Abstract
Probabilities tend to become an integral part of early childhood mathematics curricula. Research has shown that at the age of 4, children indicate basics of probabilistic reasoning and can engage with probabilistic tasks and uncertainty. The aim of this study is to examine whether methodological and design alterations influence children’s inferences of the most probable event. Children (N = 480), aged 4–6 years, participated in choice tasks involving probabilistic predictions after repeated random draws, in groups of 3. Participation was either through the interaction with tangible manipulatives (Condition 1) or through computer-based manipulatives (Condition 2). During participation, children recorded their initial predictions and the actual outcomes on specially designed sheets and each task was repeated three times. Findings imply that preschoolers appreciate what is more probable and show a significantly better understanding of the likelihood of events when interacting with tangible rather than computer-based manipulatives and when the sample space is simpler (p < .01); thus, repetition was not found to be significant. Such results are important when designing and embedding basic probabilistic notions in the early childhood classroom, aiming at promoting children’s probability literacy.
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Alcoholado, C., Diaz, A., Tagle, A., Nussbaum, M., & Infante, C. (2016). Comparing the use of the interpersonal computer, personal computer and pen-and-paper when solving arithmetic exercises. British Journal of Educational Technology, 471, 91–105.
Australian Curriculum, Assessment and Reporting Authority (ACARA) (2015). Australian curriculum: Mathematics v8.1. Sydney NSW. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/ Accessed 18 Feb 2019.
Balfanz, R. (1999). Why do we teach young children so little mathematics? Some historical considerations. In J. V. Copley (Ed.), Mathematics in the early years. Reston and Washington, DC: National Council of Teachers of Mathematics and National Association for the Education of Young Children.
Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sanchez, E. (2016). Essential research on teaching and learning probability [ICME-13 topical surveys series]. Cham: Springer.
Betsch, T., Lehmann, A., Jekel, M., Lindow, S., & Glöckner, A. (2018). Children’s application of decision strategies in a compensatory environment. Judgment and Decision Making, 13, 514–528.
Borovcnik, M. (2016). Probabilistic thinking and probability literacy in the context of risk. Educação Matemática Pesquisa: Revista do Programa de Estudos Pós-Graduados em Educação Matemática, 18(3), 1491–1516.
Boyer, T. W. (2007). Decision-making processes: Sensitivity to sequentially experienced outcome probabilities. Journal of Experimental Child Psychology, 97, 28–43.
Bruner, J. (1960). The process of education. Cambridge: Harvard University Press.
Bruner, J. S. (1966). Toward a theory of instruction. Cambridge: Harvard University Press.
Bujak, K. R., Radu, I., Catrambone, R., MacIntyre, B., Zheng, R., & Golubski, G. (2013). A psychological perspective on augmented reality in the mathematics classroom. Computers & Education, 68, 536–544.
Bulf, H., Johnson, S. P., & Valenza, E. (2011). Visual statistical learning in the newborn infant. Cognition, 121, 127–132.
Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400.
Claessens, A., & Engel, M. (2013). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115, 1–29.
Denison, S., Bonawitz, E., Gopnik, A., & Griffiths, T. L. (2013). Rational variability in children’s causal inferences: The sampling hypothesis. Cognition, 126, 285–300. https://doi.org/10.1016/j.cognition.2012.10.010.
Denison, S., & Xu, F. (2014). The origins of probabilistic inference in human infants. Cognition, 130(3), 335–347. https://doi.org/10.1016/j.cognition.2013.12.001.
EECERA (2015). EECERA ethical code for early childhood researchers (Revised version 1.2). http://www.eecera.org/custom/uploads/2016/07/EECERA-Ethical-Code.pdf Accessed 3 Feb 2019.
Falk, R., Yudilevich-Assouline, P., & Elstein, A. (2012). Children’s concept of probability as inferred from their binary choices—Revisited. Educational Studies in Mathematics, 81, 207–233. https://doi.org/10.1007/s10649-012-9402-1.
Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordecht: D. Reidel Publishing Company.
Fisk, J. E., Bury, A. S., & Holden, R. (2006). Reasoning about complex probabilistic concepts in childhood. Scandinavian Journal of Psychology, 47, 497–504. https://doi.org/10.1111/j.1467-9450.2006.00558.x.
Froebel, F. (1912). Froebel’s Chief Writings on Education. (trans: Fletcher, S.F. and Welton, J.). London: Edward Arnold.
Gal, I. (2005). Towards ‘probability literacy’ for all citizens. In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 43–71). Dordrecht: Kluwer.
Gal, I. (2012). Developing probability literacy: Needs and pressures steeming from frameworks of adult competencies and mathematics curricula. Proceedings of the 12th International Congress on Mathematical Education, 8 July–15 July, Seoul, Korea.
Garfield, J. B., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Netherlands: Springer Publishers.
Girotto, V., Fontanari, L., Gonzalez, M., Vallortigara, G., & Blaye, A. (2016). Young children do not succeed in choice tasks that imply evaluating chances. Cognition, 152, 32–39. https://doi.org/10.1016/j.cognition.2016.03.010.
Gopnik, A., & Schulz, L. (2007). Causal learning: Psychology, philosophy, computation. New York: Oxford University Press.
Gopnik, A., Seiver, E., & Buchsbaum, D. (2013). How causal learning helps us to understand other people, and how other people help us to learn about causes: Probabilistic models and the development of social cognition. In M. R. Banaji & S. A. Gelman (Eds.), Navigating the social world: What infants, children, and other species can teach us (pp. 186–190). Oxford: Oxford University Press.
Government of Western Australia 2016. The Western Australian curriculum: Mathematics. School curriculum and standards authority. https://k10outline.scsa.wa.edu.au/ Accessed 15 Feb 2019.
Hannula-Sormunen, M. M., Lehtinen, E., & Rasanen, P. (2015). Preschool children’s spontaneous focusing on numerosity, subitizing, and counting skills as predictors of their mathematical performance seven years later at school. Mathematical Thinking and Learning, 17, 155–177. https://doi.org/10.1080/10986065.2015.1016814.
Hodnik Čadež, T., & Maja Škrbec, M. (2011). Understanding the concepts in probability of pre-school and early school children. Eurasia Journal of Mathematics, Science & Technology Education, 7(4), 263–279.
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(5), 487–519.
Kinnear, V., & Clark, J. (2014). Probabilistic reasoning and prediction with young children. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: Research guided practice (pp. 335–342). Sydney: MERGA.
Kushnir, T., & Gopnik, A. (2007). Conditional probability versus spatial contiguity in causal learning: Preschoolers use new contingency evidence to overcome prior spatial assumptions. Developmental Psychology, 43(1), 186–196. https://doi.org/10.1037/0012-1649.43.1.186.
Laski, E. V., Jordan, J. R., Daoust, C., & Murray, A. K. (2015). What makes mathematics manipulatives effective? Lessons from cognitive science and Montessori education. SAGE Open, 5(2), 1–8. https://doi.org/10.1177/2158244015589588.
Lillard, A. S. (2005). Montessori: The science behind the genius. New York: Oxford University Press.
Manning, J. (2005). Rediscovering froebel: A call to re-examine his life & gifts. Early Childhood Education Journal, 32(6), 371–376. https://doi.org/10.1007/s10643-005-0004-8.
McNeil, N. M., & Jarvin, L. (2007). When theories don’t add up: Disentangling the manipulatives debate. Theory into Practice, 46, 309–316. https://doi.org/10.1080/00405840701593899.
Ministry of Education, Science and Technology. (2011). Mathematics curriculum. Seoul: Korea Institute for Curriculum and Evaluation (KICE).
Montessori, M. (1964). The advanced Montessori method. Cambridge: R. Bentley.
