Desoete A., Veenman M. (eds): Metacognition in mathematics education

Abstract

Although metacognition is seen as important in learning outcomes in mathematics education, the rapid development of metacognition research has resulted in a proliferation of definitions and methodologies, which has led to confusion and, sometimes, contradictions. Flavell (1976, 1979) defined metacognition as the knowledge and the active regulation of one’s own cognitive processes. The aim of the book is to aid in summarising and clarifying some of the issues with respect to this conceptualisation, as well as the assessment and the training of metacognition in students with and without mathematics learning disabilities. According to the editors, this book presents a ‘‘kaleidoscopic view of European research for the role of metacognition in mathematics performance’’ (Desoete & Veenman, 2006 p. 3). The book consists of ten chapters. Chapter 1, written by the editors, introduces the chapters and the critical issues to be addressed concerning the nature, theory, assessment and treatment of metacognition in mathematics. In this chapter, the relationship between metacognition and mathematical problem-solving skills is discussed and a comparison summary of the different European studies on metacognition in the book is presented. After the introductory chapter, the following nine chapters present theoretical and empirical metacognition research using a quantitative approach involving statistical tests such as ANOVA and MANOVA. There are overlaps for the various metacognitive components under study, which are well defined by the authors (metacognitive experiences; metacognitive skills including goal setting, planning, control, prediction, monitoring, evaluation and reflection on problem-solving strategies; and metacognitive beliefs). In addition, there is some overlap in the various assessment techniques utilised. These include questionnaires, interviews, observations, thinking aloud protocols, eye movements, computer registrations of activities, note taking and stimulated recall. Chapters 2, 3, 4, 5, 6, 7, 8 and 9 focus on assessment. Chapters 2, 5, 7, 9 and 10 focus on the training of metacognition including using the instructional methods, IMPROVE (Introducing the new material, Metacognitive questioning, Practicing, Reviewing, Obtaining mastery on higher and lower cognitive processes, Verification, and Enrichment and remedial) (Mevarech & Kramarski, 1997) and MASTER (Mathematics Strategy Training for Educational Remediation) (Van Luit, Kaskens & Van de Krol, 1999). Chapters 2, 3, 4, 5 and 6 focus on metacognition in average-performing subjects, whereas in chapters 7, 8, 9, and 10 metacognition is investigated in studies involving subjects with mathematics learning disabilities. There was some commonality between the chapters with respect to grade in school of the participants in the studies. The various studies involved primary students from the third to sixth grade and secondary students up to the tenth grade. A review of a selection of the chapters follows. In chapter 2, the purpose of the study by Efklides, Kiorpelidou and Kiosseoglou (2006) was to investigate the differential effect of type of mathematical worked-out examples on students’ problem-solving performances, selfexplanations and metacognitive experiences. This comparative study’s metacognitive component focused on metacognitive experiences of feeling of difficulty, estimate of effort and feeling of confidence in the solution produced. The participants involved were seventh and eighth grade students without mathematics learning disabilities. Students had to self-explain their solutions and answered M. Kahwagi-Tarabay (&) Melbourne, Australia e-mail: mariekahwagi@hotmail.com