図形指導における視覚化の機能に関する研究

概要

論文の詳細を見る
The main purpose of this study is to reflect upon the teaching of geometry from a viewpoint of visualization. If the meanings and the roles of visualization in the teaching of geometry would be recognized, then the characteristics of the teaching of geometry in elementary mathematics are also to be clarified. There have been many researchers who investigated the characteristics of visual recognition on the concept of geometry: Pimm, Bishop, van Hiele, Hoffer, Triadafillidis, Vinner, Fischbein and so on. But their works were restricted within narrow specific regions that were to regard the visual recognition as an initial stage in the developmental process of the concept of geometry or as a nuisance in the teaching of geometry. I insist on the need to recognize the important roles of visual recognition and to make the best use of it positively. From reference to the researches about visualization, the functions of visualization in the teaching of geometry can be prescribed as follows. Functions of Visualization ◎Visual Interpreting Function: Understanding, reading and interpreting the visual representations and spatial vocabulary used in geometrical works, graphs, diagrams of all types. (It also involves meanings of figural representation) ◎Visual Processing Function: Visualizing and translating abstract relationships and nonfigural information into visual terms. It also includes the manipulation and transformation of visual representation and visual imagery. ○Translating Function ・translation between different types of representations ・dimensional change from 3D to 2D, from 2D to 3D and so on ○Mental manipulating Function ・transformation (geometrical transformations) ・figural change (partition and composition) A keen interest has been shown only into the visual interpreting function because of the progress of information processing researches about a way of looking at figures and developmental process of the concept of geometry. But the visual processing function has not so interested in. Therefore I investigated the characteristics of the visual processing function both in problem solving situation and in reasoning process. In problem solving situation, the translating function from linguistic representation to figural representation and the mental manipulating function were recognized. For example in "rectangle problem", mental manipulation of partial figure fills crucial role. From the result of questionnaire I identified the weakness of visual strategies and the necessity of visualization in problem solving situation. In reasoning process, there exist three types of cognitive stages: a purely configural stage (visualization), a natural discursive stage, and a theoretical discursive stage. Visualization embodies an initial stage of reasoning process that is independent from other stages and indispensable for next discursive stages. Therefore it cannot to be lacked in reasoning process. What is significant on the teaching of geometry in elementary mathematics from a viewpoint of visualization is to become conscious of the mental manipulating function which would be a key function as a strategy of problem solving and as a basis of reasoning process.

図形指導における視覚化の機能に関する研究

スポンサーリンク

概要

著者

関連論文

スポンサーリンク