國中生建構幾何概念之研究暨統整式合作學習的幾何教學策略效果之評估

A Study of the Way of Students' Constructing Geometry Concept and the Evaluation of the Effects of Geometry Teaching Strategies with Integrated Cooperative Learning

本研究目的有四：1．瞭解國中生學習幾何概念時所產生的錯誤概念。2．分析學生建構幾何概念的認知歷程。3．針對國中生在建構幾何概念時所可能發生的錯誤概念，設計出適合國中生建構幾何概念的教學策略方案。4．以統整式合作學習的方式進行幾何教學，並以實徵研究的方式考驗幾何教學策略方案對國中生幾何概念學習時的學習效果。研究工具包括：幾何測驗卷、動機信念量表、後設認知量表等。研究方法包含兩部份，一是針對學生幾何學習時的錯誤概念進行質的研究，另一方面是以實徵研究的方法進行統整式合作學習的幾何教學策略效果的評估。資料分析時，先以三角檢核法進行質的研究部分的效度考驗，再以單因子共變數分析、單因子多變項共變數分析進行量的研究部分的假設考驗。結果發現：1．國中生在幾何學習時有系統性錯誤概念存在。2．「學生生手」思考幾何概念與「學生專家」思考模式有差異存在；而「學生專家」思考模式也與「教師專家」思考模式有差異存在。3．進行統整式合作學習的幾何教學策略後，實驗組的受試在幾何測驗卷上的得分高於控制組的受試。4．進行統整式合作學習的幾何教學策略後，實驗組的受試在「後設認知」中的「自我調整」因素上的自我監控與自我評鑑的得分高於控制組的受試。5．進行統整式合作學習的幾何教學策略後，實驗組與控制組學生在「後設認知」中的「執行控制」與在「動機信念」兩大因素上整體的得分有差異存在。本研究建議：教師在幾何教學時，可採統整式合作學習的方式，以幫助學生瞭解個別學習、競爭學習與合作學習的方法，並建構出正確的幾何概念。

The purposes of the study were: (1) to understand junior high school students' misconceptions in learning geometry; (2) to analyze students' cognitive process in constructing geometry concept; (3) to design an appropriate teaching strategy program for junior high school students to improve their misconceptions in geometry; and (4) to examine the effects of the teaching strategy program with integrated cooperative learning on students' concept in geometry learning. The research instruments in the study included Geometry Test, Motivational Belief Inventory, and Metacognition Inventory. The study was divided into two parts. The first part was to explore the students' misconceptions in learning geometry with the use of qualitative analysis. The second part was to examine the effects of taching strategy program with integrated cooperative learning by means of empirical study. The collected data were analyzed by triangulation, one-way ANCOVA, and one-way MANCOVA. The results were as follows: (1) Junior high school students students have systematic misconceptions in geometry learning. (2) There were differences between novice and expert students in geometry concept thinking modes, and there were differences between teachers and expert students, too. (3)After the experimental group accepted the teaching strategy program, the subjects of Experimental Group had higher scores on Geometry Test than those of control group. (4) The subjects of experimental group had higher scores on self monitoring and self evaluation than those of control group. (5) There were differences on executive control and motivational belief between experimental group and control group. Based on the findings, the study suggested that the teachers should use integrated cooperative learning in teaching geometry to help the students know the methods of individualized learning, competetive learning and cooperative learning, and to help them construct correct geometry concepts.