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Critical Maths for Innovative Societies

The Role of Metacognitive Pedagogies

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How can mathematics education foster the skills that are appropriate for innovative societies? Mathematics education is heavily emphasised worldwide, nevertheless it is still considered to be a stumbling block for many students. While there is almost a consensus that mathematics problems appropriate for the 21st century should be complex, unfamiliar and non-routine (CUN), most of the textbooks still mainly include routine problems based on the application of ready-made algorithms.

The time has come to introduce innovative instructional methods in order to enhance mathematics education and students’ ability to solve CUN tasks. Metacognitive pedagogies can play a key role in this. These pedagogies explicitly train students to “think about their thinking” during learning. They can be used to improve not just academic achievement (content knowledge and understanding, the ability to handle unfamiliar problems etc.) but also affective outcomes such as reduced anxiety or improved motivation. This strong relationship between metacognition and schooling outcomes has implications for the education community and policy makers.

This book is designed to assist practitioners, curriculum developers and policy makers alike in preparing today’s students for tomorrow’s world.

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Metacognitive pedagogies in mathematics education

This chapter reviews the five main metacognitive pedagogies used in maths education, their benefits and trade-offs. The models are: Polya, Schoenfeld, IMPROVE, Verschaffel and Singapore. All of them use some form of self-directed questions but differ in their details, scope and age range. Polya’s and Schoenfeld’s models are designed to be used with university students and on single CUN problems, whereas IMPROVE, Verschaffel’s model and the Singapore model can be used with younger learners and for a set of problems or even a whole curriculum. IMPROVE has also been modified for use in other domains, and for teachers’ professional development with or with no advanced technologies. Comparing the models highlights the advantages and challenges associated with each one of them.

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