The effects of IMPROVE on mathematical knowledge, mathematical reasoning and meta-cognition

The purpose of the present study is to examine the effects of IMPROVE, a meta-cognitive instructional method, on students' mathematical knowledge, mathematical reasoning and meta-cognition. Participants were 81 students who studied a pre-college course in mathematical. Students were randomly assigned into one of two groups and groups were randomly assigned into one of two conditions: IMPROVE vs. traditional instruction (the control group). Both groups were exposed to the same learning materials, solved exactly the same mathematical problems, and were taught by the same experienced teacher. The IMPROVE students were explicitly trained to activate meta-cognitive processes during the solution of mathematical problems. The control group was exposed to traditional instruction with no explicit exposure to meta-cognitive training. Results indicate that the IMPROVE students significantly outperformed their counterparts on both mathematical knowledge and mathematical reasoning. In addition, the IMPORVE students attained significantly higher scores then the control group on the three measures of meta-cognition: (a) general knowledge of cognition; (b) regulation of general cognition; and (c) domain-specific meta-cognitive knowledge. The theoretical and practical implications are discussed.