Predictive Models of Students' Mathematical Beliefs, Self-Regulated Learning and Thinking Skills on Mathematics Ability of University Students - Suthar, Velo (2010)
In spite of a general agreement on the imperative impact of students’ mathematics beliefs, self-regulated learning, thinking skills on mathematics ability of students among mathematics education researchers, still there is a lack of clarity from the conceptual viewpoint. A cultivating body of research consistently pointed out that mathematics beliefs, self-regulation and thinking skills play a vital role in facilitating and regulating students learning of mathematics and hence ability in mathematics. Previous research also indicated that self-regulated learning has extensive effects on students’ thinking and specifically on mathematical thinking. This study examined both the cognitive and affective factors contributing to mathematics ability in Malaysian higher education situation. This study was conducted to investigate the impact of students’ mathematics beliefs, self-regulated learning and thinking skills on mathematics ability of Malaysian undergraduate mathematics students using two predictive models namely, multiple linear regression model (MLR) and binary logistics regression (BLR). A self-reported questionnaire was used to assess students’mathematics beliefs, self-regulated learning and thinking skills. Findings indicated that the significantly correlations between mathematics ability and sub-constructs of students’ mathematics beliefs construct: “beliefs about one’s ability in mathematics” (r = .47, p < .001), “students’ beliefs about mathematics” (r = .31, p <.001), “beliefs about importance of mathematics” (r = .25, p < .001) and mathematics ability was also significant and positively related with overall students’ mathematics beliefs (r =. 38, p < .001). The students’ mathematics ability was significantly correlated with sub-constructs of self-regulated learning construct were time and study environment (r = .42, p < .0.001), organization (r = .39, p < .0.001), elaboration (r =.372, p < .0.001), rehearsal (r = .33, p < .0.001), meta-cognitive self-regulation (r = .31, p < 0.001 and mathematics ability was highly correlated with overall self-regulated learning construct (r = .53 p < .0.001). Similarly, the positive and strong correlations were obtained between mathematics ability and sub constructs of thinking skills construct: critical thinking skills, (r = .76, p < .001), problem solving skills, (r = .403, p< .0.001) and overall thinking skills construct, (r = .676, p < .0.001). This indicated that both critical thinking and problem solving skills are good predictors to enhance the students’ mathematics ability. Both the MLR and BLR were performed to assess the impact of students’ mathematical beliefs, self-regulated learning and thinking skills on the likelihood that respondentshave high or low mathematics ability. An ANOVA test of the strength of significance of the multiple linear regression model was found to be highly significant [F (1, 456) =73.912, p < .001], protecting against the likelihood of Type-I errors, with a moderate effect size above the 90 percentile standing (R2 = 0.722). Using the logistic regression analysis, eight predictors among the complete model containing all 13 predictors were statistically significant, χ2 (15, N= 473) = 287.55, p <0.001 indicating that the model was able to distinguish between respondents of high or low mathematical ability. The model as a whole explained 45.6% (Cox & Snell R2) and 64.5% (Nagelkerke R~2 ) of the variance in undergraduate students’ mathematical ability. This model also correctly classified 85.4% of the cases. Overall analysis indicated that the twelve and nine independent variables of made a unique statistically significant contribution using the MLR and BLR models respectively. The strongest predictor of mathematics ability was beliefs about ones’ ability in mathematics, recording an odds ratio of 2.58. Based on these findings, the study recommended that a longitudinal future research should be initiated to examine the influence of beliefs about ones’ ability in mathematics on the students’ mathematics ability. In addition, self-regulated learning, and thinking skills can also be attributed to the complex and dynamic interaction between cognitive and affective variables on mathematics ability.