Abstract
Through visualisation, geometry can mediate understanding of some demanding arithmetic and algebraic concepts, relationships, processes and situations for pupils. This thesis is explained by the method of genetic parallel and of a didactic analysis of two educationally interesting problem situations. Theoretical considerations are illustrated by several real experiences. Suggestions for the application of theoretical results are given in conclusion.
Highlights
IntroductionIntroduction and MethodologyGeometry appears at two levels in school mathematics. At the first level, plane and space shapes, relationships, constructions, proofs, etc. are introduced to pupils
Introduction and MethodologyGeometry appears at two levels in school mathematics
A deeper consideration of the cognitive structure of this didactic problem shows that geometry helps to transform arithmetic or algebraic thinking of a procedural nature to the conceptual level
Summary
Introduction and MethodologyGeometry appears at two levels in school mathematics. At the first level, plane and space shapes, relationships, constructions, proofs, etc. are introduced to pupils. Geometry provides support for arithmetic and algebra. Pupils can be strongly dependent on the visualisation of arithmetic and algebra. Some pupils are able to understand the additive structure of integers already in the second grade of the primary school with the help of a number line, but without it, they cannot carry out additive operations with negative numbers even in the eighth grade. The goal of the study is to provide examples of how geometry can help in understanding arithmetic or algebraic concepts, processes, relationships and arguments. A superficial approach which enables pupils to “meet the requirements of knowledge reproduction” changes due to visualisation into a deep approach which enables them to “really understand the subject matter” A superficial approach which enables pupils to “meet the requirements of knowledge reproduction” changes due to visualisation into a deep approach which enables them to “really understand the subject matter” (Mareš, 1998, p. 39)
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