International Journal of Curriculum Development and Practice
Online ISSN : 2424-1415
Print ISSN : 1344-4808
ISSN-L : 1344-4808
Geometric Construction as a Threshold of Proof : The Figure as a Cognitive Tool for Justification
Hideki IwasakiMasakazu Okazaki
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2001 Volume 3 Issue 1 Pages 57-64

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Abstract
Geometric construction is usually considered as the procedure of drawing a figure bounded by a straightedge ruler and a compass. It, however, could be didactical intermediate between a cause-effect and an assumption-conclusion explanation because it is not only a series of systematic activities using only two tools but also mathematical proof of existence in itself. We, therefore, consider it as a educational threshold of proof in system although most mathematics teachers emphasize its procedural aspect. We analyzed the justification of the geometric constructions made by seventh grade students in the classroom lessons in terms of image schema. Image schema was developed for a meaning-making function by Dörfler(1991). It was made available for us to clarify the logical or cognitive base of the students' justification and change of thought. This research finally showed some factors for the transition from construction to proof in geometry.
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© 2001 Japan Curriculum Research and Development Association
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