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Spatial reasoning is a cognitive process that allows us to transform and manipulate mental images. There is a significant link between spatial reasoning and achievement in STEM subjects (Wai et al., 2009). There are many spatial reasoning skills but the three most commonly identified by the research are spatial visualisation, spatial orientation and mental rotation (Ramful et al., 2017). Spatial reasoning skills are malleable and prone to training (Uttal et al., 2013).
Whilst males often do better on spatial reasoning tests this is most likely due to the differences in strategy choice. Females tend to use analytic strategies that are less successful when rotating a whole object and simultaneously processing (Logan & Lowrie, 2017). Exposure to challenging tasks requiring different types of spatial reasoning can encourage girls’ STEM participation (Woolcott et al., 2020).
Implications for Practice
Spatial skills development can have wide ranging benefits to all STEM subjects
The proportional reasoning developed through greater spatial visualisation has direct impact on students’ ability to predict, plan and solve visual problems. This is often evident in mathematical topics such as graphs, measurement, ratio, geometry and fraction but also impacts students’ ability to build in technology, make predictions about robotic movement and analyse scientific phenomena.
There is also evidence that spatial processing is one of the underlying means by which humans make sense of numbers (Patro et al., 2016). When we think of number lines, ordering, place value or the manipulation of algebraic equations we begin to see the fingerprints of spatial reasoning because of the way we think about and understand numerical magnitude and quantity.
This link is further supported by the neurological studies positing that spatial and numerical processes may have shared neural pathways due to their shared processes of mental transformations (Piazza et al., 2009).
This is still a developing area of science but points to unknown potential of greater spatial reasoning in our students.
Another way in which spatial skills can improve student outcomes is the development of visual-spatial working memory – a key component of executive function and memory (McAfoose & Baune, 2009). Visual-spatial working memory development is particularly pertinent to middle school education as it develops in late childhood and early adolescence.
It is important to note that spatial skills can be developed in each of the STEM subjects. Engaging students in tasks which actively require them to visualise objects from different perspectives and make judgements about changes to their orientation or size can help further develop these important skills.
Technology can allow students to explore and test spatial concepts
The training of spatial skills requires varied and dynamic representations of objects.
Whilst this can be obtained through interactions with the real world, new technologies are providing effective means by which to engage students’ spatial skills (Fowler et al., 2021).
There are a multitude of ways this can be done but we will outline two that are effectively explored in Connect programs.
(1) The first is through Dynamic Geometric Environments (DGEs). These virtual spaces allow students to explore an infinite number of 2D shapes and 3D objects from different perspectives and orientations whilst allowing manipulation, leading to the identification of aspects of the shape that don’t move.
This can be important in teaching about the properties of geometric shapes as it highlights the required features of a shape (e.g. a rectangle needs exactly four right angles) rather than the student comparing it to previous figures they may have seen (i.e. they may mistake a square for a diamond as it is not orientated the way they remember).
Many DGEs such as Geogebra have a particular educative focus with teacher-designed applets to explore particular concepts. DGEs can be expanded by using the related Computer Aided Design Programs (CAD). Created for engineers, CAD programs give students the ability to combine, manipulate and rotate 3D objects in order to build their own constructions.
This puts spatial skills into a real-world context and can result in objects which can be shared with others through 3D printing or Augmented Reality. These student-created objects can then be rich sources for reasoning discussions.
(2) Robotics embodies spatial reasoning in a slightly different way and it encourages students to think carefully about how their robot will interact with a set environment. Robotics ties computational thinking to spatial reasoning as students need to break down the path in which their robot will go and identify spatial patterns in order to effectively create a coded algorithm for the robot’s instructions. It is important to note though that this can also be flipped by working back from the code to predict the path of the robot.
Navigational skills are still important even though we have automated maps
Navigation hits many of the key aspects of spatial reasoning especially spatial orientation. It requires an understanding of scale, the ability to visualise objects from different perspectives, translation between 2D maps and 3D environments and mental simulation of movement.
We live in a world where many of these tasks have become automated, but this does not negate the importance of teaching this important skill due to its related cognitive benefits. Navigation can be explored through standard maps, computerised versions such as google maps, robotic paths, floorplans and even evacuation procedures.
Students require specific training on perspective
One of the more difficult spatial skills is the visualisation of 3D objects from different perspectives. This requires students to think of the front view, the plan view, and the side view.
Students are often tricked by these tasks as they fail to recognise that aspects of what they see may be hidden or separate to the main shape. This is particularly evident when students are working in CAD programs from only one perspective before they are shown that none of the objects they have added are actually touching.
Training for perspective can come from navigational tasks, working with blocks, using cameras to document different views of an object, building in CAD programs, or isometric drawing.
Many of these types of tasks can be integrated into various STEM topics but it is important that discussions of reasoning follow in order to demonstrate to students different techniques that they can use to improve their spatial reasoning.
Further Reading and References
- Fowler, S., Cutting, C., Kennedy, J., Leonard, S. N., Gabriel, F., & Jaeschke, W. (2021). Technology enhanced learning environments and the potential for enhancing spatial reasoning: a mixed methods study. Mathematics Education Research Journal, 1-24. https://doi.org/10.1007/s13394-021-00368-9
- Harris, D. (2021). Spatial ability, skills, reasoning or thinking: What does it mean for mathematics? Excellence in mathematics education: Foundations and pathways (Proceedings of the 43rd annual conference of the Mathematics Education Research Group of Australasia), Singapore.
- Harris, D., Logan, T., & Lowrie, T. (2020). Unpacking mathematical-spatial relations: Problem-solving in static and interactive tasks. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-020-00316-z
- Hawes, Z., & Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin & Review, 27(3). https://doi.org/10.3758/s13423-019-01694-7
- Logan, T., & Lowrie, T. (2017). Gender perspectives on spatial tasks in a national assessment: a secondary data analysis. Research in Mathematics Education, 19(2), 199-216. https://doi.org/10.1080/14794802.2017.1334577
- McAfoose, J., & Baune, B. T. (2009). Exploring Visual–Spatial Working Memory: A Critical Review of Concepts and Models. Neuropsychol Rev, 19(1), 130-142. https://doi.org/10.1007/s11065-008-9063-0
- Patro, K., Fischer, U., Nuerk, H. C., & Cress, U. (2016). How to rapidly construct a spatial–numerical representation in preliterate children (at least temporarily). Dev Sci, 19(1), 126-144. https://doi.org/10.1111/desc.12296
- Piazza, M., Dehaene, S., Pinel, P., & Hubbard, E. M. (2009). Numerical and Spatial Intuitions: A Role for Posterior Parietal Cortex? In: The MIT Press.
- Ramful, A., Lowrie, T., & Logan, T. (2017). Measurement of Spatial Ability: Construction and Validation of the Spatial Reasoning Instrument for Middle School Students. Journal of Psychoeducational Assessment, 35(7), 709-727. https://doi.org/10.1177/0734282916659207
- Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817-835. https://doi.org/10.1037/a0016127
- Woolcott, G., Logan, T., Marshman, M., Ramful, A., Whannell, R., & Lowrie, T. (2020). The Re-emergence of Spatial Reasoning Within Primary Years Mathematics Education. In J. Way, C.
- Attard, J. Anderson, J. Bobis, H. McMaster, & K. Cartwright (Eds.), Research in Mathematics Education in Australasia 2016–2019 (pp. 245-268). Springer Singapore. https://doi.org/10.1007/978-981-15-4269-5_10
