The purpose of this study was to investigate the effects of four instructional methods on students’ mathematical reasoning and metacognitive knowledge. The participants were 384 eighth-grade students. The instructional methods were cooperative learning combined with metacognitive training (COOP+META), individualized learning combined with metacognitive training (IND+META), cooperative learning without metacognitive training (COOP), and individualized learning without metacognitive training (IND). Results showed that the COOP+META group significantly outperformed the IND +META group, which in turn significantly outperformed the COOP and IND groups on graph interpretation and various aspects of mathematical explanations. Furthermore, the metacognitive groups (COOP+META and IND +META) outperformed their counterparts (COOP and IND) on graph construction (transfer tasks) and metacognitive knowledge. This article presents theoretical and practical implications of the findings.

The purpose of the present research was to design an innovative instructional method for teaching mathematics in heterogeneous classrooms (with no tracking) and to investigate its effects on students’ mathematics achievement. The method is based on current theories in social cognition and metacognition. It consists of three interdependent components: metacognitive activities, peer interaction, and systematic provision of feedback-corrective-enrichment. The method is called IMPROVE, the acronym of which represents all the teaching steps that constitute the method: Introducing the new concepts, Metacognitive questioning, Practicing, Reviewing and reducing difficulties, Obtaining mastery, Verification, and Enrichment. The research includes two studies, both implemented in seventh grades: One focused on in-depth analyses of students’ information processing under the different learning conditions (N = 247), and one investigated the development of students’ mathematical reasoning over a full academic year (N = 265). Results of both studies showed that IMPROVE students significantly outperformed the nontreatment control groups on various measures of mathematics achievement. The theoretical and practical implications of the research are discussed.

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