Chapters in Proceedings of the annual conference of the international group for the Psychology of Mathematics Education (PME-14), Volume 3 Edited by G. Booker, P. Cobb & T. de Mendicuti. PME, Mexico, 1990.

Thompson P. W. & Thompson A. G. (1990) Salient aspects of experience with concrete manipulatives. In: Booker G., Cobb P. & de Mendicuti T. (eds.) Proceedings of the annual conference of the international group for the Psychology of Mathematics Education (PME-14), Volume 3. PME, Mexico: 337–343. https://cepa.info/6881

A current hypothesis among many mathematics educators is that it is helpful, and perhaps necessary, for students to be able to represent mathematical ideas in several equivalent ways. This sentiment is embodied in Dienes’ Multiple Embodiment Principle. From a constructivist perspective, if manipulatives are effective, it is due to the their constraints on students actions and thereby the greater number of occasions where students are prompted to reflect on their understanding in relation to their goals. This study investigated the hypothesis that the more pronounced in students’ experience is the constraining nature of a notational system, the more likely they are to conceive of notational algorithms as deriving from adaptations to the system’s constraints.

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