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題名:透過列聯表探討國小學童資料解讀的能力與認知
作者:施懿珊
作者(外文):Yih-Shan Shih
校院名稱:國立臺中教育大學
系所名稱:教育測驗統計研究所
指導教授:楊志堅
學位類別:博士
出版日期:2014
主題關鍵詞:列聯表比率推理機率contingency tableproportional reasoningprobability
原始連結:連回原系統網址new window
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本研究的主要目的是透過列聯表來探討國小二到六年級學童資料解讀的能力與認知。並將成功解讀列聯表所需的數學概念分為比率推理與機率兩個概念。主要透過統計分析來整體了解學童在概念上的認知,並利用個案晤談方式進行學童解題策略上的暸解。
研究對象包含北市某公立國小277位國小二至六年級的學童,其中男生有127位,女生有150位;之後輔以其中5位學童的個案晤談。研究工具包含比率推理、機率與列聯表三個分測驗,試題共計20題。
研究結果顯示:四年級以上的學童約有一半以上的人有比率推理的概念;約有近六成的學生有機率概念或列聯表解讀的能力。五年級男生在列聯表的解題表現顯著高於五年級女生;二年級學童在三個分測驗中的解題表現都顯著低於中、高年級,而三、四年級學童在機率上的解題表現也顯著低於六年級學童。
The purpose of this study is to explore the performance in interpreting data through contingency table in second grade to sixth grade students. Proportional reasoning and probability is the main concept in interpreting contingency table successfully. The cognitive of concept are evaluated by analyzing data. Furthermore, problem-solving strategies is analyzed by interview.
127 boys and 150 girls in second grade to sixth grade are recruited at an elementary school in Taipei, in which 5 students are interviewed. The test are composed of three sub-tests, proportional reasoning, probability and contingency table. It totally has 20 items.
The results indicated that:More than half of fourth grade students have proportional reasoning concept. There are about 60% students have probability concept or the performance in interpreting contingency table. Fifth-grade boys in interpreting contingency table is significantly higher than fifth-grade girls. Second grade students problem solving in three subtests are significantly lower than in other students. Third and fourth grade students on the probability of solving performance significantly lower than sixth grade students.
參考文獻
Andrew, L. (2009). Experimental probability in elementary school. Teaching Statistics, 31 (2), 34–36.
Bar, V. (1987) Comparison of the development of ratio concepts in two domains. Science Education, 71(4), 599-613.
Batanero , C., Godino, J.D. , Vallecillos, A. , Green, D. R., & Holmes, P. (1994). Errors and difficulties in understanding elementary statistical concepts, International Journal of Mathematical Education in Science and Technology, 25(4), 527-547.
Batanero,C., Estepa, A., Godino, J.D. , & Green, D. R. (1996). Intuitive Strategies and Preconceptions about Association in Contingency Tables. Journal for Research in Mathematics Education, 27(2), 151-169.
Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and Equivalence of Rational Numbers: A Clinical Teaching Experiment. Journal for Research in Mathematics Education. 15(5), pp. 323-341.
Behr, M. & Post, T. (1992). Teaching rational number and decimal concepts. In T. Post (Ed.), Teaching mathematics in grades K-8: Research-based methods (2nd ed.) (201-248). Boston: Allyn and Bacon.
Cramer, K., & Post, T. (1993). Connecting Research To Teaching Proportional Reasoning. Mathematics Teacher, 86(5), 404-407.
delMas, R. C. (2002). A Review of the Literature on Learning and Understanding Probability. The Annual Meeting of the American Educational Research Association New Orleans, LA.
Falk, Ru., Falk, Ra., & Levin, I. (1980). A potential for learning probability in young children. Educational Studies In Mathematics, 11(2), 181–204.
Fujimura, N. (2001). Facilitating Children's Proportional Reasoning: A Model of Reasoning Processes and Effects of Intervention on Strategy Change. Journal of Educational Psychology. 93(3), 589-603.
Godino, J. D., & Batanero, C. (1998). Clarifying the meaning of mathematical objects as a priority area of research in mathematics education. Mathematics Education as a Research Domain: A Search for IdentityNew ICMI Studies Series Volume 4, 177-195.
Hiebert, J., & Tonnessen, L. H. (1978). Development of the Fraction Concept in Two Physical Contexts: An Exploratory Investigation. Journal for Research in Mathematics Education ,9(5), 374-378.
HodnikČadež, T., & Škrbec, M. (2011). Understanding the Concepts in
