT achievement via performance-approach goals. The results indicate that different types of achievement goals play unique roles in mediating the relation between changes in implicit theories and SAT achievement.

1. Introduction As adolescents transition to middle school and to high school, they undergo significant changes in academic and social environments, often finding such changes to be challenging (Berndt & Mekos, 1995; Seidman, Allen, Aber, Mitchell, & Feinman, 1994). When students enter high school, for example, the curriculum becomes more demanding and students are expected to take more responsibility for their educational outcomes (Benner, 2011; Benner & Graham, 2009). Some students feel helpless and withdraw from engaging with their schoolwork; others rise to the challenge, persisting in the face of difficulty and putting more effort into their academic work. Research suggests that students who believe intelligence is malleable and can grow (i.e., incremental theory) are more likely to adapt to challenging situations than those who believe intelligence is fixed (i.e., entity theory). This belief that intelligence is malleable in turn results in more successful outcomes, such as higher academic achievement (Dweck & Leggett, 1988; Rattan, Savani, Chugh, & Dweck, 2015). Prior studies have shown the relations between students’ implicit theories of intelligence and a range of outcomes, but most have measured implicit theories at a single time point (e.g., Chen & Pajares, 2010; Cury, Elliot, Da Fonseca, & Moller, 2006). However, there has

been theoretical discussion that implicit theories of intelligence may be sensitive to environmental stimuli (Dweck & Molden, 2005) and empirical evidence shows the changes in implicit theories of intelligence over time in a natural learning setting without experimental manipulations (e.g., Dai & Cromley, 2014; Gonida, Kiosseoglou, & Leondari, 2006; Shively & Ryan, 2013). Such changes in implicit theories of intelligence may importantly relate to subsequent academic motivation and performance (Carr & Dweck, 2011; Dai & Cromley, 2014) especially in the face of difficulties and obstacles (Dweck, 1986). Therefore, the current study focuses on changes in implicit theories during the high school transition period in South Korea, where students’ academic stress may increase substantially. Examining how 8th grade South Korean students’ implicit theories change over three years, and how these changes relate to subsequent outcomes, may enable us to explain how and why helping students maintain or increase their belief in the malleability of intelligence can be crucial during the secondary school period. In addition to identifying the developmental trajectories of secondary school students’ implicit theories of intelligence over three years, based on Dweck’s social-cognitive model of achievement motivation (Dweck, 1986; Dweck & Leggett, 1988), this longitudinal study also investigates the potential mediating role of achievement goals in

We thank Kristy Robinson and Rebecca Steingut for their insightful feedback on earlier versions of this manuscript. Corresponding author at: School of Family and Consumer Sciences, Texas State University, 601 University Drive, FCS 123C, San Marcos, TX 78666-4684, USA. Present address: Population Research Center, The University of Texas at Austin, 305 E. 23rd Street, RLP 2.702A, Austin, TX 78712, USA. E-mail address: [email protected] (E. Seo). ☆ ⁎

https://doi.org/10.1016/j.cedpsych.2019.101800

Available online 17 September 2019 0361-476X/ © 2019 Elsevier Inc. All rights reserved.

Contemporary Educational Psychology 59 (2019) 101800

Y.-k. Lee and E. Seo

mastery-avoidance goals in the current research.2

the relation between two distinct implicit theories and subsequent academic achievement (i.e., SAT scores). This modeling allows us test Dweck’s social-cognitive model in a more comprehensive way to reveal one of the key mechanisms by which students’ implicit theories relate to academic achievement.

1.2. Trajectories of implicit theories of intelligence Implicit theories of intelligence are often conceptualized at a dispositional level, but there is evidence of changes in implicit theories of intelligence through laboratory experiments (e.g., Spray, Wang, Biddle, Chatzisarantis, & Warburton, 2006) or long-term interventions (e.g., Blackwell, Trzesniewski, & Dweck, 2007; Burnette & Finkel, 2012). Furthermore, Dweck and Molden (2005) maintain that individuals’ implicit theories of intelligence may change without manipulated stimuli because these beliefs are sensitive to environment. In other words, changes in the learning environment in secondary school may prompt changes in students’ implicit theories. For example, students may not strongly endorse an entity theory in earlier grades due to the context of elementary school which tends to focus on learning processes rather than performance outcomes (Eccles et al., 1993). After transitioning to secondary school, however, students may experience greater emphasis on relative performance outcomes given the prevalent nature of the normative evaluations (Eccles et al., 1993). To worsen the situation, students tend to experience challenges in a lot of requirements of classwork and several subjects perceived to be difficult such as algebra or calculus (Benner, 2011; Benner & Graham, 2009). Consequently, students could often feel that being a top student in these subjects requires special talent that cannot be taught or changed. These changes in the learning environment during the period of transitioning to secondary school may lead some students to revise their implicit theories and believe more in entity theory. As such, one may expect the changeability of students’ implicit theories of intelligence over time. Evidence for the changes in implicit theories based on the longitudinal field observation studies are relatively rare, but a few studies have found the pattern in which entity theory increases whereas incremental theory decreases over time (e.g., Dai & Cromley, 2014; Flanigan, Peteranetz, Shell, & Soh, 2017; Shively & Ryan, 2013), though this was not always the case (e.g., stable entity theory over four years; Robins & Pals, 2002). It is unclear whether the discrepant findings are due to different research designs, such as different lengths of the study periods or different educational contexts (e.g., the highly selective university setting in Robins & Pals, 2002). While most extant literature has shown the trajectory of either entity theory or incremental theory, Dai and Cromley (2014) investigated changes in both entity theory and incremental theory among college students, and how the change patterns were related to each other, using parallel process models. Although entity theory and incremental theory are often considered to be in conceptual opposition to each other, Dai and Cromley (2014) found empirical evidence for the multidimensionality of this construct by proposing a two-factor model of implicit theories as opposed to a one-factor model. That is, students simultaneously hold two distinct implicit theories, although one theory can be stronger in certain contexts than the other (Dweck et al., 1995). For example, students may think that ability determines their achievement outcomes (i.e., high in entity theory) but also believe that effort, over a long period of time, leads to high levels of ability (i.e., high in incremental theory; Muenks & Miele, 2017). In addition, Dai and Cromley found that both the intercepts and the slopes of the two theories were negatively related to each other, suggesting that the development of these two theories over time is not independent but rather

