本研究的目的是希望在數列收斂的概念上，比較傳統的講述式教學與使用數學臆測活動的教學。討論數學臆測活動這個以學生為主體，教師擔任協助角色，有別於現行教科書規劃的學習模式，是否比傳統的講述式教學在促進學生於數學課室中主動思維與建構，進而讓具體的概念心像與抽象的概念定義互動更有所助益？
本研究採教學實驗的方式。研究對象是採方便樣本，選取研究者任教的兩個同質性高班級。研究時一班為實驗組使用數學臆測活動學習單；另一班為對照組採用講述式教學法。收集兩班上課錄影及錄音記錄、訪談記錄、學習單、學習後問卷與延後測問卷，進行質的分析。
研究結果發現，使用數學臆測活動對數列收斂概念有以下助益：
一、概念心像較為多樣，思考較為靈活。
二、學生會傾向用「說理」的方式來描述數列收斂，更能注意數列的全貌。
根據研究結果，研究者提出以下使用數學臆測活動的建議：
一、教師先訓練學生命題的表達，可以更有效率。
二、教師慎選命題，可以啟發學生例子的分類。
三、教師注意學生舉例種類的完整性，可以讓其有更完整的臆測。
四、教師引導學生反思原命題，有助於誘發概念心像。

中文部分：

王惠中(2003)。青少年無限概念發展研究(2/2) 。行政院國家科學委員會補助專題研究計劃成果報告。(計畫編號：NSC91-2521-S-003-002)，未出版。
余文卿(主編)(2008)。普通高級中學數學第一冊。台南市：翰林出版事業股份有限公司。
林福來(2007)。青少年數學論證「學習與教學」理論之研究：總計畫(4/4)。行政院國家科學委員會專題研究計畫期末報告。(計畫編號：NSC94-2521-S-003-001)，未出版。
林福來(2008)。數學臆測活動的設計、教學與評量：總計畫(1/3)。行政院國家科學委員會專題研究計畫期中報告。(計畫編號：NSC 96-2521-S-003-001-MY3)，未出版。
陳英娥(1998)。數學臆測：思維與能力的研究。國立台灣師範大學科學教育研究所博士班博士學位論文。台北市。未出版。
鄭英豪(2000)。學生教師數學教學概念的學習：以「概念啟蒙例」的教學概念為例。國立台灣師範大學數學系博士班博士學位論文。台北市。未出版。

英文部分：

Boero, P. (1999). Argumentation and mathematical proof：A complex, productive, unavoidable relationship in mathematics and mathematics education. International Newsletter on the Teaching and Learning of Mathematical Proof.
Duval, R. (1999). Questioning argumentation. International Newsletter on Teaching and Learning in Mathematics Proof.
Fischbein, E. (1987). Intuition in Science and Mathematics：An Educational Approach. Dordrecht, The Netherlands：Reidel. (pp.143-153)
Fischbein, E. (1996). The Psychological Nature of Concepts. In H. Mansfield, N. A. Pateman, & N. Bednarz (Eds.), Mathematics For Tomorrow’s Young Children (pp.105-110). London:Kluwer Academic Publishers.
Fischbein, E., Tirosh, D., & Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics, 10, 3-40.
Fischbein, E., Tirosh, D., & Melamed, U. (1981). Is it possible to measure the intuitive acceptance of a mathematical statement? Educational Studies in Mathematics, 12, 491-512.
Healy, L. & Hoyles, C.(1998). Justifying and Proving in School Mathematics. Summary of the Results Rorm a Survey of the Proof Conceptions of Students in the UK. Research Report Mathematical Sciences, Institute of Education, University of London.
Lakatos, I. (1976). Proofs and Refutations：The Logic of Mathematical Discovery. 6-105, Cambridge University Press.
Lin,F.L.(2006).Designing Mathematics Conjecturing Activities to Foster Thinking and Constructing Actively. Keynote Address in the APEC-TSUKUBA International Conference.Japan, Dec 2-7.
Lin,F.L.(2007).How Can We Enhance Students’ Mathematical Thinking Through Discourse. Keynote Address on the APEC-Khon Kaen International Symposium. Thailand, Aug. 16-20.
Lin, F.L. & L.C. Tsao (1999) , EXAM MATH Re-examined, in Hoyles C, C.Morgan and G.Woodhouse(eds.). Rethinking Mathematics Curriculum. The Falmer press,chap.18,228-239.
Lin, F. L. & Yu, J.W.(2005). False Proposition As a Means for Making Conjectures in Mathematics Classrooms. Invited Speech in Asian Mathematical Conference 2005. Singapore July 20-23.
Schwarz, B. B. & Hershkowitz, R. (1999). Prototypes：Brakes or Levers in Learning the Function Concept？ The Role of Computer Tools. Journal for Research in Mathematics Education, 30(4), 362-389.
Schwarzenberger, R. L. E. & Tall, D. O. (1978). Conflict in the Learning of Real Numbers and Limits. Mathematics Teaching 82, 44–9.
Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of limit of a function. Journal for Research in Mathematics Education, 31(3), 258-276.
Tall, D. O. (1992). The Transition to Advanced Mathematical Thinking: Functions, Limits, Infinity and Proof. In A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 495-511). New York: Macmillan.
Tall, D., Gray, E., Bin Ali, M., Crowley, L., DeMarois, P., McGowen, M., Pitta, D., Pinto, M., Thomas, M., ＆ Yusof, Y. (2001). Symbols and Bifurcation between Procedural and Conceptual Thinking. Canadian Journal of Science, Mathematics and Technology Education. , 1, 81–104.
Tall, D. & Tirosh, D. (Eds.), (2001). Infinity－The Never Ending Struggle. Special Issue：Educational Studies in Mathematics, 48(2&3).
Tall, D. & Vinner, S. (1981). Concept Image and Concept Definition in Mathematics with Particular Reference to Limits and Continuity. Educational Studies in Mathematics, 12, 151–169.
Tirosh, D. (1991). The Role of Students’ Intuitions of Infinity in Teaching the Cantorian Theory. In D. Tall (Ed), Adnvanced Mathematical Thinking (pp. 199-214). Dordrecht：Kluwer Academic Publishers.
Tsamir, P., & Tirosh, D. (1994). Comparing Infinite Sets：Intuition and Representations. In Proceedings of the 18th Annual Conference of the International Group for the Psychology of Mathematics Education, 345-352, Portugal, London.
Vinner, S. (1983). Concept Definition, Concept Image and the Notion of Function. International Journal of Mathematical Education in Science and Technology, 14(3), 293-305.
Vinner, S. (1991). The Role of Definitions in Teaching and Learning Mathematics. In D. Tall(Ed.), Advanced Mathematical Thinking(pp.65-81). Netherlands：Kluwer Academic Publishers.
Vinner, S. & Dreyfus, T. (1989). Images and Definitions for the Concept of Function. Journal for Research in Mathematics Education, 20(4), 356-366.