From Motivation to Engagement: The Role of Effort Regulation of Virtual High School Students in Mathematics Courses

Transcription

1 Kim, C., Park, S. W., Cozart, J., & Lee, H. (2015). From Motivation to Engagement: The Role of Effort Regulation of Virtual High School Students in Mathematics Courses. Educational Technology & Society, 18 (4), From Motivation to Engagement: The Role of Effort Regulation of Virtual High School Students in Mathematics Courses ChanMin Kim 1*, Seung Won Park 2, Joe Cozart 3 and Hyewon Lee 1 1 Learning, Design, and Technology, University of Georgia, Athens, Georgia, USA // 2 Department of Medical Education, Sungkyunkwan University, South Korea // 3 Georgia Virtual Learning, Georgia Department of Education, Atlanta, Georgia, USA // chanmin@uga.edu // parkswon@skku.edu // joe.cozart@gavirtualschool.org // ehyewon@uga.edu * Corresponding author (Submitted June 5, 2014; Revised December 10, 2014; Accepted May 3, 2015) ABSTRACT Engagement and motivation are not one and the same, but motivation can be transformed into engagement with proper design of support. In this study, we examined the differences between high performers and low performers with regard to changes in their motivation, regulation, and engagement throughout the semester. Participants were 100 students enrolled in online self-paced asynchronous mathematics courses offered at a virtual high school in the United States. A survey was administered to participants at three times throughout the semester. Data were analyzed using repeated measures MANOVAs. Overall, high performers and low performers differed with regard to their changes in motivation and regulation throughout the course, specifically, in self-efficacy and effort regulation. The study findings offer implications for teaching and research on creating potentially effective support for virtual learning. Keywords Virtual high school, Motivation, Regulation, Engagement, Mathematics education Introduction In recent years, online education has drastically increased, including at the K-12 level (Watson, Murin, Vashaw, Gemin, & Rapp, 2011). The enrollment of K-12 school students in online courses continues to grow along with the popularity of virtual schooling (Tucker, 2007). Every state in the United States and the District of Columbia has a K- 12 virtual school (Kennedy & Archambault, 2012). The rapid growth of virtual schooling has been attributed to numerous factors, especially its perceived benefits such as provision of individualized instruction and broadening educational access (Barbour & Reeves, 2009). The effectiveness of online and face-to-face education is now largely considered equal, which may have added momentum to the growth of virtual schooling (Hughes, McLeod, Brown, Maeda, & Choi, 2007). However, as with face-to-face schooling, high enrollment does not necessarily imply a high success rate. Challenges in virtual schooling include low performance and high course dropout rates (Barbour & Reeves, 2009). Motivation is critical in learning. This is no less true in online learning (Carpenter & Cavanaugh, 2012). However, motivated students do not always engage in learning (Keller, 2008). Motivation to learn is only a desire to be involved in activities for learning (Kim & Bennekin, 2013). What makes students actually learn is their mindful engagement in those learning activities because engagement leads to outcomes such as achievement and motivation underpins engagement (Martin, 2012, p. 305). There has been much research on motivation and engagement in a variety of face-to-face learning contexts (e.g., Junco, Elavsky, & Heiberger, 2013). However, what has been learned from such research may not apply to virtual schooling because of the unique characteristics of online learning environments (Cho, Demei, & Laffey, 2010) such as the lack of social presence, defined as the degree of salience of the other person in the interaction and the consequent salience of the interpersonal relationship (Short, Williams, & Christie, 1976, p. 65). Social presence and its lack have been researched in many studies to understand learning processes in online courses (e.g., Shea & Bidjerano, 2010). Student motivation can be different depending on the quantity and quality of social presence (Borup, Graham, & Davies, 2012; Shea & Bidjerano, 2010). This may apply even more to adolescents who tend to heavily weigh the importance of peers (Berten, 2008). In fact, the K-12 online education literature highlights the role of students interactions with their instructor and classmates (e.g., DiPietro, Ferdig, Black, & Preston, 2008). In ISSN (online) and (print). This article of the Journal of Educational Technology & Society is available under Creative Commons CC-BY-ND-NC 3.0 license ( For further queries, please contact Journal Editors at ets-editors@ifets.info. 261

