Young children exploring probability – with focus on their documentations
DOI:
https://doi.org/10.7146/nomad.v21i4.148744Abstract
This article reports on an intervention where possibilities and limitations with problem-solving as a basis for mathematics education in pre-school class were studied. In the article we explore how 50 children use non-guided documentation when working with a problem-solving task about probability. The results show that the task was possible to work with for these young children, and in the follow-up interviews many of the children seemed familiar with the mathematical concepts used, as well as with a relevant sample space. The children’s non-guided documentation showed a diversity of strategies and contributed positively to their exploration of probability, both during the lesson and in the final discussions.
References
Alderson, P. & Morrow, V. (2011). The ethics of research with children and young people. A practical handbook. Los Angeles: SAGE. https://doi.org/10.4135/9781446268377
Amir, G.S. & Williams, J.S. (1999). Cultural influences on children's probabilistic thinking. Journal of mathematical behaviour, 18 (1), 85-107. https://doi.org/10.1016/S0732-3123(99)00018-8
Benko, P. & Maher, C. A. (2006). Students constructing representations for outcomes of experiments. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 137-144). Prague: PME.
Bennett, J. & Tayler, C. P. (2006). Starting strong II. Early childhood education and care. Paris: OECD.
Brooker, L., Blaise, M. & Edwards, S. (2014) (Eds.). The SAGE handbook of play and learning in early childhood. Los Angeles: SAGE. https://doi.org/10.4135/9781473907850
Cai, J. (2010). Commentary on problem solving heuristics, affect, and discrete mathematics: a representational discussion. In B. Sriraman & L. English (Eds.), Theories of mathematics education. Seeking new frontiers (pp. 251-258). London: Springer. https://doi.org/10.1007/978-3-642-00742-2_25
Casey, B. (2009). Applying developmental approaches to learning math. In O.A. Barbarin & B.H. Wasik, (Eds.), Handbook of child development & early education. New York: The Guilford Press.
Charlesworth, R. & Leali, S.A. (2012). Using problem solving to assess young children's mathematics knowledge. Early Childhood Educational Journal, 39, 373-382. https://doi.org/10.1007/s10643-011-0480-y
Chick, H. & Baker, M. (2005). Teaching elementary probability: not leaving it to chance. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough et al. (Eds.), Building connections: research, theory and practice (proceedings of MERGA28) (pp. 233-240). Sydney: MERGA.
Claessens, A. & Engel, M. (2013). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115, 403-434. https://doi.org/10.1177/016146811311500603
Clements, D. H. & Sarama, J. (2009). Learning and teaching early mathematics. The learning trajectory approach. New York: Routledge. https://doi.org/10.4324/9780203883389
Cobb, P., Wood, T., Yackel, E. & Perlwitz, M. (1992). A follow-up assessment of a second-grade problem-centered mathematics project. Educational Studies in Mathematics, 23 (5), 483-504. https://doi.org/10.1007/BF00571469
Cross, C.T, Woods, T.A. & Schweingruber, H. (2009). Mathematics learning in early childhood. Paths toward excellence and equity. Washington: The National Academies Press.
Duncan, G.J, Dowsett, C.J., Claessens, A., Magnuson, K., Huston, A.C. et al. (2007). School readiness and later achievement. Developmental Psychology, 43 (6), 1428-1446. https://doi.org/10.1037/0012-1649.43.6.1428
English, L.D. & Mulligan, J.T. (2013). Perspectives on reconceptualizing early mathematics learning introduction. In L.D. English & J.T. Mulligan (Eds.), Perspectives on reconceptualizing early mathematics learning (pp. 1-4). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-6440-8
English, L.D. & Watson, J. (2016). Development of probabilistic understanding in fourth grade. Journal for Research in Mathematics Education, 47 (1), 28-62. https://doi.org/10.5951/jresematheduc.47.1.0028
EU (2007). Nyckelkompetenser för livslångt lärande. En europeisk referensram. Luxembourg: Byrån för Europeiska gemenskapernas officiella publikationer.
Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel. https://doi.org/10.1007/978-94-010-1858-6
Hiebert, J. & Grouws, D. A. (2002). The effects of classroom mathematics teaching on students' learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371-404). Charlotte: Information Age.
Jones, G. A., Langrall, C. W., Thornton, C. A. & Mogill, A. T. (1997). A framework for assessing and nurturing young children's thinking in probability. Educational Studies in Mathematics, 32, 101-125. https://doi.org/10.1023/A:1002981520728
Lesh, R. & Zawojewski, J. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning, (pp. 763-804). Charlotte: Information Age.
McKenney S. & Reeves, T. (2012). Conducting educational design research. London: Routledge. https://doi.org/10.4324/9780203818183
National Agency for Education (2011). Curriculum for the primary school, preschool class and leisure time centre 2011. Stockholm: National Agency for Education.
National Agency for Education (2014). Förskoleklassen - uppdrag, innehåll och kvalitet. Stockholm: National Agency for Education.
NCTM (2000). Principles and standards for school mathematics. Charlotte: National Council of Teachers of Mathematics.
Newton, K. J. & Alexander, P. A. (2013). Early mathematics learning in perspective: eras and forces of change. In L. D. English & J. T. Mulligan (Eds.), Perspectives on reconceptualizing early mathematics learning (pp. 5-28). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-6440-8_2
Palmér, H. & Bommel, J. van (2016). Problemlösning som utgångspunkt - matematikundervisning i förskoleklass. Stockholm: Liber.
Piaget, J. & Inhelder, B. (1975). The origin of the idea of chance in children. Routledge and Kegan Paul.
Pramling, N. & Pramling Samuelsson, I. (2008). Identifying and solving problems: making sense of basic mathematics through storytelling in the preschool class. International Journal of Early Childhood, 40 (1), 65-79. https://doi.org/10.1007/BF03168364
Prediger, S., Gravemeijer, K. & Confrey, J. (2015). Design research with a focus on learning processes: an overview on achievements and challenges. ZDM, 48, 877-891. https://doi.org/10.1007/s11858-015-0722-3
Saracho, O. N. & Spodek, B. (2008). Trends in early childhood mathematics research. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives in early childhood education (pp. vii-xx). Charlotte: Information Age.
Seo, K.-H. & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 91-104). Mahwah: Lawrence Erlbaum.
Sowder, J., Sowder, L., Cobb, P., Yackel, E., Wood, T. et al. (1988). Creating a problem-solving athmosphere. The Arithmetic Teacher, 36 (1), 46-47. https://doi.org/10.5951/AT.36.1.0046
Swedish Research Council (2002) Forskningsetiska principer inom humanistisk- samhällsvetenskaplig forskning. Stockholm: Vetenskapsrådet.
Watson, J. (2006). Statistical literacy in schools: growth and goals. Mahwah: Lawrence Erlbaum.
Way, J. (2003). The development of children's notions of probability (unpublished doctoral dissertation). University of Western Sydney.
Westwood P. (2011). The problem with problems: potential difficulties in implementing problem-based learning as the core method in primary school mathematics. Australian Journal of Learning Difficulties, 16 (1), 5-18. https://doi.org/10.1080/19404158.2011.563475
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.