Dynamic reasoning in elementary geometry – how to achieve it?
Treść / Zawartość
Theories of creating mathematical concepts and mathematicalreasoning do not say much about the way in which dynamic reasoningis associated with the development of geometrical thinking. Historicalreview shows that using movement in geometry was differently seen byits creators. Also, approach by psychology does not indicate a simpleway how to connect visual thinking (present at preparatory stage of reasoning)with operational thinking and movement in geometric reasoning.Therefore identification of the way a pupil, working in a geometrical environment,uses physical or imaginary movement has a significant meaningfor didactical designing. In this article results of research led among 4-6years old children is presented. The aim of the research was to investigatethe role of gestures and manipulation in solving geometrical problems.Children were subject to a series of observations during an experiment,aimed at finding a special placement for the figures in the symmetricalpattern. Results show, that rotation was taken as the first, most intuitivemovement for them. Manipulation with rotation was taken independentlyon visual recognition of the relation of axis symmetry. It suggests thatsuch approach can have a great impact on “tacit knowledge” used in furtherlearning about geometrical transformations, and as consequence thedynamic imagination of rotation could be closer to acquaintance thanother rigid movements on the plane.