Emotion regulation, homework completion, and math achievement: Testing models of reciprocal effects

Journal Pre-proofs Emotion Regulation, Homework Completion, and Math Achievement: Testing Models of Reciprocal Effects Jianzhong Xu, Jianxia Du, Fangtong Liu, Bosu Huang PII: DOI: Reference:

S0361-476X(19)30415-1 https://doi.org/10.1016/j.cedpsych.2019.101810 YCEPS 101810

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Contemporary Educational Psychology

Received Date: Revised Date: Accepted Date:

7 February 2019 20 September 2019 21 October 2019

Please cite this article as: Xu, J., Du, J., Liu, F., Huang, B., Emotion Regulation, Homework Completion, and Math Achievement: Testing Models of Reciprocal Effects, Contemporary Educational Psychology (2019), doi: https://doi.org/10.1016/j.cedpsych.2019.101810

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Emotion Regulation, Homework Completion, and Math Achievement: Testing Models of Reciprocal Effects

Jianzhong Xu Mississippi State University, USA Jianxia Du, Fangtong Liu, and Bosu Huang University of Macau, China

Author Note Correspondence concerning this article should be addressed to Jianzhong Xu, Department of Counseling, Educational Psychology, and Foundations, P.O. Box 9727, Mississippi State

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University, Mississippi State, MS 39762, USA. Email: [email protected]. Phone: (662) 325-2186.

Abstract The current investigation employs models of reciprocal effects among emotion management, cognitive reappraisal, homework completion, and achievement, based on two measurement points from 1,450 Chinese 8th graders. Results revealed that emotion management and math achievement were reciprocally related. Furthermore, higher prior achievement led to higher subsequent cognitive reappraisal and homework completion. Additionally, significant interactions were found between emotion management and cognitive reappraisal in the prediction of subsequent emotion management, cognitive reappraisal, and homework completion. Specifically, these findings indicated that emotion management had a more positive influence on subsequent emotion management, cognitive reappraisal, and homework completion when prior cognitive reappraisal was low (compensatory effect by decreasing the gap between students with prior high and low cognitive reappraisal). Keywords: Achievement; cognitive reappraisal; emotion management; emotion regulation; homework completion.

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Emotion Regulation, Homework Completion, and Math Achievement: Testing Models of Reciprocal Effects 1. Introduction From theoretical framework of emotion regulation (Gross & Thompson, 2007; Peixoto, Sanches, Mata, & Monteiro, 2017; Troy, Shallcross, & Mauss, 2013), homework emotion regulation, homework completion, and academic achievement may affect one another over time. This is likely to have important implications for homework research and practice (e.g., regulating homework emotion and improving student achievement; Cooper, Lindsay, Nye, & Greathouse, 1998; Troy et al., 2013; Xu, 2018). However, it is surprising that no prior research, to our knowledge, has employed models of reciprocal effects to examine longitudinal relationships among these constructs. Our present study attempts to fill this important gap in homework research, by testing the temporal ordering of these constructs in math homework for Chinese eighth-grade students at two time points (from November to June). A study such as this is particularly important, as homework becomes an emotionally charged task for many students across nations (Knollmann & Wild, 2007; Verma, Sharma, & Larson, 2002; Xu & Corno, 1998), and as the relationship between homework completion (i.e., the amount of homework completed by students) and academic achievement could be bidirectional (Cooper et al., 1998). Yet, previous studies were relied on cross-sectional data (Cooper et al., 1998; Núñez et al., 2015; Regueiro, Suárez, Valle, Núñez, & Rosário, 2015; Xu, Fan, & Du, 2016). Additionally, despite the acknowledgement that emotion regulation may be affected by cultural norms (Gross & John, 2003; Mesquita, Leersnyder, & Albert, 2014; Tsai & Lau, 2013), previous studies have been largely carried out in

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Western nations (Arens, Balkir, & Barnow, 2012; Jacobs & Gross, 2014), with homework emotion regulation in particular (Xu, 2018). Our justification for focusing on 8th graders is that these students, on the edge of moving to high school, have accumulated rich experience of working on math homework. Previous research has indicated that students’ attitude towards homework becomes increasingly negative as they make transition from elementary to middle and high schools (Cooper et al., 1998; Xu, 2004). Thus, it would be important to investigate reciprocal influences of emotion regulation, homework completion, and math achievement at this grade level. Finally, our justification for choosing math homework is that math, as a main subject, is critically important in different countries (e.g., the role of math competencies in a wide variety of disciplines; Hagger et al., 2015). Not surprisingly, students often receive disproportion more homework in math (e.g., devoting one- to two-fifth of homework time to math assignments; Xu, 2015). Yet, for many students, working math homework is frequently perceived as a daunting challenge (e.g., math avoidance and anxiety; Lee, 2009). Our investigation is guided by three lines of literature. First, we discuss theoretical framework regarding the linkages among emotion regulation, homework completion (as one type of task completion), and academic achievement (as one type of performance). We then turn to related previous studies that have tapped into the linkages among these constructs based on cross-sectional studies. Finally, we examine how the linkages among these constructs may be affected by cultural differences. 1.1. Theoretical Framework According to Gross’s model (1998), emotion regulation is referred to as “the process by which individuals influence emotion they have, when they have them, and how they experience

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and express these emotions” (p. 275). In this model, Gross and his colleagues (Gross, 1998, 2002; Gross & Thompson, 2007) have highlighted the importance of cognitive change in emotion regulation in that “changing how we appraise the situation we are in to alter its emotional significance, either by changing how we think about the situation or about our capacity to manage the demands it poses” (Gross & Thompson, 2007, p. 14). This conceptualization suggests that cognitive change takes two distinct forms: (a) cognitive reappraisal (i.e., how we think about the situation), and (b) emotion management (i.e., how we manage the demands). Previous research based on Gross’s model focuses on one form of cognitive change (cognitive reappraisal; Gross, 2002; Gross & Thompson, 2007). Cognitive reappraisal is posited to influence academic outcomes (e.g., task completion and performance) on stressful tasks or tasks embedded in temptation, in which individuals reinterpret the meaning of their situation in a positive light, by decreasing or qualitatively altering the stress level (e.g., from threat to challenge), and by reducing goal inconsistent behavior (Cole, Mating, & Dennis, 2004; Leroy, Grégoire, Magen, Gross, & Mikolajczak, 2012; Schmader, Johns, & Forbes, 2008). Additionally, emotion regulation may be particularly pertinent in disliked tasks (e.g., homework), as individuals likely experience unpleasant emotions both prior to and during these tasks. Thus, given that emotions facilitate psychological processes including attention and problem-solving (Cole et al. 2004), emotion regulation would be particularly important for successful completion in disliked tasks (e.g., homework completion; Ben-Eliyahu & Linnenbrink-Garcia, 2015). Furthermore, students’ experiences concerning their prior academic outcomes such as task completion and performance may feed back on their emotions and emotion regulation (Pekrun, 2006; Peixoto et al., 2017).

