Recent research suggests that children could be engaged in probability tasks at an early age and task characteristics seem to play an important role in the way children perceive an activity. To this direction in the present article we investigate the role of some basic characteristics of probabilistic tasks in their design and implementation. In order to do so, we present the structure and the content of a series of tasks that were implemented in a kindergarten school focusing on two characteristics: the context and the materials used. In our case, the performance of the experiment together with the use of dice and spinners seemed to be critical in children's development of probabilistic thinking.
Arbaugh, F. and Brown, C. (2005) `Analyzing mathematical tasks: a catalyst for change ?' Journal of Mathematics Teacher Education8: 499-536.
2.
Becker, P.J. and Selter, C. (1996) `Elementary school practices', in A. Bishop, K. Clements, C. Keitel, J. Kilpatrick and C. Laborde (eds) International Handbook of Mathematics Education, pp. 511-64. Dordrecht : Kluwer Academic.
3.
Byrnes, P. and Beilin, H. (1991) `The cognitive basis of uncertainty'. Human Development34: 189-203.
4.
Christiansen, B. and Walter, G. (1986) `Task and activity', in B. Christiansen, A.G. Howson and M. Otte (eds) Perspectives on Mathematics Education, pp. 243-307. Dordrecht: Reidel.
5.
Cobb, P. and Bauersfeld, H., eds (1995) The Emergence of Mathematical Meaning: Interaction in Classroom Cultures. Mahweh, NJ : Lawrence Erlbaum Associates.
6.
Cyprian Institute of Education (CIE) (1997 ) National Curriculum (in Greek).
7.
DCFS (2007) `Department for children, schools and families: the standards site'. Available at http://www.standards.dfes.gov.uk (accessed 19 December 2007).
8.
Doyle, W. (1988) `Work in mathematics classes: the context of students' thinking during instruction'. Educational Psychologist23: 167-80.
9.
Fischbein, E. (1975) The Intuitive Sources of Probabilistic Thinking in Children. New York: Reidel USA .
10.
Fischbein, E. and Schnarch, D. (1997) `The evolution with age of probabilistic, intuitively based misconceptions'. Journal for Research in Mathematics Education28(1): 96-105.
11.
Freudenthal, H. (1973) Mathematics as an Educational Task. Dordrecht: Reidel.
12.
Gellert, U. (2004) `Didactic material confronted with the concept of mathematical literacy'. Educational Studies in Mathematics55: 163-79.
13.
Gravemeijer, K. and Doorman, M. (1999) `Context problems in realistic mathematics education: a calculus course as an example'. Educational Studies in Mathematics39: 111-29.
14.
Gravemeijer, K. and Stephan, M. (2002) Emergent models as an instructional design heuristic' , in K. Gravemeijer, R. Lehrer, B. van Oers and L. Verschaffel (eds) Symbolizing, Modeling and Tool Use in Mathematics Education, pp. 145-69. Dordrecht : Kluwer Academic.
15.
Greer, B. (2001) `Understanding probabilistic thinking: the legacy of Efraim Fischbein'. Educational Studies in Mathematics45: 15-33.
16.
Hellenic Mathematical Society (HMS) (1998) `New mathematics curriculum'. Euclides γ Review of Mathematics Education47-50: 7-63 (in Greek).
17.
Jones, G. and Thornton, C. (1992) Data, Chance and Probability: Grades 1-3. Vernon Hills, IL: Learning Resources.
18.
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 Mathematics32: 101-25.
19.
Kafoussi, S. (2004) `Can kindergarten children be successfully involved in probabilistic tasks?' Statistics Education Research Journal3(1): 29-39.
20.
Koshy, V., Ernest, P. and Casey, R. (1999) Mathematics for Primary Teachers. New York: Routledge.
21.
Langrall, W.C. and Mooney, S.E. (2005) `Characteristics of elementary school students' probabilistic reasoning', in G. Jones (ed.) Exploring Probability in School: Challenges for Teaching and Learning, pp: 95-119. New York: Springer.