2 addition, mathematics educators and researchers have underscored social aspects of mathematics learning (Davydov & Kerr, 1995). In sum, there is a need to understand how students motivation and engagement influence their achievement in virtual high school mathematics courses so that support can be planned and implemented accordingly. The aims of the present study were to (a) explore and document how students motivation and engagement were related to their mathematics achievement at a virtual high school and (b) determine what support is needed in order to improve their motivation, engagement and achievement. This research can potentially provide a new lens through which to view how motivation and engagement interrelate with student achievement in virtual schooling. In the following sections, we discuss the definitions of engagement with an emphasis on its difference from motivation. We then discuss what is needed to transform motivation into engagement. Our research question is then posed. What is engagement? There is no straightforward way of defining the construct of engagement. Rather, it may be reasonable to define engagement as a multi-component construct comprised of subsets with associated indices. The engagement definition of Fredricks, Blumenfeld, and Paris (2004) encompasses three kinds of engagement: behavioral, cognitive, and emotional engagement. Behavioral engagement refers to involvement in learning tasks and environments such as time-on-task and attendance; cognitive engagement refers to psychological investment in the process of learning such as the use of learning strategies; and emotional engagement refers to affective reactions to learning tasks and environments such as emotions (Fredricks et al., 2004). The multi-component approach to considering engagement as a meta-construct can be conceptually and practically useful in research on and development of interventions to improve student engagement (Fredricks et al., 2004). Such an approach can broaden understanding of engagement (Finn & Zimmer, 2012; Fredricks et al., 2004; Lawson & Lawson, 2013). For example, if students emotional experience is examined along with their off-task behaviors such as disrupting a peer (Skinner, Kindermann, & Furrer, 2008), one could better understand how to improve their engagement by providing relevant support for negative emotions such as boredom. In the present study, we define engagement as cognitive and affective participation in learning activities. We included only cognitive engagement (i.e., using shallow and deep cognitive strategies; Pintrich, Smith, Garcia, & McKeachie, 1993) and emotional engagement (i.e., experiencing boredom, anxiety, enjoyment, anger, shame, pride, and hopelessness; Pekrun, Goetz, & Frenzel, 2005) in our definition. We recognize that behavioral engagement is critical. However, in asynchronous online education, there are no face-to-face or synchronous virtual classes to attend and thus, the notion of behavioral engagement is not conceptually clear. For example, students login time does not necessarily mean how many hours they studied. They may log in just to download course materials. In addition, although Fredricks and her colleagues (2004) view of engagement as a meta-construct was applied in the present study, we excluded motivation from cognitive engagement unlike their definition of cognitive engagement. Engagement does not occur without desire to engage (Martin, 2012) but engagement and motivation are not one and the same. How can motivation be transformed into engagement? Motivation and engagement do not always coexist. In other words, there could be motivation but without engagement (e.g., only wanting something but not actually doing it). What transforms motivation to engagement is the effort and metacognitive regulation that students put into the process of their learning (Pintrich et al., 1993). Effort regulation is to control one s effort expenditure (Halisch & Heckenhausen, 1977, p. 724). Metacognitive regulation is to control one s own cognition (Pintrich et al., 1993, p. 803). Effort regulation is part of resource management (Pintrich et al., 1993). To display the role of the effort and metacognitive regulation in transforming motivation to engagement, here is an example. Reviewing class notes over and over (i.e., rehearsal, one of the cognitive strategies) is one way to engage in learning activities (Fredricks et al., 2004). This action of rehearsal (i.e., engagement) would not happen without the desire to learn (i.e., motivation); at the same time, the desire alone does not guarantee engagement and the student should also make an effort to rehearse (i.e., effort regulation) and monitor 262

