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。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。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。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