本研究目的在從思考實驗、拖曳行動和動態表徵三個面向來探討與分析學生的幾何探索和推理論證過程。研究方法主要採取半結構的診斷活動方式，對二十四位數學系大學生在進行幾何作業時的觀察與訪談。以錄音及錄影方式收集原案資料，再採用質性分析，詮釋個案的探索歷程。
研究結果顯示：1.學生在動態幾何環境下的幾何探索架構包含拖曳行動、動態表徵以及思考實驗三個主要元素，三者的交互作用會影響個體的幾何探索與推理。拖曳行動的認知行為影響個體對動態表徵的解讀，動態表徵的解讀會激發內在思考實驗，思考實驗會引導拖曳行動，三者之間的交互作用形成一個幾何探索的循環系統。
2.學生在DGE下所發展出的思考實驗運作模式主要是以動態表徵外在的動態行為和內在的數學性質激發個體產生猜測，並透過模擬操作物件的動態行為來驗證猜測，進而產生宣告。學生通常模擬操作完後，會用GSP具體操作驗證自己的想法，或是當問題情境過於複雜或簡單時，會跳過模擬操作直接朝向具體操作圖形的方式來驗證猜測。
3.學生在作思考實驗的過程中，有時會發生有如與第三者論證的自我對話現象。這個虛擬的第三者常常扮演提供解題或反思的角色，而電腦的作用則是激發第三者的產生。
4.學生在DGE下所進行的幾何推理方式可分為幾何實驗、思考實驗和形式證明三大部分，其中思考實驗在推理過程中橋接幾何實驗(實驗歸納)與形式證明(演繹推理)。學生在幾何實驗中產生猜測或觀察動態表徵的變化，經由思考實驗來驗證猜測，並將推論的結果轉化為形式證明。

一、中文部分
左台益(2007)。動態心像與幾何學習之研究(3/3)。行政院國家科學委員會補助專題研究計畫期末成果精簡報告。
黃哲男(2001)。於動態幾何環境下國中生動態心像建構與幾何推理之研究。國立台灣師範大學數學研究所碩士論文，台北市。
鄭勝鴻(2005)。於動態幾何巨集環境下國中生證明概念與技能發展之研究。國立臺灣師範大學數學研究所碩士論文，台北市。

二、英文部分
Almeqdadi, F. (2000). The effect of using the geometer's sketchpad (GSP) on Jordanian students' understanding of geometrical concepts. Proceedings of the International Conference on Technology in Mathematics Education. July 2000. (ERIC Document Reproduction Service No. ED 477317).
Anapolitanos, D. A. (1991). Thought experiments and conceivability conditions in mathematics. In Horowitz. and Massey (Eds), Thought Experiments in Science and. Philosophy, pp. 87–97.
Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practices in Cabri environments. ZDM, 34(3), pp.66-72.
Balacheff, N.（1988）. ‘Aspects of proof in pupils’ practice of school mathematics’, in D. Pimm (ed.), Mathematics, Teachers and Children, Hodder & Stoughton, London, pp.216-235.
Chazan, D. (1993). High school geometry students’ justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24, pp.359-387.
Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2 , pp.215-222.
Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processing. In R. Sutherland & J. Mason (Eds.), Exploiting Mental Imagery with Computers in Mathematics Education, pp.142-157. New York, NY: Springer-Verlag.
Emmorey, K,. & Casey, S. (2001). Gesture, thought and spatial language. Gesture, 1, 35-50.
Fishbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics , 24, pp.139-162.
Furinghetti, F., & Paola, D. (2003). To produce conjectures and to prove them within a dynamic geometry environment: a case study.In Pateman, N. A. & Dougherty, B. J. & Zilliox, J. T.(eds), Proc. of the joint meeting PME 27 and PMENA, 2, pp.397-404.
Garuti, R., Boero, P., & Lemut, E. (1998). Cognitive Unity of Theorems and Difficulties of Proof, in Proceedings of the 22th PME Conference, Stellenbosch, South Africa, vol. 2 pp. 345-352.
Harel, G., & Sowder, L.(1996) Classifying processes of proving , Proceedings of the 20th PME International Conference, vol.3,Valencia, Spain, pp.59-66.
Hazzan, O., & Goldenberg, P., E. (1997). Students’ understanding of the notion of function in dynamic geometry environments. International Journal of Computers for Mathematical learning. 1. pp.263-291.
