為探討七年級學生在對於數列題型中「未知結果」及「辨別真偽」兩種題目上的表現及思維歷程，本研究將不同成就學生各兩位，施測完後，為了可以更加清楚學生的猜想過程，再透過結構訪談，最後繪製出不同成就學生的臆測思維歷程圖。
研究結果發現辨別真偽與未知結果的任務類型中，臆測思維歷程都是以觀察為起點，歷程都具有方向性；但在數字題型與圖形題型中，臆測思維歷程並無明顯差異。
而在不同成就學生臆測思維歷程的差異發現，高成就學生在面對辨別真偽與未知結果不同類型的題目時，臆測思維歷程並無明顯差異，唯有透過語錄才可以發現未知結果的題型臆測思維歷程較辨別真偽來的複雜，且高成就學生解題較有自信；中成就學生則是在辨別真偽的題型臆測思維歷程較未知結果來的複雜，且中成就學生因缺乏自信最後結果只停留在反駁與檢驗的階段；低成就學生則是在辨別真偽的題型臆測思維歷程較未知結果來的複雜，但往往只停留在觀察或猜測階段。
最後在形成猜想與檢驗猜想的方式發現，學生在形成猜測最常使用的方法是擴展和特殊化；而在檢驗猜想時最常使用的方法則是代數字進行檢驗，當代到ㄧ到兩個實例正確時，便會對此猜測深信不疑。

The aim of the research is to explore the 7th grade students’ performance and thinking processes on “unknown result question” and “tell the true from the false question”. The object of the study is the six students picked from three different achievement performance groups and two for each. To get more deep understanding of the students’ conjecturing thinking processes, the researcher interviews the students through constructive questions and draw the conjecturing thinking processes charts of the students with different achievement performance.
Major findings are as follows. First, in “tell the true from the false question” task, the students’ conjecturing thinking processes are based from observation and the processes are directionality. However, in number type questions and figure type questions, there is no significant difference on the students’ conjecturing thinking processes. Second, the result of the difference in different achievement performance students shows that there is no significant difference on the high achievement performance students’ conjecturing thinking processes when doing “unknown result question” and “tell the true from the false question”. In this group, only when analyzing the interviewing data, we can see the high achievement performance students’ conjecturing thinking processes are more complicated when doing “unknown result question” than doing “tell the true from the false question” and the high achievement performance students have more confidence when solving questions. On the other hand, in the group of medium achievement performance students, their conjecturing thinking processes are more complicated when doing “tell the true from the false question” than doing “unknown result question”. Besides, due to the lacking of confidence, the medium achievement performance students can only achieve the step of refutation and examination in the end. As for the last group of low achievement performance students, their conjecturing thinking processes are more complicated when doing “tell the true from the false question” than doing “unknown result question”, and also can only achieve the step of observation and conjecture in the end.
Finally, in the research of forming conjecture and examining the methods, the researcher finds that the most using methods when the students form conjecture are extension and specialization. Furthermore, the most using methods when the students examine conjecture is to substitute numbers into questions, and when one or two examples are fitted to the question, the students will be convinced of the conjecture.

一、中文部分
李立凱（2009）。以臆測為中心的數學教學模組之研發－以數列與級數單元為例。國立彰化師範大學科學教育研究所碩士論文，彰化市。
李佩玟(2005)。國小六年級學童發現數列樣式的推理歷程之分析。國立臺北教育大學，教育心理與諮商學系碩士論文，臺北市。
李美蓮(2004)。一位國二學生在等差數列解題表現之研究。國立嘉義大學數學教育研究所碩士論文，嘉義市。
李惠如(2010)。在以臆測活動為中心的教學情境下八年級學生臆測思維歷程的展現與其數學解題歷程之研究。立彰化師範大學科學教育研究所碩士論文，彰化市。
何鳳珠(2004)。國小六年級學童以七巧板發展分數基準化能力之研究。國立嘉義大學數學教育研究所碩士論文，嘉義市。
張佩琦(2007)。運用臆測教學提昇國三學生數學學習成效-以相似形為例。高雄師範大學數學教學碩士班碩士論文，高雄市。
陳英娥、林福來（1998）。數學臆測的思維模式。科學教育學刋，6，191-218。
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論文，未出版，台北市。
陳威任(2011)。台南地區八年級學生在「數列與等差級數」單元之錯誤類型分析。國立台南大學應用數學研究所碩士論文，未出版，台南市。
陳勝楠(2003）。國一學生關於樣式解題歷程之分析研究。國立高雄師範大學數學教育研究所碩士論文，未出版，高雄市。
曹亮吉 (2003)。阿草的數學聖杯¬–探索無所不在的胚騰。台北市：天下遠見出版社。
教育部 (2002)。國民中小學九年一貫課程綱要數學領域。台北市：教育部。
教育部（2006）。國民中小學九年一貫課程綱要。台北市：教育部
廖志偉(2009)。高雄市國中學生等差數列解題之錯誤類型分析研究。高雄師範大學數學系碩士論文，高雄市。
蔡忠翰(2011)。高一數理資優班與普通班學生在數列級數單元的解題歷程中所展現的臆測思維與數學素養之比較研究。國立彰化師範大學資賦優異研究所碩士論文，彰化市。
二、英文部分
Balacheff, N. (1988a). Aspects of in pupils’ practice of school mathematics. In D. Pimm(Ed.), mathematics, teachers and children (pp. 316-230). London: Hodder and Stoughton.
Cañadas, M. C., Deulofeu, J., Figueiras, L., Reid, D., & Yevdokimov, A. (2007). The conjecturing process: Perspectives in theory and implications in practice. Journal of Teaching and Learning, 5(1), 55-72
Cantlon, D.(1998). Kids + conjecture=mathematics power. Teaching Children Mathematics, 5(2), 108-112.
Carlson, M. P., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58(1), 45-75.
David, P. L., & Hersh, R. (1995). The mathematical experiment. Birkhauser, Boston.
Douek, N. (1999). Argumentative aspects of proving: Analysis of some undergraduate mathematics students’ performances. In O. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, 2, 273-280.
de Villier, M(1990). The role and function of proof in mathematics. Pythagoras, 24, 17-24.
Lin, M. L., & Wu C. J. (2007). Uses of examples in geometric conjecturing. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceeding of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol, 3(pp. 209-216). Seoul, Korea (7/8/2007-7/13/2007). (NSC 94-2524- S-152- 001)
Latkatos, I.(1976). Proofs and refutations: The logic of mathematical discovery. New York: Cambridge University Press.
Mason, J.,Burton L., & Stacey K.(1985). Thinking mathematically. Great Britain: Addison-Wesley Publishing Company.
Melanie, H., Diane, S. T., & John, T. (1998). Children's strategies with number patterns. Educational Studies, 24(3), 315-331.
National Council of Teachers of Mathematics [NCTM](1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics [NCTM](2000). Principles and Standards for School Mathematics. Reston, VA: Author.
Orton, A., & Orton, J. (1994). Student's perception and use of pattern and generalization. In proceeding of the 18th annual conference of international group for the psychology of mathematics education, 3, 407-414.
Polya, G. (1945). How to solve it. Princeton: Princeton University Press.
Polya, G. (1954). Mathematics and plausible reasoning. London: Oxford University Press. National Council of Teachers of Mathematics. (2000). Principal and standards for school mathematics. Reston, VA: Author.
Popper, K. R. (1963). Conjectures and Refutations. London: Routledge.
Reid, D. A. (2002). Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education, 33(1), 5-29.
Stylianides, A. J.,& Ball, D. L.(2008). Understanding and describing mathematical knowledge for teaching：knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education 11：307-322