实验几何、勾股定理与蒙特梭利

Q3 Multidisciplinary
Circe Mary Silva Silva
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引用次数: 0

摘要

背景:一些19世纪和20世纪的几何教科书显示了与遵循欧几里得逻辑演绎建议的传统书籍相关的方法论创新。目的:分析玛丽亚·蒙台梭利(1934)所著的《几何学:婴幼儿几何学estúdio》一书中,她提出的毕达哥拉斯定理的教学方法是否适合实验几何视角。设计:采用文献分析的方法,我们分析了以下作者的著作:ho(1867),姆萨雷(1874),莱桑(1898,1906),卡尔金斯(1861),伯特(1886),普雷斯特斯(1895),莱拉·达·西尔瓦(1923),温特沃斯和希尔(1901)和蒙台梭利(1916,1934),以了解几何教学的方法。环境和参与者:法国国家图书馆(BNF)和圣卡塔琳娜联邦大学(UFSC)数字资源库中收集的研究来源是指来自四个国家的作者的地理环境数据收集和分析:所选和分析的文件可以在BNF - Gallica找到数字化版本,也可以在UFSC数字资源库中找到。基于对这些书籍的文献分析,我们发现,方法论建议试图摆脱初等几何的演绎呈现,并在其文本中包含介绍初等几何概念和视觉演示的经验。结果:来自不同国家的作者对初等几何教学提出了批评,尤其是教科书的作者,因为他们在初等课程中采用演绎几何的方法,倾向于用演绎的方式来表达数学。蒙台梭利的书展示了毕达哥拉斯定理的实验几何方案。结论:我们发现蒙台梭利的提议除了呈现出实验几何的特征外,还插入了一些演绎推理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Experimental Geometry, Pythagorean Theorem and Montessori
Background: Some 19th and 20th-century geometry textbooks show methodological innovations in relation to the traditional books that followed Euclid's logical-deductive proposal. Objective: To analyse in the book Psico Geometria: el estúdio de la geometria basado en la psicologia infantil by Maria Montessori (1934) as the didactic approach of the Pythagorean theorem, proposed by her, fits into an experimental geometry perspective. Design: Using documentary analysis, we analysed the books of the following authors: Hoüel (1867), Méray (1874), Laisant (1898, 1906), Calkins (1861), Bert (1886), Prestes (1895), Lyra da Silva (1923), Wentworth and Hill (1901) and Montessori (1916, 1934) to understand the approach to teaching geometry.Environment and participants:The research sources collected in the National Library of France (BNF) and in the Universidade Federal de Santa Catarina (UFSC) Digital Repository refer to the geographic environment of authors from four countries Data collection and analysis: The selected and analysed documents can be found at BNF – Gallica in a digitized version, as well as at the UFSC Digital Repository. Based on the documentary analysis of these books, we found that the methodological proposals seek to escape from a deductive presentation of elementary geometry and include in their texts experiences for the introduction of concepts and visual demonstrations of elementary geometry. Results: The authors of the analysed works, from different countries, criticized the elementary teaching of geometry, especially the authors of textbooks, for the fact that they approach deductive geometry in the initial classes, favouring a deductive presentation of mathematics. Montessori's book shows an experimental geometry proposal for the Pythagorean theorem. Conclusion: We found that Montessori's proposal, besides presenting characteristics of an experimental geometry, also inserts some deductive reasoning.
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来源期刊
Acta Scientiae
Acta Scientiae Multidisciplinary-Multidisciplinary
CiteScore
0.70
自引率
0.00%
发文量
43
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