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題名：小六學童在探究教學中的樣本空間概念發展
書刊名：臺中教育大學學報. 數理科技類
作者：陳欣民／劉嘉茹 引用關係／柳賢
作者(外文)：Chen, Hsin-min／Liu, Chia-ju／Leou, Shian
出版日期：2011
卷期：25:1
頁次：頁67-91
主題關鍵詞：樣本空間概念；數學探究教學；排列組合；Sample space；Mathematics inquiry teaching；Permutation
原始連結：連回原系統網址new window
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本研究旨在探討小六學童於數學探究教學的情境脈絡下，樣本空間概念的發展與轉變情形。研究採取詮釋性研究法，收集的資料包括課堂錄影錄音、研究者課堂札記和學生數學日誌等資料，研究對象為南部地區某公立小學一個小六班級的 31 位學童。結果發現在探究教學前，學童會受個人生活經驗影響而具有質樸的初始樣本空間概念。另外，骰子上的點數可視為一種明顯組合的線索，能協助學童思考樣本點的排列組合。經由探究教學後，所有的學童皆能根據樣本空間觀點解機率問題，大部份的學童皆能列出二維、甚至三維樣本空間。此外對小六學童而言，理解並列出兩個硬幣樣本空間的難度比較高。並提出對於課程與教學上的建議。
This study adopted an interpretative research method in order to investigate the development of the concept of sample space among sixth graders during mathematics inquiry teaching. The data comprised videotapes and audiotapes of classroom teaching practices, the researchers’ journals, and the notes of 31 sixth graders of an elementary school in southern Taiwan. The results indicated that before inquiry teaching, most students had a naive concept of sample space, affected by their daily experiences. Moreover, the numbers on the sides of dice are potential cues for students to understand permutation. After inquiry teaching, all students were able to solve probability problems based on sample space and list two-stage or even three-stage sample spaces. In addition, sixth graders experience difficulty in listing the sample space of tossing two coins. Furthermore, the study provides some suggestions to improve the mathematics curriculum and teaching practices.
期刊論文
1.Tirosh, D.、Stavy, R.(1996)。Intuitive rules in science and mathematics: the case of 'everything can be divided by two。International Journal of Science Education，18(6)，669-683。  new window
2.Fischbein, E.、Schnarch, D.(1997)。The evolution with age of probabilistic, intuitively based misconceptions。Journal for Research In Mathematics Education，28(1)，96-105。  new window
3.Goos, M.(2004)。Learning mathematics in a classroom community of inquiry。Journal for Research in Mahtematics Education，35(4)，258-291。  new window
4.林原宏；羅友任(2009)。國小學童機率概念測驗之編製與答題類型分析。測驗統計年刊，17，39-60。  延伸查詢new window
5.Siegel, M.、Borasi, R.、Fonzi, J.(1998)。Supporting students’ mathematical inquiries through reading。Journal for Research in Mathematics Education，29，378-413。  new window
6.Tyson, L. M.、Venville, G. J.、Harrison, A. G.、Treagust, D. F.(1997)。A multidimensional framework for interpreting conceptual change events in the classroom。Science Education，81，387-404。  new window
7.Watson, J. M.、Kelly, B. A.(2007)。Development of student understanding of outcomes involving two or more dice。International Journal of Science and Mathematics Education，7，25-54。  new window
8.Watson, J. M.、Moritz, J. B.(1998)。Longitudinal development of chance measurement。Mathematics Education Research Journal，10，103-127。  new window
9.White, H.(1984)。The Development of Combinatorial Reasoning: The Role of Cognitive Capacity。The Journal of Genetic Psychology，145，185-194。  new window
10.Aspinwall, L.、Shaw, K. L.(2000)。Enriching students’ mathematical intuition with probability games and tree diagrams。Mathematics Teaching In the Middle School，6，214-220。  new window
11.Batanero, C.、Navarro-Pelayo, V.、Godino, J.(1997)。Effect of the Implicit Combinatorial Model on Combinatorial Reasoning in Secondary School Pupils。Educational Studies in Mathematics，32，181-199。  new window
12.Eizenberg, M. M.、Zaslavsky, O.(2004)。Students’ verification strategies for combinatorial problems。Mathematical Thinking and Learning，6，15-36。  new window
13.English, L. D.(1993)。Children’s strategies for solving two- and three-dimensional combinatorial problems。Journal for Research in Mathematics Education，24，255-273。  new window
14.Fischbein, E.(1991)。Factors affecting probabilistic judgments in children and adolescents。Educational Studies in Mathematics，22，523-549。  new window
15.White, H.(2001)。Breakdowns in Combinatorial Reasoning: The Role of Memory。The Journal of Genetic Psychology，146，431-432。  new window
16.Fischbein, E.、Gazit, A.(1984)。Do the teaching of improve probability intuitions?。Educational Studies in Mathematics，15，1-24。  new window