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Much less attention, however, has been given to emotion management – another distinct form of cognitive change. It is not until recently that, informed by Gross’s model, Xu and his colleagues have conducted several validation studies to test whether emotion management could be distinguished from cognitive reappraisal in the context of homework (Xu, Fan, & Du, 2016, 2017, 2018). In these studies, emotion management is defined as students’ efforts to up-regulate pleasant homework emotions (e.g., to cheer myself up) and down-regulate unpleasant homework emotions (e.g., to calm myself down). Cognitive reappraisal is defined as students’ efforts to recontextualize or reframe an unpleasant stimulus in less emotional ways during a homework session (e.g., to look on “the bright side” when a child was upset with a homework assignment). Results from studies based on students at middle school level (Xu et al., 2016), high school level (Xu et al., 2017), and college level (Xu et al., 2018) supported the presence of emotion management and cognitive reappraisal as two distinct forms of cognitive change. Troy et al. (2013) hypothesized that different emotion regulation strategies interact over time; for individuals who think their situations are controllable or manageable, they are more likely to employ problem-focused coping. Meanwhile, for individuals who think their situations are less controllable or manageable, they are more apt to use cognitive reappraisal. It follows then that, as two forms of cognitive change, cognitive reappraisal and emotion management may interact with each other over time. This implies, for example, that students with low prior cognitive reappraisal may modify their subsequent emotion management in two ways: (a) they may more likely to resort to emotion management (i.e., to compensate prior cognitive reappraisal); and (b) they may less likely to use emotion management (i.e., to magnify prior cognitive reappraisal). Thus, prior emotion management may have a differential influence for students with low and high prior cognitive reappraisal.

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Taken together, this body of literature points to possible linkages among cognitive reappraisal, emotion management, task completion, and achievement. Thus, in line with the recent calls to employ longitudinal designs to study reciprocal relations between self-regulation capacities (e.g., emotion regulation) and learning over time (Ben-Eliyahu & Linnenbrink-Garcia, 2015; Peixoto et al., 2017), there is a critical need to investigate these variables in models of reciprocal influences. 1.2. Studies Relating to Homework Whereas no previous research has studied the reciprocal effects among emotion regulation, homework completion, and achievement, several studies tapped into potential linkages among them based on cross-sectional data (Cooper et al., 1998; Núñez et al., 2015; Regueiro et al., 2015; Xu, 2017; Xu et al., 2016, 2017). Using 796 students in grade 8, Xu et al. (2016) found that emotion management was positively related to homework completion and math achievement, and that cognitive reappraisal was positively related to homework completion, but not math achievement. Another study based on 915 10th graders (Xu et al., 2017) found that emotion management was positively related to homework completion and math achievement, and that cognitive reappraisal was positively related to homework completion, but not math achievement. In another study involving 1,799 students in grades 10-11, Xu (2017) found that emotion management was positively related to cognitive reappraisal, and that homework completion was positively related to emotion management, cognitive reappraisal, and math achievement. In addition, math achievement was positively associated with emotion management, but not cognitive reappraisal.

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Taken together, using cross-sectional data, these studies have tapped into possible linkages among homework emotion regulation, completion, and achievement. What is unknown is the longitudinal relationships among these constructs. For instance, regarding the direction of influence between homework completion and achievement; homework completion was found to influence achievement in some studies (Bryan & Burstein, 2004; Cooper et al., 1998; Núñez et al., 2015; Xu, 2017) whereas prior achievement was found to influence homework completion in other studies (Núñez et al., 2017; Piñeiro et al., 2019; Regueiro et al., 2015). Thus, there is a critical need to use models of reciprocal effects to unpack the complex interplay of these constructs, particularly as homework-related emotions and achievement were found to be reciprocally (Trautwein, Schnyder, Niggli, Neumann, & Lüdtke, 2009). 1.3. Cultural Influences Emotion regulation is likely to be shaped by cultural differences, as cultural norms provide specific parameters for emotion regulation (Gross & John, 2003; Hofstede, 2001; Mesquita et al., 2014; Tsai & Lau, 2013; Xu, 2018). National culture dimensions (Hofstede, 2001) including individualism/collectivism, uncertainty avoidance, power distance, and shortversus long-term orientation may affect emotion regulation (e.g., how individuals experience and express their emotions). The Confucian Heritage Culture (CHC) is dominant in China and its neighboring nations heavily influenced by China (e.g., Korea, Japan, Vietnam, Malaysia, and Singapore; Nguyen, Terlouw, & Pilot, 2006). Relating to individualism/collectivism, CHC places a high value on harmony, interpersonal relationship, and emotional dependence among group members (Ho & Ho, 2008; Hofstede, 2001). In particular, CHC emphasizes the relationship between individuals of different statues including (a) the father-son relationship and (b) the teacher-student

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relationship. The teacher-student relationship is modeled after the father-son relationship and guided by the same ethic of filial piety, which is illustrated by a popular saying: “One day as teacher amounts to a lifetime as father” (Ho & Ho, 2008). In comparison with students from Western countries, CHC students tend to display a stronger uncertainty avoidance (Hofstede, 2001), are less tolerant of ambiguous or less structured tasks (Radclyffe-Thomas, 2007), and are more concerned with providing the “correct” answer (Smith, Coldwell, Smith, & Murphy, 2005). For instance, CHC students often exhibit higher levels of anxiety than Australian students: CHC students tended to show more anxiousness than Australian students in making sure that they were doing what they were supposed to do to ensure that they contributed to the task resolution, and also showed more anxiousness that their contributions were received and noted by the facilitator, such that their assessment obligations were being met. (Smith et al., 2005, p. 130) Additionally, students in countries with higher power distance are more frequently monitoring and controlling unpleasant emotions (e.g., stronger rules for monitoring the expression of anger; Grandey, Rafaeli, Ravid, Wirtz, & Steiner, 2010; Moran, Diefendorff, & Greguras, 2013). Therefore, CHC students find it more important to regulate and control unpleasant emotions in achievement-related activities such as homework. Further adding to this perceived importance is that (a) CHC places a high value on education and educational activities (e.g., homework; Cai, 2003; Chen & Stevenson, 1989) and on long-term orientation towards future goals (Hofstede, 2001; Tsikriktsis, 2002), (b) CHC emphasizes effort over ability in educational activities (Chen & Uttal, 1988; Li, 2005), and (c) CHC students are more concerned with losing face (e.g., relating to personal desires; Nguyen et al., 2006).

