臺灣博碩士論文加值系統

本研究主要的目的在探討七年級學生在學習三種多邊形內角和解題方法後，對學生形成一般化解題公式的影響以及推論一般化解題公式的過程可能遭遇之困難。研究對象為桃園縣楊梅市某七年級數學學習低成就三十位學生。本研究使用動態幾何軟體設計出三種解決多邊形內角和的方法，分別是除了使用課本所教授「切割多邊形成多個三角形以求多邊形內角和」方法，另外還多加了「堆砌三角形以求多邊形內角和」與「多邊形內一點與各頂點做連接線以求多邊形內角和」兩種解題方法。研究結果為：
1. 傳統課本的解題方法對學生求解固定邊數的多邊形內角和較容易，但非課本討論的解題方法（多邊形內一點與各頂點做連接線以求多邊形內角和）對看出多數形邊數與內角和的關係是較容易的。
2. 學生推導多邊形內角和一般化公式的困難，除了是因為沒有掌握構成多邊形邊數與三角形個數的關係之外，最大的困難仍是對文字符號意義的不了解。

The study aimed to explore the influence of the 7th graders to formulate the general formula after learning one of the solutions to the Angle Sum of Polygon. The researcher also examined the difficulties of the ratiocinated process. The chosen participates were the 30 lower achiever students at a selected junior high school in Taoyuan County in Taiwan. The research designed three solutions to angle sum of polygon with dynamic geometry software. It included the first solution of “computing angle sum of polygon by cutting polygon to triangles” from the textbooks; the second solution of “to compute angle sum of polygon by piling triangles”; and the third solution of to calculate angles by making lines between one point in the polygon and the other vertexes”. Results of the study generated from qualitative way as following:
1. Traditional solutions were easier for participants when solving the Angle Sum which had fixed sides, such as the Angle Sum of quadrilateral, pentagon, hexagon, and heptagon. However, from the result of findings, the third solution was helpful for participants to solve the questions of Angle Sum of Polygon.
2. The difficulties of the ratiocinated process that participants encounter included two aspects. In addition to the incomprehensible relationship between the side of Polygon and the amount of triangle, the participants could not realize the meaning of words or phrases literally caused the biggest baffle.

目次
摘要 I
Abstract II
謝詞 III
目次 V
圖次 VII
第一章 緒論 1
第一節 研究背景與動機 1
第二節 待答問題 3
第三節 名詞釋義 3
第四節 研究範圍與限制 5
第二章 文獻探討 7
第一節 資訊科技融入教學的意義與目的 7
第二節 數學論證 10
第三節 算術思維與代數思維 12
第四節 國小與國中有關多邊形內角和探索的教材分析 23
第三章 研究方法 31
第一節 前置研究 31
第二節 研究設計 32
第三節 研究對象 33
第四節 研究工具 34
第五節 實施步驟 38
第六節 資料處理與統計 40
第四章 研究結果與討論 41
第一節 學生對三角形內角和與多邊形的基本認識 41
第二節 以堆砌三角形以求多邊形內角和的過程對推論多邊形內角和
一般化公式的影響與學生的學習困難 46
第三節 以切割多邊形成多個三角形以求多邊形內角和的過程對推論
多邊形內角和一般化公式的影響與學習困難 55
第四節 以多邊形內一點與各頂點做連接線以求多邊形內角和的過程
對推論多邊形內角和一般化公式的影響與學習困難 69
第五章 結論與建議 79
第一節 結論 79
第二節 建議 81
參考文獻 85
一、中文部份 85
二、英文部份 87
附錄 95

圖次
圖2-1 Toulmin的論證模式 11
圖2-2 國小求三角形內角和的剪紙活動 24
圖2-3 各式多邊形的名稱介紹 24
圖2-4 切割多邊形成多個三角形以求多邊形內角和 25
圖2-5 國中三角形內角和的剪紙活動 26
圖2-6 切割四邊形成兩個三角形以求多邊形內角和 27
圖2-7 切割五邊形成三個三角形以求多邊形內角和 28
圖2-8 切割六邊形成四個三角形以求多邊形內角和 28
圖3-1 研究步驟實施流程圖 38
圖4-1 編號10號學生的作答情形 53
圖4-2 編號18號學生的作答情形 64
圖4-3 編號19號學生的作答情形 65
圖4-4 編號21號學生的作答情形 66
圖4-5 編號22 號學生的作答情形 68

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