本研究比較使用與不使用GSP之解題情境對於幾何解題時間、表徵方式、解題策略與反思行為之影響。採質性研究取向。研究對象取自台北縣市三所學校之四名學生，具高數學學習成就與熟練操作GSP，並非隨機取樣。研究工具有兩項，一為《幾何評量測驗》，內容為四道幾何問題，問題內容包括幾何變換、四點共圓、全等證明及平行線性質，其特色為難度高且圖形複雜。此工具由兩位具有豐富經驗的老師建立專家效度，所建立用以分析解題表徵、過程策略及反思行為之編碼原則的評分者信度(inter-rater reliability)為.82。另一工具為《GSP操作檢定》，該工具之設計係根據本研究之幾何評量測驗中可能用到的GSP操作技能，進行檢測，目的為確認受測者具備相關幾何知識且熟練操作GSP的動作技能。內容為八道作圖題，其評分者信度為.98，重測信度為.80。先施測《GSP操作檢定工具》，通過者進行放聲思考的訓練，實施《幾何評量測驗》，每一道題均有兩位受測者以GSP解題，另兩位以紙筆解題，針對施測內容進行訪談。研究結果如下：一、GSP組的解題者較非GSP組的解題者解題平均時間約快12分鐘，原因在於GSP能提供較固定且清晰、精確與可操作的圖象表徵以及動態操弄圖形的功能，易形成視覺發現；二、GSP環境有利於圖像表徵的形成與操弄，卻可能抑制代數符號的運算；三、紙筆解題者對問題的表徵方式為符號與圖象並重，進而影響其採用多元的解題策略與較多的反思行為；四、使用GSP解題者對問題的表徵方式以圖形為主，解題策略受GSP圖形操弄功能之影響，反思行為中質疑多於預見；五、非GSP解題者的繪圖反應解題者對於問題的整體理解，GSP解題者則透過繪圖理解問題：六、幾何知識、GSP操作技能、空間操弄能力以及與GSP的「對話」能力均為採GSP進行幾何解題成功與否的關鍵因素。研究對於GSP的解題者、幾何教學及未來研究等三方面提出建議。

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