Preparing pre-school teachers for teaching probability



Contemporary mathematics curricula introduce probabilistic activities as early as pre-school. Through a long term pre-school teacher professional development programme we tried to investigate pre-school teachers’ beliefs about teaching probability in pre-school as well as their self-efficacy probabilistic teaching beliefs and whether these beliefs were possible to change. The programme was designed based on the assumption that teachers’ beliefs, which are formulated through knowledge and experiences, inform and formulate their classroom practice. We worked with a small group, thus our findings can only be viewed as trends rather than generalizable conclusions. Nevertheless these findings show encouraging trends towards the verification of our initial assumption.


Mathematics curricula, professional development, teacher beliefs, pre-school mathematics, probability

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Ajzen, I., & Fishbein, M. (2000). Attitudes and the attitude-behavior relation: reasoned and automatic processes. In W. Stroebe & M. Hewstone (Eds), European Review of Social Psychology (Vol. 11, pp. 1–33). Chichester, UK: Wiley.

Amir, G. S., & Williams, J. S., (1999). Cultural influences on children’s probabilistic thinking. Journal of Mathematical Behavior, 18(1), 85-107.

Antonopoulos, K., & Zacharos, K. (2013). Probability constructs in preschool education and how they are taught. Teachers and Teaching: Theory and Practice, 19(5), 575-589.

Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: the unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (pp. 433-456). Washington, DC: American Educational Research Association.

Bandura, A. (1997). Self-efficacy: the exercise of control. NY: W. H. Freeman and Company.

Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In G. A. Jones (Ed.), Exploring probability in school. Challenges for teaching and learning (pp. 15-37). N.Y, U.S.A: Springer.

Batanero, C., Burrill, G., & Readin, C. (2011). Overview: challenges for teaching statistics in school mathematics and preparing mathematics teachers. In C. Batanero, G. Burrill & C. Reading (Eds), Teaching statistics in school mathematics-challenges for teaching and teacher education: a joint ICMI/IASE study, (pp. 407-418). Heidelberg etc: Springer.

Batanero, C., & Diaz, C. (2012). Training school teachers to teach probability: reflections and challenges. Chilean Journal of Statistics, 3(1), 3-13.

Batanero, C., Arteaga, P., Serrano, L., & Ruiz, B. (2014). Prospective primary school teachers’ perception of randomness. In E. J. Chernoff & B. Sriraman (Eds), Probabilistic thinking. Presenting plural perspectives (pp. 345-366). Dordrecht etc: Springer.

Baturo, A., Cooper, T., Doyle, K., & Grant, E. (2007). Using three levels in design of effective teacher-education tasks: the case of promoting conflicts with intuitive understandings in probability. Journal of Mathematics Teacher Education, 10(4/6), 251-259.

Begg, A., & Edwards, R. (1999). Teachers’ ideas about teaching statistics. Proceedings of the 1999 Combined Conference of the Australian Association for Research in Education and New Zealand Association for Research in Education. Melbourne: AARE & NZARE. Retrieved from

Borim, C., & Coutinho, C. (2008). Reasoning about variation of a univariate distribution: a study with secondary mathematics teachers. In C. Batanero, G. Burrill, C. Reading & A. Rossman (Eds), Joint ICMI/IASE study: teaching statistics in school mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference, ICMI and IASE, Monterrey. Retrieved from

Borovcnik, M., & Peard, R. (1996). Probability. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Eds), International Handbook of Mathematics Education (pp. 239-288). Dordrecht: Kluwer.

Chester, M. D., & Beaudin, B. Q. (1996). Efficacy beliefs of newly hired teachers in urban schools. American Educational Research Journal, 33(1), 233-257.

Copley, J. V. (2004). The early childhood collaborative: a professional development model to communicate and implement. In D. H. Clements & J. Sarama (Eds), Engaging young children in mathematics, standards for Early Childhood Mathematics Education, (pp. 401-414). London: Lawrence Erlbaum Associates.

Estrada, A., Batanero, C., & Lancaster, S. (2011). Teachers’ attitudes towards statistics. In C. Batanero, G. Burrill & C. Reading (Eds), Teaching statistics in school mathematics. Challenges for teaching and teacher education (pp. 163-174). Dordrecht etc: Springer.

Fullan, G. M. (1991). The new meaning of educational change. New York: Cassell.

Franklin, C., Kader, G., Mewborn, D. S., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2005). A curriculum framework for K-12 statistics education. GAISE Report. American Statistical Association. Retrieved from

Ghaith, G., & Shaaban, K. (1999). The relationship between perceptions of teaching concerns, teacher efficacy, and selected teacher characteristics. Teaching and Teacher Education, 15, 487-496.

Greer, B., & Mukhopadhyay, S. (2005). Teaching and learning the mathematization of uncertainty: historical, cultural, social and political contexts. In G. A. Jones (Ed.), Exploring probability in school. Challenges for teaching and learning (pp. 344-366). N.Y, U.S.A: Springer.