1.1. Dweck’s social-cognitive model of achievement motivation Dweck and colleagues proposed a social-cognitive model of achievement motivation (Dweck, 1986, 1999; Dweck, Chiu, & Hong, 1995; Dweck & Leggett, 1988). In this model, implicit theories of intelligence influence the endorsement of different types of achievement goals. In turn, achievement goals determine adaptive or maladaptive patterns of learning outcomes in achievement settings. The key proposition of Dweck’s social-cognitive model is that individuals who believe they have a fixed amount of intelligence (i.e., entity theory) focus, when they encounter obstacles, on gaining favorable judgment of their ability or avoiding negative judgments (i.e., performance goals). Conversely, individuals who believe their intelligence is malleable (i.e., incremental theory) focus on developing their competence through hard work (i.e., mastery goals) and embrace challenging tasks as learning opportunities when obstacles are introduced. Thus, Dweck’s social-cognitive model posits that entity theory usually leads to maladaptive behavioral patterns in achievement settings. The incremental theory, in contrast, usually leads to adaptive behavioral patterns. This model also adds an important point that entity theory may result in maladaptive patterns of behavior only when confidence in present ability is low; thus, implicit theories would play an important role especially in the face of challenges, such as a transition to high school. In terms of achievement goals, Dweck’s social-cognitive model (1986) introduces two types of goals: mastery goals (or learning goals) focusing on developing competence and understanding a task, and performance goals focusing on gaining favorable judgments of the individual’s competence or avoiding negative judgments. Later, the 2 × 2 achievement goal model (Elliot & McGregor, 2001) was introduced1 based on the definition (mastery vs. performance) and valence (approach vs. avoidance) of competence, which comprises mastery-approach (focusing on developing competence), mastery-avoidance (focusing on avoiding failing to develop competence), performanceapproach (focusing on outperforming others), and performance-avoidance (focusing on avoiding doing worse than others) goals. Accounting for both approach and avoidance forms of achievement goals may provide more precise explanations of the predictive utility of achievement goals (see Elliot, 2005), especially considering that Dweck’s social-cognitive model posits that the outcomes of performance goals would vary depending on individuals’ perceived competence. In fact, some achievement goal theorists maintain that individuals endorse performance-approach goals or performance-avoidance goals depending on the level of perceived competence and these two performance goals in turn uniquely relate to various outcomes (Elliot & Church, 1997; Law, Elliot, & Murayama, 2012). Combining the socialcognitive model and the views of achievement goal theorists, therefore, we tested whether performance-approach and performance-avoidance goals played differential roles in the relations between implicit theories and achievement. Regarding mastery-avoidance goals, however, there is no clear theoretical expectation for their role based on Dweck’s social-cognitive model, because the model theorizes that achievementrelated outcomes of mastery goals would be consistently positive regardless of the level of perceived competence. Thus, we did not focus on

2 There has also been discussion about the nature of mastery-avoidance goals, because they tend to be observed relatively less frequently among students and are not easily understood by them (Ciani & Sheldon, 2010; Maehr & Zusho, 2009). Some researchers have suggested that the multifaceted components of mastery-avoidance goals (e.g., intrapersonal and task-based standards of competence) may be a possible reason for this gap (Madjar, Kaplan, & Weinstock, 2011).

1

In addition to the 2 × 2 goal model, there have been additional refinements to achievement goal frameworks by introducing a 3 × 2 goal model (Elliot, Murayama, & Pekrun, 2011) or by identifying various components of performance goals (e.g., appearance or normative components; Hulleman et al., 2010; Senko et al., 2011). 2

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are related to each other. Specifically, college students with high levels of initial entity theory tended to have low levels of initial incremental theory, and college students with an increasing entity theory tended to have a decreasing incremental theory. One critical gap within the extant longitudinal field observation studies on implicit theories is that most of them focused on college students (Dai & Cromley, 2014; Flanigan et al., 2017; Robins & Pals, 2002; Shively & Ryan, 2013). Only one study focused on elementary school students (Gonida et al., 2006) and no study, to our knowledge, has yet examined the changing pattern of implicit theories in secondary school years. The secondary school period, however, is extremely crucial for understanding changes in individuals’ beliefs about malleability of their intelligence due to the many contextual changes students may experience during this period (Benner, 2011; Benner & Graham, 2009). Furthermore, many middle school transition studies have demonstrated students’ motivation declines during this period in relation to their increasing perceptions of academic pressure and social comparison (Eccles, Lord, & Midgley, 1991; Eccles et al., 1993; Stipek & MacIver, 1989). Considering that incremental theories may function as a protective factor for the declining motivation in the face of challenges, it is important to understand how students’ implicit theories of intelligence may change during this period and how these patterns may be distinct from or similar to those in other periods (e.g., college, elementary school).

1.4. Mediational roles of achievement goals Implicit theories of intelligence have been posited as one of the key antecedents of achievement goals (Dweck, 1986). Namely, students who strongly endorse entity theory are theorized to endorse goals for doing better than others (i.e., performance-approach goals), because it is important for them to make others think they have strong abilities that are unlikely to change. Even though Dweck’s social-cognitive model did not explicitly mention performance-avoidance goals, one may speculate that students with a strong entity theory would also endorse goals focusing on avoiding doing worse than others (i.e., performance-avoidance goals), because it is important for them to ensure that others to not think that their ability is low and will not change. Conversely, according to Dweck’s social-cognitive model, students with a strong incremental theory are hypothesized to endorse goals focusing on learning even in the face of difficulties because they believe their abilities and intelligence are malleable and that their outcomes depend on their efforts. Prior studies (e.g., Corrion et al., 2010; Cury et al., 2006; Howell & Buro, 2009) and a meta-analysis study (Burnette et al., 2013) have provided empirical support for the hypothesized relations. Specifically, the meta-analysis revealed that incremental theory, relative to entity theory, was positively correlated to mastery goals (r¯ = 0.19), but negatively correlated to performance goals (r¯ = −0.15), with a stronger negative relation to performance-avoidance goals than to performanceapproach goals. Turning to the relations between achievement goals and achievement outcomes, the relations have been extensively examined in the extant literature. Prior research, including meta-analytic research, suggests that performance-avoidance goals are typically associated with maladaptive outcomes, including lower achievement, whereas masteryapproach goals are associated with adaptive outcomes, including greater achievement (for meta-analysis: Cellar et al., 2011; Hulleman, Schrager, Bodmann, & Harackiewicz, 2010; Payne, Youngcourt, & Beaubien, 2007). Performance-approach goals have often been related to mixed outcomes, but a meta-analysis (Hulleman et al., 2010) found that appearance-approach goals in which individuals desire to show their competence to others (e.g., “It is important to me that my peers think I am good at math”) negatively related to achievement outcomes (r¯ = −0.14), whereas normative-approach goals in which individuals desire to outperform others (e.g., “My goal is to get a better grade than other students”) positively related to them (r¯ = 0.14). In the current study, we measured normative-approach goals as performance-approach goals; as such, we expected that performance-approach goals would be positively related to academic achievement. Taken together, different implicit theories may relate to different types of achievement goals, which in turn may uniquely relate to academic achievement, as Dweck’s social-cognitive model theorized. Although previous studies found supporting evidence for Dweck’s social-cognitive model by testing the mediating roles of achievement goals in the relation between implicit theories and academic achievement (e.g., Chen & Pajares, 2010; Dinger, Dickhäuser, Spinath, & Steinmayr, 2013; Dupeyrat & Mariné, 2005), most of these previous studies had cross-sectional designs, limiting their ability to make inferences about directional relations. The present study’s mediational models, which consider the temporal order of the variables, may facilitate interpreting the relations among implicit theories, achievement goals, and academic achievement more clearly, though these relations still do not provide evidence for causality.

