Affective and motivational factors of learning in online mathematics courses

We investigated what factors would be related to students’ achievement in mathematics courses offered at a virtual high school. This was an attempt to understand why some succeed and some do not as well as to suggest what should be done to help with student success. Seventy-two students responded to a self-report survey on motivation (ie, selfefficacy, intrinsic value), mathematics achievement emotions (ie, anxiety, anger, shame, hopelessness, boredom, enjoyment, pride), and cognitive processes (ie, cognitive strategy use, self-regulation). A three-step hierarchical multivariate regression was employed to examine which of the factors predict student achievement. Results showed that motivation accounted for approximately 13% of the variance in student achievement and self-efficacy was the significant individual predictor of student achievement. However, when achievement emotions were added to the analysis, self-efficacy failed to predict student achievement and emotions accounted for 37% of the variance in student achievement. Cognitive strategy use and self-regulation did not explain any additional variance in the final scores. Findings are discussed and implications for future research and development are also suggested. Mathematics is a core academic subject, not just for the domains of science, technology, engineering and mathematics but for nearly all students in nearly any domain (National Mathematics Advisory Panel [NMAP], 2008). It is important to develop the “means for reducing the mathematics achievement gaps that are prevalent in U.S. society” due to increased expectations in mathematics education (NMAP, 2008, p. xx). In response to national pressure to improve education in K-12 schools, many states have introduced new standards. Typically, these standards have raised the bar for mathematics in serious ways because of the ongoing struggle in the USA to demonstrate higher levels of mathematical proficiency on international assessments such as Trends in International Mathematics and Science Study (Martin, Mullis, Gonzalez & Chrostowski, 2004). Learning mathematics online can be even more challenging for students due to a sense of isolation and a lack of social support in online learning environments (Erichsen & Bolliger, 2011; Muilenburg & Berge, 2005; Murphy & Rodríguez-Manzanares, 2008; Song, Singleton, Hill & Koh, 2004). Online education has shown phenomenal growth in its use and development (Watson, Murin, Vashaw, Gemin & Rapp, 2011). In the 2004–05 school year, there were 65% more K-12 public school students enrolled in online courses than there were in 2002–03 in the British Journal of Educational Technology Vol 45 No 1 2014 171–185 doi:10.1111/j.1467-8535.2012.01382.x © 2012 British Educational Research Association USA (Zandberg & Lewis, 2008). Over 1 million students took online courses in the 2007–08 school year, and it is estimated that 5 million students (ie, 10% of K-12 students) will take online courses in 5 years in the USA (Picciano & Seaman, 2007, 2009; Picciano, Seaman & Allen, 2010). The enrollment keeps rapidly increasing along with the growth of online virtual schools (Tucker, 2007). In the USA, all but one state has virtual schools according to a national investigation (Watson et al, 2011). The promise that virtual schooling will equal or exceed the quality of education in face-to-face schools (Cavanaugh, 2001; Cavanaugh, Gillan, Kromrey, Hess & Blomeyer, 2004; Hughes, McLeod, Brown, Maeda & Choi, 2007) partly explains the widespread needs and expectations for virtual schooling (Hawkins, Barbour & Graham, 2012). Studies specifically on learning mathematics online also indicate that online courses are effective enough to become an alternative to face-to-face courses (Cavanaugh, Gillan, Bosnick & Hess, 2008; Hughes et al, 2007). Hughes and her colleagues (2007) found that students in algebra classes offered at virtual schools outperformed students in algebra classes offered at traditional schools in a content knowledge test. Learning gains were observed in online algebra learning classes regardless of the use of interactive technologies (Cavanaugh et al, 2008). However, research findings are still inconsistent (Barbour, 2011; Hughes et al, 2007), and effectiveness comparison research does not necessarily provide much information of how to improve the design of online teaching and learning environments (Murphy, Rodríguez-Manzanares & Barbour, 2011). Over 10 years ago, Cavanaugh (2001) emphasized that online education can be as effective as face-to-face education “when implemented with the same care as effective face-toface instruction” (p. 84). Exactly what care is needed remains unresolved. Recent research attempts to understand K-12 teachers’ perspectives on online teaching as a way of examining what support (eg, professional development) could help improve virtual schooling (DiPietro, Ferdig, Black & Preston, 2008; Hawkins et al, 2012; Murphy et al, 2011). It would be also helpful Practitioner Notes What is already known about this topic • Motivation is important in students’ learning and performance. • Self-efficacy is a significant predictor for student motivation and learning. What