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

Oughton, Rachel and Nichols, Kathryn and Bolden, David S. and Dixon-Jones, Sarah and Fearn, Sam and Darwin, Sophia and Mistry, Mrita and Peyerimhoff, Norbert and Townsend, Adam (2022) 'Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: A collaborative study between early years teachers and University-based mathematicians.', Mathematical Thinking and Learning .


Mathematics in early years settings is often restricted to learning to count and identifying simple shapes. This is partly due to the narrow scope of many early years curricula and insufficient teacher training for exploring deeper mathematical concepts. We note that geometry is an area particularly neglected. In an innovative year-long project, a group of university-based mathematicians and early years teachers collaborated on a child-led exploration of ‘patterns in nature.’ The early years teachers ran the project within the setting, meeting regularly with the mathematicians to discuss potential areas of interest, and to highlight the children’s mathematical thinking. We found that, with the appropriate environment and guidance, the children naturally displayed deep levels of geometrical thinking and found enjoyment and satisfaction in the exploration of mathematical ideas. We define what we mean by the term ‘deep geometrical thinking’ and demonstrate this by looking at three excerpts through the lens of the van Hiele levels of geometric thought, finding that the children are capable of exhibiting thought at level 3 (abstraction), more advanced than previously thought of children of this age. Using a second taxonomy we also assess the range of skills across which they are demonstrating such geometric thought.

Item Type:Article
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Publisher statement:© 2022 The Author(s). Published with license by Taylor & Francis Group, LLC. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Date accepted:27 August 2022
Date deposited:27 September 2022
Date of first online publication:06 September 2022
Date first made open access:27 September 2022

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