1.3. The relations of implicit theories of intelligence to academic motivation and achievement Although Dweck’s social-cognitive model posits the positive relation of incremental theory to achievement-related outcomes, empirical research has produced confounding results about their relations to academic achievement. On the one hand, some research has found that students with high levels of endorsement of incremental theory or low levels of endorsement of entity theory tend to achieve higher course grades or exhibit slower decreases in grades over time (e.g., Aronson, Fried, & Good, 2002; Blackwell et al., 2007; Cheung, Wang, Monroy, & Couch, 2016; Dai & Cromley, 2014; McCutchen, Jones, Carbonneau, & Mueller, 2016). On the other hand, there is research showing only a weak positive relation (Leondari & Gialamas, 2002; Stump, Husman, & Corby, 2014) or even a negative relation (Bahník & Vranka, 2017; Flanigan et al., 2017) between incremental theory and achievement. To integrate these mixed findings, researchers conducted metaanalyses, and two meta-analytic studies consistently found an overall weak and positive correlation between incremental theory and achievement outcomes, relative to entity theory (r¯ = 0.095 in Burnette, O’Boyle, VanEpps, Pollack, & Finkel, 2013; r¯ = 0.10 in Sisk, Burgoyne, Sun, Butler, & Macnamara, 2018). In particular, Burnette et al. (2013) found that incremental theory tenuously but positively correlated with goal achievement outcomes as compared to entity theory. The metaanalytic research has also found high heterogeneity in the relations between implicit theories and achievement across studies as a potential reason for the weak relations. Accordingly, to identify the potential reasons for high heterogeneity in the relations, Sisk et al. (2018) tested several possible moderators, including types of outcome measures (e.g., standardized test scores vs. course grades), students’ academic risk status, socioeconomic status, and developmental stage, but these variables were identified as not significant or as weak moderators at most. Instead of examining potential moderators of inconsistent relations between implicit theories and achievement, Burnette et al. (2013) focused on the mediators to better understand the relation between incremental theories and goal achievement, on the basis of Dweck’s social-cognitive model. We delineate this mediational model in the following section.

2. The present study Guided by Dweck’s social-cognitive model (Dweck, 1986, 1999; Dweck & Leggett, 1988), this study examined how secondary school students’ entity and incremental theories in 8–10th grade were associated with achievement goals in 11th grade, which in turn related to 3

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academic achievement in 12th grade. Compared to a cross-sectional design, this longitudinal temporal ordering of the variables helps depict the theorized pathway from implicit theories to academic outcomes via achievement goals. Two main research questions were posed, along with their associated hypotheses. First, how do students’ implicit theories of intelligence change over the course of three years, from 8th grade to 10th grade? We hypothesized that students’ entity theory would increase and their incremental theory would decrease over time (Hypothesis 1a), based on the contextual changes in secondary school (Eccles et al., 1993) and empirical evidence from prior longitudinal studies (e.g., Dai & Cromley, 2014; Flanigan et al., 2017). In addition, given the prior finding from parallel process modeling (Dai & Cromley, 2014), we hypothesized that the intercept and slope of entity theory would be negatively related to the intercept and slope of incremental theory, respectively (Hypothesis 1b). Second, to what extent do implicit theories (for both initial levels and subsequent changes) relate to SAT achievement via each type of achievement? For the mastery-approach goal, we hypothesized that not only the initial level but also an increase in incremental theory would be positively related to mastery-approach goals (Hypothesis 2a), based on Dweck’s social-cognitive model and research (Burnette et al., 2013). Accordingly, we expected to find positive indirect effects for the initial level and changes in incremental theory on SAT scores via masteryapproach goals. For the performance-approach goal, we hypothesized that the initial level and an increase in entity theory would be positively related to performance-approach goals (Hypothesis 2b) based on Dweck’s socialcognitive model and research (Burnette et al., 2013), which would in turn positively relate to SAT scores. Because we measured normativeapproach goals (Hulleman et al., 2010) as performance-approach goals, we expected to find positive indirect effects for the initial level and changes in entity theory on SAT scores via performance-approach goals. For the performance-avoidance goal, we hypothesized that the initial level and an increase in entity theory would be positively related to performance-avoidance goals (Hypothesis 2c) based on the prior metaanalysis finding (Burnette et al., 2013), which would in turn negatively relate to SAT scores (Cellar et al., 2011; Hulleman et al., 2010). Thus, we expected to find negative indirect effects of the initial level and changes in entity theory on SAT scores via performance-avoidance goals. Although we based our hypotheses on Dweck’s social-cognitive model’s theoretical propositions and a majority of the empirical findings, we should note that our sample of students is somewhat different from those focused on in most prior work (e.g., students from Western cultures). Specifically, we investigated South Korean students’ implicit theories of intelligence and their related outcomes. Given the relative scarcity of studies based on non-Western samples of adolescents on this topic, it is still unclear how the cultural background of South Korea, such as its strong emphasis on the role of effort in education (Chen & Stevenson, 1995; Cheung, Monroy, & Delany, 2017; Suprawati, Anggoro, & Bukatko, 2014) and the importance of SAT scores in social success (Diamond, 2016), may contribute to different trajectories of implicit theories and their relations to achievement goals and SAT achievement. As such, we took an exploratory approach to understanding Dweck’s social-cognitive model in a Korean educational context. In testing these models, we controlled for three key factors—gender (Matthews, Ponitz, & Morrison, 2009; Stipek & Gralinski, 1991), prior achievement (Hemmings, Grootenboer, & Kay, 2011), and socioeconomic status (Reardon, 2011; Sirin, 2005; Tibbetts et al., 2016)—related to student motivation and outcomes. In particular, socioeconomic status (SES) has been found to be a crucial factor in explaining the relation between students’ implicit theories and academic success, in that those with low SES may benefit from mindset interventions more than those with high SES (Claro, Paunesku, & Dweck,

