Looking within and beyond the geometry curriculum: connecting spatial reasoning to mathematics learning
- 1.5k Downloads
This commentary adopts a broad perspective in considering the contributions of papers from cross- and interdisciplinary fields of mathematics education, psychology, child development and neuroscience. The discussion aims to complement the commentary by Dindyal, focused on background research on geometry and implications for pedagogy and curricula. Spatial reasoning is considered as a common underlying theme salient to most of the papers in this issue. The fundamental role of spatial ability or visual thinking skills in young children is traced through the various theoretical approaches of studies ranging from concepts such as perspective taking, symmetry, and two- and three-dimensional shape, to the role of technological tools in mapping and location. Intervention studies to promote early spatial reasoning also provide insight into effective transformative practices. New questions are raised about the crucial development of spatial reasoning in Science, Technology, Engineering and Mathematics (STEM) education. The commentary suggests the need for a more strategic research agenda that aims to coordinate the key questions and methodologies that investigate what may seem common problems.
KeywordsMathematics Education Spatial Ability Perspective Taking Mathematics Education Research Spatial Reasoning
- Bartolini-Bussi, M., & Baccaglini-Frank, A. (2015). Geometry in early years: sowing seeds for a mathematical definition of squares and rectangles. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-014-0636-5 (this issue).
- Battista, M. C. (1999). Spatial structuring in geometric reasoning. Teaching Students Mathematics, 6, 171–177.Google Scholar
- Bishop, A. J. (2008). Spatial abilities and mathematics education—a review. In P. Clarkson & N. Presmeg (Eds.), Critical issues in mathematics education. New York: Springer. Google Scholar
- 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). doi: 10.1007/s11858-014-0637-4 (this issue).
- Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: from brain to education. Science 27, 332 (6033), 1049–1053.Google Scholar
- Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D. H. Clements, J. Sarama, & A. M. Di Biase (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 267–298). Mahwah: Lawrence Erlbaum.Google Scholar
- Davis, B. (Ed.). (2015). Spatial reasoning in the early years: principles, assertions, and speculations. New York: Routledge.Google Scholar
- Dehaene, S. (2009). Reading in the brain: the new science of how we read. New York: Penguin.Google Scholar
- Devlin, K. (2012). Introduction to mathematical thinking. Palo Alto: Keith Devlin.Google Scholar
- Dindyal, J. (2015). Geometry in the early years. ZDM Mathematics Education, 47(3) (this issue). Google Scholar
- Grandin, T. (2009). Thinking in pictures. London: Bloomsbury.Google Scholar
- Hallowell, D., Okamoto, Y., Romo, L. & LaJoy, J. (2015). First-Grader’s spatial mathematical reasoning about plane and solid shapes and their representations. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-015-0664-9 (this issue).
- Hawes, Z., Tepylo, D., & Moss, J. (2015). Developing spatial reasoning. In B. Davis (Ed.), Spatial reasoning in the early years (pp. 29–44). New York: Routledge.Google Scholar
- Kaur, H. (2015). Two aspects of young children’s thinking about different types of dynamic triangles: prototypicality and inclusion. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-014-0658-z (this issue).
- Kotsopoulos, D., Cordy, M. & Langemeyer, M. (2015). Children’s understanding of large-scale mapping tasks: an analysis of talk, drawings, and gesture. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-014-0661-4 (this issue).
- Lehrer, R., & Chazan, D. (1998). Designing learning environments for developing understanding of geometry and space. Erlbaum: Lawrence.Google Scholar
- Lehrer, R., Slovin, H., Dougherty, B., & Zbiek, R. (2014). Developing essential understanding of geometry and measurement for teaching mathematics in grades 3–5. Reston: National Council of Teachers of Mathematics.Google Scholar
- Mamolo, A., Ruttenberg-Rozen, R., & Whiteley, W. (2015). Developing a network of and for geometric reasoning. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-014-0654-3 (this issue).
- 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 Mathematics Education, 47(3). doi: 10.1007/s11858-015-0679-2 (this issue).
- Mulligan, J. T., & Woolcott, G. (2015). What lies beneath? Conceptual connectivity in whole number arithmetic. In. X. Sun, B. Kaur, J. Novotná (Eds.), Proceedings of the International Commission of Mathematical Instruction (ICMI) Study Group 23 conference, University of Macau, 2–8 June 2015. Macau: ICMI Organising Committee (in press).Google Scholar
- Newcombe, N. S. (2010). Picture this: increasing math and science learning by improving spatial thinking. American Educator, 34(2), 29–43.Google Scholar
- Ng, O. & Sinclair, N. (2015). Young children reasoning about symmetry in a dynamic geometry environment. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-014-0660-5 (this issue).
- Papic, M. M., Mulligan, J. T., & Mitchelmore, M. C. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42, 237–268.Google Scholar
- Piaget, J., & Inhelder, B. (1956). The child’s conception of space. London: Routledge and Kegan Paul.Google Scholar
- Rivera, F., Steinbring, H., & Arcavi, A. (2014). Visualization as an epistemological learning tool (special issue). ZDM—The International Journal on Mathematics Education, 46(1), 79–93.Google Scholar
- Sinclair, N. & Bruce, C. (2015). New opportunities in geometry education at the primary school. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-015-0693-4 (this issue).
- Sinclair, N., & Bruce (coordinators), C. D. (2014). Research forum: spatial reasoning for young learners. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36 (Vol. 1, pp. 173–203). Vancouver: PME.Google Scholar
- Soury-Lavergne, S. & Maschietto, M. (2015). Articulation of spatial and geometrical knowledge in problem solving with technology at primary school. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-015-0694-3 (this issue).
- Tahta, D. (1980). About geometry. For the Learning of Mathematics, 1(1), 2–9.Google Scholar
- Thom, J., & McGarvey, L. (2015). The act and artifact of drawing(s): observing geometric thinking with, in, and through children’s drawings. ZDM Mathematics Education, 47(3) (this issue).Google Scholar
- Tsamir, P., Tirosh, D., Levenson, E., Barkai, R. & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: triangles, circles, and cylinders. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-014-0641-8 (this issue).
- van den Heuvel-Panhuizen, M., Iliade, E., & Robitzsch, A. (2015). Kindergartners’ performance in two types of imaginary perspective-taking. ZDM Mathematics Education, 47(3). doi: 10.1007/s11858-015-0677-4 (this issue).
- van Hiele, P.M. (1985). The child’s thought and geometry. In D. Geddes & R. Tischler (Eds.), English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele (pp. 243–252). Brooklyn: Brooklyn College, School of Education (original work published 1959).Google Scholar
- van Nes, F., & de Lange, J. (2007). Mathematics education and neurosciences: relating spatial structures to the development of spatial sense and number sense. The Montana Mathematics Enthusiast, 2, 210–229.Google Scholar