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In summary, this body of literature implies that, affected by cultural differences, CHC students may approach emotion regulation differently (e.g., stronger need for regulating unpleasant emotions in achievement-related activities). Thus, it would be critical to study possible linkages among emotion regulation, homework completion, and achievement for Chinese students, particularly as prior work on emotion regulation focuses on younger students and adults in Western nations (Arens et al., 2012; Jacobs & Gross, 2014). 1.4. The Present Investigation The investigation aims to study the reciprocal effects of emotion regulation, homework completion, and math achievement, based on data from Chinese eighth-grade students. Models of reciprocal effects are particularly informative for longitudinal relations among constructs (e.g., testing the direction of influence by controlling for autoregressive estimates and cross-lagged estimates; Selig & Little, 2012). Particularly, models of reciprocal effects permit researchers to control for prior levels (through autoregressive paths), which is an internal validity threat in nonexperimental research when not conducted. This is a major advantage as the effects may be attenuated or magnified without controlling for prior levels. Additionally, the direction of influence can be empirically investigated instead of assumed (as opposed to cross-sectional studies). Hence, models of reciprocal effects allow more rigorous test of the directional influence among constructs over time. Research Questions and Hypotheses Hypothesis (Path coefficients): We used models of reciprocal effects (see Figure 1) to study temporal relationships of homework emotion regulation, homework completion, and achievement.

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(a) Emotion regulation and achievement. Prior work on emotion regulation (Cole et al., 2004, Pekrun, 2006; Peixoto et al., 2017; Schmader et al., 2008) suggests that emotion regulation and achievement may be reciprocally related. Yet, related homework studies using cross-sectional data revealed that achievement was positively related to emotion management, but not cognitive reappraisal (Xu et al., 2016, 2017, 2018). Therefore, it is hypothesized that emotion management and achievement are reciprocally related. On the other hand, we do not have any prediction concerning the association between cognitive reappraisal and achievement. (b) Homework completion and achievement. Although prior studies focused on and found that homework completion positively influenced achievement (Bryan & Burstein, 2004; Cooper et al., 1998; Núñez et al., 2015; Xu, 2017), recent studies found that prior achievement positively influenced homework completion (Núñez et al., 2017; Regueiro et al., 2015). Thus, it is hypothesized that homework completion and achievement are reciprocally related. (c) Emotion regulation and homework completion. We do not have a specific hypothesis concerning emotion regulation and homework completion, as there is little research concerning the linkages between emotion regulation and homework completion. Thus, we leave it as a research question. (d) Emotion management × cognitive reappraisal interaction (see Figure 2). According to Troy et al. (2013), the use of other emotion regulation strategies may vary as a function of cognitive reappraisal. Thus, we expect an interaction between these

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variables. However, we do not have a hypothesis concerning emotion management × cognitive reappraisal interaction, as no prior research examined this issue. _______________________ Insert Figure 2 about here _______________________ Prior literature examined gender difference in emotion regulation in general (e.g., McRae, Ochsner, Mauss, Gabrieli, & Gross, 2008), with homework in particular (Xu, 2018; Xu et al., 2017, 2018). Even though gender difference is not the focus in our present study, it would be important to examine the following research question, that is, whether longitudinal relations among emotion regulation, homework completion, and achievement vary by gender for Chinese students. 2. Method 2.1. Participants One thousand and four hundred and fifty 8th graders (51.4% males; 100% Han nationality) participated our current study. They were from four public schools in East and South China. These were regular schools (i.e., not key schools with the priority of selecting high-achieving students). Educational level for mother and father was 9.9 years (SD = 3.2) and 10.4 years (SD = 3.1), and they were positively correlated (r = .70, p < .001). Consistent with prior research on the proper time span for examining emotion and student achievement (Pekrun, Hall, Goetz, & Perry, 2014), students were measured at two time points: Time 1 (T1, at the beginning of November, after students had approximately two months of experiences with math homework), and Time 2 (T2, approximately seven and half months later). With respect to math homework assignments, the percentages of participants who did homework

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four days or more in a week was T1 (69.4%) and T2 (69.0%). Time spent on math homework on a typical day was 34.5 minutes (SD = 25.7) at T1, and 35.3 minutes (SD = 28.2) at T2. Taken together, these homework practices were largely parallel to other studies carried out in China (e.g., Xu, 2016). 2.2. Measures Normally, the following three sources may be used to assess constructs such as emotion regulation and homework completion – teacher ratings, observer ratings, and student ratings. Each source has theoretical and methodological advantages and disadvantages (Dettmers et al., 2010; Turner & Meyer, 2000). Teachers, who could be viewed expects on homework, may seem to be the perfect source of information relating to emotion regulation and homework completion. Yet, teachers are not exposed to what occurs at home (e.g., each student’ emotional responses while doing homework). Additionally, it would have been too burdensome to have teachers rate each student in class about the amount of homework he or she completes (Cooper et al., 1998). Furthermore, teaching ideals, self-serving strategies, and vested interest may compromise the validity of their ratings (Dettmers et al., 2010). Direct observations at home by trained observers are often intrusive, labor intensive, and time-consuming (Xu, 2011; Xu & Corno, 1998), with longitudinal studies such as ours in particular (i.e., following up with a relatively large sample of students in private settings over time). Direct observations by parents may alleviate some of the above issues. Yet, it may present its own challenge, as parents tended to observe homework across all subjects, not just homework in one subject area (e.g., math; Cooper et al., 1998). In our current investigation, student ratings was used to assess emotion regulation and homework completion. Students could also be viewed experts and their ratings is a highly

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valuable source of information about emotions (Kouzma & Kennedy, 2002; Youngstrom & Green, 2003) and homework completion (Cooper et al., 1998). They have some advantages as observers of their homework emotions in that certain aspects of homework emotions are not readily observable and their ratings of their emotion regulation are likely to be more veridical than observer ratings (Xu, 2011). Another important reason for using self-ratings is that, as discussed above, constructs such as emotion regulation can be influenced by cultural norms (Gross & John, 2003; Moran et al., 2013; Tsai & Lau, 2013). Thus, in line with a phenomenological perspective (Dettmers et al., 2010), student ratings is more appropriate data source for tapping into their emotions than ratings by Western observers (or based on Western criteria). 2.2.1. Homework emotion regulation. Homework emotion regulation was assessed using two subscales – emotion management and cognitive reappraisal – using the Homework Emotion Regulation Scale (HERS; Xu et al., 2016, 2017). In their validation study using 796 students in grade 8, Xu et al. (2016) found that the HERS included these two related yet distinct subscales (CFI = .985; RMSEA = .069; SRMR = .025). Both emotion management (α = .83) and cognitive reappraisal (α = .87) were related positively to mastery orientation and negatively to avoidance orientation, in line with theoretical expectations (Radosevich, Vaidyanathan, Yeo, & Radosevich, 2004). Similarly, their findings based on 915 10th graders (Xu et al., 2017) supported the existence of two subscales (CFI = .993; RMSEA = .045; SRMR = .020), including emotion management (α = .82) and cognitive reappraisal (α = .89). Additionally, in both validation studies (Xu et al., 2016, 2017), math achievement was associated with emotion management, but not cognitive reappraisal.

