Fairness of dice: A longitudinal study of students' beliefs and strategies for making judgments

Journal for Research in Mathematics Education

Volumn 34, Issue 4, 2003, Pages 270-304

  Watson, Jane M ^a   Moritz, Jonathan B ^a  

^a UNIVERSITY OF TASMANIA   (Australia)

Author keywords

Beliefs; Children's strategies; Cognitive development; Longitudinal studies; Probability; Qualitative methods

Indexed keywords

EID: 30244524301     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: 10.2307/30034785     Document Type: Article

References (53)

1. Amir, G. S., & Williams, J. S. (1999). Cultural influences on children's probabilistic thinking. Journal of Mathematical Behavior, 18, 85-107.
2. Australian Education Council. (1991). A national statement on mathematics for Australian schools. Carlton, Australia: Author.
3. Australian Education Council. (1994). Mathematics - work samples. Carlton, Australia: Author.
4. Batanero, C., & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30, 558-567.
5. Bennett, D. J. (1998). Randomness. Cambridge, MA: Harvard University Press.
6. Bernstein, P. L. (1998). Against the odds: The remarkable story of risk. New York: John Wiley and Sons.
7. Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy (structure of the observed learning outcome). New York: Academic Press.
8. Biggs, J. B., & Collis, K. F. (1991). Multimodal learning and the quality of intelligent behaviour. In H. A. H. Rowe (Ed.), Intelligence: Reconceptualisation and measurement (pp. 57-76). Hillsdale, NJ: Lawrence Erlbaum Associates.
9. Borovcnik, M., & Bentz, H. J. (1991). Empirical research in understanding probability. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 73-105). Dordrecht, The Netherlands: Kluwer Academic Publishers.
10. Bright, G. W., Harvey, J. G., & Wheeler, M. M. (1981). Fair games, unfair games. In A. P. Shulte (Ed.), Teaching Statistics and Probability (pp. 49-59). Reston, VA: National Council of Teachers of Mathematics.
11. Burrill, G., & Romberg, T. A. (1998). Statistics and probability for the middle grades: Examples from Mathematics in Context. In S. P. Lajoie (Ed.), Reflections on statistics: Learning, teaching and assessment in grades K-12 (pp. 33-59). Mahwah, NJ: Lawrence Erlbaum Associates.
12. Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? An exploratory research study. Educational Studies in Mathematics, 15, 1-24.
13. Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96-105.
14. Garfield, J., & Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: Implications for research. Journal for Research in Mathematics Education, 19, 44-63.
15. Green, D. R. (1983). Shaking a six. Mathematics in Schools, 12(5), 29-32.
16. Green, D. R. (1986). 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, BC: The Organizing Committee, ICOTS2.
17. Green, D. (1991). A longitudinal study of pupils' probability concepts. In D. Vere-Jones (Ed.), Proceedings of the Third International Conference on Teaching Statistics. Volume 1: School and general issues (pp. 320-328). Voorburg, The Netherlands: International Statistical Institute.
18. Green, D. (1993). Data analysis: What research do we need? In L. Pereira-Mendoza (Ed.), Introducing data analysis: Who should teach it and how? (pp. 219-239). Voorburg, The Netherlands: The International Statistical Institute.
19. 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 on statistics: Learning, teaching and assessment in grades K-12 (pp. 121-148). Mahwah, NJ: Lawrence Erlbaum Associates.
20. Jacobs, V. R. (1999). How do students think about statistical sampling before instruction? Mathematics in the Middle School, 5, 240-263.
21. Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3, 430-454.
22. Kerslake, D. (1974). Some children's views on probability. Mathematics in School, 3(4), 22.
23. Konold, C., Pollatsek, A., Well, A., Lohmeier, J., & Lipson, A. (1993). Inconsistencies in probabilistic reasoning of novices. Journal for Research in Mathematics Education, 24, 392-414.
24. Lajoie, S. P., Jacobs, V. R., & Lavigne, N. C. (1995). Empowering children in the use of statistics. Journal of Mathematical Behavior, 14, 401-423.
25. Lidster, S. T., Pereira-Mendoza, L., Watson, J. M., & Collis, K. F. (1995, November). What's Fair for Grade 6? Paper presented at the Annual Conference of the Australian Association for Research in Education, Hobart, Tasmania.
26. Lidster, S. T., Watson, J. M., Collis, K. F., & Pereira-Mendoza, L. (1996). The relationship of the concept of fair to the construction of probabilistic understanding. In P. C. Clarkson (Ed.), Technology in mathematics education: Proceedings of the Nineteenth Annual Conference of the Mathematics Education Research Group of Australasia (pp. 352-359). Melbourne: Mathematics Education Research Group of Australasia.
