When I read the recent curriculum and assessment review, and the government’s response to it, there was a gap that immediately jumped out at me: spatial reasoning.
On further reading, it became clear that spatial reasoning underpins many of the review’s maths recommendations. So, why isn’t this foundational skill more explicitly mentioned?
What is spatial reasoning?
Spatial reasoning includes the ability to understand the properties of objects (shape, size and location), and the relationships between them, as well as the ability to mentally visualise and manipulate objects and numbers.
In England, spatial reasoning is under-emphasised in the current national curriculum for maths. Lessons are filled with recalling multiplication facts, learning calculation algorithms, and applying specific strategies to answer questions in context. But how often are children asked to apply spatial strategies to solve problems?
Are children asked to explore different ways of describing an array of counters (for example: 3 x 4 versus 4 x 3) to mentally rearrange numbers in arithmetic, before applying a calculation procedure? Are they asked to visualise word problems to build a mental model before they put pen to paper?
These examples draw on spatial reasoning and spatial problem solving - skills that are foundational for maths and yet rarely get the attention they deserve.
The importance of spatial skills
Ahead of the curriculum and assessment review, several policy documents emphasised the central role of spatial reasoning for maths. For example, the Royal Society’s Mathematical Futures report called for “a stronger focus on spatial reasoning”, while 2024 Ofsted research found that “understanding number and spatial reasoning are crucial to later development”.
Similarly, the 2025 report from the Maths Horizons project stated that “spatial reasoning is a powerful but under-utilised foundation for mathematical learning with broad benefits for maths, including geometry, measures, number, algebra and statistics”.
While reference to spatial reasoning in the curriculum and assessment review was not particularly explicit, many of the review’s recommendations for maths can only be realised by incorporating spatial reasoning. For instance, the review recommends that children are provided with “opportunities for more complex problem-solving”, including “non-routine problems”, and that assessments “include a stronger focus on mental arithmetic and reasoning”.
Research evidence consistently shows that teaching children to think spatially has broad benefits for mathematics. Those drafting the new curriculum must recognise this. For example, applying a spatial visualisation strategy has been shown to be particularly important for non-routine problem solving, mathematical word problems and arithmetic, all of which are key features of the review’s recommendations.
Spatial reasoning is also inclusive. Independent evaluation of our teacher-led spatial training programme reported that “children otherwise identified as having lower abilities found that they could quickly grasp the concept”.
Teaching children to think and work spatially, therefore, offers a powerful means to unlock potential, particularly for “left behind” groups, providing a route to closing attainment gaps - a central goal of the curriculum and assessment review.
How to teach spatial reasoning
So, how can teachers incorporate more of this learning into their lessons? The good news is that spatial reasoning can easily be embedded into existing maths planning - it does not require additional content or extra activities. Here are three simple ideas:
- Ask children to compare spatial representations of the same data (for example, a tally versus a bar chart) or to visualise a frog jumping in twos and threes to calculate equivalence and which combinations make 10. (Adapted from NRICH)
- A non-routine problem, such as sharing four chocolate bars between three people, can be solved using the ability to split wholes into parts and other spatial strategies such as visualisation. Children can then check their answers using strips of paper. (Adapted from White Rose Maths)
- Practising skills like “mental folding” (for example, visualising what shape would be made by folding a square along its diagonal) and “mental rotation” (for example, imagining what a shape would look like if it were rotated a three-quarter turn clockwise) as part of geometry content can bolster flexible problem solving and is hugely beneficial for many aspects of mathematics including statistics, arithmetic, measurement and algebra.
As these examples show, strong evidence and scalable practice already exists, ready for implementation in the curriculum. There are plenty of resources available to support this, including our trajectory of development of spatial reasoning (birth to age 7 and 7 to 11), as well as professional development such as the NCETM spatial reasoning pathway.
However, embedding spatial reasoning in the maths curriculum is not without challenge. The current lack of teacher confidence in teaching children spatially highlights that professional development in spatial reasoning should be prioritised.
The message that spatial reasoning is not another topic to be taught, but that existing content can be “spatialised” must be communicated well. National coherence across curriculum, assessment and classroom practice will be essential if spatial reasoning is to be effectively implemented in the curriculum.
The evidence base is robust, and scalable practice already exists, so it’s time to make this learning explicit. Teaching children to think spatially will equip the next generation to meet the heightened demands for critical thinking, problem solving and data use brought about by technological and AI-enabled change.
Emily Farran is professor in developmental psychology at the University of Surrey. Find out more about spatial reasoning at the University of Surrey’s spatial reasoning platform
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