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In our present study, for each measurement (Time 1 and 2), the same three-item subscale assessed emotion management (i.e., to up-regulate pleasant emotions and down-regulate unpleasant emotions; see Table 1; α/T1/T2 = .79/.84). Similarly, for each measurement, the same three-item subscale measured cognitive reappraisal (i.e., to reframe an unpleasant stimulus in less emotional ways; see Table 1; α/T1/T2 = .75/.82). _______________________ Insert Table 1 about here _______________________ 2.2.2. Homework completion. For each time point, students answered one item on homework completion, based on the National Education Longitudinal Study of 1988 and other related homework studies (Cooper et al., 1998; Cooper et al., 2006; Piñeiro et al., 2019; Xu, 2008, 2017; Yang & Xu, 2018). Specifically, the item asked: “Some students often complete math homework on time; others rarely do. How much of your assigned math homework do you usually complete?” Ratings included none, some, about half, most, and all. A converging line of evidence from prior research has indicated that this item provides reasonably valid information about homework completion. For example, one study with secondary school students (Xu, 2017) found that, in line with theoretical expectations, math homework completion was related negatively to homework distractions and positively to math homework expectancy, value, effort, emotion management, cognitive reappraisal, and standardized math achievement. 2.2.3. Achievement. We used standardized math achievement at each time point. Guided by national math curriculum standards in China (Li & Li, 2018), the test measured math competence and knowledge in probability, fraction, circle, triangle, linear function, inverse function, trigonometric function, quadratic function, axial symmetry, and rotation of figures and central symmetry. It included both short-answer and multiple-choice items. Anchor items were

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incorporated to link T1 to T2, and students were given 120 minutes to complete the test. Reliability estimate (coefficient alpha) was .87 for T1 and .88 for T2. 2.3. Analyses Our analyses were carried out using Mplus (Muthén & Muthén, 1998-2012). Emotion management and cognitive reappraisal were measured by latent factors using the same items at two measurement points. We included autoregressive and cross-lagged paths, the correlations among emotion management, cognitive reappraisal, homework completion, and achievement at T1 and T2, and correlated uniqueness for the same items across T1 and T2. The missing data for eight indicators were: T1 (M = 5.9%, SD = .3%), and T2 (M = 13.4%, SD = 1.8%). Our models were conducted using MLR, along with FILM, which is found to produce unbiased estimates for missing values (Marsh et al., 2016). 2.3.1. Measurement invariance across time. Given that metric and scalar measurement invariance are highly important in longitudinal studies (Niepel, Brunner, & Preckel, 2014; Van de Schoot, Lugtig, & Hox, 2012), we tested whether the two latent variables (emotion management and cognitive reappraisal) captured the same target constructs across T1 and T2, by examining configural, metric, and scalar invariance. 2.3.2. Measurement invariance across gender. Consistent with recommended practices regarding multiple group invariance (Hong, Malik, & Lee, 2003), we examined measurement invariance over gender by testing configural model, metric model, correlated uniqueness, and scalar models. 2.3.3. Path invariance across gender. We examined the paths relating these constructs (emotion management, cognitive reappraisal, homework completion, and achievement) from T1 to T2. Further incorporated were paths regarding the same construct from T1 to T2. For

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example, T2 emotion management was predicted by T1 cognitive reappraisal, T1 homework completion, and T1 achievement, but also by T1 emotion management. Therefore, to examine path invariance, 16 paths were constrained to be equal across gender (12 cross paths and 4 horizontal paths; see Figure 1). _______________________ Insert Figure 1 about here _______________________ 2.3.4. Latent interaction. Using the latent moderated structural equations (LMS) (Maslowsky, Jager, & Hemken, 2015; Marsh et al., 2016), we studied the influences of the emotion management × cognitive reappraisal interaction on subsequent emotion management, cognitive reappraisal, homework completion, and achievement. Although latent interaction does not affect the model fit, LMS did not provide goodness-of-fit measures (Maslowsky et al., 2015). Thus, we examined the model fit (Figure 1), and then added the autonomy support × effort interaction (Figure 2; see black circles and thick paths). 2.3.5. Model evaluation criteria. We applied a number of goodness-of-fit measures: (a) comparative fit index (CFI) ≥ .95 (Hu & Bentler, 1999); (b) Tucker-Lewis index (TLI) ≥ .95 (Hu & Bentler, 1999); (c) root mean square error of approximation (RMSEA) ≤ .08 (Browne & Cudeck, 1993); and (d) standardized root mean square residual (SRMR) ≤ .08 (Hu & Bentler, 1999). Because of the sensitivity of the chi-square test, we used the following guidelines concerning multigroup invariance; there is a support for more parsimonious model when ΔCFI < .01 and RMSEA < .015 (Chen, 2007; Cheung & Rensvold, 2002). 3. Results Our results are displayed in two sections. Section 1 studies the factor structure represented by the 16 indicators (as mentioned above). Section 2 examines models of reciprocal

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influences among emotion management, cognitive reappraisal, homework completion, and math achievement over these two measurements points. 3.1. Preliminary analysis Kurtosis and skewness values for the 16 indicators were satisfactory; only one indicator had skewness value larger than the absolute value 1 (-.1.185) and three indicators had kurtosis values larger than the absolute value 1 (from -1.303 to 1.032). Table 1 shows descriptive statistics for these indicators at each wave. All measures revealed adequate to good internal consistencies. Table 2 displays the findings from tests of measurement invariance for emotion management and cognitive reappraisal across time. Configural invariance models resulted in an excellent fit; CFI ≥ .993, TLI ≥ .979, RMSEA ≤ .044, and SRMR ≤ .018. The change in fit between configural and metric models was ΔCFI ≤ .002 and ΔRMSEA ≤ .014. The change in fit between metric and scalar models was ΔCFI ≤ .004 and ΔRMSEA ≤ .006. Thus, there is a support for scalar invariance for emotion management and cognitive reappraisal. _______________________ Insert Table 2 about here _______________________ Following the recommendation by Maslowsky et al. (2015), we compared the fit of the between following two models: Model 0 (without the latent interaction), and Model 1 (with the latent interaction). We tested the fit of the model without latent interaction (Model 0; Figure 1). Model 0 yielded an excellent fit (MLRχ2 = 208.951; df = 74; CFI = 0.981; TLI = .970; SRMR = 0.025; RMSEA = .035; 90% CI = [.030, .041]). Model 0 explained 33.3% variance in T2 emotion management, 24.1% variance in T2 cognitive reappraisal, 22.9% variance in T2 homework completion, and 72.9% variance in T2 achievement.

