圓內接四邊形的解題策略

本研究主要目的是探討數學教學上相關的理論，應用其中理論，針對國中教材中「幾何」主題中的「圓心角、圓周角與弦切角」中的「圓內接四邊形」單元做解題設計，協助學生幾何中圓形相關概念的學習，並藉由相關文獻，了解學生學習上問題的所在，填補學生不熟或不易掌握的概念，進而建構針對圓內接四邊形的解題策略。普遍的教育學者、包括在前線教導的教師都認為，任何知識的學習都是由淺而深、循序漸進的，數學也不例外，是由最基本的觀念開始；所以在撰寫這篇解題策略時也是依照這點原則，由淺而深的編序方式讓學生理解圓內接四邊形幾何的概念，讓學生能夠充分的運用這些概念進而理解題目本身的意義。本研究主要是分析各版本的教科書，並進行一定程度上的整合，提供授課教師做為參考，此研究分成四部分一、緒論二、文獻探討三、解題策略四、反思與結論自從學生的教材不由國立編譯館統一提供，而是改為一綱多本的方式讓學校教師自行選用，各種版本的教科書教師有了多元的選擇，是優點也是缺點，教師在教學上應該依照學生的程度以及學生學習進度做調整，在幾何圖形上對於圓內接四邊形的教學上應由淺入深，先由圖形開始，循序漸進的教學，進而讓學生得到最完美的學習效果。本研究先針對學生對於幾何圖形的思考模式做探討，進而針對圓內接四邊形解題策略做分析。

關鍵字

解題策略；圓內接四邊形

並列摘要

The aim of this research is to explore the mathematics teaching theories. With applying to these theories, the researchers take advantage of Geography, named ‘Quadrilateral Inscribed in a Circle’ to create question solving design for the purpose of making students understand the learning concepts of Geography. Moreover, by means of literature review, understanding students' learning problems are capable of help the researchers to build new teaching materials Most educators as well as teachers think people must learn knowledge step by step, and mathematics is no exception. As a result, this teaching material is also based on this principle. By doing so, students are able to realize the concepts of ‘Quadrilateral Inscribed in a Circle’ so that they can fully utilize it to understand the meaning of the question itself. The purpose of this research is to analyze and integrate every version of textbooks into a brand new teaching material, which can be provided for teachers for reference. This research is divided into four parts: 1. Introduction 2. Literature Review 3. Problem-Solving Strategies 4. Discussion and Results Since the teaching materials are not provided by NICT, teachers can choose different teaching materials . Teachers must adjust students' learning progress via their levels. Students learned with the basic concepts of graphs initially before learning with the cyclic quadrilateral in the geometry. The method helped students to make significant progress from learning with basic concepts to advanced concepts. The present study investigated the students' thinking models involving in geometry and analyzed their problem-solving strategies of the cyclic quadrilateral.