Metacognition has been accorded a role in both mathematical problem solving and in the learning of mathematics. There has been consistent advocacy of the need for the promotion of metacognitive activity in both domains. Such advocacy can only be effective if the advocated process is well understood. In this paper we have four goals: to describe a multi-method technique developed to study student mathematical metacognition; to set out the structural elements and configuration of a coherent model of metacognition in the domain of mathematical problem solving; to report on the empirical utility (and validity) of this model; and, to report the insights into student mathematical metacognition arising from the research.
This research investigates the perceptions of ®rst-year Bachelor of Teaching students (primary and secondary) and Diploma of Education students (secondary) about their peer teaching experience in a postgraduate subject called Curriculum and Assessment. Peer teaching is a learner-centred approach to teaching and learning that is intended to provide signi®cant bene®ts for learners' knowledge, skills and metacognition. However, concerns have been raised over the quality of the learning and teaching and the risks associated with such a pedagogy. In the present study, student responses to questionnaires and semi-structured interviews were analysed, using a mixed methods approach, with respect to three broad and somewhat interconnected categories: process, people and product. These responses suggested a wide range of reactions to peer teaching, but overall students feel they bene®ted from the experience. The ®ndings of this study should be of interest to lecturers and students in pre-service teacher education courses, especially. Knowledge about peer teaching, learning and assessment would be especially valuable for both education lecturers and beginning teachers seeking to design and manage learner-centred pedagogy in their own primary, secondary and tertiary classrooms. However, the results of this research would have far-reaching appeal for all teaching and learning contexts.
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