The intuitive perceptions of Kindergarten children , Primary School and High School School in problems of sum of two dice with the help of a microcosm

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Published: Dec 1, 2017
DOI: https://doi.org/10.12681/enedim.15033
Keywords:
ITC Probabilities Intuitive perceptions
Γιώργος Φεσάκης (Giorgos Fesakis)
University of Aegean
Σόνια Καφούση (Sonia Kafoussi)
University of Aegean
Ελευθερία Μαλισιόβα (Eleftheria Malisiova)
University of Aegean
Abstract

Children from a young age construct intuitive perceptions about the probability concepts that are adaptable through appropriate learning interventions. The computers with the capability of generating large sequences of random numbers and multiple dynamic representations of phenomena offer new opportunities to stochastic concepts learning. In this paper we present a case study on the impact of a software microworld-game in intuitive concept of probability development. The proposed microworld problem is based on the sum of two dice and the study of its impact concerns to kindergarten, middle school, and junior high school children. The experimental fi ndings support the learning value of the proposed microworld in the diagnosis of primary and secondary intuitive perceptions of probabilistic concepts in the context of an attractive and engaging learning activity.

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Author Biographies
Γιώργος Φεσάκης (Giorgos Fesakis), University of Aegean
Lecturer
Σόνια Καφούση (Sonia Kafoussi), University of Aegean
Ass. Professor
Ελευθερία Μαλισιόβα (Eleftheria Malisiova), University of Aegean
Kindergarten Teacher
References
Drier, H. S., (2000). Children’ s probabilistic reasoning with a computer microworld. Διδακτορική μελέτη που παρουσιάστηκε στο Curry School of Education University of Virginia.
Fesakis G., Kafoussi S.. (2009). Kindergarten children capabilities in combinatorial problems using computer microworlds and manipulatives. In the proceedings of the 33rd Conference of the IGPME (PME33), Thessaloniki, Greece, 19-24 July, 2009,
Vol. III, pp. 41-48.
Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht, The Netherlands: Reidel.
Fischbein, E., & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? Educational Studies in Mathematics, 15, 1-24.
Fischbein, E., Pampu, I., & Manzat, I. (1970a). Comparisons of ratios and the chance concept in children. Child Development, 41,377-389.
Fischbein, E. and Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education 28 (1), 96-105.
Freudenthal, Η. (1973). Mathematics as an educational task. Reidel Publishing Company/ Dordrecht – Holland.
Frykholm, J., A. (2001). Reasearch, refl ection, practice. Building on intuitive notions of chance, Teaching Children Mathematics, 8(2,), NCTM, pp. 112-118.
Green, D. R. (1983). A survey of probability concepts in 3000 pupils aged 1 1-16 years. In D. R. Grey, P. Holmes, V. Barnett, & G. M.. Constable (Eds.), Proceedings of the First International Conference on Teaching Statistics (pp. 766-783). Sheffi eld, UK: Teaching Statistics Trust.
Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York: Basic Books.
Jones, G. A., & Thornton, C. A. (2005). An overview of research into the teaching and learning probability. Mathematics Education Library, 40 (1).
Jones, G., Langrall, C., Thornton, C. and Mogill, T. (1997). A framework for assessing and nurturing young children’s thinking in probability. Educational Studies in Mathematics, 32, 101-125.
Kafoussi, S. (2004) Can kindergarten children be successfully involved in probabilistic tasks?. Statistics Education Research Journal 3(1), 29-39.
Kahnernan, D., & Tversky, A. (1972). Subjective Probability: A judgement of representativeness. Cognitive Psychology, 3, 430-454.
Kahnernan, D., & Tversky, A. (1973). On the psychology of prediction. Psychological review, 80 (4), 237- 251.
Konold, C. (1983). Conceptions about probability: Reality between a rock and a hard place. Unpublished doctoral dissertation, University of Massachusetts, Boston.
Konold, C. (1989). Informal conceptions of probability. Cognition and Instruction, 6, 59-98.
Konold, C. (1991). Understanding students’ beliefs about probability. In E. von Glaserfeld (Ed.), Radical Constructivism in Mathematics Education (pp. 139-156). Holland:Kluwer.
Langrall, W. C. and Mooney, S. E. (2005). Characteristics of elementary school students’ probabilistic reasoning. Ιn G. Jones (Εd.), Exploring probability in school:Challenges for teaching and learning ( pp. 95-119). Springer.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Pratt, D. (2000). Making sense of the total of two dice. Journal of Research in Mathematics Education, 31(5),602-625.
Resnick, M., Maloney, J., Monroy-Hernández, A., Rusk, N., Eastmond, E., Brennan, K., Millner, A., Rosenbaum, E., Silver, J., Silverman, B., Kafai, Y., (2009). Scratch: Programming for All, November 2009, Communications of the ACM, 52(11), pp. 60- 67.
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.
Shepler, J. L. (1970). Parts of a systems approach to the development of a unit in probability and statistics for the elementary school. Journal for Research in Mathematics Education, 1, 197-205.
Steinbring, H. (1984). Mathematical concepts in didactical situations as complex systems: The case of probability. In H. Steiner & N. Balacheff (Eds.), Theory of mathematics education (TME: ICME 5): Occasional paper 54 (pp. 56-88). Bielefeld: IDM.
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1 124- 1 13 1.
Vahey, P. (1998). Promoting Student Understanding of Elementary Probability Using a Technology-Mediated Inquiry Environment. Unpublished doctoral dissertation, University of California-Berkeley, Berkeley, CA.
Way, J. (2003). The development of children’s notions of probability. Unpublished doctoral dissertation, University of Western Sydney.
Φεσάκης Γ., Καφούση Σ., Σκουμπουρδή Χρ., (2008). Δημιουργώντας στοχαστικές εμπειρίες για την εξέλιξη των διαισθητικών αντιλήψεων νηπίων με τη βοήθεια διαδικτυακών μικρόκοσμων, 6ο Πανελλήνιο συνέδριο, οι ΤΠΕ στην εκπαίδευση, Κύπρος 25-28 Σεπ. 2008, από http://www.etpe.gr.
Φεσάκης, Γ. , Καφούση, Σ. , (2008). Ανάπτυξη συνδυαστικής σκέψης νηπίων με τη βοήθεια ΤΠΕ: παραγωγή συνδυασμών με επανατοποθέτηση. Πιλοτική έρευνα, 6ο Πανελλήνιο συνέδριο, Οι ΤΠΕ στην εκπαίδευση, Κύπρος 25-28 Σεπ. 2008, από http://www.etpe.gr.