National Council of Teachers of Mathematics. (2012). Common Core State Standards for Mathematics. http://www.nctm.org/uploadedFiles/Standards_and_Positions/Common_Core_State_Standards/Math_Standards.pdf. Accessed 15 Feb 2019.
Nikiforidou, Z., & Pange, J. (2010). The notions of chance and probabilities in pre-schoolers. Early Childhood Education Journal, 38(4), 305–311. https://doi.org/10.1007/s10643-010-0417-x.
Nikiforidou, Z., Pange, J., & Chadjipadelis, T. (2013). Intuitive and informal knowledge in preschoolers’ development of probabilistic thinking. International Journal of Early Childhood, 45(3), 347–357.
Nunes, T., Bryant, P., Evans, D., Gottardis, L., & Terlektsi, M. (2014). The cognitive demands of understanding the sample space. ZDM—International Journal on Mathematics Education, 46(3), 437–448. https://doi.org/10.1007/s11858-014-0581-3.
Outhwaite, L. A., Faulder, M., Gulliford, A., & Pitchford, N. J. (2019). Raising early achievement in math with interactive apps: A randomized control trial. Journal of Educational Psychology, 111(2), 284–298. https://doi.org/10.1037/edu0000286.
Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2018). The effectiveness of computer and tablet assisted intervention in early childhood students’ understanding of numbers. An empirical study conducted in Greece. Education and Information Technologies, 23, 1849. https://doi.org/10.1007/s10639-018-9693-7.
Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children (trans: Leake, L., Jr., Burrell P., & Fischbein, H. New York: Norton.
Saracho, O. N., & Spodek, B. (2006). Roots of early childhood education in America. In M. Takeuchi & R. Scott (Eds.), New directions for early childhood education and care in the 21st century: International perspectives (pp. 252–277). Waterloo: G & R Publishing.
Sarama, J., & Clements, D. H. (2009). ‘‘Concrete’’ computer manipulatives in mathematics education. Child Development Perspectives, 3, 145–150.
Schlottmann, A., & Wilkening, F. (2012). Judgment and decision making in young children. In M. K. Dhami, A. Schlottmann, & M. R. Waldmann (Eds.), Judgment and decision making as a skill: Learning development and evolution (pp. 55–83). New York: Cambridge University Press.
Sharma, S. (2016). Probability from a socio-cultural perspective. Statistics Education Research Journal, 15(2), 126–144.
Skoumpourdi, C., Kafoussi, S., & Tatsis, K. (2009). Designing probabilistic tasks for kindergartners. Journal of Early Childhood Research, 7(2), 153–172. https://doi.org/10.1177/1476718X09102649.
Swan, P., & Marshall, L. (2010). Revisiting mathematics manipulative materials. Australian Primary Mathematics Classroom, 15(2), 13–19.
Tenenbaum, J. B., Kemp, C., Griffiths, T. L., & Goodman, N. D. (2011). How to grow a mind: Statistics, structure, and abstraction. Science, 331, 1279–1285. https://doi.org/10.1126/science.1192788.
Van de Walle, J., Karp, K., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally (10th ed.). New York, NY: Pearson Education Inc.
Watts, T. W., Duncan, G. J., Clements, D. H., & Sarama, J. (2018). What is the long-run impact of learning mathematics during preschool? Child Development, 89(2), 539–555.
Yurovsky, D., Boyer, T., Smith, L. B., & Yu, C. (2013). Probabilistic cue combination: Less is more. Developmental Science, 16(2), 149–158. https://doi.org/10.1111/desc.12011.
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Nikiforidou, Z. Probabilities and Preschoolers: Do Tangible Versus Virtual Manipulatives, Sample Space, and Repetition Matter?. Early Childhood Educ J 47, 769–777 (2019). https://doi.org/10.1007/s10643-019-00964-2
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DOI: https://doi.org/10.1007/s10643-019-00964-2