Predicting Algebra Achievement: Cognitive and Meta-cognitive Aspects

Abstract

Click One of the most important goals of mathematics learning is to enhance students’ mathematical achievement and also develop skills in mathematics problem solving. The purposes of this study were to consider: How well algebra problem solving performance, meta-cognitive strategies, and cognitive strategies (IVs) predict students’ mathematical achievement (DV)? How much variance in mathematical achievement score can be explained by scores of algebra problem solving performance, meta-cognitive strategies, and cognitive strategies? Which is the best predictor of mathematical achievement: algebra problem solving performance, meta-cognitive strategies, or cognitive strategies? The subjects of this study were selected from first year mathematics students who took Algebra course in a public university in Malaysia. The Cognitive Strategy Questionnaire comprises of 18 items, was used to assess the students’ specific cognitive strategy for solving the given Algebra problems. Algebra problem solving performance was measured using a test includes routine and non-routine problems, based on the covered topics in the course. The results indicated that there is no significant correlation between independent variables (Algebra problem solving performance, meta-cognitive strategies, deep cognition and shallow cognition). ALGPS and overall meta-cognition are two independent variables which make a strong and significant unique contribution to the prediction of mathematical achievement as a dependent variable, when the explained variance is controlled by all other variables in the model (Beta=0.686, p<0.05), (Beta=0.157, p<0.05). The value of R square is 0.546 which is indicating 54.6 percent of the variance in the mathematical achievement as independent variable is explained by the model of regression (which includes the variance of algebra problem solving performance, meta-cognitive awareness, deep cognitive strategies and shallow cognitive strategies). The F Change shows the relationship between the set of IVs and the DV is significantly large [F(4,83)=24.914, p<0.0005]. The answer of the first question of research is: 54.6 percent of the variance in the mathematical achievement as independent variable is explained by the model of regression (which includes the variance of algebra problem solving performance, meta-cognitive awareness, deep cognitive strategies and shallow cognitive strategies). The answer of the second question of research is: among these four variables, ALGPS makes the largest unique contribution, although overall meta-cognition also made a statistically significant contribution.