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We then tested the fit of the model with latent interaction between emotion management and cognitive reappraisal (Model 1; Figure 2). The relative fit of Model 1 versus Model 0 was determined by using a log-likelihood ratio comparing the log-likelihood values of Model 0 (36241.909) and Model (-25238.609), leading to a log-likelihood difference value of D = -2 × [(36241.909) – (-25238.609)] = 22006.600. Given free parameters of Model 0 (78) and Model 1 (82), the log-likelihood ratio test was statistically significant (p < .001), showing that Model 1 represents a significant better fit relative to Model 0. Overall, Model 1 explained additional 29.0% variance in T2 emotion management, additional 27.4% variance in T2 cognitive reappraisal, and additional .5% variance in T2 homework completion. We then examined factor structure invariance over gender. As shown in Table 3, the fit of scalar model was very good (CFI = .980), barely differing from that of configural model (ΔCFI = .001). Therefore, these findings offered strong support for the factor structure invariance across gender. _______________________ Insert Table 3 about here _______________________ As displayed in Table 4, across two measurement points, the standardized factor loadings all exceeded .600, ranging from .724 to .829 for emotion management, and .609 to .822 for cognitive reappraisal. _______________________ Insert Table 4 about here _______________________ As displayed in Table 5, emotion management, cognitive reappraisal, homework completion, and achievement were all positively correlated at both time points. Within T1 and

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T2, there were large correlations between emotion management and cognitive reappraisal (.54 to .75). There were medium correlations between emotion management and homework completion (.32 to .33), between emotion management and achievement (.33 to .38), and homework completion and achievement (.24 to .28). Additionally, there were small to medium correlations between cognitive reappraisal and homework completion (.14 to .21) and between cognitive reappraisal and achievement (.07 to .24). _______________________ Insert Table 5 about here _______________________ 3.2. Reciprocal Effects among Emotion Regulation, Homework Completion, and Achievement We assessed structural path invariance across gender. As dispalyed in Table 3, this model yielded an excellent fit (CFI = .980; SRMR = .035; RMSEA = .033; 90% CI [.027 .038]), barely differing from scalar model (ΔCFI < .001). Thus, there is a support for structural path invariance across gender. 3.2.1. Emotion management and achievement. As displayed in Table 6, there is a support for reciprocal influence of emotion management and achievement. The path from prior emotion management to subsequent achievement was significant (β = .155, p < .001). Similarly, the path from prior achievement to subsequent emotion management was significant (β = .071, p = .003). _______________________ Insert Table 6 about here _______________________

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3.2.2. Cognitive reappraisal and achievement. There was no support for reciprocal effects between cognitive reappraisal and achievement. Whereas T1 achievement was positively related to T2 cognitive reappraisal (β = .090, p = .001), T1 cognitive reappraisal was unrelated to T2 achievement (β = -.059, p = .065). 3.2.3. Homework completion and achievement. We found no support for reciprocal effects between homework completion and achievement. The path from T1 achievement to T2 homework completion was significant (β = .092, p = .001), but not the other way around (β = .004, p = .813). 3.2.4. Emotion management and cognitive reappraisal. There was no reciprocal influences of emotion management and cognitive reappraisal. Whereas higher T1 emotion management led to higher T2 cognitive reappraisal (β = .178, p = .002), higher T1 cognitive reappraisal did not lead to higher T2 emotion management (β = .052, p = .282). 3.2.5. Emotion management and homework completion. There was no support for reciprocal influences of emotion management and homework completion. T1 emotion management was unrelated to T2 homework completion (β = .040, p = .525), and T1 homework completion was unrelated to T2 emotion management (β = .018, p = .446). 3.2.6. Cognitive reappraisal and homework completion. Likewise, there was no support for reciprocal effects between cognitive reappraisal and homework completion. The path from T1 cognitive reappraisal to T2 homework completion was not significant (β = .049, p = .420), neither was the path from T1 homework completion to T2 cognitive reappraisal (β = .008, p = .756). 3.2.7. Emotion management × cognitive reappraisal. As displayed in Table 6, the emotion management × cognitive reappraisal interaction was not related to subsequent

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achievement (β = .037, p = .161). On the other hand, significant interactions were found between emotion management and cognitive reappraisal in the prediction of T2 emotion management (β = -.096, p = .010), T2 cognitive reappraisal (β = -.115, p = .014), and T2 homework completion (β = -.138, p < .038). To facilitate our interpretation, we plotted interaction effects on T2 emotion management (Figure 4), T2 cognitive reappraisal (Figure 5), and T2 homework completion (Figure 6). These plots showed that emotion management had a more positive influence on subsequent emotion management, cognitive reappraisal, and homework completion when prior cognitive reappraisal was low (i.e., compensatory effect by decreasing the gap between students with prior high and low cognitive reappraisal). _______________________ Insert Figures 4-6 about here _______________________ 4. Discussion Our current investigation tested the reciprocal effects of homework emotion regulation, homework completion, effort, and math achievement over the two waves. Informed by theory and research on emotion regulation, we investigated several hypotheses concerning the relationships among these important constructs relating to math homework. 4.1. Emotion regulation and achievement We found reciprocal influences of emotion management and achievement (see Figure 3). Additionally, we found an asymmetrical form of reciprocal influences of cognitive reappraisal and achievement: higher prior achievement resulted in higher subsequent cognitive reappraisal, whereas prior cognitive reappraisal was not related to subsequent achievement.

