幼兒幾何形體概念發展研究

Young Children's Conception of Geometry

本研究透過文獻探討建立幼兒幾何形體概念發展架構並發展幼兒幾何形體概念評量工具，藉以及瞭解幼兒幾何形體概念發展現況。研究對象為台北市小、中、大班共217 位幼兒。研究結果如下：一、幼兒幾何形體概念發展架構乃基於皮亞傑拓樸為先，歐氏幾何與投影幾何在後的概念，並以完形心理學知覺說與福祿貝爾、蒙特梭利的教具哲學為基礎，假設幼兒的立體幾何概念發展先於平面幾何概念。二、本研究發展之幼兒幾何形體概念的評量可有效蒐集幼兒描述立體及平面幾何所使用的詞彙與其分類表現、以及幼兒透過觸覺對立體幾何的認知，並可檢測幼兒對立體幾何的正投影映象。三、幼兒能以日常生活中的物件形容立體幾何，但說出正確名稱則非常困難；就平面幾何，能說出圓形者最多；幼兒均能表現合宜的分類亦有其分類理由；幼兒對立體幾何的觸覺認知與正投影平面幾何視覺映象已發展良好。建議幼兒園的幾何形體課程可由日常生活物件開始介紹立體幾何正確名稱，再引導幼兒由立體幾何的正面投影來認識平面幾何。

This study was to establish the framework of young children’s conception of geometry, to develop an evaluation tool for young children’s conception of geometry, and to understand the development of young children’s conception of geometry. The subjects of this research included 217 preschool children from three classes in three different public preschools in Taipei. By using one-to-one interviews conducted through the evaluation tool for young children’s conception of geometry developed by the author, the results of this study were as follows: A. The first part of the framework of young children’s conception of geometry was established firstly from Piaget’s Topological primacy studies and secondly from Euclidean Geometry, Projective Geometry studies, the Cognitive Theory ofGestalt Psychology , and the instructional philosophies of Froebel and Montessori. This framework then assumes that the conception of 3-dimensional shapes is developed prior to the conception of 2-dimensional shapes. B. The evaluation for young children’s conception of geometry in this study was to collect the vocabulary and classification of 3-dimensional shapes used in young children’s descriptions, the vocabulary and classification of 2-dimensional shapes used in young children’s escriptions, the recognition of 3-imensional shapes through their touching the objects, and the projected images of 3-dimensional shapes perceived by young children.C. Young children can describe 3-dimensional shapes by referring to daily-life objects. However, it is rather difficult for them to name the shapes. For 2-dimensional shapes, what they can name correctly is circles. Young children also possess relevant reasons for their appropriate classifications, where they exhibit focus of thought. Their recognition of 3-dimensional shapes through touching and their visual projections of 2-dimensional shapes have already well developed. This indicated that young children was already well-equipped with good judgment and perception of geometrical shapes in their early years.