2016; for meta-analysis, Sisk et al., 2018). Thus, controlling for these confounding variables would provide a clearer picture of the relations among implicit theories, achievement goals, and achievement outcomes. 3. Method 3.1. Dataset We utilized the Korean Educational Longitudinal Study (KELS: 2005), a nationally representative longitudinal study of secondary school students. The Korean Educational Development Institute (KEDI), a non-profit institution funded by the South Korean government, recruited 150 middle schools using stratified cluster random sampling. Initially, 6908 participants in one of the 150 schools completed the baseline surveys. The base year data were collected in 2005 when the participating students were in 7th grade. Follow-up data have been collected every subsequent year or two and will continue to be collected until 2020 when most participants become 26 and 27 years old. Based on our research focus and the availability of focal variables, we utilized the data from five waves (see the following section for details), starting in Grade 8 when most participants were 13–14 years old (n = 6491; 47.9% female) and ending in Grade 12 when most participants were 17–18 years old. Retention rates for each wave and missing data analysis are described in the Missing Data section. 3.2. Measures Items for implicit theories of intelligence and achievement goals were consistently measured using a four-point Likert scale, with responses ranging from not at all (1) to very much so (4) in KELS: 2005. Reliability information is presented in Table 1. The evidence for appropriate item properties, including the estimates of standardized factor loadings, residual variances, and R squares of items for all confirmatory factor analysis models, is presented in Table S1. 3.2.1. Implicit theories of intelligence (Grades 8–10) We used students’ responses to questions about their implicit theories in Grades 8–10, because this period includes the transition from middle school to high school (i.e., 9th grade to 10th grade). We also included the 8th grade time point based on the availability of the variables in the dataset and to allow for latent growth modeling, which requires at least three time points. KELS: 2005 used six items to measure implicit theories of intelligence in Grades 8–9, but used only five items in Grade 10. Therefore, we used only the five items that were consistently measured every year, dropping the one item that was not measured in Grade 10 (“Intelligence continues to change throughout life”). Of the included five items, three items assessed entity theory (“Smart people were born to be smart”; “Intelligence does not change much over time”; “Even if people learn new things, they cannot change their basic intelligence”) and two items assessed incremental theory (“People can develop their ability regardless of their current ability levels”; “People can be smart as long as they put forth their effort”). These measures were similar to those developed by Dweck (1999), which have commonly been used to examine relations between implicit theories of intelligence and academic outcomes (e.g., Blackwell et al., 2007; Chen & Pajares, 2010; Cury et al., 2006; Dai & Cromley, 2014; Dweck et al., 1995). 3.2.2. Achievement goals (Grade 11) Mastery-approach goals (“I want to learn as much as possible in class”; “I want to understand the content of the course as thoroughly as possible”; “It is important for me to develop my ability in class”), performance-approach goals (“It is important for me to do better than other students in class”; “I want to do well compared to others in school”; “My goal in class is to get a better grade than other students”), 4

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Table 1 Descriptive Statistics, Reliabilities, and Intercorrelations among Study Variables.

1. Female 2. Grade 8 test scoresa 3. Family incomea 4. Grade 8 Ent. theory 5. Grade 8 Inc. theory 6. Grade 9 Ent. theory 7. Grade 9 Inc. theory 8. Grade 10 Ent. theory 9. Grade 10 Inc. theory 10. Grade 11 MAP 11. Grade 11 PAP 12. Grade 11 PAV 13. Grade 12 SATa N Mean Standard Deviation Cronbach’s α

1

2

3

4

5

6

7

8

9

10

11

12

13

– 0.15*** −0.05*** −0.05*** 0.06*** −0.05*** 0.08*** −0.03** 0.06*** 0.06*** 0.03* 0.01 0.05** 6908 0.48 0.50 –

– 0.20*** −0.10*** 0.14*** −0.03* 0.12*** 0.04** 0.04** 0.25*** 0.16*** 0.07*** 0.66*** 6466 3.99 0.60 –

– 0.002 0.01 −0.01 0.000 0.01 −0.01 0.05*** 0.04** −0.01 0.17*** 6207 0.35 0.23 –

– −0.36*** 0.37*** −0.24*** 0.31*** −0.23*** −0.09*** −0.02 0.03 −0.02 6483 1.93 0.63 0.77

– −0.25*** 0.33*** −0.19*** 0.26*** 0.15*** 0.08*** 0.02 0.05** 6470 3.25 0.67 0.74

– −0.37*** 0.40*** −0.28*** −0.09*** 0.000 0.04** 0.03* 6559 1.99 0.64 0.77

– −0.24*** 0.36*** 0.16*** 0.08*** 0.01 0.03 6548 3.23 0.61 0.57

– −0.47*** −0.08*** 0.03* 0.04** 0.07*** 6284 2.07 0.62 0.74

– 0.17*** 0.06*** 0.01 −0.02 6264 3.28 0.60 0.78

– 0.53*** 0.35*** 0.26*** 5732 3.03 0.52 0.73

– 0.72*** 0.19*** 5732 2.79 0.60 0.75

– 0.05** 5731 2.57 0.62 0.75

– 3857 0.98 0.18 –

Note. Ent. theory = Entity theory; Inc. theory = Incremental theory; MAP = mastery-approach goals; PAP = performance-approach goals; PAV = performance avoidance goals; SAT = scholastic aptitude test scores. a Original scores were rescaled for model convergence. See the methods section for details. * p < .05. ** p < .01. *** p < .001.

and performance-avoidance goals (“My goal is not to get a worse grade than other students”; “I pay attention to classes so that I do not fall behind other students”; “I study because I do not want other students to think that I am not smart”) were each measured by three items. These items were developed on the basis of those in Elliot and McGregor’s (2001) Achievement Goal Questionnaire, and have often been used in prior research on Korean students’ achievement goals (Lee, 2014; Yang & Cheong, 2012). A three-factor model showed adequate model fit indices, χ2(24) = 847.32, p < .001, CFI = 0.939, RMSEA = 0.077 [90% CI = 0.073, 0.082].

scores were calculated based on 8th graders’ relative performance on the test with a mean of 400 and standard deviation of 50. We rescaled the average scores by dividing them by 100, as we did for SAT scores, for model convergence. Parents’ report of total monthly household income was included as the indicator of socioeconomic status. The unit represents approximately US$10, where $1 is approximately 1000 Korean won, and we rescaled the values by dividing them by 1000 for model convergence.

3.2.3. Achievement on the national scholastic aptitude test (Grade 12) Participants’ national scholastic aptitude test (SAT) scores were collected through institutional records. We created an average score based on standardized scores of three subjects (i.e., Korean, English, and Mathematics). The SAT scores for these three subjects are the most commonly required in college applications; in fact, many researchers examining Korean students’ achievement have focused on these three subjects (e.g., Bong, 2004; Park, Byun, & Kim, 2011). SAT standardized scores were available based on students’ relative performance on a given test with a mean of 100 and a standard deviation of 20. To assist model convergence, we rescaled the scores by dividing them by 100. This rescaling approach has often been used (e.g., Seo & Lee, 2018; Duncan, Duncan, Strycker, & Chaumeton, 2007; Hitlin, Erickson, & Brown, 2015) when the units of included variables are substantially different from one another, and a difference in units can cause model convergence issues due to problems in estimating standard errors of coefficients (Muthén, 2010).

