幼兒幾何形體概念發展研究

Young Children's Conception of Geometry

李文貞

指導教授 ： 鍾志從博士

國立臺灣師範大學/教育學院/人類發展與家庭學系在職進修碩士班/碩士(2003年)

摘要

本研究之目的在於：建立幼兒幾何形體概念發展架構、發展幼兒幾何形體概念評量工具、以及瞭解幼兒幾何形體概念發展現況。研究方法以自編的幼兒幾何形體概念評量工具進行一對一施測晤談，輔以觀察、書面紀錄，以及錄影、錄音等方式蒐集資料。研究對象為台北市三所公立托兒所小班、中班、大班共217位幼兒。本研究主要結果如下：
一、幼兒幾何形體概念發展架構乃先基於皮亞傑拓樸為先，歐氏幾何與投影幾何在後的概念建立第一層架構，再依完形心理學知覺說與福祿貝爾、蒙特梭利的教具哲學，假設幼兒的立體幾何概念發展先於平面幾何概念的發展。立體幾何概念包括球體、正方體、長方體、圓柱體、橢圓體、三角柱、三角錐、圓錐、四角錐等。平面幾何概念包括圓形、正方形、長方形、三角形、橢圓形、菱形、梯形等。
二、幾何形體概念是指個體對平面幾何與立體幾何之名稱、外形、屬性等之認知。本研究發展之幼兒幾何形體概念的評量包含（一）「小蜜蜂奇遇記」藉以收集幼兒描述立體幾何所使用的詞彙與其分類表現；（二）「恐龍生病了」藉以瞭解幼兒描述平面幾何所使用的詞彙與其分類表現；（三）「神秘寶物」觀察透過觸覺幼兒對立體幾何的認知；（四）「小朋友眼睛照過來」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，但說其正確的名稱非常困難。對平面幾何的認識，能說出正確名稱的次序是圓形最多，其次依序為三角形、正方形、長方形。幼兒均能表現合宜的分類亦有其分類理由，其判準有思考集中傾向。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。此結果顯示：對於幾何形體概念的知覺判斷能力，幼兒已具備完好。幾何形體確與幼兒的生活經驗相關。只是，對於幾何形體概念的命名幼兒並不純熟，似乎與學習經驗有關。建議幼兒園的幾何形體課程可由日常生活物件與立體幾何相聯結，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。

關鍵字

幼兒幾何形體 ； 立體幾何 ； 平面幾何

並列摘要

This study is 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 include 217 preschool children from three classes, levels one to three, in three different public preschools in Taipei. The method of this research involves collecting data from one-on-one interviews conducted through the evaluation tool for young children’s conception of geometry developed by the author. More data are collected from supplementary observations and other sources of written, audio and video records. The results of this study are as follows:
A. The first part of the framework of young children’s conception of
geometry is established firstly from Piaget’s Topological primacy studies and secondly from Euclidean Geometry and Projective Geometry studies. This framework then assumes that the conception of 3-dimensional shapes is developed prior to the conception of 2-dimensional shapes, following the Cognitive Theory of Gestalt Psychology and the instructional philosophies of Froebel and Montessori Three-dimensional shapes include spheres, cubes, rectangular solids, cylinders, ellipsoids, triangular columns, triangular awls, circular awls, rectangular awls, and so on. Two-dimensional ional shapes include circles, squares, rectangles, triangles, ellipses, rhombuses, trapezoids, and so on.
B. The conception of geometry indicates an individual’s recognition of the name, shape and characteristics of a geometrical shape. The evaluations for young children’s conception of geometry in this study include 1) “Adventures of a Little Bee” is to collect the vocabulary and classification of 3-dimensional shapes used in young children’s descriptions, 2) “The Dinosaur Is Sick” is to understand the vocabulary and classification of 2-dimensional shapes used in young children’s descriptions, 3) “Mysterious Treasures” is to observe young children’s recognition of 3-dimensional shapes through their touching the objects, and 4) “Kids, Look Over Here” is to examine 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, and then triangles, squares, and rectangles respectively. 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 indicates that young children are already well-equipped with good judgment and perception of geometrical shapes in their early years. The recognition of geometrical shapes is indeed related to life experiences. However, the naming of the shapes seems to be more closely related to learning experiences, since most children scored lower in naming the shapes. Therefore, our suggestion is that preschools should teach 3-dimensional shapes by associating them with daily-life objects, introducing the correct names of those shapes, and guiding the children to identify 2-dimensional shapes from the projected images of 3-dimensional shapes.

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