- Top of page
- Practitioner Notes
- Motivation, emotion and cognitive process
- Research questions
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, self-efficacy, 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 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-to-face 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 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
- Top of page
- Practitioner Notes
- Motivation, emotion and cognitive process
- Research questions
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 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 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 & Rodríguez-Manzanares, 2008); however, students' motivational and emotional experiences were not systematically investigated.
- Top of page
- Practitioner Notes
- Motivation, emotion and cognitive process
- Research questions
A three-step hierarchical multivariate regression was computed to explore the relation between student achievement and the motivation, emotion and cognitive process variables. The motivation variables (ie, self-efficacy, intrinsic value) were entered in the first step of these analyses, the achievement emotion variables (ie, boredom, anxiety, enjoyment, anger, shame, pride and hopelessness) were entered in the second step, and the cognitive process variables (ie, cognitive strategy use, self-regulation) were entered in the last step. This analysis strategy was selected because (1) achievement emotions are often viewed as a result of motivation despite the bidirectional influence between the two and (2) both influence students' use of cognitive strategies and their self-regulation (eg, Carver & Scheier, 1990; Op t'Eynde et al, 2006; Pekrun, 2006; Pekrun et al, 2002). Table 2 presents means, standard deviations and correlations of the variables in the study.
Table 2. Means, standard deviations, zero-order correlations and reliabilities for the study variables (n = 72)
| 1. Self-Efficacya||45.79||9.65||—|| || || || || || || || || || || |
| 2. Intrinsic valueb||46.47||9.22||0.74**||—|| || || || || || || || || || |
| 3. Cognitive Strategyc||66.43||12.34||0.43**||0.61**||—|| || || || || || || || || |
| 4. Self-Regulationd||42.00||7.26||0.57**||0.73**||0.57**||—|| || || || || || || || |
| 5. Boredome||8.95||3.66||−0.45**||−0.67**||−0.39**||−0.57**||—|| || || || || || || |
| 6. Anxietyf||31.94||12.94||−0.49**||−0.24*||0.01||−0.21||0.28*||—|| || || || || || |
| 7. Enjoymentg||17.01||4.52||0.58**||0.64**||0.34**||0.56**||−0.74**||−0.42**||—|| || || || || |
| 8. Angerh||12.45||5.48||−0.61**||−0.49**||−0.09||−0.44**||0.63**||0.61**||−0.62**||—|| || || || |
| 9. Shamei||11.48||5.57||−0.46**||−0.27*||−0.05||−0.31**||0.27*||0.74**||−0.40**||0.64**||—|| || || |
|10. Pridej||13.87||3.73||0.52**||0.66**||0.23*||0.56**||−0.61**||−0.27*||0.64**||−0.57**||−0.47**||—|| || |
|11. Hopelessnessk||16.66||7.93||−0.63**||−0.46**||−0.15||−0.44**||0.44**||0.84**||−0.58**||0.74**||0.78**||−0.44**||—|| |
Pearson correlations indicate that final scores were correlated significantly with self-efficacy but not with cognitive strategy use and self-regulation. The correlational results also indicate that final scores were related significantly to all mathematics achievement emotions but boredom. Students with a higher final score tended to report the lower levels of anxiety (r = −0.33, p < 0.01), anger (r = −0.51, p < 0.01), shame (r = −0.37, p < 0.01) and hopelessness (r = −0.44, p < 0.01) but the higher levels of enjoyment (r = 0.41, p < 0.01) and pride (r = 0.30, p < 0.01).
The correlations between the motivational variables and the achievement emotions were significant. Students with a higher self-efficacy tended to report the lower levels of boredom (r = −0.45, p < 0.01), anxiety (r = −0.49, p < 0.01), anger (r = −0.61, p < 0.01), shame (r = −0.46, p < 0.01) and hopelessness (r = −0.63, p < 0.01) but the higher levels of enjoyment (r = 0.58, p < 0.01) and pride (r = 0.52, p < 0.01). Students who perceived a higher intrinsic value tended to report the lower levels of boredom (r = −0.67, p < 0.01), anxiety (r = −0.24, p < 0.05), anger (r = −0.49, p < 0.01) and shame (r = −0.27, p < 0.05), hopelessness (r = −0.46, p < 0.01) but the higher levels of enjoyment (r = 0.64, p < 0.01) and pride (r = 0.66, p < 0.01).
The correlations between motivation and cognitive processes were significant. Students with a higher self-efficacy tended to report the higher levels of cognitive strategy use (r = 0.43, p < 0.01) and self-regulation (r = 0.57, p < 0.01). Students with a higher perception of intrinsic value tended to report the higher levels of cognitive strategy use (r = 0.61, p < 0.01) and self-regulation (r = 0.73, p < 0.01).
With regard to correlations between emotions and cognitive processes, students with the lower levels of boredom (r = −0.39, p < 0.01) but with the higher levels of enjoyment (r = 0.34, p < 0.01) and pride (r = 0.23, p < 0.05) tended to report a higher level of cognitive strategy use. Students with the lower levels of boredom (r = −0.57, p < 0.01), anger (r = −0.44, p < 0.01), shame (r = −0.31, p < 0.01) and hopelessness (r = −0.44, p < 0.01) but with the higher levels of enjoyment (r = 0.56, p < 0.01) and pride (r = 0.56, p < 0.01) tended to report a higher level of self-regulation.
As illustrated in Table 3, results from the first step of multiple regression analysis show that self-efficacy and intrinsic value accounted for approximately 13% of the variance in students' final scores, F(2, 69) = 5.241, p < 0.01. Self-efficacy (β = 0.45, p < 0.01) was the significant individual predictor of the final scores. Results from the second step analysis indicate that the achievement emotion variables increase the amount of variance explained by all of the predictors in the equation to approximately 37%, ΔF(7, 62) = 3.449, p < 0.01. In this analysis, self-efficacy failed to individually predict the final scores (β = 0.04, p = 0.83). Among the achievement emotion variables, boredom (β = 0.43, p < 0.05), enjoyment (β = 0.38, p < 0.05) and anger (β = −0.56, p < 0.01) were the significant individual predictors of the final scores. Finally, the third step analysis revealed that cognitive strategy use and self-regulation did not explain any additional variance in the final scores, ΔF(2, 60) = 0.858, p = 0.42. Cognitive strategy use (β = −0.01, p = 0.91) and self-regulation (β = −0.20, p = 0.22) failed to individually predict the final scores. Consistent with the second step analysis, boredom, enjoyment and anger remained the significant individual predictors of the final scores.
Table 3. Summary of multiple regression analysis for variables predicting achievement (n = 72)
|Step1|| || || |
|Step 2|| || || |
|Step 3|| || || |