3 when to rehearse (i.e., metacognitive regulation). Managing both cognition (i.e., metacognitive regulation) and effort (i.e., effort regulation) is important in learning (Pintrich et al., 1993) because it transforms motivation to engagement. Such regulation happens more easily when students engage in the learning tasks that are (a) perceived easy to execute and (b) interesting and enjoyable. Self-efficacy is defined as one s perceived ability to successfully complete a task (Bandura, 1977). Intrinsic task value is defined as the value one perceives in a task that is inherently interesting and enjoyable (Schunk, Pintrich, & Meece, 2008). In many different learning environments, self-efficacy has been steadily found to be a strong predictor for motivation and performance (e.g., Multon, Brown, & Lent, 1991). Self-efficacious students also tend to control their learning process (Bandura, 1977). Thus, when a task is perceived to be easy to perform, students are likely to perceive high self-efficacy and to self-regulate. Self-efficacy influences motivation directly and engagement indirectly (Schunk & Mullen, 2012). Students engage in tasks also for their own interests (Ainley, 2012) and enjoyment (Csikszentmihalyi, 1988) when the intrinsic value of the tasks is high (e.g., Deci & Ryan, 2008). Not every student enjoys mathematics. Still, students can engage in learning tasks for which they do not perceive high intrinsic value when there is no obstacle that they believe they cannot overcome. In other words, when students have high expectancy of success (Wigfield & Eccles, 2000), motivation can be transformed into engagement. However, not every task is easy. Especially in online mathematics courses, not only do many students not enjoy math, but also they are not self-efficacious due to previous failure of math courses. Thus, such students often experience negative emotions like anger in math classes (Kim, Park, & Cozart, 2014). Research question This study investigated how differently virtual high school students engage and achieve in mathematics courses and what quality of theirs makes such differences. We addressed the following research question: How do high performers and low performers differ with regard to their changes in motivation, regulation, and engagement throughout the course? We compared such changes from the beginning of the semester to the middle of and the end of the semester. In this study, motivation variables included self-efficacy and intrinsic value, regulation variables included metacognitive regulation and effort regulation, and engagement variables included cognitive engagement (i.e., using deep cognitive strategy use and shallow cognitive strategy use) and emotional engagement (i.e., experiencing boredom, anxiety, enjoyment, anger, shame, pride, and hopelessness). Table 1 summarizes each construct and variable. Table 1. Variable description (Operationalization of the constructs in this study) Construct Construct definition Variable Variable description Motivation Desire to be involved with learning activities/tasks Self-efficacy Beliefs about own abilities to complete learning tasks in a certain circumstance Intrinsic value Perception of the value of learning tasks in relation to his or her interest Regulation Management of cognition and other resources such as effort, emotions, Metacognitive regulation Management of cognition in learning activities and environments Effort regulation Management of effort in learning Engagement Cognitive and affective participation in learning activities Cognitive engagement Emotional engagement activities in the face of difficulties Involvement with learning activities using shallow and deep cognitive strategies Emotional reactions, such as boredom, anxiety, enjoyment, anger, shame, pride, and hopelessness, to learning activities 263