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The finding concerning reciprocal influences of emotion management and achievement is consistent with literature on emotion regulation (Cole et al., 2004, Pekrun, 2006; Peixoto et al., 2017; Schmader et al., 2008) and recent homework studies using cross-sectional data (Xu et al., 2016, 2017, 2018). On the other hand, what do we make out of the result that higher prior achievement led to higher subsequent cognitive reappraisal but not the other way around? One plausible explanation for the nonsignificant path from cognitive reappraisal to achievement is that it may need an extended period of time before cognitive reappraisal takes effect (e.g., becoming more optimistic about negative emotions and facilitating problem solving; Leroy & Gregoire, 2007; Xu et al., 2016, 2017). Another possible explanation is that cognitive reappraisal might be less effective for CHC students (Zhang & Fung, 2009) due to its perceived importance of monitoring, controlling, and suppressing negative emotions (Gross & John, 2003; Moran et al., 2013; Tsikriktsis, 2002). This explanation is further supported by our results from the present study that higher prior emotion management led to higher subsequent cognitive reappraisal, but not the other way around. 4.2. Homework completion and achievement About twenty years ago, Cooper et al. (1998) hypothesized that for lower grades, standardized test scores maybe viewed as determinants of homework practices (e.g., homework completion) as homework is often minimal during the first years of schooling. However, this causal ordering (i.e., from standardized test scores to homework completion) maybe problematic at upper grades. Thus, our present study based on models of reciprocal effects has examined and provided new insights into this two-decades-old hypothesis.

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We found an asymmetrical form of reciprocal influences of homework completion and math achievement: higher prior achievement led to higher later homework completion whereas prior homework completion was not related to subsequent achievement. As some cross-sectional studies found the positive path from homework completion to achievement (Bryan & Burstein, 2004; Cooper et al., 1998; Núñez et al., 2015; Xu, 2017) and other cross-sectional studies found the positive path from prior achievement to homework completion (Núñez et al., 2017; Piñeiro et al., 2019; Regueiro et al., 2015), our investigation extends prior research by using models of reciprocal effects. Our finding suggests that prior experience of academic success plays a more important role in homework completion, not the other way around. This is to some extent substantiated by previous work concerning the important role of prior achievement on student engagement (Chen, Yeh, Hwang., & Lin, 2013; Trautwein, Köller, Schmitz, & Baumert, 2002), with homework engagement in particular (Piñeiro et al., 2019). This is further in line with the recent call to control important variables such as students’ prior achievement in homework research (Moroni et al., 2015). As for nonsignificant path from homework completion to achievement, one possible explanation is that many students are often concerned with bringing their homework to class completed so as to avoid reproaches or to please their significant others (e.g., teachers and parents; Valle et al., 2015; Xu & Corno, 1998). As a result, more homework completion may not necessarily lead to increased academic achievement. This might be more of an issue for Chinese students, as CHC places a high value on interpersonal relationship and emotion dependence among members of the group, particularly relating to the hierarchical relationships including the father-son relationship and the teacher-student relationship (Ho & Ho, 2008; Hofstede, 2001). Given that this is the first study that we are aware of that examined reciprocal influences of

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homework completion and achievement in China, future research is needed, consistent with the recent call by Núñez et al (2015), to investigate the direction of influence between these important variables with longitudinal data in cross-cultural settings. 4.3. Emotion regulation and homework completion There was no support for reciprocal effects between (a) emotion management and homework completion, and (b) cognitive reappraisal and homework completion, although both sets of constructs were positively related within each wave. This pattern of findings were not surprising, as reciprocal effects models incorporated cross-lagged and autoregressive paths, thereby providing a more rigorous examination of the relations between these two sets of constructs (Marsh, Trautwein, Lüdtke, Köller, & Baumert, 2005; Selig & Little, 2012). Another plausible explanation was that there was a significant interaction between emotion management and cognitive reappraisal in the prediction of homework completion, one area that has been overlooked in prior investigation (discussed below). 4.4. Emotion management × cognitive reappraisal interaction In light of the work by Troy et al (2013) that the use of other emotion regulation strategies may vary as a function of cognitive reappraisal, we tested the emotion management × cognitive reappraisal interaction on subsequent emotion management, cognitive reappraisal, homework completion, and achievement. The emotion management × cognitive reappraisal interaction had a negative influence on subsequent cognitive reappraisal, emotion management, and homework completion. These results indicated that emotion management had a more positive influence on subsequent emotion management, cognitive reappraisal, and homework completion when prior cognitive reappraisal was low (i.e., to compensate prior cognitive reappraisal). Given that “negative emotions can be adaptive because they motivate people to

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take action to solve a problem” (Troy et al., 2013, p. 2511), it could be that students with low prior cognitive reappraisal tend to resort to or more rely on emotion management as a regulatory strategy. Hence, they are more motivated to control and manage homework emotion (compared with students with high prior cognitive reappraisal). Another plausible explanation could be cultural in the sense that CHC places more importance on education and homework as a major achievement-related activity (Cai, 2003; Chen & Stevenson, 1989) and on controlling, monitoring, and managing unpleasant emotions (Grandey et al., 2010; Moran et al., 2013; Tsikriktsis, 2002). In addition, CHC places more importance on effort in achievement-related activities (Chen & Uttal, 1988; Li, 2005), and Chinese children are encouraged and expected to work hard even if the likelihood of success is not promising (Hau & Salili, 1996). Thus, in light with Troy’s hypothesis, unpleasant emotions maybe particularly adaptive for Chinese students. As a result, emotion management plays a more important role for subsequent emotion management, cognitive reappraisal, and homework completion for Chinese students with low cognitive reappraisal. Informed by past theorizing that the controllability of a situation may influence the adaptiveness of one’s regulatory efforts (e.g., problem-focused coping vs emotion-focused coping such as cognitive reappraisal; Heth & Somer, 2002; Lazarus, 1993), Troy et al (2013) showed that in the context of uncontrollable stress, high cognitive reappraisal was related to enhanced well-being. Yet, in the context of controllable stress, high cognitive reappraisal was related to decreased psychological health. They concluded that “these findings support a novel theoretical model in which the effects of emotion-regulation strategies depend on the context in which they are used” (p. 2511). Thus, our present investigation takes another significant step

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forward, by suggesting that the influences of emotion-regulation strategies depend on how the context was perceived or experienced by individuals. 4.5. Implications, limitations, and future investigation Our current study represents an important advance over prior research by employing models of reciprocal influences to investigate temporal relations among emotion regulation, homework completion, and achievement. Although our study concerning reciprocal and unidirectional influences over time remains correlational (i.e., not causal due to a lack of random assignment and control; Marsh et al., 2016; Serbin, Kingdon, Ruttle, & Stack, 2015), it permits a more rigorous test of relations among different constructs (e.g., compared with cross-sectional models concerning the strength and direction of the relationships; Selig & Little, 2012). Thus, we extend prior research by indicating (a) the reciprocal influences of emotion management and achievement, (b) the positive path from prior achievement to subsequent emotion management, cognitive reappraisal, and homework completion, and (c) the negative path from the emotion management × cognitive reappraisal to emotion management, cognitive reappraisal, and homework completion. Furthermore, our investigation regarding structural path invariance suggests that these findings are applicable across gender. Our findings concerning the reciprocal influences of emotion management and achievement suggests that the more beneficial way to promote emotion management and achievement at the same time. Thus, it would be desirable for teachers to pay close attention to these two areas simultaneously – from providing explicit instructions to help students to manage homework emotions, to encouraging students to take more initiatives to monitor and control unpleasant homework emotions, and to improving and developing their math competences. This approach is particularly desirable, given our findings concerning the other positive paths from