17.Fischbein, E.、Grossman, A.(1997)。Schemata and intuitions in combinatorial reasoning。Educational Studies in Mathematics，34，27-47。  new window
18.Godino, J. D.、Batanero, C.、Roa, R.(2005)。An onto-semiotic analysis of combinatorial problems and the solving processes by university students。Educational Studies in Mathematics，60，3-36。  new window
19.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。  new window
會議論文
1.蔡欣潔；葉啟村(2004)。國小六年級學童機率概念表現之研究。  延伸查詢new window
2.劉祥通；陳欣民(2004)。一位小六學生解樣本空間問題之個案研究。  延伸查詢new window
3.McLoughlin, M. P. M. M.(2004)。On the Nature of Mathematical Thought and Inquiry: A Prelusive Suggestion。Phoenix, Arizona。  new window
4.Shin, J.、Steffe, L. P.(2009)。Seventh graders use of additive and multiplicative reasoning for enumerative combinative combinative combinatorial problems。Atlanta, GA。  new window
研究報告
1.王建都(2002)。青少年的數學概念學習研究：青少年的機率概念發展研究。臺北市。  延伸查詢new window
學位論文
1.Lefebvre, C.(2010)。Probability vs. typicality: Making sense of misconceptions。Concordia University。  new window
2.McLoughlin, M. P. M. M.(2009)。Inquiry-Based Learning: An Educational Reform Based Upon Content-Centered Teaching。Kutztown University。  new window
3.Abu-Bakare, V.(2008)。Investigating students’ understandings of probability: A Study of grade 7 classroom。The University of British Columbia，Canada。  new window
4.Polaki, M. V.(2000)。Using instruction to trace the development of Basotho elementary students’ probabilistic thinking。Illinois State University。  new window
圖書
1.Piaget, J.、Inhelder, B.、Leake, L. Jr.、Burrell, P. D.、Fischbein, H. D.(1975)。The origin of the idea of chance in children。Routledge & Kegan Paul。  new window
2.Dewey, J.(1933)。How we think: Restatement of the reflective thinking to the educative process。D. C. Health。  new window
3.劉秋木(1996)。國小數學科教學研究。臺北：五南圖書出版公司。new window  延伸查詢new window
4.Freudenthal, H.(1973)。Mathematics as an educational task。Dordrecht：D. Reidel Publishing。  new window
5.National Council of Teachers of Mathematics(2000)。Principles and standards for school mathematics。Reston, Virginia：National Council of Teachers of Mathematics。  new window
6.Miles, Matthew B.、Huberman, A. Michael、Newman, G.(1994)。Qualitative data analysis: an expanded sourcebook。Sage Publications。  new window
7.Australian Education Council(1991)。A National Statement on Mathematics for Australian Schools。Melbourne：Curriculum Corporation。  new window
8.Vygotsky, Lev Semenovich、Cole, Michael、John-Steiner,‎ Vera、Scribner, Sylvia、Souberman, Ellen(1978)。Mind in Society: The Development of Higher Psychological Processes。Harvard University Press。  new window
9.蔡文煥(1998)。國小統計教材機率初步概念之設計理念與實際。國小新課程概說。臺北。  延伸查詢new window
10.徐正梅(1987)。基礎數學第四冊。臺北。  延伸查詢new window
11.耿素雲；張立昂(1996)。機率統計。臺北。  延伸查詢new window
12.Kolmogorov, A.(1950)。Foundations of probability’s calculation。New York。  new window
13.Green, D. R.(1983)。A survey of probability concepts in 1000 students aged 11-16 years。Proceedings of the First International Conference on Teaching Statistics。Sheffield, UK。  new window
14.Jones, G. A.、Thornton, C. A.、Langrall, C. W.、Tarr, J. A.(1999)。Understanding students’ probabilistic reasoning。Developing Mathematical Analyzing in Grades K-12: 1999 year book。Reston, Va：National Council of Teachers of Mathematics。  new window
15.Watson, J. M.(1995)。Probability and statistics: An overview。Teaching Secondary School Mathematics: Theory into Practice。Sydney。  new window
16.Schroeder, T. L.(1988)。Elementary school children’s use of strategy in playing microcomputer probability games。Proceedings of the Second International Conference on Teaching Statistics。Canada。  new window
其他
1.Nikiforidou, Z.，Pange, J.(2007)。Can probability combinations/ estimations be assessed in preschoolers with the use of computers?。  new window
圖書論文
1.Richards, J.(1991)。Mathematical discussions。Radical constructivism in mathematics education。Dordrecht：Kluwer。  new window
2.Borovcnik, M.、Bentz, H. J.、Kapadia, R.(1991)。A probabilistic perspective。Chance encounters: Probability in education。Boston, MA：Kluwer Academic Publishers。  new window
3.Peirce, C. S.(1982)。The fixation of belief。Pragmatism: The classic writings。Indianapolis, IN：Hackett。  new window
 
 
 
 
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