22.
Moyer, P.S. (2001) `Are we having fun yet? How teachers use manipulatives to teach mathematics'. Educational Studies in Mathematics47: 175-97.
23.
NCTM (2007) `National Council of Teachers of Mathematics: Standards'. Available at http://www.nctm.org (accessed 19 December 2007).
24.
Nicol, C. and Crespo, S. (2005) `Exploring mathematics in imaginative places: rethinking what counts as a meaningful context for learning mathematics'. School Science and Mathematics105(5): 240-51.
25.
Piaget, J. and Inhelder, B. (1975) The Origin of the Idea of Chance in Children, trans. L. Leake, P. Burrell and H. Fischbein. London: Routledge and Kegan Paul.
26.
Pratt, D. (2000) `Making sense of the total of two dice'. Journal for Research in Mathematics Education31: 602-25.
27.
Schwartz, S. and Curcio, F. (1995) `Learning mathematics in meaningful contexts: an action-based approach in the primary grades', in P. House and A. Coxford (eds) Connecting Mathematics Across the Curriculum, pp. 116-23. Reston, VA: National Council of Teachers of Mathematics.
28.
Shaughnessy, M. (1992) `Research in probability and statistics: reflections and Directions', in D.A. Grows (ed.) Handbook of Research on Mathematics Teaching and Learning A Project of the National Council of Teachers of Mathematics, pp. 465-94. New York: Macmillan Library.
29.
Skoumpourdi, C. (2004) `The Teaching of Probability Theory as a New Trend in Greek Primary Education'. Paper presented at the 10th International Congress on Mathematical Education, Denmark, July. (Available at http://www.icme-organisers.dk/tsg01/Skoumbourdi_(rev)1.doc)
30.
Skoumpourdi, C. and Kalavassis, F. (2003) `Didactic Materials Used in Probabilistic Activities' . Paper presented at the CIEAEM 55 (pp. 35-6) Poland , July.
31.
Skoumpourdi, C., Tatsis, K. and Kafoussi, S. (2007) `Kindergarten children's informal knowledge about probability'. Paper presented at the CIEAEM 59 (pp. 59-63) Budapest, July.
32.
Sobel, A.M. and Maletsky, M.E. (1988) Teaching mathematics a sourcebook of aids, activities and strategies, 2nd edn. Englewood Cliffs, NJ: Prentice Hall.
33.
Stein, M.K. and Smith, M.S. (1998) `Mathematical tasks as a framework for reflection: from research to practice'. Mathematics Teaching in the Middle School3(4): 268-75.
34.
Steinbring, H. (1991) `The theoretical nature of probability in the classroom' , in R. Kapadia and M. Borovcnik (eds) Chance Encounters: Probability in Education , pp. 135-68. Dordrecht: Kluwer Academic.
35.
Streefland, L. (2000) Realistic Mathematics Education, ed. E. Koleza (in Greek). Athens: Leader Books.
36.
Szendrei, J. (1996) `Concrete Materials in the Classroom', in A. Bishop, K. Clements, C. Keitel, J. Kilpatrick and C. Laborde (eds) International Handbook of Mathematics Education, pp. 411-34. Dordrecht: Kluwer Academic.
37.
Treffers, A. (1987) Three dimensions: A Model of Goal and Theory Description in Mathematics Instruction: The Wiskobas Project. Dordrecht : Reidel.
38.
van den Heuvel-Panhuizen, M. (2003) `The didactical use of models in realistic mathematics education: an example from a longitudinal trajectory on percentage'. Educational Studies in Mathematics54: 9-35.
39.
Varol, F. and Farram, D. (2006) `Early mathematical growth: how to support young children's mathematical development'. Early Childhood Education33(6): 381-7.
40.
Watson, J.D. and Moritz, J.B. (2003) `Fairness of dice: a longitudinal study of students' beliefs and strategies for making judgments'. Journal for Research in Mathematics Education34: 270-304.
