topic study group no 12 teaching and learning of geometry primary level

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Mathematization of rotation as a didactic task

International audienceThe inspiration for observation was an idea of getting movement to a static school geometry. In the school curriculum, the only area where you can consciously refer to the movement are questions related to isometrics. I took the premise that the mathematization of movement should be based on student perceptions related to the physical movement of objects. Conducted observation shows that the mathematization of rotation might not be so obvious

Dynamic reasoning in elementary geometry – how to achieve it?

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

On the development of the mathematical concept - case study

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Using various representations in the process of solving mathematical problems

Mathematics uses a wide range of representations, but the mathematical symbol is not the only way to code information. Different ways of representing mathematical concepts and relationships are used, especially in the early stages of learning. Generally, the teacher decides on the choice of representational forms to use. But in the process of solving mathematical problems, it is the pupils – not the teacher – who are engaged in the problem-solving, and the coding used should support their cognitive work. This paper analyses how different representations can influence the results of work on an untypical mathematical problem. The task was solved by a group of 7–8 year-old pupils participating in a mathematics club. The examples selected for analysis indicate a strong relationship between the choice of representations and the final result of the pupils’ work