臺灣博碩士論文加值系統

本研究採用半結構式晤談法(semi-structured interview)進行訪談，以探討三位未曾受過機率課程與教學之學童的機率概念。發現此三位研究個案對於「事件發生之可能性」已有下列認識：(一)能使用自己的用語描述事件發生之必然性或可能性。(二)能以生產性策略求出樣本空間。(三)能做兩事件發生之可能性大小比較。(四)能了解簡易之條件機率。然而，他們皆尚未能了解「機率值」之意涵。本研究最後將研究結果與前人之相關研究做對照，並根據訪談結果提出在課程及教學上的建議。

This study was to discuss three elementary school students’ concepts about probability . The students have never taken any courses about probability. The semi-structured interview approach was applied. The researcher found that the three students have the following understandings about “the possibility of something occurring”. First, they can describe in their own words if an event will certainly happen or possibly happen. Second, they can get complete sample space using productive strategies. Third, they can compare two events in terms of their possibility. Fourth, they can understand simple conditional probability; however, they can’t define the meaning of probability. Finally, the researcher compared the results of this study with others’ and provided suggestions of teaching according to the results.

目 次
第一章 緒論………………………………………………… 1
第一節 研究背景與動機………………………………………..1
第二節 研究目的………………………………………………..2
第三節 重要名詞釋義…………………………………………..3
第四節 研究範圍與研究限制…………………………………..5
第二章 文獻探討…………………………………………… 6
第一節 機率概念的內涵分析…………………………………..6
第二節 兒童機率概念的發展…………………………………..9
第三節 兒童機率迷思概念的類型…………………………….21
第四節 我國及美國國小機率課程之發展現況……………….30
第五節 改善機率教學之方法………………………………….33
第三章 研究方法………………………………………….. ……..38
第一節 研究設計……………………………………………….39
第二節 研究對象……………………………………………….41
第三節 訪談導引……………………………………………….43
第四節 資料蒐集與分析……………………………………… 48
第五節 研究者………………………………………………….49
第六節 研究程序……………………………………………….51
第四章 研究結果與討論……………………………………52
第一節 四位個案之研究結果………………………………….52
第二節 跨個案分析……………………………………………95
第五章 結論、反思及建議………………………………..110
第一節 結論…………………………………………….111
第二節 反思(與前人之研究比較)……………………………121
第三節 建議…………………..…………………………...130

