Executive summary

Spatial reasoning involves understanding and visualising spatial relations and the spatial properties of objects, including spatial aspects of quantities.

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.[1]

Spatial reasoning predicts mathematics performance at any age. Research shows that teaching children to think and work spatially results in substantially improved mathematics performance, with lifelong benefits.

Spatial reasoning is supported by spatial representation, including manipulating objects and mental images, spatial language, gesture, sketching, maps and graphic representations.

Spatialising the mathematics curriculum by emphasising thinking and working spatially has broad benefits for mathematics, including geometry, measures, number, algebra and statistics.

Spatial reasoning is important in everyday life, for interpreting data and solving problems in a range of contexts, as well as for learning mathematics. It is especially important in STEM careers, where data science is of increasing importance. However, spatial thinking is a weakness for English 15-year-olds.[2] Spatialising the mathematics curriculum would improve the skills of the STEM workforce and help the UK to move out of the ‘slow lane’.[3]

Everyone’s spatial reasoning can be improved, in a range of ways, at any age. Spatial reasoning develops as a result of genetic and developmental factors, but also environmental factors. Effective teaching strategies use spatial language, gesture and representations, with activities involving physical movement, manipulatives, robots and IT. Puzzles and problems foster visualisation, prediction and experimentation.

A spatialised mathematics curriculum is particularly helpful for disadvantaged groups, who may lack spatial experiences or vocabulary and underperform in spatial tasks. It can engage children with mathematics in different ways, drawing on interests, aptitudes and out of school experiences, in a more accessible and relevant curriculum. It can reduce the indifference and anxiety many people feel towards mathematics, including teachers as well as pupils.

[1] OECD, Organisation for Economic Co-operation and Development (2022). PISA 2022 Mathematics Framework. PISA, OECD Publishing, Paris. https://pisa2022-maths.oecd.org/

[2] OECD, Organisation for Economic Co-operation and Development (2023). PISA 2022 Results (Volume I): The State of Learning and Equity in Education, PISA, OECD Publishing, Paris. https://www.oecd-ilibrary.org/education/pisa-2022-results-volume-i_53f23881-en

[3] Royal Society (2023). A new approach to mathematics and data education: A discussion paper from the Mathematical Futures Board of The Royal Society’s Advisory Committee on Mathematics Education (ACME). https://royalsociety.org/topics-policy/projects/mathematical-futures/