4 Methods Participants and setting Participants were students enrolled in online self-paced asynchronous mathematics courses offered at a virtual high school in the southeastern United States. The virtual high school is run by the State Department of Education. Students who are enrolled in the virtual high school courses either take courses for an entire curriculum or supplement courses that they take at their local school. A survey was administered to participants at three times throughout the semester. One hundred participants who completed the survey all three times were included in the study. The participants (n = 100) were from Math 1 (n = 13), Math 2 (n = 4), Math 3 (n = 9), Algebra (n = 31), Geometry (n = 7), Pre-Calculus (n = 5), Calculus (n = 14), Statistics (n = 16), and Applied Math (i.e., Problem Solving and Money Management) (n = 1) courses. The average age was Sixty-eight out of 100 were female. 71% of the participants were Caucasian, 11% were Black/African American, 8% were Asian American, 3% were Hispanic/Latino, and 7% were multiracial. Those who had no prior experience with online math courses (n = 82) outnumbered those with experience. Data collection The Motivated Strategies for Learning Questionnaire (MSLQ) (Pintrich, & DeGroot, 1990) was used to measure motivation, regulation, and cognitive engagement. Participants responded to each of the 40 items using a 7-point Likert scale ranging from (1) Not at all true of me to (7) Very true of me. The reliability of scores on these subscales of the MSLQ ranged from.52 to.93 (Pintrich, Smith, Garcia, & McKeachie, 1991) and validity of the items were tested in a variety of school settings (e.g., Wolters & Pintrich, 1998). Some items were reworded to reflect the online context of this study (e.g., the item When reading I try to connect the things I am reading about with what I already know was revised to when reviewing online course materials I try to connect the things I am reviewing with what I already know ). Scale reliability coefficients with the reworded items ranged from.59 to.90 in a previous study (Kim et al., 2014) and from.50 to.88 in the current study (see Table 2). Measure Scale Sample item Motivation Regulation Engagement Self-efficacy Intrinsic value Metacognitive regulation Effort regulation Deep cognitive strategy use Shallow cognitive strategy use Boredom Anxiety Enjoyment Anger Table 2. Sample items and scale reliability I am sure I can do an excellent job on the problems and tasks assigned for this class. Even when I do poorly on a test I try to learn from my mistakes. Before I begin studying I think about the things I will need to do to learn. I work hard to get a good grade even when I don t like a class. When reviewing online course materials I try to connect the things I am reviewing with what I already know. When I study for a test I try to remember as many facts as I can. Just thinking of my math homework assignments makes me feel bored. I m so scared of my math assignments that I would rather not start them. The material we deal with in mathematics is so exciting that I really enjoy my class. I am so angry that I would like to throw my homework into the trash. Scale reliability (Cronbach s α) Shame I feel ashamed when I realize that I lack ability

5 Pride After having done my math homework, I am proud of myself..76 Hopelessness I would prefer to give up..91 The Achievement Emotion Questionnaire in Mathematics (AEQ-M) (Pekrun, Goetz, & Frenzel, 2005) was used to measure emotional engagement. Nineteen items were excluded from the current study because they were pertinent to attending a physical classroom (e.g., When I say something in my math class, I can tell that my face gets red. ). Only the items asking about emotional experiences before, during, and after studying (18 items) and taking an exam (23 items) were included. Participants responded to each of 41 items using a 5-point Likert scale ranging from (1) Strongly disagree to (5) Strongly agree. Some items were reworded to reflect the online context of this study. Internal consistency coefficients of scores on the various sub-scales of the AEQ-M ranged from.84 to.92 in a previous study (Frenzel, Pekrun, & Goetz, 2007) and validity of the scores was tested in a variety of applications (e.g., Frenzel, Thrash, Pekrun, & Goetz, 2007). Scale reliability coefficients with the reworded items ranged from.67 to.93 in a previous study (Kim et al., 2014) and from.75 to.93 in the current study (see Table 2). Achievement was measured using students final grades. The possible range of the final grades was Final grades were determined using scores from asynchronous discussions, homework assignments, quizzes, tests, and the final exam. There was no grade directly tied to attendance. Each course used a standard weighting system to distribute grades across