include the ability to understand the spatial properties of objects, such as their size and location, and the ability to visualise and . We use spatial abilities every day: to pack a bag, read timetables and find our way.
A robust finding in cognitive psychology is that training children’s spatial abilities can significantly improve mathematics performance. However, in England these research findings have yet to be translated into classroom practice and spatial reasoning remains underrepresented in the national curriculum.
This neglect in teaching children to think and work spatially is already evident in England’s latest Programme for International Student Assessment (Pisa) and Trends in International Mathematics and Science Study (Timss) results, where “shape and space” and geometry sub-domains are weak relative to other areas of mathematics.
We should be concerned by that because spatial abilities in childhood are strong predictors of adult expertise in (Stem).
Teaching spatial skills in schools
If spatial reasoning remains a low priority in schools, there is a risk that the next generation will not be equipped to meet the heightened demands for critical thinking, problem solving and data use (skills that are underpinned by spatial abilities) brought about by technological and AI-enabled change. In the words of the report published this month, we need to “reform maths education for the age of AI”.
To help with this, at the University of Surrey, we aimed to translate the evidence base into practice through the project. We worked with practitioners to implement teacher-delivered spatial training in the classroom, targeted at six- to seven-year-olds (Year 2 in England).
Teachers received professional development on the value of spatial reasoning for mathematics, and a suite of . Following this, they delivered a six-week LEGO brick construction training programme to their class during their normal maths lesson time. In each of 12 30-minute SPACE sessions, children worked through a booklet instructing them to build up to six LEGO models using pictorial instructions, while teachers prompted children to engage with spatial thinking and spatial language.
So, what did we find?
In our paper, , we report that the training was effective: spatial ability and mathematics improved significantly for the children who took part in the SPACE programme, relative to a control group. Furthermore, as an of the pilot study found, teachers reported benefits for inclusion with otherwise “left behind” groups revealing “an aptitude that they had not previously been able to express”.
Our findings demonstrate that classroom opportunities to engage in structured block building are an effective activity for mathematics improvement, and that all children can be taught to think and work spatially.
Encouragingly, the value of spatial reasoning for mathematics and Stem is starting to gain recognition in national discussions. For example, spatial reasoning features strongly in the report and the report, whilst recently stated that “understanding both number and spatial reasoning is crucial to later achievement”, listing spatial reasoning as one of three key areas of development in the early years foundation stage. This recognition has direct relevance for the ongoing review of curriculum and assessment.
But there are also ways in which teachers can enhance the work they do around spatial reasoning right now.
Use spatial vocabulary
Teaching children to think and work spatially does not require additional activities - existing content can be spatialised. For many activities, we can model the use of spatial language using words like “on”, “next to”, “between” and “parallel”. This helps children to .
Visualise number lines
When using , ask children to imagine a number line in their head. This prompts the use of visualisation, which can then be further supported by asking children to check their predictions on a physical number line.
Make use of arrays
Using arrays, meanwhile, is a spatial way of exploring multiplication. In a 3x4 array, children need to understand the spatial relationships between the rows and columns. Recognising that the same set of objects can be viewed as either three groups of four or four groups of three requires them to mentally reorientate their viewpoint of the array. This draws on a form of perspective-taking as a spatial skill.
Shade fractions
For fractions, present children with a set of different shapes and ask them to shade in half of each shape. To prompt spatial thinking, we can ask, “How many different ways can you shade half of the shape? How will you know that you have shaded half of the shape?” This encourages spatial skills like visualisation and representation.
Approach data in various ways
Children can also be encouraged to in different ways. We can ask them to translate data from a table to a bar chart, or to compare the same data represented with horizontal bars, vertical bars or a tally chart. We can ask, “What is the same and what is different?” “Is one easier to understand?”
Incorporate nets
Working with nets and symmetry are also a great way of prompting visualisation. We can ask, “How many different nets could make a cube?” Or, “Reflect a letter over a diagonal line of symmetry.”
Encourage children to visualise their solutions, sketch them on paper and check using physical objects: for example, by cutting and folding nets using paper or painting and folding paper to .
Teaching children to think and work spatially is an evidence-based, inclusive way to future-proof the next generation to meet the demands of the AI and data-driven employment revolution. As policymakers become more aware of this, schools can get a head start on leading the way.
For more ideas on how to help children to think spatially, have a look at the resources tab on our .
Emily Farran is professor in developmental psychology at the University of Surrey
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