The spatial reasoning toolkit: Enhancing children’s early mathematical learning

SARAH MCCARTHY AND EMILY K FARRAN, SCHOOL OF PSYCHOLOGY, UNIVERSITY OF SURREY, UK 

SUE GIFFORD, SCHOOL OF EDUCATION, UNIVERSITY OF ROEHAMPTON, UK

Spatial reasoning – the ability to understand the properties of objects and how they relate to other objects – is important for supporting children’s development of mathematics understanding (Mix et al., 2016). Spatial reasoning can be trained from an early age (Yang et al., 2020), and spatial activities are highly engaging and enjoyable for children, providing an accessible way of teaching mathematics. Despite this research evidence, the early learning goal of ‘shape, space and measures’ has been removed from the Early Years Foundation Stage (EYFS) curriculum (DfEDepartment for Education - a ministerial department responsible for children’s services and education in England, 2021), and the Key Stage 1 curriculum understates spatial reasoning in favour of number-related content (DfE, 2013).

Hawes et al. (2023) outline four key reasons why academics believe that spatial reasoning is important for mathematics. Firstly, neural evidence suggests that spatial and numerical thinking activate common brain areas and processing systems (Hawes and Ansari, 2020). Secondly, mathematics is inherently spatial – curriculum topics such as geometry and measurement involve numbers related to space. Thirdly, spatial visualisation is thought to help children to use a ‘mental blackboard’ to support mathematical problem-solving (Hawes et al., 2023). Finally, the solving of mathematics problems is often facilitated by spatial representations. Resources such as number frames, number lines, rulers and protractors are used to support children’s mathematical understanding (Mix, 2010).

Recognising the importance of spatial reasoning skills, a group of practitioners and researchers examined psychological research from the last 20 years on spatial reasoning and children’s mathematics understanding. Drawing together the findings, the group translated the research evidence into practical guidance for practitioners, and developed the spatial reasoning toolkit (SRT) (www.earlymaths.org/spatial-reasoning; Gifford et al., 2022). The resources in the toolkit are designed to help practitioners supporting children from birth to seven years. The toolkit provides information about different spatial skills and how to support these skills in Early Years settings. Examination of the use and impact of the SRT determined that practitioners who actively use the toolkit resources are more confident in their understanding of spatial reasoning than practitioners who have not actively used them. In addition, active users observed more impact on children’s spatial skills and mathematics understanding through integration of the suggested activities into their teaching, compared to those who were yet to use the materials in practice (McCarthy et al., in prep). The case studies of practitioner use of the toolkit presented here provide ideas for practitioners to incorporate evidence-based strategies into curriculum planning and teaching and learning practice. Three settings – a small rural primary school, a special school and a large urban primary school – used the toolkit materials in diverse ways to support practitioners and students in increasing spatial reasoning and developing children’s mathematics understanding (McCarthy et al., in prep). The following case studies are based on interviews with practitioners in each setting. These are drawn from a wider analysis of practitioner feedback on the SRT (Farran et al., submitted).

Case study 1: A small primary school in a coastal setting

The toolkit facilitated a strategic decision in this small school to embed spatial reasoning objectives into the Key Stage 1 mathematics curriculum. Staff invested considerable time in exploring the content in the toolkit’s research summaries and learning trajectory, to understand what spatial reasoning encompassed. The toolkit’s videos were used for staff training and prompted discussions about how to introduce spatial reasoning into lessons, which led to activities being incorporated into planning. The toolkit’s posters were displayed in classrooms to provide spatial reasoning ideas and language prompts that would support practitioners in teaching moments. Similarly, in Early Years, existing spatial reasoning objectives were extended within the medium-term mathematics planning. As a result, continuous provision was adapted to incorporate elements of spatial reasoning to support the age-related development steps. In Reception, books such as Rosie’s Walk were used as a basis for teaching a range of spatial skills across a whole week. Topics such as perspective-taking allowed children to consider objects and places from different viewpoints and develop their prepositional language. As a result of this work, practitioners have an increased understanding and awareness of the importance of spatial reasoning and how teacher-led and continuous provision environments can support it. One of the biggest impacts on children’s learning has been an increased comprehension of spatial language and children’s ability to use it in the appropriate context. Developing spatial language skills is critical in supporting spatial reasoning (Gilligan-Lee et al., 2021).