We obtained descriptive statistics using SPSS 24, and conducted factor analyses and latent growth models using Mplus 8 (Muthén & Muthén, 1998–2017) based on robust maximum likelihood estimator (MLR) in conjunction with full information maximum likelihood (FIML) to account for missing data (Enders, 2010; Peugh & Enders, 2004). To address the nested structure of the data (i.e., students within schools), we adjusted cluster-robust standard errors while preserving the covariance matrix for estimating parameters (McNeish, Stapleton, & Silverman, 2017) for all analyses including factor analyses and latent growth models. Model fit was determined via the Comparative Fit Index (CFI; values ≥0.90 for adequate fit; values ≥0.95 for excellent fit; Hu & Bentler, 1999) and root mean square error of approximation (RMSEA; values < 0.08 for acceptance). When comparing two models, we used changes in CFI less than 0.01 and RMSEA less than 0.015 as criteria for retaining the more parsimonious model (Chen, 2007; Cheung & Rensvold, 2002).

3.3. Data analysis

3.3.1. Factor analyses We conducted confirmatory factor analyses (CFA) on implicit theories of intelligence (entity theory and incremental theory) at each time point (Grades 8–10) to examine the factor structure. We then conducted longitudinal confirmatory factor analyses on implicit theories to examine measurement invariance across time (Meredith, 1993; Vandenberg & Lance, 2000).

3.2.4. Covariates (Grade 8) Gender (male = 0, female = 1), prior achievement, and family socioeconomic status were included in the conditional models. We used students’ standardized test scores on Korean, English, and Mathematics in Grade 8 as an indicator of prior achievement. Multiple-choice tasks were developed and validated by the Korean Educational Development Institute with strong evidence of reliability and predictive validity according to a Korean official technical report (Lee, Kang, Noh, Yu, & Lew, 2006). Further, students’ mean score on this standardized test was significantly correlated with our focal outcome variable (i.e., r = 0.66 with SAT scores), supporting the convergent validity. The standardized

3.3.2. Latent growth curve models We tested a series of latent growth curve models in a structural equation modeling (SEM) framework for two implicit theories measured at three time points over three years (i.e., parallel process models, 5

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Fig. 1. Unconditional intercept-only model (Model A) where entity and incremental theories were assumed to be constant over three grade levels. ***p < .001.

Fig. 2. Unconditional linear growth model (Model B) where entity and incremental theories were assumed to linearly grow over three grade levels. *p < .05, ***p < .001.

Byrne, 2012; Muthén & Muthén, 1998–2017). We tested a non-growth model (Model A), an unconditional linear latent growth model (Model B), and conditional latent growth models (Models C-E) with two outcomes (i.e., SAT scores, achievement goals) and three covariates (i.e., gender, prior achievement, family income). We did not test quadratic growth models, as these models require at least four time points. For the unconditional models, latent intercepts and latent slopes were specified based on the average scores on implicit theory items measured at each time point as indicators (see Figs. 1 and 2). The variances of the intercepts and the slopes and their covariances were freely estimated. We specified the residual covariance between entity and incremental theories at each time point, consistent with prior research utilizing parallel process models of implicit theories (e.g., Dai & Cromley, 2014). For the conditional models, we specified paths from the intercepts and the slopes of implicit theories to each type of achievement goal,3 which in turn related to SAT scores. The direct paths from the intercepts and the slopes of implicit theories to SAT scores were also assumed (see Figs. 4–6). Three covariates were included as predictors of the intercepts and the slopes of implicit theories, achievement goals, and SAT scores. We tested indirect effects of implicit theories on the SAT scores via each type of achievement goal using the bootstrapping procedure, which is considered to provide robust estimations for indirect effects under most conditions (MacKinnon, Lockwood, & Williams, 2004; Pituch, Stapleton, & Kang, 2006; Preacher & Hayes, 2008).

achievement and family income in all conditional models to assist FIML estimation by reducing potential bias in parameter estimates caused by missing values (Peugh & Enders, 2004; Schafer & Graham, 2002). Furthermore, in an effort to reduce potential concerns about the missingness of the SAT scores, we conducted a supplementary analysis with the same model using a different indicator of students’ academic achievement. Specifically, we used students’ self-reported achievement on the National Academic Achievement Examination, measured in Grade 11, which had a smaller percentage of missing data (35%) than that for SAT scores. The results were substantially similar to findings using the actual SAT scores in Grade 12 (see Table S2 in the online supplemental materials). 4. Results 4.1. Preliminary analyses: factor structure of implicit theories We performed confirmatory factor analysis on items for entity theory and incremental theory by each year (Grades 8–10) to compare two different models of implicit theories: (a) a one-factor model, in which all items for entity and incremental theories were loaded onto the same factor, but the scores on incremental theory were reversely coded; and (b) a two-factor model, in which all items for entity theory were loaded onto one factor and those for incremental theory were loaded onto the other factor, and these two factors were correlated with each other. We found that the two-factor model exhibited better model fit indices than the one-factor model across all three years based on the changes in CFI and RMSEA values (see Table 2). Accordingly, we proceeded with the two-factor model of implicit theories for the following analyses. Next, we examined measurement invariance of implicit theories over three years to ensure any observed change in implicit theories of intelligence over time could be attributed to true changes in students’ beliefs rather than changes in the meaning of the construct over time. We found evidence for configural, weak, and partial strong invariance4 (see Table S3). Table 1 presents descriptive statistics for all study variables.

3.4. Missing data Numbers of completed responses for each variable based on composite scores are presented in Table 1. Across Grades 8–11, missing values were relatively small, ranging from 5% to 17%. In the Grade 12 data, however, only 3857 (56%) students’ SAT scores were available. Missing data analysis showed that students with lower achievement scores in Grade 8 were more likely to have missing data on SAT scores, t (5865.12) = 22.76, p < .001. In addition, students with lower family income were also more likely to have missing data on SAT scores, t (5302.21) = 4.63, p < .001. Based on the analyses, we included prior 3

Including all three types of achievement goals in a single model caused a model convergence issue, which was due either to the model complexity or to the collinearity issue (the relation between performance-approach and performance-avoidance goals, in particular). Thus, we specified a model for each achievement goal.

4 The intercept for one of the incremental theory items in Grade 10 was lower (3.13) than the intercepts in Grades 8–9 (3.29). The lower intercept at the later time point suggests that our finding of the increasing pattern of incremental theory over time cannot be undermined by this partial invariance result.

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Table 2 Model Comparison: 1-Factor vs. 2-Factor CFA Models for Implicit Theories of Intelligence in Grades 8–10.

