中學數學實習教師之數學教學概念心像探究－以學生數學思考面向為例

Mathematics Intern Teachers' Mental Images for Mathematics Teaching: Students' Mathematical Thinking in Classroom

10.6249/SE.2012.63.3.04

謝佳叡(Chia-Jui Hsieh)

數學思考 ； 數學教學概念心像 ； 數學實習教師 ； Concept Image for Mathematics Teaching ； Mathematics Thinking ； Mathematics Intern Teacher

中等教育

63卷3期（2012 / 09 / 01）

48 - 67

繁體中文

在觀察教師課堂工作時，不難發現教師們必須在短時間內做出大量的決策以便解決課堂上所發生的各項狀況，不禁令人好奇，教師進行教學決策之依據為何？本研究則試圖從數學教學概念心像（Concept Image for Mathematics Teaching）的角度切入，探討臺灣中學數學實習教師在面對數學教學情境問題時，所展現出的教學決策其背後之依據；更具體地說，本研究試圖透過實習教師對於教學情境問題的反應，推測其數學教學概念心像的內涵與結構。在各個不同的教學面向中，本文特別從學生數學思考面向著眼，檢視中學數學實習教師在面對教學問題時所喚起之數學教學概念心像，以及其與教學決策之間的關聯。研究發現大多數中學數學實習教師肯定學生思考在數學課堂上所扮演的角色，然而，當他們面對教學問題時，這些實習教師並不常喚起「讓學生思考」的概念心像以作為教學決策的依據，比現象反映在教學情境問題的回應上則表現出他們很少給予學生思考的機會與時間。研究也發現多數展現學生思考心像的實習教師同時也經常伴隨著學生數學認知發展心像的產生。

When observing teachers working, we will find that they must make the large number of decisions to deal with the situations that take place in a few moments. Based on the idea ”concept image for mathematics teaching (CIMT)”, the study was to investigate the bases on which secondary school mathematics intern teachers in Taiwan choose strategies when facing teaching tasks.This paper focuses on the concept of student's mathematics thinking in the mathematics classroom, as well as examines what kind of CIMT is evoked when mathematics intern teachers face the tasks related to students' mathematical thinking. We found that even mathematics intern teachers do know how important ”student thinking” is for mathematics-learning, they do not usually evoke the image of ”make students think” as their bases of teaching strategy when facing teaching situation. In other words, they barely give students opportunities and time to think in the classroom. The study also found that most mathematics intern teachers who evoke the image of student thinking usually evoke the image of students' cognitive development at the same time.

1. Carpenter, T. P.,Fennema, E.,Frank, M. L.(1997).Cognitive guided instruction: A knowledge base for reform in primary mathematics instruction.The elementary School journal,97(1),3-20.
2. Cochran, K. F.,DeRuiter, J. A.,King, R. A.(1993).Pedagogical content knowing: An integrative model for teacher preparation.Journal of Teacher Education,44(4),263-272.
3. Cooney, T. J.(1985).A beginning Teacher's view of problem solving.Journal for Research in Mathematics Education,16(5),324-336.
4. Ernest, P.(ed.)(1989).Mathematics teaching: The state of the art.London:Falmer Press.
5. Griffin, L.(1996).Pedagogical content knowledge for teachers: Integrate everything you know to help students learn.Journal of Physical Education, Recreation & Dance,67(9),58-61.
6. Grossman, P. L.(1989).A study in contrast sources of pedagogical content knowledge for secondary English.Journal of Teacher Education,40(5),24-31.
7. Grossman, P. L.(1991).The Making of a teacher: Teacher knowledge and teacher education.New York:Teachers College Press.
8. Hoyles, C.(1992).Mathematics teaching and mathematics teachers: A meta-case study.For the Learning of Mathematics,12(3),32-44.
9. Jones, M. R.(ed.)(1965).Human motivation: A symposium.Lincoln:University of Nebraska Press.
10. Levin, B.,He, Y.(2008).Investigating the content and sources of preservice teachers' personal practical theories (PPTs).Journal of Teacher Education,59(1),55-68.
11. Lin, F. L.(ed.)(2001).Making sense of mathematics teacher education.Dordrecht:Kluwer Academic Publish.
12. Mayer, R. E.(1983).Thinking, problem solving, cognition.NY:W. H. Freeman and Company.
13. Niess, M. L.(2005).Preparing teachers to teach science and mathematics with technology: developing a technology pedagogical content knowledge.Teaching and Teacher Education,21(5),509-523.
14. Patton, M. Q.、吳芝儀譯、李奉儒譯(1995)。質的評鑑與研究。臺北:桂冠出版社。
15. Polya, G.(1957).How to solve it.NY:Doubleday Anchor.
16. Raymond, A. M.(1997).Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice.Journal for Research in Mathematics Education,28(5),550-576.
17. Shulman, L. S.(1987).Knowledge and teaching: Foundation of the new reform.Harvard Educational Review,57,1-22.
18. Sierpinska, A.(ed.),Kilpatrick, J.(ed.)(1998).Mathematics education as a research domain: A search for identity: an ICMI study.Boston:Kluwer Academic Publishers.
19. Stacey, K.(2005).The place of problem solving in contemporary mathematics curriculum documents.Journal of Mathematical Behavior,24,341-350.
20. Su, Y.-N(2012).Teach to live or live to teach: A case study on the educational beliefs displaced teachers in Taiwan.International Journal of Research Studies in Education,1(1),3-20.
21. Tall, D.(ed.)(1991).Advanced mathematical thinking.Netherlands:Kluwer Academic Publishers.
22. Tall, D.,Vinner, S.(1981).Concept image and concept definition in mathematics with particular reference to limits and continuity.Educational Studies in Mathematics,12(2),151-169.
23. Thompson, A. G.(1984).The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice.Educational Studies in Mathematics,15(2),105-128.
24. Vinner, S.(1983).Concept definition, Concept image and the Notion of Function.International Journal of Mathematical Education in Science and Technology,14(3),239-305.
25. 任樟輝(1999)。數學思維論。廣西教育出版社。
26. 林進材(1997)。博士論文(博士論文)。臺灣師範大學教育研究所。
27. 林褔來(1997)。行政院國科會專題研究計畫報告行政院國科會專題研究計畫報告,臺北市:臺灣師大數學系。
28. 邱美虹(1997)。行政院國科會專題研究計畫報告行政院國科會專題研究計畫報告,臺北市:臺灣師大科學教育研究所。
29. 謝佳叡(2011)。博士論文(博士論文)。國立臺灣師範大學數學系。
30. 謝佳叡(2001)。碩士論文(碩士論文)。國立臺灣師範大學數學系碩士班。
31. 魏姿玟(2010)。碩士論文(碩士論文)。國立臺灣師範大學數學系。

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