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prior achievement to cognitive reappraisal and homework completion (i.e., not the other way around). Additionally, our findings regarding the emotion management × cognitive reappraisal suggest that prior emotion management may compensate prior cognitive reappraisal. These findings are important, as there could be many instances when at least some students are not optimistic about certain math homework assignments. These findings, along with the finding concerning the positive path from prior emotion management to subsequent cognitive reappraisal, further add to the desirability of simultaneously promoting homework emotion management and math achievement. The effect sizes in our present study were small. Yet, they are common in longitudinal design, as they reflect additive effects and could have a meaningful and substantial influence on the outcome variables over an extended period (Trautwein et al., 2009; Willoughby, Heffer, & Hamza, 2015). This is particularly, as our models controlled for moderate-to-large stability effects (see Table 6), thus removing a considerable proportion of the variance in T2 constructs. Although our current study used standardized math achievement, we assessed emotion management, cognitive reappraisal, and homework completion based on students’ self-report. Therefore, it would be beneficial to include multiple measures in future research (e.g., observation and teacher report). For example, although prior research has indicated that selfreported homework completion provides reasonably valid information about homework completion (Cooper et al., 1998; Xu, 2017; Yang & Xu, 2018), although it may be burdensome to have teachers to rate each student’s homework completion (Cooper et al., 1998) and with longitudinal studies in particular, it would be informative to have teachers to do so whenever

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possible. Additionally, it is likely that other variables might influence emotion regulation, homework completion, and achievement had they been included in our current study. Moreover, the current study focused on middle school students. Therefore, it would be important to continue this line of investigation at the elementary or high school level, as (a) students may increasingly employ different emotion regulation strategies over time (John & Gross, 2004), and as (b) prior meta-analyses revealed that the relationship between homework and achievement is moderated by school level (Cooper, Robinson, & Patall, 2006; Fan, Xu, Cai, He, & Fan, 2017). Finally, in light of our findings that the longitudinal relationships among emotion management, cognitive reappraisal, homework completion, and achievement maybe influenced by cultural differences, there is a need to conduct qualitative research to better capture students’ perspectives of the complex interplay among these constructs in cross-cultural settings. For examine, given with our results concerning significant interactions between emotion management and cognitive reappraisal, it would be beneficial to conduct interviews and observations with low/high cognitive reappraisal students to better understand how and under what condition these constructs may relate or interact over time.

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Xu, J. (2016). A study of the validity and reliability of the Teacher Homework Involvement Scale: A psychometric evaluation. Measurement, 93, 102-107. https://doi.org/10.1016/j.measurement.2016.07.012. Xu, J. (2017). Homework Expectancy Value Scale for high school students: Measurement invariance and latent mean differences across gender and grade level. Learning and Individual Differences, 60, 10-17. https://doi.org/10.1016/j.lindif.2017.10.003. Xu, J. (2018). Emotion regulation in mathematics homework: An empirical study. Journal of Educational Research, 111, 1-11. https://doi.org/10.1080/00220671.2016.1175409. Xu, J., & Corno, L. (1998). Case studies of families doing third grade homework. Teachers College Record, 100, 402-436. Xu, J., Fan, X., & Du, J. (2016). Homework Emotion Regulation Scale: Psychometric properties for middle school students. Journal of Psychoeducational Assessment, 34, 351-361. https://doi.org/10.1177/0734282915603542. Xu, J., Fan, X., & Du, J. (2017). Homework Emotion Regulation Scale: Confirming the factor structure with high school students. Journal of Psychoeducational Assessment, 35, 437441. https://doi.org/10.1177/0734282916640438. Xu, J., Fan, X., & Du, J. (2018). A study of the validity and reliability of the Online Homework Emotion Regulation Scale. Measurement, 115, 243-248. https://doi.org/10.1016/j.measurement.2017.10.050. Yang, F., & Xu, J. (2018). Homework Expectancy Value Scale: Measurement invariance and latent mean differences across gender. Journal of Psychoeducational Assessment, 36, 863-868. https://doi.org/10.1177/0734282917714905.

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Youngstrom, E. A., & Green, K. W. (2003). Reliability generalization of self-report of emotions when using differential emotions scale. Educational and Psychological Measurement, 63, 279-295. https://doi.org/10.1177/0013164403253226. Zhang, X., & Fung, H. H. (2009). Does graduation give rise to increased poignancy? Moderation roles of university identity and emotion regulation. Personality and Individual Differences, 47, 722-727. https://doi.org/10.1016/j.paid.2009.06.010.

HOMEWORK

42 Time 1

;

;

Time 2

;

Emotion management

;

;

;

;

;

;

Emotion management

;

;

;

Cognitive reappraisal

Cognitive reappraisal

;

;

Homework completion

Homework completion

;

;

Achievement

Achievement

Figure 1. The model of reciprocal effects between emotion management, cognitive reappraisal, homework completion, and achievement.

HOMEWORK

43 Time 1

;

;

Time 2

;

Emotion management

;

;

;

;

;

;

Emotion management

;

;

;

Cognitive reappraisal

Cognitive reappraisal

;

;

Homework completion

Homework completion

;

;

Achievement

Achievement

Figure 2. The model of reciprocal effects between emotion management, cognitive reappraisal, homework completion, achievement, and emotion management × cognitive reappraisal interaction. The latent interaction between emotion management and cognitive reappraisal (represented by the black circle) is added to the model, with thick black paths representing interaction effects.

HOMEWORK

44 Time 1

;

;

Time 2

;

;

Emotion management

;

;

Emotion management

.493 -.096 .071

;

;

; -.115

Cognitive reappraisal

.178

;

;

;

Cognitive reappraisal

.399

.090

;

; -.138

Homework completion

; Achievement

Homework completion

.423

.092 .814

.155

; Achievement

Figure 3. Structural paths relating Time 1 to Time 2. Only statistically significant paths are displayed.

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45

Figure 4. Interaction of emotion management (T1EM) and cognitive reappraisal (T1CR) predicting T2 emotion management (T2EM) – a plot of the effect of T1EM on T2EM at 1 SD below the zero mean of T1CR (LOWT1EF; 95% confidence bands [Lower for LOWT1CR – Upper for LOWT1CR]) and 1 SD above the zero mean of T1EF (HIGHT1CR; 95% confidence bands [Lower for HIGHT1CR – Upper for HIGHT1CR]).