Probability of Pre-School and Early School Children. Eurasia Journal of Mathematics, Science & Technology Education, 7(4), 263-279.
Hunting, R. P., & Sharpley, C. F.(1988). Fraction Knowledge in Preschool Children. Journal for Research in Mathematics Education, 19(2), 175-180.
Koerber, S., Sodian, B., Thoermer, C., & Nett, U. (2005). Scientific reasoning in young children. Preschoolers’ ability to evaluate covariation evidence. Swiss Journal of Psychology, 64, 141–152.
Lamon, S. J. (1993). Ratio and Proportion: Connecting Contect and Children’s Thinking. Journal for Research in Mathematics Education. 24(1), 41-61.
Lamon, S. J. (1999). Teaching fractions and rations for understanding essential content knowledge and instructional strategies for teachers. Mahwah, New Jersey:Lawrence Erlbaum Associates, Pumlushers.
Langrall, C. W., & Swafford, J. (2000). Three Balloons for Two Dollars: Developing Proportional Reasoning. Mathematics Teaching in the Middle School, 6(4), 54-61.
Ledesma, E. F. R. (2010). Using an Interactive Computer System to Support
the Task of Building the Notions of Ratio and Proportion. Creative Education, (2), 115-120.
Noelting, G. (1980). The Development of proportional reasoning and the ratio concept (PART I - DIFFERENTIATION OF STAGES). Educational Studies in Mathematics, 11, 217-253.
Polaki, M. V. (2002). Using Instruction to Identify Key Features of Basotho Elementary Students' Growth in Probabilistic Thinking. Mathematical Thinking and Learning. 4(4), 285-313.
Reiss, Barchfeld, Lindmeier, Sodian, & Ufer (2011). Interpreting scientific evidence: primary student's understanding of base rates, sampling procedures, and contingency tables. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, 4, 4-33. Ankara, Turkey: PME.
Rodrigo, M. J., Castaneda, J., & Camacho, J. (1999). Mental Models in Predictive Reasoning with Perceptual and Semantic Base Rates: A Developmental Perspective. European Journal of Cognitive Psychology, 11 (4), 499- 529.
Ruffman, T., Perner, J., Olson, D. R., & Doherty, M. (1993). Reflecting on scientific thinking: Children’s understanding of the hypothesis-evidence relation. Child Development, 64, 1617–1636.
Shtulman, A., & Carey, S. (2007). Improbable or impossible? How children reason about the possibility of extraordinary events. Child Development, 78, 1015 – 1032.
Singh, P. (2000). Understanding the concepts of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics. 43, 271-292.
Sophian, C., & Wood, A. (1997). Proportional Reasoning in Young children : The Parts and the Whole of It. Journal of Educational Psychology, 89(2), 309-317.
Spinillo, A. G. & Bryant, P. (1991). Children's Proportional Judgments: The Importance of "Half". : Child Development, 62(3), 427-440.
Tourniaire, F. (1986). Proportions in elementary school. Educational Studies in Mathematics, 17, 401-412.
Tversky, A. & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science,185, 1124-1131.
Wallsten, T. S. & Fillenbaum, S., & Cox, J. A. (1986). Base rate effects on the interpretations of probability and frequency expressions. Journal of Memory and Language, 25(5), 571–587.
Yost, P. A., Siegel, A. E., & Andrews, J. M. (1962). Nonverbal Probability Judgments by Young Children. Child Development, 33(4), 769-780.
沈明勳、劉祥通(2002)。分析學生解比例問題文獻-國小數學課程與教學的建議。科學教育研究與發展季刊,27,81-96。
林福來、黃敏晃、呂玉琴(1996)。分數啟蒙的學習與教學之發展性研究。科學教育學刊,4(2),161-196。new window
周玉秀(2006)。 從PISA 看數學素養與中小學數學教育。科學教育月刊,293,2-21。
洪繼賢、劉祥通(2004)。一位小五學生解分數單位量等分割問題的表現。
科學教育研究與發展季刊,35,53-75。
教育部(2007)。國民中小學九年一貫課程綱要。台北:教育部。new window
陳欣民、劉祥通(2002)。從兒童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。
蘇國樑(1995)。國小兒童統計概念分析之研究(I):資料分佈概念之分析。new window
空大人文學報,4,205-226。
美國數學教師學會 (National Council of Teachers of Mathematics):
  http://www.nctm.org/
紐西蘭國家教育部數學與統計課程的學習標準(Ministry of Education, The New Zealand Curriculum online):http://nzcurriculum.tki.org.nz/National-Standards/Mathematics-standards/The-standards

 
 
 
 
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