Case study 2: A special school, working with children with learning and additional needs 

Inspired by the launch event for the SRT, the lead mathematics practitioner in this special school was excited by the resources and shared them with practitioners across the school. Staff had an A4 copy of the toolkit’s posters in their in-trays to which to refer in planning and preparation. The posters were also displayed in the staffrooms and family spaces in the school. Staff training, supported by this wide communication of the materials, ensured the development of a consistent approach to supporting spatial reasoning. This is important, given the flexible staffing structure required to meet students’ needs, where practitioners may work in different classes each day. The learning trajectory information in the toolkit relating to how to extend children’s progress ‘in the moment’ facilitated the school’s approach of allowing students to direct their own learning to achieve their potential. It also supported teachers to ensure that every child could be moved onto the next stage, depending upon their individual pathway, without being constrained by what year group they were in. Content, such as what language to use, what questions to ask and knowing what the next development step would be, allowed staff to offer improved support to students and progress their learning while they were engaged in activities. Play-based learning is used from Reception to Year 6, and the toolkit inspired the introduction of large-scale block play equipment, such as giant interlocking shapes and big wooden blocks, to provide more opportunities for children to develop their spatial reasoning. In addition, these activities resulted in children working together, and both practitioners’ and children’s confidence in mathematics grew. The development steps for spatial reasoning have now been embedded in the curriculum, reflecting teaching and learning practice. The toolkit also enabled practitioners to share ideas for how to support children’s spatial reasoning at home with parents and caregivers, via the parent newsletter and in parent workshops.

Case study 3: A large primary school in an urban setting

In conjunction with researchers from the University of Surrey, practitioners used the SRT to design a focus week on spatial reasoning for Year 2 children. Practitioners committed time to developing their understanding of spatial reasoning and gathering appropriate resources from across the school. Spatial Week ran in the summer term. Spatial reasoning activities were incorporated into many parts of the school day across different subjects, such as geography, PE, mathematics and reading time. The days started with spatial language games, such as ‘Teacher Says’, asking the children to draw shapes in certain orientations and in relation to other shapes. In PE, children created obstacle courses and completed them while being supported with spatial language words such as ‘over’, ‘under’ and ‘through’. In geography, children navigated the school grounds to locate items and drew maps. In mathematics, 2D nets of the faces of an object were used to discuss 3D shape properties. During reading, books relating to shapes, space and measures were used to support children’s understanding of spatial reasoning concepts. In ‘choosing time’, jigsaw puzzles allowed children to practise their spatial skills, such as mental rotation. All the activities were engaging and fun and provided a contrast to desk-based tasks. The result from one week of focused spatial reasoning training showed a significant improvement in children’s spatial language skills, measured via researcher-led assessments. An added benefit was the social development opportunity provided by these team-based, child-led activities. Practitioners have now incorporated some of these ideas into their curriculum planning for Year 2.

Conclusion

In summary, these case studies highlight the main themes identified through practitioner feedback on the SRT (Farran et al., submitted; McCarthy et al., in prep). Firstly, the SRT is perceived as a useful tool that practitioners are using for professional development and curriculum planning. This echoes the success of other professional development programmes used in spatial reasoning research that contributed to the development of the SRT (see Hawes et al., 2017, Lowrie and Logan, 2023).  Secondly, an initial investment of time is needed to plan how the SRT is most effectively used and to identify appropriate resources. This is challenging given the time constraints facing practitioners (Drill et al., 2013) and potentially limits the use of the SRT in practice. Thirdly, practitioners observed that the SRT has a positive impact on children’s spatial reasoning and their social development. Additionally, it has helped to improve practitioners’ knowledge of spatial reasoning and increase their confidence in sharing their understanding. Nevertheless, practitioners reported the need for the SRT to extend past children aged 7 years. Future research is therefore focused on extending the trajectory of spatial reasoning development in the toolkit, to support spatial reasoning in 7- to 11-year-olds.