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An evidence-based trajectory of spatial reasoning development for 7- to 11-year-olds.

Gifford S, Farran EK, Borthwick A · 21 Sept 2026

Abstract

Spatial reasoning involves understanding and visualising spatial relations and the spatial properties of objects, including spatial aspects of quantities. Spatialising the mathematics curriculum by emphasising thinking and working spatially has broad benefits for mathematics, including geometry, measures, number, algebra and statistics. Research shows that teaching children to think and work spatially results in substantially improved mathematics performance, with lifelong benefits.This trajectory of spatial reasoning development for 7- to 11-year-olds complements the trajectory of spatial reasoning development for birth to seven years developed by the Early Childhood Maths Group (see ECMG Spatial Reasoning Toolkit). These two trajectories are informed by extensive review of research in this area and together offer activities for children from birth to 11 years. This trajectory is presented in four sections, covering space (spatial relations) and shape (objects and properties) for 7- to 9-year-olds and 9- to 11-year-olds. Three columns identify the areas of spatial reasoning, the progression in children’s learning and developmentally appropriate activities. Each child develops in their own unique way: age bands are approximate and dependent on previous experience, so should be used as a guide rather than age-related expectations. Spatial reasoning is wider than traditional geometry, including aspects of space and shape such as position and direction, navigation, perspective-taking, scaling, transformations, shape properties and structure, composition and decomposition; the document could be used to substitute a geometry curriculum, with activities integrated throughout the curriculum. This document forms part of a series of Royal Society publications on spatial reasoning which can be found at: Royal Society Curriculum and Assessment and accompanies our earlier work on the ECMG Spatial Reasoning Toolkit. The series includes: •RS ACME Primary and early years expert panel perspective: Spatial reasoning - June 2024 (royalsociety.org) •Progression of Spatial Reasoning across age bands (Appendix 1 of document listed above)•This document, An evidence-based trajectory of spatial reasoning development for 7- to 11-year-olds.•Whole-school approach case studies: Supporting Primary Children’s Spatial Reasoning in Geography and Design & Technology