A Study on the Meanings of Geometrical Sense in the Teaching of Geometry

Abstract

There are many students who have suitable knowledges about geometry but can't solve geometrical problems due to lack of the sensorial aspect of geometry. Generally speaking geometrical sense has a crucial feature for the teaching of geometry in the following days. But the meanings of geometrical sense is very vague for us. The main purpose of this study is to clarify the meanings of geometrical sense in the teaching of geometry. To clarify the nature of geometrical sense I classified it from phenomenological viewpoint as below. <Geometrical Sense> ◎External Sense: geometrical perception about external object or figure ◇Perceptual Intuition: perception of concrete entity (visual perception about the spatial aspects of geometrical figure: shape, size, position) ◇Essential Intuition: perception about ideal meaning of geometrical figure (linguistic perception about the essential meanings of geometrical figure or geometrical relation) ◎Internal Sense: perception about individual situation to the external object ◇Value Judgement: perception about "goodness" (directional and intellectual perception for judgement and selection of geometrical information) ◇Emotional Sensibility: perception about "beauty" (individual perception about sensibility for geometrical figure: beauty, stability) The characteristics of geometrical sense are explained by next five points of view: individuality, unconsciousness, interest, simplification and perception. Especially "perception" is an essential feature which characterizes geometrical sense. So I tried to enumerate the perceptual functions of geometrical sense and analyzed each of them by case-study. <Perceptual Functions> ・Plane Perception Part and Whole: "Gestalt" and "Figure and Ground" Synthesis and Analysis: "Perceptual Construction" and "Perceptual Transformation" ・Spatial Perception "Perceptual Constancy" and "Back and Forward Perception" To promote the growth of geometrical sense is an essential aim of the teaching of geometry both in elementary school and in junior high school. Especially in elementary school, the sensibility for "beauty" of geometrical figure and the "richness" of geometrical sense are taken notice of. And in juniore high school, the "sharpness" of geometrical sense is particularly considered.