Abstract
This chapter provides an overview of the growing body of evidence regarding the nascent geometrical capabilities of young children. We focus on spatial awareness and shape which are two broad concepts that underpin geometrical thinking from 0 to 8 years. In relation to each concept, we identify key indicators of informal learning trajectories, the mathematical underpinnings of these concepts and how they manifest themselves in early infancy through the preschool years and into the early primary school years. In parallel with these informal trajectories, we explain ‘big ideas’ which may include obstacles to learning or key misconceptions. Finally, we outline ways of supporting the development of geometrical understandings across the early years making reference to informal mathematics and play-based activities within the home and community setting and acknowledge the important role that language, gesture and context play in the development of children’s geometrical capacities and understandings.
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References
Athey, C. (2007). Extending thought in young children. London: Sage.
Battista, M. T. (2007). The development of geometric and spatial thinking. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–908). Reston: National Council of Teachers of Mathematics.
Bruce, C., & Hawes, Z. (2015). The role of 2D and 3D mental rotations in mathematics for young children: What is it? Why does it matter? And what can we do about it? ZDM Mathematics Education, 47(3), 331–343.
Bussi, M. G., & Baccaglini-Frank, A. (2015). Geometry in early years: Sowing seeds for a mathematical definition of squares and rectangles. ZDM Mathematics Education, 47, 391–405.
Cartwright, S. (1996). Learning with large blocks. In E. S. Hirsch (Ed.), The block book (3rd ed.). Washington, DC: National Association for Education of Young Children (NAEYC).
Casey, B. M., Andrews, N., Schindler, H., Kersh, J. E., Samper, A., & Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26(3), 269–309.
Charles, R. (1980). Exemplification and characterization moves in the classroom teaching of geometry concepts. Journal for Research in Mathematics Education, 11(1), 10–21.
Clements, D., & Sarama, J. (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Mahwah: Erlbaum.
Clements, D., & Sarama, J. (2007). The development of geometric and spatial thinking, students and learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching learning (pp. 489–517). Reston, VA: NCTM.
Clements, D., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge.
Cook, S., & Goldin-Meadow, S. (2006). The role of gesture in learning: Do students use their hands to change their minds? Journal of Cognition and Development, 7(2), 211–232.
Copley, J. (2010). The young child and mathematics (2nd ed.) Washington: National Association for the Education of Young Children (NAEYC).
DeLoache, J. S., Miller, K. F., & Rosengren, K. S. (1997). The credible shrinking room: Very young children’s performance with symbolic and non-symbolic relations. Psychological Science, 8, 308–313.
DeLoache, J. S., Pierroutsakos, S. L., Uttal, D. H., Rosengren, K. S., & Gottlieb, A. (1998). Grasping the nature of pictures. Psychological Science, 9, 205–210.
Department of Education, Employment and Workplace Relations [DEEWR]. (2009). Belonging, being & becoming—The early years learning framework for Australia. Canberra, ACT: Commonwealth of Australia.
Diezmann, C., & Yelland, N. J. (2000). Developing mathematical literacy in the early childhood years. In N. J. Yelland (Ed.), Promoting meaningful learning (pp. 47–58). Washington: NAEYC.
Elia, I., Gagatsis, A., Michael, P., Georgiou, A. S., & van den Heuvel, M. (2014). The role of gestures in making connections between space and shape aspects and their verbal representations in the early years: Findings from a case study. Mathematics Education Research Journal, 26, 735–761. doi:10.1007/s13394-013-0104-5.
Flavell, J. H., Abrahams Everett, B., Croft, K., & Flavell, E. R. (1981). Young children’s knowledge about visual perception: Further evidence for the level 1–level 2 distinction. Developmental Psychology, 17(1), 99–103.
Fox, T. B. (2000). Implications of research on children’s understanding of geometry. Teaching Children Mathematics, 6, 572–576.
Gentner, D. (2003). Why we’re so smart. In D. Gentner & S. Goldin-Madow (Eds.), Language in mind: Advances in the study of language and thought (pp. 195–235). Cambridge: MA: MIT Press.
Goldenberg, E. P., Clements, D., Zbiek, R. M., & Dougherty, B. (2014). Developing essential understanding of geometry and measurement for teaching mathematics in pre-K–grade 2. Reston, VA: NCTM.
Goldschmeid, E., & Jackson, S. (1994). People under three: Young children in daycare (1st ed.). London: Routledge.
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.
Hallowell, D. A., Okamoto, Y., Romo, L. F., & La Joy, J. R. (2015). First-graders’ spatial-mathematical reasoning about plane and solid shapes and their representations. ZDM Mathematics Education, 47, 363–375.
Hershkowitz, R. (1989). Visualization in geometry: Two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61–76.
Hewitt, K. (2001) Blocks as a tool for learning: Historical and Contemporary Perspectives in Young Children 56 (1): 6–11. Washington: National Association for the Education of Young Children (NAEYC).
Hock, T. T., Rohani A. T., Aida S. M., Yunus, & Ahmad, F. (2015). Understanding the primary school students’ van Hiele levels of geometry thinking in learning shapes and spaces: A Q-methodology. Eurasia Journal of Mathematics, Science & Technology Education, 11(4), 793–802.
Hourigan, M., & Leavy, A. (2015). What’s a real shape? Designing appropriate geometric instruction. Australian Primary Mathematics Classroom, 20(1), 24–29.
