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Characteristics of Elementary School Students' Probabilistic Reasoning

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Book cover Exploring Probability in School

Part of the book series: Mathematics Education Library ((MELI,volume 40))

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References

  • Acredolo, C., O'Connor, J., Banks, L., & Horobin, K. (1989). Children's ability to make probability estimates: Skills revealed through application of Anderson's functional measurement methodology, Child Development, 60, 933–945.

    Google Scholar 

  • Australian Education Council. (1994). Mathematics: A curriculum profile for Australian schools. Carlton, VIC: Curriculum Corporation.

    Google Scholar 

  • Benson, C. T. (2000). Assessing students' thinking in modeling probability contexts. Unpublished doctoral dissertation, Illinois State University, Normal.

    Google Scholar 

  • Benson, C. T., & Jones, G. A. (1999). Assessing students' thinking in modeling probability contexts. The Mathematics Educator, 4(2), 1–21.

    Google Scholar 

  • Biggs, J. B., & Collis, K. F. (1991). Multimodal learning and the quality of intelligent behaviour. In H.A.H. Rowe (Ed.), Intelligence: Reconceptualization and measurement (pp. 57–76). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Borovcnik, M. & Bentz, H. (1991). Empirical research in understanding probability. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 73–106). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Borovcnik, M. & Peard, R. (1996). Probability. In A. Bishop et al. (Eds.), International handbook of mathematics education (Part 1, pp. 239–287). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Byrnes, J. P., & Beilin, H. (1991). The cognitive basis of uncertainty. Human Development, 34, 189–203.

    Article  Google Scholar 

  • Dessart, D. J. (1995). Randomness: A connection to reality. In P. A. House, & A. F. Coxford (Eds.), Connecting mathematics across the curriculum (pp. 177–181). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Department of Education and Science and the Welsh Office. (1991). National curriculum: Mathematics for ages 5 to 16. York, UK: Central Office of Information.

    Google Scholar 

  • English, L.D. (1993). Children's strategies for solving two-and three-dimensional combinatorial problems. Journal for Research in Mathematics Education, 22, 255–273.

    Article  Google Scholar 

  • Falk, R. (1983). Children's choice behaviour in probabilistic situations. In D. R. Grey, P. Holmes, V. Barnett, & G. M. Constable (Eds.), Proceedings of the First International Conference on Teaching Statistics (pp. 714–716). Sheffield, UK: Teaching Statistics Trust.

    Google Scholar 

  • Falk, R., & Wilkening, F. (1998). Children's construction of fair chances: Adjusting probabilities. Developmental Psychology, 34(6), 1340–1357.

    Article  Google Scholar 

  • Fay, A. L., & Klahr, D. (1996). Knowing about guessing and guessing about knowing: Preschoolers' understanding of indeterminacy. Child Development, 67, 689–716.

    Google Scholar 

  • Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht, The Netherlands: Reidel.

    Google Scholar 

  • Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht, The Netherlands: Reidel.

    Google Scholar 

  • Fischbein, E., Barbat, I., & Minzat, I. (1971). Intuitions primaires et intuitions secondaires dans l'initiation aux probabilities [Primary and secondary intuitions in the introduction to probability]. Educational Studies in Mathematics, 4, 264–280.

    Article  Google Scholar 

  • Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgments in children in adolescence. Educational Studies in Mathematics, 22, 523–549.

    Article  Google Scholar 

  • Fischbein, E., Pampu, I., Minzat, I. (1970). Comparison of ratios and the chance concept in children. Child Development, 41, 377–389.

    Google Scholar 

  • Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96–105.

    Article  Google Scholar 

  • Green, D. R. (1983). A survey of probability concepts in 3000 pupils aged 11–16 years. In D. R. Grey, P. Holmes, V. Barnett, G. M. Constable (Eds.), Proceedings of the First International Conference on Teaching of Statistics (pp. 766–783). Sheffield, UK: Teaching Statistics Trust.