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46

Figure 5. Interaction of emotion management (T1EM) and cognitive reappraisal (T1CR) predicting T2 cognitive reappraisal (T2CR) – a plot of the effect of T1EM on T2CR at 1 SD below the zero mean of T1CR (LOWT1EF; 95% confidence bands [Lower for LOWT1CR – Upper for LOWT1CR]) and 1 SD above the zero mean of T1EF (HIGHT1CR; 95% confidence bands [Lower for HIGHT1CR – Upper for HIGHT1CR]).

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47

Figure 6. Interaction of emotion management (T1EM) and cognitive reappraisal (T1CR) predicting T2 homework completion (T2HC) – a plot of the effect of T1EM on T2HC at 1 SD below the zero mean of T1CR (LOWT1EF; 95% confidence bands [Lower for LOWT1CR – Upper for LOWT1CR]) and 1 SD above the zero mean of T1EF (HIGHT1CR; 95% confidence bands [Lower for HIGHT1CR – Upper for HIGHT1CR]).

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HOMEWORK Table 1 Emotion Management, Cognitive Reappraisal, Homework Completion, and Achievement Kurtosis Indicators

Skewness

Time 1 Time 2 Time 1 Time 2

Emotion Tell myself not to be bothered with previous mistakes. -.734 a management Tell myself to calm down. -.217

-.709

-.072

-.069

-.169

-.530

-.491

Cheer myself up by telling myself that I can do it.

-.679

-.710

-.197

-.203

I think that there are good sides to it as well.

-.643

-.721

.061

.004

I think that I can learn something from the situation.

-.788

-.717

.011

-.106

I think that it is not all bad.

-.808

-.668

.029

-.101

Homework completionb

1.032

.010 -1.185 -.848

Achievement

-1.187 -1.303

Cognitive reappraisala

a Rating:

1 = Never, 2 = Rarely, 3 = Sometimes, 4 = Often, and 5 = Routinely.

b Rating:

1 = None, 2 = Some, 3 = About half, 4 = Most, and 5 = All.

.111

Mean (SD)

α

Time 1

Time 2

3.38 (.91)

3.34 (.95)

.79

.84

3.00 (.94)

3.18 (.97)

.75

.82

4.16 (.94)

3.94 (1.04) .87

.88

.034 47.15 (31.06) 54.69 (34.25)

Time 1 Time 2

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HOMEWORK Table 2 Measurement Invariance Tests for Emotion Management and Cognitive Reappraisal Across Two Waves Measure Emotion management

Cognitive reappraisal

Invariance

CFI

TLI

RMSEA

SRMR

Configural

.993

.979

.044

.018

Metric

.992

.982

.040

.023

Scalar

.988

.979

.043

.024

Configural

1.000

1.001

.000

.008

Metric

.998

.995

.014

.015

Scalar

.999

.999

.008

.016

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HOMEWORK Table 3 Tests for Gender Invariance Invariance models

MLRχ2

df

RMSEA

RMSEA 90% CI

CFI

TLI

SRMR

1. Configural (baseline)

283.494

148

.036

.029 - .042

.981

.970

.029

2. Metric (factor loading)

292.467

156

.035

.029 - .041

.981

.971

.031

3. Correlated uniqueness

305.210

162

.035

.029 - .041

.980

.971

.031

4. Scalar (intercept)

316.067

170

.034

.028 - .040

.980

.972

.031

5. Path coefficient

330.003

186

.033

.027 - .038

.980

.974

.035

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HOMEWORK Table 4 Standardized Factor Loadings Time 1 constructs Variables

EM

T1EM1 T1EM2 TIEM3 T1CR1 T1CR2 T1CR3 T1HC T1TEST

.758 .724 .754

T2EM1 T2EM2 T2EM3 T2CR1 T2CR2 T2CR3 T2HC T2TEST

CR

HC

Time 2 constructs Test

EM

CR

HC

Test

.724 .787 .609 1 1 .758 .792 .829 .812 .822 .683 1 1

Note. Each variable was given an identifier that specifies the Time (e.g., T1), the construct (e.g., EM = emotion management). Across two measurement points, emotion management was measured with the same three items (EM1-EM3), cognitive reappraisal was measured with the same three items (CR1-CR3), whereas homework completion (HC) and math achievement (TEST) were represented by a single measure.

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HOMEWORK Table 4 Factor Correlations Time 1

Time 2

EM

CR

HC

Time 1 EM CR HC Test

1.00 .54*** .32*** .38***

1.00 .14*** .07*

1.00 .28***

Time 2 EM CR HC Test

.57*** .40*** .22*** .40***

.32*** .44*** .10** .08*

.22*** .13*** .47*** .25***

Test

EM

CR

HC

Test

1.00 .75*** .33*** .33***

1.00 .21*** .24***

1.00 .24***

1.00

1.00 .29*** .20*** .22*** .85***

Note. EM = emotion management, CR = cognitive reappraisal, HC = homework completion, and Test = math achievement. *p <.05. **p <.01. ***p <.001.

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HOMEWORK Table 6 Path Coefficients for Models of Reciprocal Effects Between Emotion Management (EM), Cognitive Reappraisal (CR), Homework Completion (HC), Achievement (test), and EM × CR Interaction Dependent variable/ Independent variable

Without EM × CR Interaction Path coefficient

Standard error

With EM × CR Interaction Path coefficient

Standard error

T2EM T1EM

.512***

.048

.493***

.054

T1CR

.031

.046

.052

.049

-.096*

.037

T1EM × T1CR T1HC

.025

.032

.018

.024

T1TEST

.089**

.031

.071**

.024

T1EM

.185***

.052

.178**

.056

T1CR

.334***

.051

.399***

.059

-.115*

.047

T2CR

T1EM × T1CR T1HC

-.008

.031

-.008

.025

T1TEST

.106**

.031

.090**

.026

T1EM

.048

.047

.040

.062

T1CR

.009

.040

.049

.061

-.138*

.067

T2HC

T1EM × T1CR T1HC

.424***

.033

.423***

.033

T1TEST

.087**

.029

.092**

.029

T1EM

.113***

.026

.155***

.035

T1CR

-.038

.022

-.059

.032

.037

.026

T2TEST

T1EM × T1CR T1HC

-.004

.017

-.004

.017

T1TEST

.810***

.014

.814***

.017

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

HOMEWORK

Highlights ► We found positive reciprocal effects between emotion management (EM) and achievement. ► Prior achievement affected later cognitive reappraisal (CR) and homework completion. ► EM × CR had negative effects on subsequent EM, CR, and homework completion.

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