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Research Article

Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: a collaborative study between early years teachers and university-based mathematicians

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Pages 306-325 | Received 28 Oct 2021, Accepted 27 Aug 2022, Published online: 06 Sep 2022

References

  • Aksu, Z., Gedik, S. D., & Konyalıoglu, A. C. (2021). Mathematics teacher candidates’ approaches to using topology in geometry. School Science and Mathematics, 121(4), 192–200. https://doi.org/10.1111/ssm.12464
  • Alcock, L., & Simpson, A. (2009). Ideas from mathematics education: An introduction for mathematicians. The Higher Education Academy. Maths Stats and OR Network (MSOR Network).
  • Andrews, A. G., & Trafton, P. R. (2002). Little kids–powerful problem solvers: Math stories from a kindergarten classroom. ERIC.
  • BERA. (2018, October). Ethical guidelines for educational research (4th ed.). British Educational Research Association. https://www.bera.ac.uk/researchers-resources/publications/ethical-guidelines-for-educational-research-2018
  • Björklund, C. (2012). What counts when working with mathematics in a toddler-group? Early Years, 32(2), 215–228. https://doi.org/10.1080/09575146.2011.652940
  • Bolden, D., Harries, T., & Newton, D. (2010). ‘Pre-service primary teachers’ conceptions of creativity in mathematics. Educational Studies in Mathematics, 73(2), 143–157. https://doi.org/10.1007/s10649-009-9207-z
  • Carpenter, T. P., Ansell, E., Franke, M. L., Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children’s problem-solving processes. Journal for Research in Mathematics Education, 24(5), 428–441. https://doi.org/10.2307/749152
  • Charles, R. I., & Carmel, C. A. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Education Leadership, 7(3), 9–24. https://jaymctighe.com/wp-content/uploads/2011/04/MATH-Big-Ideas_NCSM_Spr05v73p9-24.pdf.
  • Clements, D. (2001). Mathematics in the preschool. Teaching Children Mathematics, 7(5), 270–275. https://doi.org/10.5951/TCM.7.5.0270
  • Clements, D. H., & Samara, J. (2000). Young children’s ideas about geometric shapes. Teaching Children Mathematics, 6(8), 482–488. https://doi.org/10.5951/TCM.6.8.0482
  • Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14(2), 133–148. https://doi.org/10.1007/s10857-011-9173-0
  • Clements, D. H., & Sarama, J. (2018). Myths of early math. Education Sciences, 8(2), 71. https://doi.org/10.3390/educsci8020071
  • Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. In M. M. Lindquist (Ed.), Learning and teaching geometry, K-12, (1987) yearbook of the National Council of teachers of mathematics (pp. 1–16). National Council of Teachers of Mathematics.
  • Department for Education. (2017). Statutory framework for the early years foundation stage. Statutory Framework for the Early Years Foundation Stage. https://www.icmec.org/wp-content/uploads/2018/01/EYFS_STATUTORY_FRAMEWORK_2017.pdf
  • Dindyal, J. (2015). Geometry in the early years: A commentary. ZDM, 47(3), 519–529. https://doi.org/10.1007/s11858-015-0700-9
  • Edwards, C. P., Gandini, L., & Forman, G. E. (1998). The hundred languages of children: The Reggio Emilia approach–advanced reflections. Greenwood Publishing Group.
  • Fujita, T., & Jones, K. (2006). Primary trainee teachers’ understanding of basic geometrical figures in Scotland 30th Conference of the International Group for the Psychology of Mathematics Education July 2006 Prague.