Hourigan, M., & Leavy, A. M. (2016). Practical problems: Introducing statistics to Kindergarteners. Teaching Children Mathematics, 22(5), 283–291.
Kaur, H. (2015). Two aspects of young children’s thinking about different types f dynamic triangles: Prototypicality and inclusion. ZDM Mathematics Education, 47, 407–420.
Knaus, M., & Featherstone, S. (2014). Maths is all around you. London: Featherstone.
Leavy, A., & Hourigan, M. (2015). Budding architects: Exploring the designs of pyramids and prisms. Australian Primary Mathematics Classroom, 20(3), 17–23.
Murphy, A., & Nicholson, A. J. (2011). Baby walkers in Europe-time to consider a ban. Irish Medical Journal, 104(3), 69.
National Council for Curriculum and Assessment (NCCA). (2009). Aistear: The early childhood curriculum framework. Principles and themes. Dublin, Ireland: Author.
National Council for Curriculum and Assessment (NCCA). (2014). Mathematics in early childhood and primary education. Dublin, Ireland: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.
National Research Council (NRC). (2009). Mathematics learning in early childhood: Paths towards excellence and equity. In C. Cross, T. Woods, & H. Schweingruber (Eds.), Committee on Early Childhood Mathematics, Center for Education, Division of Behavioral and Social Sciences. Washington, DC: The National Academies Press.
Nutbrown, C. (2011). Threads of thinking. London: Sage.
Örnkloo, H., & von Hofsten, C. (2007). Fitting objects into holes: On the development of spatial cognition skills. Developmental Psychology, 43(2), 404–416.
Pillow, B., & Flavell, J. (1986). Young children’s knowledge about visual perception: Projective size and shape. Child Development, 57, 125–135.
Ping, R., & Goldin-Meadow, S. (2008). Hands in the air: Using ungrounded iconic gestures to teach children conservation of quantity. Developmental Psychology, 44(5), 1277–1287.
Pound, L. (2006). Supporting mathematical development in the early years. Oxford: Open University Press.
Pruden, S. M., Levine, S. C., & Huttenlocher, J. (2011). Children’s spatial thinking: Does talk about the spatial world matter? Developmental Science, 14(6), 1417–1430. doi:10.1111/j.1467-7687.2011.01088.x.
Pytlak, M. (2015). Learning geometry through paper-based experiences. Conference proceedings of Congress of European Research in Mathematics Education (CERME9). Prague.
Rodrigues, M.P., & Serrazina, L. (2015). Six years old pupils intuitive knowledge about triangles. Conference proceedings of Congress of European Research in Mathematics Education (CERME9). Prague.
Roth, W. M., & Lee, Y. J. (2004). Interpreting unfamiliar graphs: A generative, activity-theoretic model. Educational Studies in Mathematics, 57, 265–290.
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research. Learning trajectories for young children. New York: Routledge.
Sinclair, N., & Moss, J. (2012). The more it changes, the more it becomes the same: The development of the routine of shape identification in dynamic geometry environments. International Journal of Education Research, 51&52, 28–44.
Siraj-Blatchford, I. (2004). Quality teaching in the early years. In A. Anning, J. Cullen, & M. Fleer (Eds.), Early childhood education: Society and culture (pp. 137–148). London, Sage Publications.
Skemp, R. (1969). The psychology of learning mathematics. Harmondsworth, UK: Penguin.
Stannard, L., Wolfgang, C. H., Jones, I., & Phelps, P. (2001). A longitudinal study of the predictive relations among construction play and mathematical achievement. Early Child Development and Care, 167(1), 115–125.
Thom, J.S., & McGarvey, L. (2015). The act and artifact of drawing(s): Observing geometric thinking with, in, and through children’s drawings. ZDM Mathematics Education (Special issue: Geometry in primary school), 47(3), 465–481.
Tovey, H. (2013). Bringing the Froebel approach to your early years practice. New York: Routledge.
Tucker, K. (2005). Mathematics through play in the early years. London: Paul Chapman.
Tucker, K. (2010). Mathematics through play in the early years (2nd ed.). London: Paul Chapman.
Valenzeno, L., Alibali, M. A., & Klatzky, R. (2003). Teachers’ gestures facilitate students’ learning: A lesson in symmetry. Contemporary Educational Psychology, 28, 187–204.
Van den Heuvel-Panhuizen, M., Elia, I., & Robitzsch, A. (2015). Kindergartners’ performance in two types of imaginary perspective-taking. ZDM Mathematics Education, 47(3), 345–362.
Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Orlando, FL: Academic Press.
Wilson, S. (1986). Feature frequency and the use of negative instances in a geometric task. Journal for Research in Mathematics Education, 17(2), 130–139.
World Health Organisation. (2006). WHO motor development study: Windows of achievement for six gross motor development milestones. Acta Paediatr Suppl. Apr; 450: 86–95.
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Leavy, A., Pope, J., Breatnach, D. (2018). From Cradle to Classroom: Exploring Opportunities to Support the Development of Shape and Space Concepts in Very Young Children. In: Kinnear, V., Lai, M., Muir, T. (eds) Forging Connections in Early Mathematics Teaching and Learning. Early Mathematics Learning and Development. Springer, Singapore. https://doi.org/10.1007/978-981-10-7153-9_7
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