Grade 8 1-Factor 2-Factor Grade 9 1-Factor 2-Factor Grade 10 1-Factor 2-Factor

χ2(df)

CFI

ΔCFI

RMSEA [90% CI]

ΔRMSEA

Standardized factor loadings

Inter-factor correlation

1994.375 (5) 119.237 (4)

0.610 0.977

– 0.367

0.248 [0.239, 0.257] 0.067 [0.057, 0.077]

– −0.181

≥0.382 ≥0.645

– −0.464

773.731 (5) 128.417 (4)

0.847 0.975

– 0.128

0.153 [0.144, 0.162] 0.069 [0.059, 0.079]

– −0.084

≥0.269 ≥0.441

– −0.503

1744.254 (5) 155.660 (4)

0.687 0.973

– 0.286

0.235 [0.226, 0.245] 0.078 [0.067, 0.088]

– −0.157

≥0.565 ≥0.569

– −0.588

Note. All chi-square values were statistically significant, p < .001. CFI = comparative fit index; RMSEA = root-mean-square error of approximation. Table 3 Model Fit for Unconditional and Conditional Growth Models. Model A B C D E

Description

χ2(df)

CFI

RMSEA [90% CI]

Unconditional: Intercept-only Unconditional: Linear Conditional: Mastery-approach goals Conditional: Performance approach goals Conditional: Performance avoidance goals

377.863 (18) 71.182 (9) 308.967 (36) 530.188 (36) 348.168 (36)

0.911 0.985 0.974 0.953 0.970

0.054 0.032 0.034 0.046 0.037

[0.049, [0.025, [0.031, [0.043, [0.033,

0.059] 0.039] 0.038] 0.050] 0.040]

Note. All chi-square values were statistically significant, p < .001.

4.2. Unconditional growth models: joint trajectories of implicit theories

model fit indices of the three conditional models were all excellent (see Table 3). Growth parameter estimates of implicit theories were similar across all models (see Figs. 3–6 and Table S5). Across the three models, neither of the latent intercepts nor the slopes of the two implicit theories directly related to SAT scores, but unique patterns of indirect effects of the implicit theory trajectories on SAT scores were found, depending on which type of achievement goal was included as a mediator. In the mastery-approach goal model (Model C, Fig. 4), consistent with Hypothesis 2a, both the intercept and the slope of incremental theory positively related to mastery-approach goals, which in turn positively related to SAT scores. Unexpectedly, however, the intercept of entity theory, but not the slope of entity theory, also had a significant and positive indirect effect on SAT scores via mastery-approach goals. In the performance-approach goal model (Model D, Fig. 5), consistent with Hypothesis 2b, both the intercept and the slope of entity theory positively related to performance-approach goals, which in turn positively related to SAT scores. Inconsistent with the hypothesis, however, the intercept of incremental theory, though not its slope, also had a significant and positive indirect effect on SAT scores via performance-approach goals. In the performance-avoidance goal model (Model E, Fig. 6), consistent with Hypothesis 2c, the intercept of entity theory positively related to performance-avoidance goals; however, the slope of entity theory was not significantly related to performance-avoidance goals, different from our hypothesis. Unexpectedly, the intercept of incremental theory, though not its slope, also positively related to performance-avoidance goals. Neither the intercepts nor the slopes of implicit theories had significant indirect effects on SAT scores. As supplementary analyses, we compared explained variance in SAT scores by each type of achievement goal and checked r-squared values in each model. Although the amount of explained variance in SAT scores was similar across models (mastery-approach: 0.51, performance-approach: 0.49, performance-avoidance: 0.47; all p-values < 0.001), pairwise comparisons of r-squared values using Fisher r-to-z transformations (Lee & Preacher, 2013) showed that the explained variance in SAT scores in the mastery-approach goal model was significantly larger than for the other two models (vs. performance approach: z = 2.15, p = .03; vs. performance avoidance: z = 3.02, p = .001). In contrast, the variance in SAT scores explained by the performance-approach goal model was not significantly different from

To address the first research question, we compared a non-growth model (Model A, Fig. 1) with a linear growth model (Model B, Fig. 2). Overall, the intercept-only model showed adequate, but not excellent fit, and the linear growth model showed a better model fit, with changes in the CFI value of 0.075 and the RMSEA value of 0.022 (see Table 3). This result suggests that the levels of implicit theories changed over time rather than remaining constant, and thus we chose the linear growth model as a basis for our conditional growth models.5 The linear growth model revealed that the intercepts and the slopes of both implicit beliefs were statistically significant (ps < 0.05; see Table S4 for all parameter estimates). Consistent with Hypothesis 1a, the slope of entity theory was positive (Ment = 0.07 [0.06, 0.08]). Inconsistent with the hypothesis, however, the slope of incremental theory was also positive (Minc = 0.02 [0.003, 0.03]). This means that both entity and incremental theories increased from Grades 8–10, but entity theory increased more quickly (see Fig. 3). Consistent with Hypothesis 1b, the intercept of entity theory was negatively correlated with the intercept of incremental theory (r = −0.66), and the slope of entity theory was negatively correlated with the slope of incremental theory (r = −0.60). This indicates that individuals with a higher initial level of entity theory tended to have lower initial levels of incremental theory, and those with a more rapidly increasing trajectory of entity theory tended to have a less rapidly increasing trajectory of incremental theory. 4.3. Conditional growth models: relations among changes in implicit theories, achievement goals, and SAT achievement To address the second research question, we examined the relations among implicit theories, achievement goals, and SAT achievement. The 5 We also tested latent growth models by including one implicit theory at a time. The results still supported the linear growth models over the interceptonly models for both entity theory (intercept-only: χ2(6) = 174.221, p < .001, CFI = 0.851; linear: χ2(3) = 23.386, p < .001, CFI = 0.982) and incremental theory (intercept-only: χ2(6) = 123.366, p < .001, CFI = 0.888; linear: χ2(3) = 43.238, p < .001, CFI = 0.962).

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that in the performance-avoidance goal model (z = 0.87, p = .38). This suggests that, even though both goals significantly predicted SAT scores, mastery-approach goals explained significantly more variance in SAT scores than did performance-approach goals. The relations of covariates (i.e., gender, prior achievement, and family income) to the intercepts and slopes of implicit theories, achievement goals, and SAT scores are reported in Table S6.

4.0 3.5

3.24

3.25

3.27

2.00

2.07

3.0 Entity

2.5 2.0

1.93

Incremental

5. Discussion

1.5 1.0

Grade 8

Grade 9

The purpose of this study was to examine trajectories of adolescents’ implicit theories of intelligence, and their relations to achievement on Scholastic Aptitude Tests in a sample of secondary school students in South Korea. As an extension of prior research on the outcomes of implicit theories (e.g., Bahník & Vranka, 2017; Dai & Cromley, 2014;

Grade 10

Fig. 3. Model-implied trajectories of entity and incremental theories of intelligence in Model B (Fig. 2). Entity theory increased more quickly than incremental theory.

