國中生線對稱概念學習研究

陳天宏

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College of Science > In-service Master's Program, Department of Mathmatics

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國中生線對稱概念學習研究

The Study of Junior High School Student’s Symmetry Concept Learning

陳天宏 , Masters　　Advisor：左台益　　

繁體中文

線對稱；概念心像；概念定義；典範現象；動態連結多重表徵（GSP）之實徵教學； Line-symmetry ； Concept image ； Concept Definition ； Prototypical ； Dynamic-Link multiple characteristics

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Abstract
Symmetry is not only one of the most beautiful modeling in the natural world, but also the important concept in Mathematics.　Recently, the ‘6-15 Curriculum Syllabus’ for elementary and junior high schools in Taiwan. Especially in the domain of Mathematics, was clearly defined the development of ability of symmetry concept.
The major work of the first part of this paper is researching junior high school students’ concept image which carried from their line-symmetry concept, and proceed to the next step is analyzing the lost concept and the reasons it occur. In the meantime, we select qualitative research of case studies and adopt statistic investigate of questionnaire. In accordance with the intension of the concept image ： Prototypicality 、Part-Whole Reasoning and Attribute Understanding , we designed tools for interviewing and testing .
According to their Mathematics grade , we took apart second grade students form junior high school to three levels : higher、middle and lower , and selected two students in each level for case studies to analyze their contexture of line-symmetry concept. Two classes a grade in Taipei,  about two hundred students, we used an open questionnaire to analyze the understanding、operating、enginery using and lost of their line-symmetry concept.
The second part of this paper is structured by Geometry development level ( Van Hiele,  1984)，depending on this idea, the questionnaire for line-symmetry concept was designed . Three classes a grade, we selected nine classes about three hundred students from three grade of junior high schools in Taipei area to be the object of the questionnaire. From this research we understood the development of line-symmetry concept of students who were in junior high school.
The third part of this paper is based on previous results. Collocated theories of mathematics learning and previous results, we develop teaching materials for experiment. We selected two classes in second grade of junior high school for experiment of teaching and learning of line-symmetry concept. The one recommend GSP (The Geometer’s Sketchpad) which is dynamic-link multiple characteristics teaching and learning environment, and the other in traditional teaching environment is to comparison.
 The results of our research reveal three points :
(1)    The line-symmetry concept of students of junior high school has Prototypicality of vertical or horizontal symmetry axle. Instead of using definition of concept, they always use prototype model of concept image to solve problems .
(2)    On first and second thinking levels of line-symmetry concept of junior high school’s students almost reach intermediate acquisition.
(3)    In GSP learning environment of dynamic-link multiple characteristics, the operation of students’ concept is actively, and the exclusiveness of prototypical is lower than traditional environment. In aspect of development of concept, the class of experiment has promoted to higher grade in third and fourth thinking level. But the lower level students of this class have not clear advancement in each thinking level.
So we conclusion that for the purpose of learning more smooth and more complete, the teacher should pay attention to the situation of students’ learning and summarize important concept in suitable time although in dynamic-link multiple learning environment.

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