Publication 2974

Dörfler W. (1987) Empirical investigations of the construction of cognitive schema from actions. In: Bergeron J. C., Herscovics N. & Kieran C. (eds.) Proceedings of the Eleventh Conference of the International Group for the Psychology of Mathematics Education, Volume 3. University of Montreal, Montreal: 3–9.
The theoretical basis of the interviews reported about here is a Piagetian-like approach to the origin and genesis of cognitive schemata representing mathematical concepts. Such schemata are postulated to reflect the abstract and general structure of material, imagined or mental actions and of relations induced by these actions. The main cognitive tools for the mental construction of such schemata are seen to be: Actions, symbolic representations, prototypes of objects, reflection and abstraction, schematization, generalization. The interviews were devised such that the subjects were guided appropriately in their individual cognitive constructions. The mathematical topics treated are: Place value system, divisibility, word problems, geometric sequence, Riemann integral. In general the results support the view that the individual construction of cognitive schemata is possible and effective in the proposed way.
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