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The Problems of Mathematical Reasoning on Teaching Geometry

Bulletin of the Faculty of Education, Yamaguchi University Volume 34 Page 97-108
published_at 1985-01
Title
図形指導における数学的推論の課題 (I)
The Problems of Mathematical Reasoning on Teaching Geometry
Creators Iwasaki Hideki
Source Identifiers
Proof has two aspects in the from of thinking. Plato said that one is synthesis which goes asendently in cognition, and the other is analysis which goes descently. Methematical reasoning is the key concept of new teaching gemetry of grade 7. It is clarified when we compare a new text with old one and research into the mathematical course of study. Mathematical reasoning has two educational problems. One is the Necessity of deduction and the other is the strictness of deducion. Philosophical ambiguity of the proof corresponds with two problems of mathematical reasoning. We can conprehend the problem of the necessity of deduction in the light of synthesis and the strictness of deduction in light of analysis. Necessity and Strictnss of deduction are logically interrelated and dependent upon each other in the content of teaching geometry. Locally axiomatic, which is proposed by Freudenthal, H. and Schuster, S. independently, is considered as the point of view which integrates the necessity and strictness of deduction. The problems of mathematical reasoning are oriented to solutions in the terms of locally axiomatic.
Subjects
数学 ( Other)
Languages jpn
Resource Type departmental bulletin paper
Publishers 山口大学教育学部
Date Issued 1985-01
File Version Not Applicable (or Unknown)
Access Rights metadata only access
Relations
[ISSN]0286-0597
[NCID]AN00240238
Schools 教育学部