    Google Scholar 

  • Green, D. R. (1988). Children's understanding of randomness: Report of a survey of 1600 children aged 7–11 years. In R. Davidson & J. Swift (Eds.), Proceedings of the Second International Conference on Teaching Statistics (pp. 287–291). Victoria, B.C.: University of Victoria.

    Google Scholar 

  • Greer, B. (2001). Understanding probabilistic thinking: The legacy of Efraim Fischbein. Educational Studies in Mathematics, 45, 15–33.

    Article  Google Scholar 

  • Hawkins, A. S., & Kapadia, R. (1984). Children's conceptions of probability: A psychological and pedagogical review. Educational Studies in Mathematics, 15, 349–377.

    Article  Google Scholar 

  • Horvath, J. K., & Lehrer, R. (1998). A model-based perspective on the development of children's understanding of chance and uncertainty. In S. P. Lajoie (Ed.), Reflections in statistics: Learning, teaching, and assessment in Grades K-12 (pp. 121–148). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Jones, G. A. (1974). The performances of first, second, and third grade children on five concepts of probability and the effects of grade, I.Q., and embodiments on their performances. Unpublished doctoral dissertation, Indiana University, Bloomington.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students' probabilistic thinking in instruction. Journal for Research in Mathematics Education, 30, 487–519.

    Article  Google Scholar 

  • Jones, G. A., Thornton, C. A., Langrall, C. W., & Tarr, J. E. (1999). Understanding students' probabilistic reasoning. In L. V. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning in Grades K-12: 1999 Yearbook (pp. 146–155). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Kafoussi, S. (2002). Learning opportunities in a kindergarten about the concept of probability. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26 th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 161–168). Norwich, England: UEA.

    Google Scholar 

  • Kahneman, D., & Tversky, A. (1982). Variants of uncertainty. Cognition, 11, 143–157.

    Article  Google Scholar 

  • Kelly, B.A., & Watson, J.M. (2002). Variation in a chance sampling setting: The lollies task. In B. Barton, K.C. Irwin, M. Pfannkuch, & M.O.J. Thomas (Eds.), Mathematics education in the South Pacific (Proceedings of the 26 th annual conference of the Mathematics Education Research Group of Australasia, Vol. 2, pp. 366–373). Sydney, NSW: MERGA.

    Google Scholar 

  • Konold, C. (1991). Understanding students' beliefs about probability. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 139–156). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Konold, C., Pollatsek, A., Well, A., Lohmeier, J., & Lipson, A. (1993). Inconsistencies in students' reasoning about probability. Journal for Research in Mathematics Education, 24, 392–414.

    Article  Google Scholar 

  • Kuzmak, S., & Gelman, R. (1986). Young children's understanding of random phenomena. Child Development, 57, 559–566.

    Google Scholar 

  • Lamprianou, I., & Lamprianou, T. A. (2003). The probabilistic thinking of primary school pupils in Cyprus: The case of tree diagrams In N. Pateman (Ed.), Proceedings of the 26 th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 173–180). Honolulu, Hawaii: University of Hawaii.

    Google Scholar 

  • Metz, K. E. (1998a). Emergent ideas of chance and probability in primary-grade children. In S. P. Lajoie (Ed.), Reflections on statistics: Learning, teaching, and assessment in grades K-12 (pp. 149–174). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Metz, K. E. (1998b). Emergent understanding and attribution of randomness: Comparative analysis of reasoning of primary grade children and undergraduates. Cognition and Instruction, 16, 285–365.

    Article  Google Scholar 

  • Moore, D. (1990). Uncertainity. In L. Steen (Ed.), On the shoulders of giants: A new approach to numeracy (pp. 95–137). Washington, DC: National Research Council.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston. VA: Author.

    Google Scholar 

  • Paparistodemou, E., Noss, R., & Pratt, D. (2002). Exploring in sample space: Developing young children's knowledge of randomness. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics, CapeTown, South Africa [CD-ROM]. Voorburg, The Netherlands: International Statistics Institute.

