本研究採用個案研究法，藉由對個案所搜集的資料進行分析，目的在找出個案學生對圖論概念的想法與認知架構，並探討影響個案學習成就低落的因素。本研究發現：在「圖論」課程中，學生在証明題上的作答能力與學習成就有相當的關聯；而「師生互動」和「同儕討論」對學生概念的發展有絕對正向的影響。最後根據研究中所發現的結果，提出幾項建議，以做為未來「數學課程」在教學上的參考。

A case study was used to study a junior student’s conceptual understanding of graph theory. Factors that affected the learning achievement were also explored in this study. Research results showed a relationship between proof ability and learning achievement. Teacher-student interactions and peer discussions are also found to affect the student’s conceptual development. Suggestions of teaching based on this study are included.

中文摘要 i
英文摘要 ii
目錄檢索 iii
第壹章　緒論 1
第一節　研究動機 1
第二節　研究目的 1
第三節　名詞釋義 2
第四節　研究限制 2
第貳章　文獻探討 3
第一節　建構主義的探討 3
第二節　認知發展的探討 4
第三節　概念圖的研究及其應用 6
第四節　迷思概念 7
第五節　圖論的應用與本研究探討之概念 9
第參章　　研究方法設計 14
第一節　研究問題 14
第二節　研究對象 14
第三節　研究方法與步驟 14
第四節　資料搜集 16
第五節　資料處理與分析 16
第六節　研究流程 17
第肆章　　結果與分析 18
第一節　「圖論」課程 18
第二節　個案的學習歷程 19
第三節　小強在晤談、寫作業與答考卷呈現出之錯誤概念 26
第伍章　　結論與建議 46
第一節　結論 46
第二節　個案對「數學課程」之教學提出的建議 47
第三節　研究者與「圖論」授課教師對「數學課程」之教學提出的建議 47
參考文獻 50
附錄一：同意書 55
附錄二：教室觀察記錄表 56
附錄三：課程進度表 57

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