27. Maher, C. (1998). Is this game fair? The emergence of statistical reasoning in young children. In L. Pereira-Mendoza, L. S. Kea, T. W. Kee, & W. Wong (Eds.), Statistical education: Expanding the network: Proceedings of the Fifth International Conference on Teaching of Statistics (pp. 53-59). Singapore: International Association for Statistical Education.
28. Metz, K. E. (1997). Dimensions in the assessment of students' understanding and application of chance. In I. Gal & J. B. Garfield (Eds.), The assessment challenge in statistics education (pp. 223-238). Amsterdam, The Netherlands: IOS Press.
29. Metz, K. E. (1998). 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: Lawrence Erlbaum Associates.
30. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks, CA: Sage.
31. Ministry of Education. (1992). Mathematics in the New Zealand curriculum. Wellington, New Zealand: Author.
32. Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95-137). Washington, D.C.: National Academy Press.
33. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
34. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
35. Peterson, I. (1998). The jungle of randomness: Mathematics at the edge of uncertainty. London: Penguin.
36. Ritson, R. (2000). A question of choice. Australian Primary Mathematics Classroom, 5(3), 10-14.
37. Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465-494). New York: National Council of Teachers of Mathematics and MacMillan.
38. Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Dordrecht, The Netherlands: Kluwer Academic Publishers.
39. Truran, J. (1985). Children's understanding of symmetry. Teaching Statistics, 7(3), 69-74.
40. Truran, K. (1995). Animism: A view of probability behaviour. In B. Atweh & S. Flavel (Eds.), Galtha: Proceedings of the Eighteenth Annual Conference of the Mathematics Education Research Group of Australasia (pp. 537-542). Darwin, Australia: Mathematics Education Research Group of Australasia.
41. Vidakovic, D., Berenson, S., & Brandsma, J. (1998). Children's intuition of probabilistic concepts emerging from fair play. In L. Pereira-Mendoza, L. S. Kea, T. W. Kee, & W. Wong (Eds.), Statistical education: Expanding the network: Proceedings of the Fifth International Conference on Teaching of Statistics (pp. 67-73). Singapore: International Association for Statistical Education.
42. Watson, J. M. (1993). Introducing the language of probability through the media. In M. Stephens, A. Wayward, D. Clarke, & J. Izard (Eds.), Communicating mathematics - Perspectives from current research and classroom practice in Australia (pp. 119-139). Melbourne: Australian Council for Educational Research.
43. Watson, J. M. (1994). Instruments to assess statistical concepts in the school curriculum. In National Organizing Committee (Ed.), Proceedings of the Fourth International Conference on Teaching Statistics. Volume 1 (pp. 73-80). Rabat, Morocco: National Institute of Statistics and Applied Economics.
44. Watson, J. M. (2001). Longitudinal development of inferential reasoning by school students. Educational Studies in Mathematics, 47, 337-372.
45. Watson, J. M. (2002). When 2 + 2 ≠ 4 and 6 + 6 ≠ 12 in data and chance. New England Mathematics Journal, 34(2), 56-68.
46. Watson, J. M., & Chick, H. L. (2001). Factors influencing the outcomes of collaborative mathematical problem solving: An introduction. Mathematical Thinking and Learning, 3(2 & 3), 125-173.
47. Watson, J. M., Collis, K. F., & Moritz, J. B. (1997). The development of chance measurement. Mathematics Education Research Journal, 9, 60-82.
48. Watson, J. M., & Moritz, J. B. (1998). Longitudinal development of chance measurement. Mathematics Education Research Journal, 10, 103-127.
49. Watson, J. M., & Moritz, J. B. (1999). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37, 145-168.
50. Watson, J. M., & Moritz, J. B. (2000a). Developing concepts of sampling. Journal for Research in Mathematics Education, 31, 44-70.
51. Watson, J. M., & Moritz, J. B. (2000b). The longitudinal development of understanding of average. Mathematical Thinking and Learning, 2 (1 & 2), 11-50.
52. Watson, J. M., & Moritz, J. B. (2001a). Development of reasoning associated with pictographs: Representing, interpreting, and predicting. Educational Studies in Mathematics, 48, 47-81.
53. Watson, J. M., & Moritz, J. B. (2001b). The role of cognitive conflict in developing students' under-standing of chance measurement. In J. Bobis, B. Perry, & M. Mitchelmore (Eds.), Numeracy and beyond: Proceedings of the Twenty-Fourth Annual Conference of the Mathematics Education Research Group of Australasia (pp. 523-530). Sydney: Mathematics Education Research Group of Australasia.