discussions, assignments, quizzes, tests, and exams. Procedure We recruited participants in the first and second weeks of the Fall 2011 semester. In the course website, we posted a URL of a webpage containing an online survey that includes (a) the study description, (b) consent forms, (c) demographic questions, and (d) 1 st survey questions on motivation, regulation, and engagement. Students who submitted signed parental consent and student assent forms proceeded to respond to demographic and 1 st survey questions. The same survey on motivation, regulation, and engagement was administered two more times throughout the semester: one was in the middle of the semester and the other was toward the end of the semester. We collected the final grade scores of the participants when the semester ended. Figure 1 illustrates the two groups, three measurement points, and six variables of the study. Measured at Time 1 (beginning of the semester) Measured at Time 2 (middle of the semester) Measured at Time 3 (end of the Semester) High Performers Low Performers Motivation: Self-efficacy Intrinsic value Regulation: Metacognitive regulation Effort regulation Engagement: Cognitive engagement Emotional engagement Figure 1. A summary of data collection Data analyses Four separate 3 (time) 2 (group) MANOVAs were conducted with time (Measurement Points 1, 2, and 3) as a repeated measure to investigate differences in changes in motivation, regulation, cognitive engagement, and 265

6 emotional engagement between the high-performer and low-performer groups. The participants were categorized into high, middle, and low performer groups based on their final grade scores (M = 79.11, SD = 19.43). Because the variability of the final scores was relatively high, we were concerned that grouping the participants based upon the mean ± one standard deviation may not include students who scored high enough to be considered as high performers. Thus, we categorized participants using the conventional letter grade assignment: participants with final grade scores higher than 90 (equivalent to a letter grade A) were included in the high-performer group (M = 94.13, n = 38) while participants with final grade scores lower than 80 (or, those who received a letter grade C or below) were included in the low-performer group (M = 61.68, n = 40). The rest were regarded as the middle performers. For the purpose of examining differences between high performers and low performers, the middle performers were excluded in these analyses. Partial eta- squared (ηp2) was used to calculate effect size: Small:.01 ηp2 <.06; Medium:.06 ηp2 <.14; Large: ηp2.14). Results The results of repeated measures MANOVAs indicated that high performers and low performers differed with regard to their changes in motivation, regulation, and engagement throughout the course, specifically, in self-efficacy (part of motivation) and effort regulation (part of regulation). The descriptive statistics of all dependent variables examined are presented in Table 3. The analysis results of the repeated measures are summarized in Table 4. Measurement time point Self-efficacy a Intrinsic value b Effort regulation c Meta. regulation d Deep strategy e Shallow strategy f Boredom g Anxiety h Enjoyment i Anger j Shame k Pride l Table 3. Descriptive statistics Low performer (n = 40) High performer (n = 38) (8.09) (8.14) (3.63) (3.87) (5.57) (5.07) 8.72 (3.94) (11.44) (4.66) (5.06) (5.30) (3.72) (10.57) (9.65) (4.18) (4.24) (6.61) (6.09) 9.27 (4.00) (8.41) (3.22) (4.60) (4.14) (2.96) (9.93) (9.91) (3.98) (4.29) (7.60) (6.61) 9.27 (3.72) (12.43) (4.83) (5.84) (5.22) (3.51) (8.84) (7.80) (3.71) (4.07) (5.73) (4.87) 7.86 (4.04) (11.49) (4.49) (6.27) (5.16) (3.57) (8.80) (10.19) (3.58) (4.66) (7.17) (5.55) 8.15 (3.83) (9.00) (3.75) (5.27) (4.45) (2.70) (7.81) (8.94) (3.87) (5.05) (7.99) (6.24) 8.52 (4.26) (14.50) (3.92) (6.28) (5.26) (3.72) Hopelessness m (7.05) (6.96) (7.04) (7.07) (7.54) (8.02) Notes. a Possible range of Self-Efficacy score: 9-63; b Possible range of Intrinsic Value score: 9-63; c Possible range of Effort regulation: 4-28; d Possible range of Metcognitive Regulation: 5-35; e Possible range of Deep Cognitive 266