Fig. 4. Standardized path coefficients for conditional linear growth model with mastery-approach goals as a mediator (Model C). Intercepts of both entity and incremental theories positively predicted SAT scores indirectly through mastery-approach goals. The slope of incremental theory, but not entity theory, also predicted SAT scores indirectly through mastery-approach goals. Curved rightwards arrows indicate statistically significant indirect effects. Dotted lines indicate statistically not significant paths. Covariates (i.e., gender, prior achievement, and family income) were included in the model but omitted in the figure for graphical simplicity. *p < .05, **p < .01, ***p < .001.

Fig. 5. Standardized path coefficients for conditional linear growth model with performance-approach goals as a mediator (Model D). Intercepts of both entity and incremental theories positively predicted SAT scores indirectly through performance-approach goals. The slope of entity theory, but not incremental theory, also predicted SAT scores indirectly through performance-approach goals. Curved rightwards arrows indicate statistically significant indirect effects. Dotted lines indicate statistically not significant paths. Covariates (i.e., gender, prior achievement, and family income) were included in the model but omitted in the figure for graphical simplicity. *p < .05, **p < .01, ***p < .001. 8

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Fig. 6. Standardized path coefficients for conditional linear growth model with performance-avoidance goals as a mediator (Model E). Only intercepts of entity and incremental theories positively predicted performance-avoidance goals, and there were no significant indirect effects on SAT scores through performance-avoidance goals. Dotted lines indicate statistically not significant paths. Covariates (i.e., gender, prior achievement, and family income) were included in the model but omitted in the figure for graphical simplicity. **p < .01, ***p < .001.

the age of the sample. We examined trajectories of secondary school students’ implicit theories over three years, whereas most of the prior studies showing a decreasing pattern for incremental theories examined college students’ implicit theories over the course of one semester (Flanigan et al., 2017; Shively & Ryan, 2013) or one year (Dai & Cromley, 2014). One study focused on younger students (i.e., 5th and 6th graders) but the study duration was only one year (Gonida et al., 2006). In contrast, a study that examined college students’ entity theory over four years found no meaningful mean-level change (Robins & Pals, 2002). Due to differences in both the length of the trajectories and the age of the sample, it is difficult to pin down the cause of these inconsistent results. However, one may speculate that students’ belief in incremental theory tends to decrease over time within a semester or a year, but may show a gradual increase or no meaningful change over a relatively longer period. For example, students’ optimism and hopes at the beginning of a semester are often dampened as the semester unfolds, but they also return somewhat rejuvenated at the beginning of the next semester (Schallert, Reed, & Turner, 2004), which could indirectly support the speculation that the length of the trajectory matters. Future research needs to examine both short-term and long-term changes in implicit theories with samples of students of varying ages. Our parallel process modeling approach allowed us to examine the dynamics of changes in implicit theories of intelligence based on a twofactor model of implicit theories. This approach enabled us to find a higher initial level of entity theory was related to a lower initial level of incremental theory, and a more rapidly increasing pattern of entity theory was related to a less rapidly increasing pattern of incremental theory, consistent with our hypothesis (Hypothesis 1b) and the findings of prior studies (Dai & Cromley, 2014).

Flanigan et al., 2017), we tested a mediating role of achievement goals in the relations between changes in implicit theories of intelligence and SAT achievement based on Dweck’s social-cognitive model (Dweck, 1986; Dweck & Leggett, 1988). Our results indicate that secondary school students’ implicit theories of intelligence changed over time. These changes were associated with subsequent achievement goals, which in turn related to SAT achievement. Yet, the patterns of these relations varied depending on the type of achievement goal. 5.1. Joint trajectories of implicit theories of intelligence We found that South Korean students’ implicit theories of intelligence changed from Grade 8 to Grade 10. The results revealed patterns of slow but still meaningful changes, even without any intended stimulus or intervention. In line with our hypothesis (Hypothesis 1a), Korean students’ entity theory increased over time, as has been found in different samples from other countries (e.g., Dai & Cromley, 2014; Flanigan et al., 2017). The increase in entity theory seems rather smaller than that found in prior work (Dai & Cromley, 2014), however. Given that the current research focused on domaingeneral implicit theories whereas Dai and Cromley (2014) focused on domain-specific implicit theories, it may be interesting to examine whether the rates of change between domain-specific and domaingeneral implicit theories are similar or different. Regarding students’ belief in incremental theory, it also increased over time, contradicting our hypothesis (Hypothesis 1a) based on the earlier findings (e.g., Dai & Cromley, 2014; Flanigan et al., 2017; Gonida et al., 2006; Robins & Pals, 2002; Shively & Ryan, 2013), though the pattern of change was relatively slow. To understand this surprising finding, we considered a few possible explanations. The first possibility is that cultural differences may explain the discrepancy. Unlike the current study, many of the prior studies investigating longitudinal changes in students’ implicit theories focused on students in the U.S. (e.g., Dai & Cromley, 2014; Flanigan et al., 2017; Robins & Pals, 2002; Shively & Ryan, 2013) or other Western countries (e.g., Greece; Gonida et al., 2006). It is possible that the greater emphasis on the importance of effort in East Asian countries (Chen & Stevenson, 1995; Cheung et al., 2017; Heine et al., 2001b; Hess & Azuma, 1991) could lead South Korean students to gradually increase their belief in incremental intelligence over time. Another possible explanation is related to the length of the study or

5.2. The mediating role of achievement goals Guided by Dweck’s social-cognitive model and empirical evidence on implicit theories of intelligence, we tested how trajectories of implicit theories related to SAT achievement through achievement goals. We found no significant direct effects of the intercepts and slopes of implicit theories on SAT achievement. More notable findings in the current study are the differential indirect effects of the intercept and slope of implicit theories on SAT achievement depending on which type of achievement goal was included as a mediator. Specifically, both the initial level and increasing pattern of incremental theory were 9

