空間的思考の階層性に関する考察 : 大局的特徴づけとその具体化

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概要

• 論文の詳細を見る

• In psychology and mathematics education, the variety of problems about spatial ability, visualization and the relation between students' mathematical performance and them, have been studied. But the clear definition of spatial ability among researchers is not given yet, and more important, I think that studies focus on what students think (mathematically) during working the tasks are few. Then in this article, I defined spatial thinking as the integration of spatial ability in a sense of psychology and mathematical thinking, and characterized it globally from a point of both of levels of thought and its components. And I concreted the framework after these works by aligning educational contents and possible performances to each levels and components. First, I applied van Hiele levels (except for 5th level) to 3D geometry with having the nature of spatial thinking, and labeled each 4 levels - recognition, analysis, informal reasoning, formal reasoning - taken into account the characteristic of thinking. Secondly, I made the components of spatial thinking explicit by examining preceding studies, in order to understand the mode of thinking in detail as following: ・imaging and visualization ・representation ・spatial reasoning And, I indicated according to Duval (1998) that these components interact with each other in the context of learning geometry. Finally, I constructed the framework of spatial thinking by utilizing 4 levels of thinking and 3 components and concreted it after these works by aligning educational contents and possible performances to each levels and components.

• 全国数学教育学会の論文

著者

• 影山 和也

  広島大学大学院

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• 空間的思考の階層性に関する考察 : 大局的特徴づけとその具体化

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