7 Strategy: 8-56; f Possible range of Shallow Cognitive Strategy: 5-35; g Possible range of Boredom score: 3-15; h Possible range of Anxiety score: 11-55; i Possible range of Enjoyment score: 6-30; j Possible range of Anger score: 5-25; k Possible range of Shame score: 5-25; l Possible range of Pride score: 4-20; m Possible range of Hopelessness: Table 4. Summary of univariate analyses of repeated measures Group effect Time effect Time x Group effect F P F P F P Self-efficacy Intrinsic value Effort regulation N/A N/A Meta. regulation N/A N/A Deep strategy N/A N/A N/A N/A Shallow strategy N/A N/A N/A N/A Boredom N/A N/A N/A N/A Anxiety N/A N/A N/A N/A Enjoyment N/A N/A N/A N/A Anger N/A N/A N/A N/A Shame N/A N/A N/A N/A Pride N/A N/A N/A N/A Hopelessness N/A N/A N/A N/A Note. Significant effects are in bold. The first 3 (time) 2 (group) repeated measures MANOVA was conducted with two motivation variables: selfefficacy and intrinsic value. One important assumption of a repeated measures MANOVA is the equality of covariance. Results of Box s Test of Equality Covariance Matrices yielded X 2 (21) = 36.76, p =.01, providing evidence of a violation of the equal covariance assumption. Nevertheless, because the natural logs of covariance matrices were found to be similar, we proceed with the usual MANOVA tests following Huberty and Olejnik s (2006) suggestion. Preliminary analyses were conducted to examine if there were any differences between two groups at the beginning of the semester (e.g., Time 1), and we found a significant difference in self-efficacy (p <.01) between two groups: high performers demonstrated higher self-efficacy than low performers at Time 1. On the main analysis of the repeated measures MANOVA with two motivation variables, there were a significant main effect of time, Wilks Lambda =.579, F(4, 73) = 13.23, p <.001, a main effect of group, Wilks Lambda =.759, F(2, 75) = 11.86, p <.001, and a significant time x group interaction, Wilks Lambda =.847, F(4, 73) = 3.29, p <.05. To further inspect the significant effects on the multivariate analysis, follow-up univariate analyses of repeated measures were conducted for each motivation variable. Follow-up univariate analyses for self-efficacy yielded a significant main effect of time, F(2, 75) = 10.07, p <.001, ηp2 =.21, a main effect of group, F(1, 76) = 22.74, p <.001, ηp2 =.23, and a significant time x group interaction, F(2, 75) = 6.32, p <.01, ηp2 =.14. Further analyses indicated that self-efficacy among the low-performer group gradually diminished from Time 1 to Time 3 (p <.001); the self-efficacy of the high-performer group did not change over time. Last, follow-up univariate analyses for intrinsic value yielded a significant main effect of time, F(2, 75) = 26.57, p <.001, ηp2 =.41, indicating that both high- and low-performer groups reported a gradual decrease in intrinsic value over three measurement times. The second 3 (time) 2 (group) repeated measures MANOVA was conducted with two regulation variables: metacognitive regulation and effort regulation. The equality of covariance matrices was upheld as indicated by X 2 (21) = 30.65, p =.07. Preliminary analyses indicated a significant difference in effort regulation between two groups (p <.05) at Time 1: high performers showed significantly higher effort regulation at Time 1 than low performers. Results of the repeated measures MANOVA revealed a significant main effect of time, Wilks Lambda =.851, F(4, 73) = 3.17, p <.05, and a main effect of group, Wilks Lambda =.757, F(2, 75) = 12.02, p <.001. Follow-up univariate analyses for effort regulation yielded a significant main effect of time, F(2, 75) = 4.91, p <.05, ηp2 =.11, and a main effect of group, F(1, 76) = 12.52, p <.01. While high performers maintained superior effort regulation to low performers throughout the semester, both groups demonstrated diminished effort regulation from Time 1 to Time 3 (p <.01, ηp2 =.11). Similarly, univariate analyses for metacognitive regulation indicated that both high and low performers gradually reported lesser metacognitive regulation from Time 1 to Time 3 (p <.05, ηp2 =.08). 267

8 The third 3 (time) 2 (group) repeated measures MANOVA was conducted with two cognitive engagement variables: deep strategy use and shallow strategy use. Preliminary analyses indicated that high and low performers demonstrated the similar level of both deep and shallow strategy use at Time 1. Given the equal covariance indicated by X 2 (21) = 26.44, p =.18, a significant main effect of time was found from the repeated measures MANOVA, Wilks Lambda =.829, F(4, 73) = 3.75, p <.01. Follow-up univariate analyses for deep and shallow strategies also yielded a significant time effect (p <.01, ηp2 =.12; p <.01, ηp2 =.15; respectively) indicating that both high and low performers decreased their use of deep and shallow strategies over time. The last 3 (time) 2 (group) repeated measures MANOVA