  • Gagatsis, A., Srirman, B., Elia, I., & Modestou, M. (2006). Exploring young children’s geometrical strategies. Nordic Studies in Mathematics Education, 11(2), 23–50. http://ncm.gu.se/wp-content/uploads/2020/06/11_2_025052_gagatis.pdf
  • Garvis, S., & Nislev, E. (2017). Mathematics with infants and toddlers Phillipson, Sivanes, Gervasoni, Ann, Sullivan, Peter. In Engaging families as children’s first mathematics educators (pp. 33–46). Springer. https://doi.org/10.1007/978-981-10-2553-2_3
  • Gelman, R. (2006). Young natural-number arithmeticians. Current Directions in Psychological Science, 15(4), 193–197. https://doi.org/10.1111/j.1467-8721.2006.00434.x
  • Gelman, R., Meck, E., & Merkin, S. (1986). Young children’s numerical competence. Cognitive Development, 1(1), 1–29. https://doi.org/10.1016/S0885-2014(86)80021-1
  • Ginsburg, H. P., Kaplan, R. G., Cannon, J., Cordero, M. I., Eisenband, J. G., Galanter, M., & Morgenlander, M. (2006). Helping Early Childhood Educators to Teach Mathematics Zaslow, Martha, Martinez-Beck, Ivelisse). Critical Issues in Early Childhood Professional Development (Paul H. Brookes Publishing), 171–202.
  • Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it. Social Policy Report, 22(1), 1–24. https://doi.org/10.1002/j.2379-3988.2008.tb00054.x
  • Griebling, S., Jacobs, J., Kochanowski, L., & Vaughn, L. M. (2016). What preschool children like best about school. Dimensions of Early Childhood, 44(2), 18–26. http://files.eric.ed.gov/fulltext/EJ1150272.pdf
  • Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229. https://doi.org/10.1037/a0027433
  • Gutiérrez-Rubio, D., León-Mantero, C., Maz-Machado, A., & Madrid-Martı́n, M. J. (2020). Relationship between math anxiety and perception of the utility of geometry in primary education in prospective teachers. Universal Journal of Educational Research, 8(3), 731–738. https://doi.org/10.13189/ujer.2020.080301
  • Harper, N. W., & Daane, C. J. (1998). Causes and reduction of math anxiety in preservice elementary teachers. Action in Teacher Education, 19(4), 29–38. https://doi.org/10.1080/01626620.1998.10462889
  • Hoffer, A. (1981). Geometry is more than proof. The Mathematics Teacher, 74(1), 11–18. https://doi.org/10.5951/MT.74.1.0011
  • Johnson, D. A., & Glenn, W.-L. H. (1960). Topology, the rubber-sheet geometry. (“Exploring mathematics on your own series.”) St. Webster Publishing Company.
  • Larsen, K. (2005). Stephen Hawking: A biography. Greenwood Publishing Group.
  • Lee, S. (2012). Toddlers as mathematicians? Australasian Journal of Early Childhood, 37(1), 30–37. https://doi.org/10.1177/183693911203700105
  • Linder, S. M., Powers-Costello, B., & Stegelin, D. A. (2011). Mathematics in early childhood: Research-based rationale and practical strategies. Early Childhood Education Journal, 39(1), 29–37. https://doi.org/10.1007/s10643-010-0437-6
  • MacDonald, A., & Murphy, S. (2019). Mathematics education for children under four years of age: A systematic review of the literature. Early Years 41(5), 522–539. https://doi.org/10.1080/09575146.2019.1624507
  • Mamolo, A., Ruttenberg-Rozen, R., & Whiteley, W. (2015). Developing a network of and for geometric reasoning. ZDM, 47(3), 483–496. https://doi.org/10.1007/s11858-014-0654-3
  • Mason, M. (1998). The van Hiele levels of geometric understanding. In Geometry: Explorations and applications (Professional Handbook for teachers) (pp. 4–8). McDougal-Littell/Houghton-Mifflin. http://math.fau.edu/yiu/PSRM2015/yiu/New%20Folder%20(4)/Thompson/levels.pdf
  • McLennan, D. M. (2019). Joyful number talks in kindergarten. Journal of Teaching and Learning, 13(2), 43–54. https://doi.org/10.22329/JTL.V13I2.5684
  • Mix, K. S., & Cheng, Y.-L. (2012). The relation between space and math: Developmental and educational implications. Advances in Child Development and Behavior, 42, 197–243. https://doi.org/10.1016/B978-0-12-394388-0.00006-X
  • Moss, J., Hawes, Z., Naqvi, S., & Caswell, B. (2015). Adapting Japanese lesson study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: A case study. Zdm, 47(3), 377–390. https://doi.org/10.1007/s11858-015-0679-2
  • National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence (National Council of Teachers of Mathematics).
