- 學位論文
幾何(圓)證明題的解題策略
The Strategies of Solving Geometric Proof Problems of Circles
摘要
幾何往往是國中生最容易遭遇困難的部分，尤其是圓的部分更為明顯，更容易放棄學習。一個優秀的教育者，除了觀察學生的學習狀況之外，也要建立學生對幾何的畫圖及思考能力，能給予學生引導思考。 本研究所討論的題目以國中三年級(九年級)第二單元圓為基礎，整理相關題型，並分析解題策略，以及引領學生的思考方向。 研究目的： (一) 學生有步驟及方向的思考，並完整寫出證明。 (二) 希望學生可以透過幾何思考，能活用圓的相關概念。 (三) 希望學生利用證明後的結果，延伸證明。 (四) 希望學生能了解等圓與共圓的相關性質。 本研究只針對探討利用等圓與共圓的證明提供解題策略。在教學上，建立先備的知識概念，利用片段的證明方式，引導學生思考，並建立解題的策略，以達到國中數學課程綱要上的核心能力之推理能力及連結能力。
並列摘要
Geometry is always the most difficult problem which junior high school students encounter.Students even feel frustrated and may give up learning especially when facing the chapter of circle. As excellent educators, what we need to do is not only to observe the learning situation of the students but also to build up their ability of drawing and thinking about geometry, leading them how to deal with problems. The topic of the research is based on the Unit Two “Circle” of the ninth grader of junior high school. It aims to how to clarify the related questions, how to analyze the problem-solving strategies and how to instruct the students to figure out the problems. The purpose of the study is as follows: (a) The students know how to figure out the problems step by step and estabish the ability to write out the solutions of the proof questions. (b) The students have the ability to apply the geometric thinking to the related ideas about circle. (c) The students have the ability to extend the prove by using the result of the prove. (d) The students can understand the related properties of congruent circles and concyclic. The study only focuses on how to provide the problem-solving strategies by using the proof of congruent circles and concyclic. In teaching, it’s important to build up the prerequisite knowledge, guide the students to think by using the way of the proof of the fragment and build up the problem- solving strategies. So that we can achieve the inferential capability and the linking ability of the core competencies of the junior high school mathematics curriculum guidelines.