analysis was conducted with seven emotional engagement variables: boredom, anxiety, enjoyment, anger, shame, pride, and hopelessness. Results of Box s Test of Equality Covariance Matrices provided the evidence of covariance equality. Preliminary analyses indicated that the high and low performers differed in the level of shame (p <.01), pride (p <.05), and hopelessness (p <.01) in the beginning of the semester. Two groups were not different in the levels of any other emotion variables at Time 1. Results of the repeated measures MANOVA with emotional engagement variables indicated a significant time effect, Wilks Lambda =.669, F(14, 63) = 2.23, p <.05. Conducting follow-up univariate analyses, pride was the only variable that yielded the main effect of time, F(2, 75) = 5.27, p <.01, ηp2 =.12. Both high and low performers diminished pride over time. Discussion Findings and interpretations First, we found that high performers and low performers differed throughout the course: high performers started the semester with the higher level of effort regulation than low performers and they maintained their superior level of effort regulation to low performers throughout the semester. The higher the level of effort regulation that students had, the higher their achievement was. This finding is aligned with that of Puzziferro s study (2008) with community college students enrolled in liberal arts online courses. Even when students perception of intrinsic task value was low in the current study, those who reported greater effort regulation tended to perform better than those who reported the lower level of effort regulation. Given these findings, supporting students effort regulation may be one way to help them do better in an online learning environment. Designing support for effort regulation could involve online instructors scaffolding for student effort regulation that includes monitoring and guiding student efforts (Cho & Shen, 2013). Volition theories and models can be helpful in creating such support as well since they explain how efforts can be better regulated (e.g., implementation intentions in Gollwitzer & Sheeran, 2006; action control in Kuhl, 1985). Volition refers to a dynamic system of psychological control processes that protect concentration and directed effort in the face of personal and/or environmental distractions (Corno, 1993, p.14). Second, we found that the metacognitive regulation of both high performers and low performers decreased throughout the semester. This contradicts previous findings on the role of metacognitive regulation in online learning (Artino, 2007; Cho & Shen, 2013). However, this finding along with discussions on effort regulation above suggests that students effort regulation may have compensated for the impact of decreased metacognitive regulation on achievement. This supports the notion that achievement depends not only on cognitive control and regulation, especially the different cognitive, metacognitive, and learning strategies that students may use to control their own cognition and learning but also on how students control their own motivation, emotions, behavior (including choice, effort, and persistence), and their environment (Pintrich, 1999, p. 336). Although in the current study we did not examine students regulation of other aspects such as emotions and environment, the inclusion of effort regulation is an attempt to understand the path from student motivation to achievement. This attempt may be critical especially in online learning environments where more qualities are expected than just knowing how to study (e.g., cognitive strategy use) (Kim & Bennekin, 2013). Third, high performers started the semester with higher self-efficacy than low performers. Low performers selfefficacy gradually diminished over time while there was no change in self-efficacy among high performers. The indirect effect of self-efficacy on achievement has been well documented (e.g., Multon, Brown, & Lent, 1991) also in the literature involving online learning contexts (e.g., Cho & Shen, 2013). It is conceivable that effort regulation 268