一、 中文部份
王文科(民88)。教育研究法(第五版)。台北：五南圖書出版公司。
朱雅瑋(民85)。國小學童機率的直觀概念。新竹：國立新竹師範學院未發表之碩士論文。
林燈茂(民81)。11-16歲學童之「相對差異」與「大數法則」概念初探。彰化：國立彰化師範大學科學教育研究所未發展之碩士論文。
林燈茂、曹宗萍(民86)。國小職前教師的「機率概念教學知識」與「機率概念知識」之初探。八十五學年度師範學院教育學術論文發表會刊。台東：台東師院。
吳靜瑜(民88)。國小六年級學童機率概念之研究。嘉義：國立嘉義師範學院未發表之碩士論文。
耿素雲、張立昂(民85)。機率統計。台北：儒林書局。
陳欣民、劉祥通(民91a)。從兒童機率迷思概念之文獻分析談機率單元的教學與課程。科學教育研究與發展季刊，26，40-51。
陳欣民、劉祥通(民92b)。一位國小五年級學生機率思考層次之個案研究。國民教育研究學報，8，133-158。
施能宏(民86)。國小高年級學生機率文字題表現之研究。台中：國立台中師範學院未發表之碩士論文。
黃台珠(民73)。概念的研究及其意義。科學教育月刊，66，44-56。
楊志強、洪文東(民91)。教學對概念改變之研究─以國小五年級「電磁鐵」單元為例。屏東師院月刊(15)，54-67。
Hoel, Port, & Stone(1989)。機率導論(詹世煌譯)。台北：曉園出版社。
劉秋木(民85)。國小數學科教學研究。台北：五南圖書出版公司。
臺灣省國民學校教師研習會(民86)。國民小學數學實驗課程教師手冊第十一冊。台北縣：臺灣省國民學校教師研習會。
鄭麗玉(民87)。如何改變兒童的迷思概念。教師之友，39(5)，28-36。
謝青龍(民84)。從「迷思概念」到「另有架構」的概念改變。科學教育月刊，180，23-25。
羅昭強、施登山、朱雅瑋(民84)。小學職前教師的機率直觀概念。新竹師院學報，1，43-55。
英文部份
Borovcnik, M., & Peard, R. (1996). Probability. In Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J., & Laborde, C. (Eds.), International Handbook of Mathematics Education(pp.239-286). Dordrecht, The Netherlands: Reidel.
Bognar, K. & Nemetz, T. (1977). On the teaching of probability at secondary level. Educational Studies in Mathematics, 8, 399-404.
Bruner, J. S. (1960). The Process of Education. Cambridge : Harvard University Press.
Cobb, P., & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Education, 14(2), 81-94.
Fischbein, E., & Gazit, A. (1984). Do the teaching of improve probability intuitions? Educational Studies in Mathematics, 15, 1-24.
Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, The Netherlands: Reidel.
Fischbein, E. (1991). Factors Affecting Probabilistic Judgments in Children and Adolescents. Educational Studies in Mathematics, 22(6), 523-549
Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill. A. T. (1997). A framework for assessing and nurturing young children’s thinking in Probability. Educational Studies in Mathematics, 32, 101-125.
Jones, G. A., Thornton, C. A., Langrall, C. W., & Tarr, J. A. (1999). Understanding Students’ Probabilistic Reasoning. In Stiff, L. V. & Curcio F. R. (Eds.), Developing Mathematical Analyzing in Grades k-12: 1999 year book(pp.146-155). Reston, Va: National Council of Teachers of Mathematics.
Konold, C. (1983). Conceptions about probability: Reality between a rock and a hardplace. Dissertation Abstracts International, 43, 4179B.
Konold, C. (1991). Understanding students’ beliefs about probability. In Glasersfeld E. V. (Ed.), Radical constructivism in Mathematics Education(pp139-165). Holland: Kluwer.
Konold, C. (1993). Inconsistencies in students’ Reasoning about Probability. Journal for Research in Mathematics Education, 24(5), 392-414.
Klausmeier, H. J. (1979). Cognitive Learning and Development: Information Processing an Piaget Perspectives. Washington, D. C.: Office of Education.
Kahneman, D. & Tversky, A. (1972). Subjective probability: A judgment of presentativeness. Cognitive Learning and Development: Information Processing an Piagetian Prespectives. Washington, D. C.: Office of Education.
Kahneman, D. & Tversky, A. (1973). Availability: A heuristic for judging frequency and probability. Cognitive psychology, 5, 207-232.
Leslie, A. & Kenneth L. S. (2000). Enriching Students’ Mathematical Intuition with Probability Games and Tree Diagrams. Mathematics Teaching in The Middle School, 6(4), 214-220.
Tversky, A. & Kahneman, D. (1974). Judgement under uncertainty : Heuristics and biases. Science(185),1124-1131.
Meyar, P. L. (1978). Introductory probability and statistical applications. Taipei: Mea Ya.
National Council of Teachers of Mathematics(2000). Principles and Standards for school Mathematics. Reston, Va: NCTM .
Piaget, J. & Inhelder, B. (1975). The origin of the idea of chance in children. London: Routledge kegan paul.
Robert, J. Q. (2001). Using Attribute to develop a conceptual understanding of probability. Mathematics Teaching in the Middle School, 6(5), 290-294.
Siegler, R. S. (1981). Developmental Sequences within and between concepts. Monographs of the society for research in Child Development, 46(2).
Sharge, G. (1983). Misinterpretation of stochastic models. In Scholz, R. (Ed.), Decision making under uncertainty(pp. 351-361) Amsterdam: New York North-Holland.
Shaughnessy, J. M. (1977). Misconception of probability: An experiment with a small-group, activity-based, model building approach to introductory probability at college level. Educational Studies in Mathematics, 8 (3), 295-316.
Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D.Grouws (Ed.), Handbook of research on mathematics teaching and learning(pp.465-494). New York: Macmillan.
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185,1124-1131.