this paper adds • Self-efficacy was not a predictor any more once achievement emotions were taken into account. • Achievement emotions were useful in explaining student motivation and performance in online learning environments. • The emotion of anger was the strongest individual predictor of student achievement. Lack of interpersonal interactions may have let adolescents’ anger hinder their actions of studying without the opportunity of receiving social support from peers. • The findings of this paper illustrate the interdependence of emotions, motivation and learning in a K-12 online learning setting. Implications for practice and/or policy • Unlike outcomes-oriented research that focuses on what knowledge is acquired or not, this study provides a basis that suggests diverse paths to promote student learning in online mathematics courses. 172 British Journal of Educational Technology Vol 45 No 1 2014 © 2012 British Educational Research Association to know what support students need considering that the popularity of online learning does not guarantee student success (Barbour & Reeves, 2009; Cavanaugh, Barbour & Clark, 2009). Student readiness and retention can be challenging (Barbour & Reeves, 2009) and course dropout rates can be an issue (Kozma et al, 2000). In brief, there is a need to understand why some students succeed and some do not in order to suggest what should be done to improve student success in online mathematics learning. The purpose of this study was to investigate what factors are related to students’ achievement in mathematics courses offered at a virtual high school. Three kinds of factors were explored in this study: (1) motivational factors included self-efficacy and intrinsic value (Bandura, 1977, 1997, 2004; Eccles-Parsons et al, 1983; Pintrich & Schunk, 2002), (2) affective factors included mathematics achievement emotions (ie, boredom, anxiety, enjoyment, anger, shame, pride and hopelessness) (Pekrun, Goetz & Frenzel, 2007) and (3) cognitive process factors included cognitive strategy use and self-regulation (Pintrich & DeGroot, 1990; Zusho, Pintrich & Coppola, 2003). Motivation, emotion and cognitive process Learner motivation refers to desire to engage in a learning activity; achievement emotions refer to affective experiences in relation to an achievement activity or its outcome (Kim & Pekrun, in press). The role of motivation and emotions is crucial to learning (Astleitner, 2000; Carver & Scheier, 1990; Goetz, Pekrun, Hall & Haag, 2006; Op ‘t Eynde, de Corte, & Verschaffel, 2006; Pekrun, 1992; Pekrun, Goetz, Titz & Perry, 2002). For example, when students lack motivation, their learning process is rarely initiated (Bandura, 1986; Schunk, 1991). When students feel hopeless, their learning process is easily discontinued. To understand student learning, motivation and emotions should be studied also along with cognition (Ainley, 2006; Hannula, 2006; Meyer & Turner, 2006; Op ‘t Eynde & Turner, 2006; Op ‘t Eynde et al, 2006; Pekrun, 2006; Turner & Patrick, 2008). Online learning is no exception. In fact, motivation is often included in attempts to predict and understand student performance in K-12 online courses (eg, Roblyer, Davis, Mills, Marshall & Pape, 2008; C. Weiner, 2001); however, emotions are rarely considered in relation to motivation or cognition. Figure 1 illustrates the role of motivation, emotions and cognitive processes in learning as discussed in the following. Motivation and emotions influence each other to lead to a certain action (or inaction) (Hannula, 2006; McLeod, 1988; Op ‘t Eynde & Turner, 2006; Op ‘t Eynde et al, 2006; Pekrun, 2006). Expectancy assessment is involved in this reciprocal process (Carver & Scheier, 1990). In other words, people’s motivational and emotional responses occur based on (1) their perceived value of a certain action as well as (2) expectancy stemmed from their perceived control over the outcome of the action (Carver & Scheier, 1990; Eccles, 1983; Pekrun, 2006; B. Weiner, 1985). For example, Jenny has to retake a mathematics course that she failed last semester. Because the course is required for her high school graduation but it is not offered in the current semester at her school, she is enrolled in a course offered online at a virtual high school. The value of the course motivates Jenny to study hard; at the same time, her motivation can wither away and her anxiety Figure 1: Role of motivation, emotions and cognitive processes in the process of learning Factors related to online mathematics learning 173 © 2012 British Educational Research Association level can be heightened unless she perceives control over the outcome. That is, her perception should be that her ability, not luck, would determine her success and her effort would equip her with sufficient ability for success. Typically, students’ perceived task value and self-efficacy are considered important in determining their motivation to learn (Pintrich & Schunk, 2002). The emotions of boredom, anxiety, enjoyment, anger, shame, pride, and hopelessness are considered core achievement emotions that determine students’ affective experiences (Goetz et al, 2006). Motivation and emotions impact cognitive processes (Forgas, 2000; Gläser-Zikuda, Fuß, Laukenmann, Metz & Randler, 2005; Linnenbrink, 2006; Pekrun, 2006; Pekrun et al, 2002; Schwarz, 1990, 2000). In this study, cognitive processes include cognitive strategy use and self-regulation (Zusho et al, 2003). Cognitive strategies refer to rehearsal, elaboration, and organization and self-regulation refers to “planning, monitoring, and controlling” cognition (Zusho et al, 2003, p. 1084). For example, the use of cognitive strategy can be altered by emotions (Pekrun, 2006; Pekrun et al, 2002). Information is stored and retrieved differently depending on discrete emotions (Blaney, 1986; Bower, 1981; Levine & Pizarro, 2004). For instance, in the study of Holmberg and Holmes (1994), whether people were happy or unhappy about their marriage at present made their memory of early years of their marriage different. This implies that students’ memory and recall of course materials can be different depending on their emotional experiences. Positive emotions (eg, enjoyment) tend to facilitate the flexible use of cognitive strategies and creativity whereas negative emotions (eg, anxiety) tend to lead to the rigid use of narrowly focused strategies (Isen, 2000; Levine & Pizarro, 2004). In addition, motivation and emotions influence self-regulation by facilitating or impeding self-monitoring processes (see Carver & Scheier, 1990 for review). Much research on motivation, emotions and cognitive processes was conducted in face-to-face settings. However, students tend to sense disconnectedness in online learning environments due to a lack of interactions with their instructor and classmates (Hawkins et al, 2012; Song et al, 2004; C. Weiner, 2001). The lack of interactions between students and instructors as well as among students in both quantity and quality (Kozma et al, 2000) can impact students’ motivation, emotions, and cognitive processes that typically involve social influence (Schunk, Pintrich & Meece, 2008). For example, self-efficacy, a critical factor of motivation as discussed earlier, is positively correlated with interactions within a community of inquiry (Shea & Bidjerano, 2010). Another recent study reports that students viewed their interactions with instructor as well as with peers as motivational (Borup, Graham & Davies, in press). Researchers argue that such interactions are especially important in K-12 online courses with adolescents (DiPietro et al, 2008; Murphy & Rodríguez-Manzanares, 2008; Roblyer, Freeman, Stabler & Schneidmiller, 2007; C. Weiner, 2001). This emphasis may be because peer influence is essential in adolescents’ coping with difficulties (Berndt & Perry, 1986; La Greca & Lopez, 1998). In understanding how motivation develops and changes, “the transactions among persons” are important (Turner & Patrick, 2008, p. 119). Interactions in online courses are also critical in forming students’ emotional experience. Emotions are “socially constructed” although they are “personally enacted” (Schutz, Hong, Cross & Osbon, 2006, p. 344). Cognitive processes are impacted by online interactions as well; for instance, self-regulation was found to be positively correlated with social presence that was resulted from online interactions (Shea & Bidjerano, 2010). Besides, mathematics is learned socially throughout interactions with the instructor and classmates (Balacheff, 1990; Davydov & Kerr, 1995; Van Oers, 2006). In brief, motivation, emotions and cognitive processes are influenced by interactions with their instructor and classmates; it would be interesting to see how motivation, emotion and cognition interplay in online K-12 mathematics learning environments where student–student and student–teacher interactions tend to be minimal (Hawkins et al, 2012; Kozma et al, 2000; C. Weiner, 2001). However, these three processes have rarely been studied together to understand 174 British Journal of Educational Technology Vol 45 No 1 2014 © 2012 British Educational Research Association learning processes in online courses. In an empirical study, teachers in high school online courses acknowledged that limited interactions could create students’ negative emotions such as fear and anxiety and diminish the opportunity to prompt students’ motivation (Murphy & RodríguezManzanares, 2008); however, students’ motivational and emotional experiences were not systematically investigated. Research questions To understand what factors are related to students’ achievement in mathematics courses offered at a virtual high school, we investigated the relationships between motivation, mathematics achievement emotions, cognitive process and academic achievement of students. The following research questions were addressed: 1. How do motivational factors (ie, self-efficacy and intrinsic value) predict student achievement in online mathematics courses? 2. How do affective factors (ie, mathematics achievement emotions; boredom, anxiety, enjoyment, anger, shame, pride, and hopelessness) predict student achievement in online mathematics courses? 3. How do cognitive process factors (ie, cognitive strategy use and self-regulation) predict student achievement in online mathematics courses? 4. How are students’ motivation, mathematics achievement emotions and cognitive processes related to each other in online mathematics courses?