本研究要探討的是學生對於課堂中教師作的幾何推理證明的學習情形，並且試圖從教師的教學中尋找影響學生學習的可能原因？
本研究進入學校數學課堂，實地觀察並拍攝教學實錄，作為分析教師教學對學生學習之影響的資料，並設計兩式開放程度不同的問卷，收集學生主動憶取和被動憶取教師所做推理證明的表現。
本研究藉由學生對於教師所做推理證明中所含的主要成分、局部推理、邏輯序列、重要轉折的抓取情形，來分析學生習得教師的推理證明的情形。
此外，除了分析各觀察班級學生習得幾何推理證明之情形，本研究試圖比較三個觀察班級中，學生程度相當的學生在習得教師推理證明情形之差異，再分析教師課堂教學，探討教師教學對學生習得情形差異之可能影響為何？
主要的研究結果有：第一、學生對於教師作的是「證明」或是「說明」的重視程度不同。學生較容易抓取到形式化證明的結構，而說明解釋方式的推理證明，學生反而不易抓取到主要成分。第二、學生對於應用已經形成概念之性質的局部推理，常出現的是僅寫出結論的斷言形式，或是直接應用在其他局部推理中，而不會做出該局部推理。第三、學生在憶取教師的推理證明時，鮮少與教師完全相同，有時會嵌入學生自己的局部推理、自創的紀錄格式、可接受但不同於教師的邏輯序列，也就是說某種程度可以看到學生將教師推理證明內化為自己的推理證明的現象，而不僅是完全地模仿教師的推理證明。第四、國中教師的幾何推理證明教學，仍是以講述教學為主，若能搭配問答，提出開放度較高的問題、多利用板書和圖形、避免過高的教學主題密度、提供學生重複經歷相同或相似的推理證明歷程…等教學手法及教學內容安排，應能幫助學生習得教師所做的幾何推理證明。

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