Grootenboer, P., & Hemmings, B. (2007). Mathematics performance and the role played by affective and background factors. Mathematics Education Research Journal, 19(3), 3-20.

Hannigan, A., Gill, O., & Leavy, A. M. (2013). An investigation of prospective secondary mathematics teachers’ conceptual knowledge of and attitudes towards statistics. Journal of Mathematics Teacher Education, 16(6), 427-449.

Hunter, L. T., & Markman, B. A. (2016). Proposing an operational definition of science teacher beliefs. Journal of Science Teacher Education, 27(6), 675-691.

Jones, G. A. (2005). Introduction. In G. A. Jones (Ed.), Exploring probability in school. Challenges for teaching and learning (pp. 1-12). New York: Springer.

Jones, G. A., & Thornton, C. (2005). An overview of research into the teaching and learning of probability. In G. A. Jones (Ed.), Exploring probability in school. Challenges for teaching and learning (pp. 65-92). N.Y, U.S.A: Springer.

Kafoussi, S. (2004). Can kindergarten children be successfully involved in probabilistic tasks? Statistics Education Research Journal, 3(1), 29-39.

Kyriakides, L. (2005). Evaluating school policy on parents working with their children in class. The Journal of Educational Research, 98(5), 281-298.

Markman, A. B., & Dietrich, E. (2000). In defense of representation. Cognitive Psychology, 40, 138–171.

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Retrieved from

Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children. London: Routledge & Kegan Paul.

Pajares, M. F. (1992). Teachers’ beliefs and educational research: cleaning up a messy construct. Review of Educational Research, 62(3), 307-332.

Peterson, P. L., Fennema, E., Carpenter, T. P., & Loef, M. (1989). Teachers’ pedagogical content beliefs in mathematics. Cognition and Instruction, 6(1), 1-40.

Philippou, G. N., & Christou, C. (1998). The effects of a preparatory mathematics program in changing prospective teachers’ attitudes toward mathematics. Educational Studies in Mathematics, 35, 189-206.

Ruffell, M., Mason, J., & Allen, B. (1998). Studying attitude to mathematics. Educational Studies in Mathematics, 35, 1-18.

Sachs, J. (1997). Reclaiming the agenda of teacher professionalism: an Australian experience. Journal of Education for Teaching, 23, 263–275.

Shiakalli, M. A., & Zacharos, K. (2014). Building meaning through problem solving practices: the case of four-year olds. Journal of Mathematical Behavior, 35, 58-73.

Shiakalli, M. A., & Zacharos. K. (2012). The contribution of external representations in pre-school mathematical problem solving. International Journal of Early Years Education, 20(4), 315-331.

Shulman, L. S. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57, 1-22.

Skoumpourdi, C., Kafoussi, S., & Tatsis, K. (2009). Designing probabilistic tasks for kindergartners. Journal of Early Childhood Research, 7(2), 153-172.

Soodak, L., & Podell, D. M. (1996). Teacher efficacy: toward the understanding of a multi-faceted construct. Teaching & Teacher Education, 12(4), 401-411.

Stohl, H. (2005). Probability in teacher education and development. In G. A. Jones (Ed.), Exploring probability in school. Challenges for teaching and learning (pp. 344-366). N.Y, U.S.A: Springer.

Tarr, J. E. (2002). The confounding effects of "50-50 chance" in making conditional probability judgments. Focus on Learning Problems in Mathematics, 24, 35-53.

TIMSS (2007). International version of the background questionnaires – Population 2. Retrieved from

Tschannen-Moran, M., Woolfolk Hoy, A., & Hoy, W. K. (1998). Teacher efficacy: its meaning and measure. Review of Educational Research, 68(2), 202-248.

Vacc, N. N., & Bright, G. W. (1998). Elementary preservice teacher’s changing beliefs and instructional use of children’s mathematical thinking. Journal for Research in Mathematics Education, 29(3), 89-110.

Watson, J. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: the case of chance and data. Journal of Mathematics Teacher Education, 4, 305-337.

Watson, J. M., Caney, A., & Kelly, B. A. (2004). Beliefs about chance in the middle years: longitudinal change. In I. Putt, R. Faragher & M. McLean (Eds), Mathematics education for the third millennium: towards 2010. Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 581-588). Sydney, NSW: MERGA.

Wilkins, J. L. M. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11(2), 139-164.

Williams, A., & Nisbet, S. (2014). Primary school students’ attitudes to and beliefs about probability. In J. Egan & S. Chernoff-Bharath (Eds), Probabilistic thinking. Presenting plural perspectives (pp. 683-708). Germany and USA: Springer.

Zacharos, K., Koliopoulos, D., Dokimaki, M., & Kassoumi, H. (2007). Attitudes and beliefs of prospective Early Childhood Education teachers towards mathematics and its instruction. European Journal of Teacher Education, 30(3), 305-318.


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