本研究的目的為：(1) 探討中學生在幾何證明閱讀理解認知面向上的特徵，(2) 探討知識和邏輯對中學生幾何證明閱讀理解的影響。希望基於實徵研究的結果，除了在理論上擴充數學理解的認知發展，也在實務上提出可統整獲取知識、建立邏輯與理解數學證明的假設性學習路徑。本研究係採質與量兼併的方式進行幾何證明閱讀理解的分析，希望透過調查研究法探討中學生在幾何證明閱讀理解的實際表現和自我評估，以及瞭解知識和邏輯推理因素對於此表現的解釋力。另一方面，也希望透過訪談研究法對於學生評析幾何論證有效性的思考特徵作進一步的探討。研究的主要結果為：
一、幾何證明閱讀理解的面向包含：表層理解、邏輯定位理解、摘要統整理解、一般性理解、應用推廣理解和賞析理解。
二、邏輯定位理解在學生實際表現和自我評估上佔有不同的地位。學生主要以偏向評估表層理解的標準來評估「為什麼」某些步驟是正確的，但當以區分邏輯和認識上的真以及辨識所引用的性質或事實來測量學生是否真正理解「為什麼」時，其表現結果和表層理解表現的相對關係就低於學生在這兩個面向上自我評估的相對關係。
三、以知識和概念情境中直接確認邏輯二個變項預測國三學生在一階段幾何證明閱讀理解表現，結果可以解釋總變異的54%；也以這二個變項預測國三學生在二階段幾何證明閱讀理解表現，結果可以解釋總變異的32%。
四、中學生評析幾何論證有效性的思考特徵有「不當特殊化論證過程」以及「過度一般化論證過程」。可能造成不當特殊化論證過程的認知方式有：(1)以數字檢驗形式證明；(2)受限於未畫出來的圖形；(3)把例子中的某種規律視為前提。可能造成過度一般化論證過程的認知方式有：(1)擴充演算法或動態圖形的有效性； (2)強化圖形或數字的效用；(3)開放前提或結論的位置；(4)增加前提或結論的強度。
五、除了知識和邏輯外，本研究進一步闡述述三種妨礙學生進一步理解幾何論證的因素：(1)未意識到自己誤解的可能性；(2)未區辨證明與解說的不同；(3)排斥或不喜歡不瞭解的資訊。
六、幾何證明閱讀理解層次包含：表層理解、辨識元件理解、鏈結元件理解和膠囊化理解。分析各理解層次間的實際表現，發現幾何證明閱讀理解層次的發展可能有兩類，一是從表層理解、辨識元件理解、鏈結元件理解至膠囊化理解層次循序漸進地發展，本研究稱為「關係性理解型態」；二是從表層理解跳至膠囊化理解層次，再回到辨識元件理解和鏈結元件理解間的發展，本研究稱為「工具性理解型態」。

根據上述的結果，本研究對於幾何論證的教學提出一個關於獲得知識、建立邏輯與解讀幾何論證間的假設性學習路徑，如下圖。以概念心像為學習起點，分別經由表層理解、辨識元件理解、鏈結元件理解發展至膠囊化理解，本研究所建議的學習活動有：閱讀策略的引導，情境中邏輯判斷的練習，下定義過程的經驗，局部推理的嘗試，連結概念情境和記號情境的邏輯判斷，自我評估和實際表現的衝突，圖文互相轉換的協調，應用導向的論證問題。

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