Research School Network: Improving mathematics through spatial thinking Dr Emily K. Farran and Prof. Catherine Gripton highlight the importance of spatial thinking in teaching early maths.

Spatial thinking matters for mathematics development. In addition to geometry, it is important in understanding number lines, working with pattern, interpreting graphs and using measurements.

Also referred to as ​‘spatial reasoning’ or ​‘spatial awareness’, spatial thinking involves understanding the position, dimensions and properties of objects and their relationships to one another and there is a growing evidence base for its importance in mathematical development, particularly for disadvantaged pupils.

With this in mind, we turn to the EEF’s ​‘Improving mathematics in the Early Years and Key Stage One’ guidance report to consider how the five evidence-informed recommendations can support the improvement of spatial thinking for young children.

Recommendation 1: Develop practitioners’ understanding of how children learn mathematics

In a recent questionnaire, we demonstrated that the majority of practitioners working with birth to 7‑year-olds (64%) were ​‘not at all’ or only ​‘a little’ confident in their understanding of spatial thinking. This confirmed to us that spatial thinking is a priority area for developing practitioner knowledge.

The EEF guidance report points out how useful developmental progressions are to practitioners, providing insights into the typical path that children tend to follow in order to support their teaching.

With the Early Childhood Mathematics Group, we have recently developed a spatial reasoning toolkit which includes a detailed developmental progression (or trajectory) for practitioners.

Recommendation 2: Dedicate time for children to learn mathematics and integrate mathematics throughout the day

There are opportunities to develop children’s spatial thinking in so many daily activities. Such opportunities include: cutting and sticking into exercise books, predicting whether the PE equipment will fit in the box, and matching shapes to silhouettes when tidying.

These everyday contexts provide opportunities for teachable moments in which deliberate use of spatial language, such as ​“on top”, ​“next to” or ​“between” can support spatial thinking. Using words such as ​“along”, ​“turn” and ​“left/​right” when navigating around the building is another simple way to integrate spatial learning through the day . Additionally, the EEF guidance report suggests using stories to develop mathematical talk – this is also appropriate for spatial thinking (this list of spatial books offers a good starting point).

Recommendation 3: Use manipulatives and representations to develop understanding

Recent evidence suggests that spatial interventions that include concrete materials have a greater impact on spatial and mathematical competence than spatial interventions that do not.

The physical manipulation of objects generates the perceptual information required to understand movement of objects and oneself in physical space. Many of the representations in the EEF guidance document help children to see numerical relationships spatially, such as using a staircase to explore ​‘one more than’.

Recommendation 4: Ensure that teaching builds on what children already know

There are many spatial ​‘tools’ that can support children to build on what they already know. The use of visualisation (seeing and manipulating objects in the mind’s eye), for example, is not used spontaneously by all children. Just asking children to ​‘try it in your head’ before they attempt a problem can introduce them to the benefits of visualisation.

Equally, spatial language and gesture can be used to increase children’s conceptual understanding, to draw attention to the spatial properties of objects, and to highlight the spatial relations which underpin mathematical concepts. For example, words like ​“near” and ​“far”, as well as gestures and words for ​“small”, ​“medium” and ​“large”.

Recommendation 5: Use high quality targeted support to help all children learn maths

Guided spatial play is beneficial for children and can be used effectively as part of high quality targeted support. For instance, practitioners can provide a commentary while children complete an obstacle course, to help children form a clear concept of the spatial directions.

Adult guided block play, for example, is an excellent opportunity to support children’s spatial thinking. Practitioners can model and elicit spatial language, and can support problem solving by using gesture to show motor actions such as turning a block to make desired shapes.

References

Bates, K. E., Williams, A. Y., Miss, Gilligan, K. A., Gripton, C., & Farran, E. K. (2022). Practitioner’s perspectives on spatial reasoning in educational practice from birth to 7 years. https://doi.org/10.31234/osf.i…

Bower, C., Zimmermann, L., Verdine, B., Toub, T. S., Islam, S., Foster, L., … & Golinkoff, R. M. (2020). Piecing together the role of a spatial assembly intervention in preschoolers’ spatial and mathematics learning: Influences of gesture, spatial language, and socioeconomic status. Developmental Psychology, 56(4), 686. http://dx.doi.org/10.1037/dev0…

Gilligan, K.A., Hodgkiss, A., Thomas, M.S., & Farran, E.K. (2019). The developmental relations between spatial cognition and mathematics in primary school children. Developmental Science, 22 (12786). https://doi.org/10.1111/desc.12786

Hawes, Z. C., Gilligan-Lee, K. A., & Mix, K. S. (2022). Effects of spatial training on mathematics performance: A meta-analysis. Developmental Psychology, 58(1), 112. http://dx.doi.org/10.1037/dev0…