    Google Scholar 

  • Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in students (L. Leake, Jr., P. Burrell, & H. D. Fischbein, Trans.). New York: Norton (Original work published 1951)

    Google Scholar 

  • Polaki, M. V. (2002). Using instruction to identify key feautures of Basotho elementary students' growth in probabilistic thinking. Mathematical Thinking and Learning, 4, 285–314.

    Article  Google Scholar 

  • Polaki, M. V., Lefoka, P. J., & Jones, G. A. (2000). Developing a cognitive framework for describing and predicting Basotho students' probabilistic thinking. Boleswa Educational Research Joural, 17, 1–21.

    Google Scholar 

  • Pratt, D. (1998). The co-ordination of meanings for randomness. For the Learning of Mathematics, 18(3), 2–11.

    Google Scholar 

  • Pratt, D. (2000). Making sense of the total of two dice. Journal for Research in Mathematics Education, 31, 602–625.

    Article  Google Scholar 

  • Pratt, D. & Noss, R. (2002). The micro-evolution of mathematical knowledge: The case of randomness. Journal of the Learning Sciences, 11.4, 453–488.

    Article  Google Scholar 

  • Ritson, R. (1998). The development of primary school children's understanding of probability, Unpublished thesis, Queen's University, Belfast.

    Google Scholar 

  • Ritson, R. (1999). Conceptions of probability in 5 to 12 year-old children. Australian Mathematics Teacher, 55, 25–28.

    Google Scholar 

  • Shaughnessy, J. M. (1992). Research in probability and statistics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465–494). New York: Macmillan.

    Google Scholar 

  • Steinbring, H. (1991). The theoretical nature of probability in the classroom. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 135–168). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Tarr, J. E., & Jones, G. A. (1997). A framework for assessing middle school students' thinking in conditional probability and independence. Mathematics Education Research Journal, 9, 39–59.

    Google Scholar 

  • Truran, J. (1994). Diagnosing children's probabilistic understanding. In G. Bell, B. Wright, N. Leeson, & J. Geake (Eds.), Proceedings of the 17 th conference of the Mathematics Education Research Group of Australasia (pp.623–630). Lismore, Australia: MERGA.

    Google Scholar 

  • Truran, K. (1995). Animism: A view of probability behaviour. In B. Atweh, & S. Flavel (Eds.), Proceedings of the 18 th conference of the Mathematics Education Research Group of Australasia (pp.537–541). Darwin, Australia: MERGA.

    Google Scholar 

  • Volkova, T. (2003). Assessing Russian children's thinking in probability. Unpublished master's thesis, Illinois State University, Normal.

    Google Scholar 

  • Watson, J. M. (1998). Numeracy benchmarks for years 3 and 5: What about chance and data? In C. Kanes, M. Goos, & E. Warren (Eds.), Proceedings of the 21 st Conference of the Mathematics Education Research Group of Australasia (pp.669–676). Gold Coast, Australia: MERGA.

    Google Scholar 

  • Watson, J. D., & Moritz, J. B. (2003). Fairness of dice: A longitudinal study of students' beliefs and strategies for making judgments. Journalfor Research in Mathematics Education, 34, 270–304.

    Article  Google Scholar 

  • Way, J. (1996). Children's strategies for comparing two types of random generators. In L. Puig & A. Gutierrez (Eds.), Proceedings of the 20 th conference of the International Groupfor the Psychology of Mathematics Education (Vol. 4, pp. 419–526). Valencia, Spain: Universitat de Valencia.

    Google Scholar 

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Langrall, C.W., Mooney, E.S. (2005). Characteristics of Elementary School Students' Probabilistic Reasoning. In: Jones, G.A. (eds) Exploring Probability in School. Mathematics Education Library, vol 40. Springer, Boston, MA. https://doi.org/10.1007/0-387-24530-8_5

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