  • Nicholson, S. (1972). The theory of loose parts, an important principle for design methodology. Studies in Design Education Craft & Technology, 4(2). https://ojs.lboro.ac.uk/SDEC/article/view/1204.
  • Piaget, J., & Inhelder, B. (1956). The child’s concept of space. Routledge & Paul.
  • Reikerås, E., Løge, I. K., & Knivsberg, A.-M. (2012). The mathematical competencies of toddlers expressed in their play and daily life activities in Norwegian kindergartens. International Journal of Early Childhood, 44(1), 91–114. https://doi.org/10.1007/s13158-011-0050-x
  • Rinaldi, Carlina. (2005). In Dialogue with Reggio Emilia 1, (Routledge) 9780415345040.
  • Rittle-Johnson, B., Zippert, E. L., & Boice, K. L. (2019). The roles of patterning and spatial skills in early mathematics development. Early Childhood Research Quarterly, 46(1), 166–178. https://doi.org/10.1016/j.ecresq.2018.03.006
  • Ruzzi, B. L., Eckhoff, A., & Linder, S. M. (2017). STEM resources and materials for engaging learning experiences. YC Young Children, 72(1), 90–93. https://www.jstor.org/stable/90001496
  • Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM, 47(3), 319–329. https://doi.org/10.1007/s11858-015-0693-4
  • Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9–15. https://doi.org/10.5951/AT.26.3.0009
  • Spelke, E. S., & Newport, E. L. (1998). Nativism, empiricism, and the development of knowledge. In W. Damon & R. Lerner (Eds.), Handbook of child psychology: Theoretical models of human development (pp. 275–340). John Wiley & Sons.
  • Strong-Wilson, T., & Ellis, J. (2007). Children and place: Reggio Emilia’s environment as third teacher. Theory Into Practice, 46(1), 40–47. https://doi.org/10.1080/00405840709336547
  • Takahashi, A., & McDougal, T. (2016). Collaborative lesson research: Maximizing the impact of lesson study. ZDM Mathematics Education, 48(4), 513–526. https://doi.org/10.1007/s11858-015-0752-x
  • Thom, J. S., & McGarvey, L. M. (2015). The act and artifact of drawing(s): Observing geometric thinking with, in, and through children’s drawings. ZDM, 47(3), 465–481. https://doi.org/10.1007/s11858-015-0697-0
  • Tirosh, D., Tsamir, P., Levenson, E. S., & Barkai, R. (2020). Setting the table with toddlers: A playful context for engaging in one-to-one correspondence. ZDM, 52(4), 717–728. https://doi.org/10.1007/s11858-019-01126-9
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: Triangles, circles, and cylinders. ZDM, 47(3), 497–509. https://doi.org/10.1007/s11858-014-0641-8
  • van Hiele, P. M. (1986). Structure and insight. A theory of mathematics education. Academic Press.
  • Van Oers, B. (2010). Emergent mathematical thinking in the context of play. Educational Studies in Mathematics, 74(1), 23–37. https://doi.org/10.1007/s10649-009-9225-x
  • Worthington, M., Dobber, M., & van Oers, B. (2019). The development of mathematical abstraction in the nursery. Educational Studies in Mathematics, 102(1), 91–110. https://doi.org/10.1080/1350293X.2015.1120520
  • Yopp, D. A. (2020). Eliminating counterexamples: An intervention for improving adolescents’ contrapositive reasoning. The Journal of Mathematical Behavior, 59(1), 100794. https://doi.org/10.1016/j.jmathb.2020.100794
  • Zur, O., & Gelman, R. (2004). Young children can add and subtract by predicting and checking. Early Childhood Research Quarterly, 19(1), 121–137. https://doi.org/10.1016/j.ecresq.2004.01.003