9 may have influenced self-efficacy (Komarraju & Nadler, 2013). The role of effort regulation as a mediator is pointed out in some studies (Artino, 2007; Cho & Shen, 2013; Shea & Bidjerano, 2010). Thus, combined with the finding on effort regulation, it seems that there could be other ways to promote self-efficacy than structuring learning environments to provide vicarious experiences, autonomy, clear expectations, goal specificity, and balanced task difficulty (Bandura, 1997; Jang, Reeve, & Deci, 2010; Locke & Latham, 2002). The effect of self-efficacy can be improved through effort regulation. Fourth, there was no difference between high performers and low performers in intrinsic value. This finding is counter-intuitive and we can only speculate what has happened based on relevant literature. The motivation literature describes that people tend to be persistent when they perceive intrinsic value in a certain task that satisfies their interest (Ainley, 2012) and which they enjoy (Csikszentmihalyi, 1988). Such perceived intrinsic value enhances the quality of motivation (Deci & Ryan, 2008) and provides momentum for participating in the task. With enjoyment, full engagement can occur without even a conscious effort (e.g., flow experience; Csikszentmihalyi, 1988). Nonetheless, without enjoyment and interest in a given task, people can be still engaged in a task and come to a successful completion depending on regulatory styles (Ryan & Deci, 2000). Along this line of literature, our finding on intrinsic value may have arisen as such: (a) the learning environment may have allowed students perceived intrinsic value to fade away considering that both high and low performer groups showed gradual decreases in intrinsic value throughout the semester and (b) even without enjoyment and genuine interest, students with effort regulation could succeed considering high performers had superior effort regulation to low performers. Not every student has the capability to reshape tasks and to make them more palatable in suboptimal learning contexts (Corno & Kanfer, 1993, p. 302) and those without such a capability such as low performers in this study can be educated about how to optimize contexts for themselves (e.g., exercising effort regulation) (Byman & Kansanen, 2008). Last, both high and low performers pride and uses of deep and shallow strategies significantly diminished throughout the semester. The use of shallow cognitive strategies should be better than nonuse but when shallow cognitive strategies are used without deep cognitive strategies, learning tends to stay at a shallow level. Waning pride may have been due to the decreased use of cognitive strategies and/or the lack of intrinsic value. However, resiliency occurs when negative emotions serve as a warning for students with clear goals (Turner, & Schallert, 2001). The steadily superior level of effort regulation that the high performers had may have allowed them to be resilient from decreased pride and still be successful in the course. Implications for research and practice The findings offer implications for research on and teaching at virtual schools. Understanding how students motivation and engagement as well as regulation contribute to their learning provides information of how support can be planned accordingly in virtual high school math courses. That is, comparing high and low performers changes in their motivation, regulation, and engagement provides direction for creating potentially effective support, especially for student effort regulation, for online education in K-12 virtual schools. For example, support for students effort regulation may help not only with a lack of motivation from not viewing the intrinsic value of learning tasks but also with disengagement such as nonuse of cognitive strategies, which would in turn improve achievement. This is a unique way of improving motivation, engagement, and achievement especially when every learning environment cannot be optimal for every student (Kinshuk, Liu, & Graf, 2009). Improving learning through effort regulation can also contribute to greater capacity for lifelong learning. Along this line, other qualities of students could be studied also. For example, students beliefs about intelligence valuing effort and hard work could be used to improve effort regulation (Komarraju & Nadler, 2013, p. 70). Also since self-efficacious students tend to believe that their performance can be improved by exerting effort (Komarraju & Nadler, 2013), improving selfefficacy can lead to improved effort regulation. Even when tasks are difficult, self-efficacious students tend to be persistent (Komarraju & Nadler, 2013). Limitations and suggestions for future research There are several limitations in this study. First, mainly self-reported data were used. The social desirability issue (Crowne & Marlowe, 1960) remains. Future research should consider individual or focus group interviews as well as 269

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