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positively associated with SAT achievement through mastery-approach goals; both the initial level and increasing pattern of entity theory were positively associated with SAT achievement through performance-approach goals. These results were consistent with Hypotheses 2a and 2b as well as other previous empirical studies measuring implicit theories at a single time point (e.g., Blackwell et al., 2007; Chen & Pajares, 2010; Dinger et al., 2013). However, inconsistent with Hypotheses 2c, performance-avoidance goals did not appear to be a significant mediator for the relation between implicit theories and SAT achievement. Surprisingly, the intercepts of entity and incremental theory had an unexpected positive indirect effect on SAT scores through mastery-approach goals and both types of performance goals, respectively. One potential reason is cultural differences. Prior research has found that negative motives, such as fear of failure, were not necessarily negatively related to adaptive consequences, such as mastery-oriented motivation, and were even positively related to achievement-oriented behaviors (e.g., persistence) among Asian American students (Eaton & Dembo, 1997; Heine, Kitayama, & Lehman, 2001a; Heine et al., 2001b). In line with this idea, research indicates that Asian individuals might be more motived by failure than their non-Asian counterparts (Kitayama, Markus, Matsumoto, & Norasakkunkit, 1997). These studies suggest that Korean students’ earlier belief that intelligence is fixed (i.e., entity theory), which is likely to increase the pressure to perform well on evaluative academic tasks and thus also increase the fear of failure, might function as a motivational force. Regarding the unexpected indirect effect of the intercept of incremental theory via performance goals, this finding may be explained by the highly competitive learning context in South Korea (Calonge, 2015; Koo, 2014). That is, highly normative-based evaluations during the secondary school period in South Korea might facilitate the association between the initial level of belief in incremental theory and later motivation to do better than others or avoid doing worse than others. Although it was not a focal interest of the current study, the findings regarding the relations between different achievement goals and SAT achievement are worth noting. We found a positive relation between performance approach goals and SAT achievement. This positive relation was expected, as our measure focused on normative goals rather than appearance goals (Hulleman et al., 2010). In addition, we also found that mastery-approach goals explained a significantly larger amount of variance in SAT scores compared to performance-approach and performance-avoidance goals. This suggests that the role of mastery-approach goals in predicting academic achievement should not be deemphasized, lending support to the relative importance of masteryapproach goals in the debate over which types of goals are more likely to predict academic achievement (see Lee, Wormington, LinnenbrinkGarcia, & Roseth, 2017; Linnenbrink, 2005; Senko, Hulleman, & Harackiewicz, 2011).

Third, although the longitudinal temporal ordering of the variables better depicts the theorized pathway from implicit theories to SAT achievement via achievement goals, as compared to a cross-sectional design, the relatively long intervals between measurements of implicit theories and measurements of SAT achievement (i.e., two years) could be a potential reason for the lack of direct relations between these two.6 Therefore, future research should clarify the relation between the trajectories of implicit theories and academic achievement using more proximal achievement outcomes. Fourth, including all three types of achievement goals in the same model may contribute to a more complete understanding of the roles played by implicit theories of intelligence, given that all achievement goals are related to one another and individuals can endorse multiple goals simultaneously. Yet our modeling approach also has benefits, as it reduces concerns about potential collinearity. Still, an integrative model may provide a more comprehensive understanding of Dweck’s social-cognitive model by comparing the strengths of the relations between implicit theories and different types of achievement goals. Fifth, considering students’ perceived competence in the model may be an important approach for future research to test Dweck’s (1986) social-cognitive model more fully. Dweck’s social-cognitive model posits that if students’ confidence in present ability is low, their performance goals may lead to maladaptive behavioral patterns. However, if their confidence in present ability is high, their performance goals may lead to adaptive behavioral patterns. Although researchers have found little evidence for the moderating role of perceived competence thus far (e.g., Cury et al., 2006; Kaplan & Midgley, 1997), considering both achievement goals and perceived competence in Dweck’s social-cognitive model may provide a more complete picture about the processes and outcomes of students’ implicit theories of intelligence. Finally, due to the nature of the sample in the current study, the generalizability of the findings is limited to Korean secondary school students. However, the current findings may advance our understanding of students’ implicit theories and achievement goals by suggesting the possible heterogeneity of trajectories of implicit theories and the roles of achievement goals across different ages and cultures. Future research may need to directly address the issue of age and cultural differences in the meaning of both implicit theories and achievement goals, as well as their changing patterns and longitudinal outcomes. 5.4. Theoretical contributions and practical implications The current findings suggest that South Korean secondary students’ incremental and entity theories may have separate growth trajectories that are intertwined with each other. Although previous studies have examined the developmental trajectories of implicit theories (Flanigan et al., 2017; Gonida et al., 2006; Shively & Ryan, 2013), only one study has examined separate trajectories of incremental and entity theories based on a sample of U.S. college students (Dai & Cromley, 2014). Thus, the current study is the first to examine distinct growth trajectories of incremental and entity theories in a sample of Asian adolescents. Unlike U.S. college students, Korean adolescents’ incremental theories increased over time, suggesting a potential role of culture in their adoption of incremental views on intelligence (see Cheung et al., 2017; Suprawati et al., 2014).

5.3. Limitations and suggestions for future research We should note limitations in the present study and make suggestions for future research. First, the reliability for the measure of incremental theory in Grade 9 was not sufficiently high (α = 0.57), which could be because there were only two items. Future research should replicate the findings with a more reliable measure of students’ incremental theory of intelligence. Second, we focused on students’ implicit theories of intelligence and achievement goals at the domain-general level, and examined how they related to subsequent achievement. Recent studies are beginning to suggest that domain-specific implicit theories may better predict domain-specific outcomes (e.g., implicit theories about math ability: Degol, Wang, Zhang, & Allerton, 2018; Seo, Shen, & Alfaro, 2019), but no study has yet explicitly examined the mediating roles of domainspecific achievement goals in the relations. To help clarify the relations of implicit theories to academic achievement, we encourage future research to examine these variables at the domain-specific level.

6 To reduce concerns about the distance between measurements of implicit theories and measurements of SAT achievement, we conducted an analysis using a measure of academic achievement available in Grade 11, which was students’ self-reported achievement levels on the National Academic Achievement Examination in the three subjects, including Korean, Math, and English, based on a 4-point scale ranging from very low (1) to very high (4). With a slight discrepancy in the results of the performance-avoidance goal model, the major findings remained the same (see Table S2).

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Practically, the current findings suggest that achievement goals may be one of the potential mediators linking students’ implicit theories into their achievement outcomes. Therefore, as the prior meta-analytic research suggested (Sisk et al., 2018), it would be more effective to target both implicit theories and potential mediators, such as achievement goals, at the same time. Such combined interventions designed with a theoretical basis may be able to boost the effectiveness of educational interventions for students’ learning outcomes. Among diverse achievement goals, supporting mastery-approach goals, or at least approach goals in general, should be prioritized, because mastery goals were most strongly associated with students’ SAT achievement, followed by performance-approach goals. In contrast, performance-avoidance goals were not significantly associated with SAT achievement. As one of the psychological antecedents to masteryapproach goals, incremental theories have often been found (e.g., Blackwell et al., 2007; Chen & Pajares, 2010; Dinger et al., 2013). The current study adds to the extant literature by suggesting that not only the initial level of belief in incremental (entity) theory but also its natural growth may be associated with SAT achievement via higher mastery-approach (performance-approach) goals. Therefore, again, we suggest that it is important for educators and parents to create an environment where students can develop incremental beliefs, and at the same time they can focus on developing their competence (e.g., Ames, 1992; Kaplan & Maehr, 2007; Shin, Lee, & Seo, 2017).

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