Healy, L., & Hoyles, C.(1998). Technical report on the nationwide survey: Justifying and proving in school mathematics. London: Institute of Education, University of London.
Hölzl, R. (1996). How does ‘dragging’ affect the learning of geometry. International Journal of Computer for Mathematical Learning 1(2), pp.169–187.
Hoyles, C., & Jones, K. (1998). Proof in dynamic geometry contexts. In: C. Mammana and V. Villani (Eds), Perspectives on the Teaching of Geometry for the 21st Century. Dordrecht: Kluwer. pp.121-128.
Irvine, A. D. (1991). Thought experiments in scientific reasoning. In T. Horowitz & G. J. Massey (eds.), Thought Experiments in Science and Philosophy, Rowman & Littlefield Publishers, Inc., Savage, MD, pp. 149–165.
Laborde, C. (1993). The Computer as part of the learning environment: The case of geometry. In C. Keitel and K. Ruthven (eds.), Learning from Computers: Mathematics Education and Technology, NATO ASI Series, Vol. 121, Berlin, Heidelberg, pp.48-67.
Lopez-Real, F., & Leung, A. (2006). Dragging as a conceptual tool in dynamic geometry environments. International Journal of Mathematical Education in Science and Technology, 37, pp.665-679.
Mariotti, M. A. (2001a). Justifying and proving in the Cabri environment. International Journal of Computers for Mathematical Learning, 6, pp.257-281.
Mariotti, M. A. (2001b). Introduction to proof: the mediation of a dynamic software environment, (Special issue) Educational Studies in Mathematics 44, (1&2), Dordrecht: Kluwer, pp.25-53.
Mariotti, M. A., Laborde, C., & Falcade, R. (2003). Function and graph in a DGS environment. In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PMENA, vol. 3 (pp. 237–244). University of Hawai’i, Honolulu, HI, USA: CRDG, College of Education.
Michael T. Battista. (2007). The development of geometric and spatial thinking. In Frank K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Charlotte: Information Age publishing Inc. pp.843-908.
Norton, J. (2004) "On thought experiments: Is there more to the argument?" Proceedings of the 2002 Biennial Meeting of the Philosophy of Science Association, Philosophy of Science, 71: 1139-1151.
Olivero, F. (1999). ‘Cabri-Géomètre as a mediator in the process of transition to proofs in open geometric situations’, in: W.Maull & J.Sharp (eds), Proceedings of the　4th International Conference on Technology in Mathematics Teaching, University of Plymouth, UK.
Olivero, F., Paola, D., & Robutti, O. (2002). Teaching proof in a dynamic geometry environment: what mediation? In: L. Bazzini & C. Whybrow Inchley (Eds.),Proceedings of CIEAEM53: Mathematical Literacy in the digital Era ,pp.307-312.
Pinto, M., & Tall, D. (2002). Building formal mathematics on visual imagery: a case study and a theory. For the Learning of Mathematics, 22(1) 2–10.
Schumann H., & De Villiers, M.D. (1993). Continuous variation of geometric figures: interactive theorem finding and problems in proving. Pythagoras, 31, 9-20.
Ainsworth, S. E., & Van Labeke, N. (2004). Multiple forms of dynamic representation. The Journal of the European Association for Research on Learning and Instruction, 14(3), 241-255.
Sorensen, R. A. (1992). Thought Experiments, Oxford University Press, Oxford
Straesser, R. (2001). Cabri-Geometry: does dynamic geometry software (DGS)
change geometry and its teaching and learning? International Journal of
Computers forMathematical Learning. V. 6(3), pp. 319-333.
Goldin-Meadow, S. (2003). Hearing gesture: How our hands help us think. Cambridge, MA: Harvard University Press
Tall, D. (1996). Information technology and mathematics education: Enthusiasms, Possibilities & Realities. In C. Alsina, J. M. Alvarez, M. Niss, A. Perez, L. Rico, A. Sfard (Eds), Proceedings of the 8th International Congress on Mathematical Education, Seville: SAEM Thales, pp.65–82.
Tall, D. (1999). The chasm between thought experiment and mathematical proof. In G. Kadunz, G. Ossimitz.W.Peschek, E.Schneider, B.Winkelmann (Eds.), Mathematische Bildung und neue Technologien, Teubner,Stuttgart, pp.319-343.
Talmon, V., & Yerushalmy, M. (2004). Understanding dynamic behavior: Parent-child relation in dynamic geometry environments. Educational Studies in Mathematics, 57, pp.91-119.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.