Getting better at spatial thinking

What the research says

The key study is a meta-analysis by David Uttal and colleagues, which pooled 217 spatial training studies: courses, video games and direct practice on spatial tasks.

• Trained groups, before to after0.62
• Transfer to untrained spatial tasks0.48
• Training compared with control0.47
• Control groups, before to after0.45

Read the four bars together.

• Training works. Compared with control groups, trained groups gained about half a standard deviation (g = 0.47).
• It lasts. Effects were similar whether the post-test came right after training or after a delay.
• It spreads within the spatial family. Studies that tested transfer found gains of about the same size on spatial tasks that were not trained.
• But controls improve too. Control groups gained 0.45 simply from taking the tests again, and more when they did repeated practice tests. Some of any early improvement is getting used to the format.

The three kinds of training (courses, video games and spatial task practice) all produced positive effects, and the review found no significant difference between them. The authors also note that few studies ran longer than a few weeks, so we know less about long-term training than about short bursts.

Beyond spatial: maths and engineering

• Mathematics. Hawes, Gilligan-Lee and Mix pooled 29 controlled studies with 3,765 participants aged 3 to 20. Spatial training improved spatial skill (g = 0.49) and mathematics (g = 0.28). The maths effect was larger for older participants, larger when training used physical materials rather than a screen, and larger for maths closely related to the training.
• Engineering students. Sheryl Sorby's spatial skills course at Michigan Technological University has run since 1993, using a rotation test to identify first-year engineering students with weak 3-D skills. Later reports on the programme say the intervention improved spatial skills, grades in introductory STEM courses, and retention and graduation rates.
• Video games. In Feng, Spence and Pratt, ten hours of training on an action video game improved mental rotation, with women gaining more than men. A control group trained on a non-action game showed no improvement.

What this does not mean

The implication for placement preparation is straightforward. Practise the item types and game formats you will actually face, practise them enough that the format stops costing you attention, and build the underlying strategies so that you are fast on items you have not seen.

Where our games fit

Be clear about what the spatial games in this app are. They are practice tasks from the same families as the items and games you will meet in assessments: rotation with mirror lures, route building on a grid, and steering with limited look-ahead. They have not been tested as a training programme in the way the studies above were, and nothing here promises gains beyond those tasks. Use them for what the evidence supports: getting fluent with the formats, building strategies you can apply to new items, and tracking whether your errors are changing.

Strategies that work

For mental rotation

1. Pick an anchor and a flag

   Choose one distinctive part of the reference (the anchor, such as a long tail) and one asymmetric part beside it (the flag, such as a single cell sticking out on one side). Ignore everything else at first.

2. Turn the anchor into place

   Find the anchor on the candidate and count how many quarter turns bring it to the reference's position. Turn the short way: three quarter turns clockwise is one quarter turn anticlockwise.

3. Check the flag's side

   With the anchor aligned, is the flag on the same side as in the reference? If yes, it is a rotation. If it is on the opposite side, it is a mirror image, however similar it looks.

4. Confirm with one more part

   Only if both match, check one more feature to catch shapes with a single cell moved. Stop there.

This is a deliberate ‘piecemeal’ strategy. Research by Khooshabeh, Hegarty and Shipley suggests that people with strong imagery tend to rotate whole shapes by default and switch to part-by-part strategies when a figure is fragmented or complex, while weaker imagers use piecemeal strategies regardless. The practical lesson is to have both: try to see the whole shape turn, and fall back to anchor and flag when it does not come.

For navigation and route planning

• Start from the goal and the bottlenecks. Find the places where your route has only one option, then work back to where you are. The route in between usually follows.
• Translate egocentric to allocentric. For direction questions, draw a map with a north arrow before you think in rights and lefts.
• Commit to one frame. Either rotate the map to match your heading or rotate yourself on the map. Switching halfway is how people turn the wrong way.

For spatial construction

• Place corners and edges first; they have the fewest possible positions.
• Group pieces into chunks you can name (‘the dark row across the top’) so there is less to hold in mind.
• When rebuilding from memory, spend your study time on the parts that are hard to name, not the obvious ones.

Read your own numbers

Practice pays off faster when you know which error you are fixing. The session report for each spatial game breaks your results down further than a single score.

• ShapeDance reports the share of rotated matches you found, how often you picked a mirror image or another non-match (mirror confusion), and how much extra time each degree of turning costs you. High mirror confusion means you are matching on appearance: slow down and check the flag's side. A steep time-per-degree figure means you are turning the long way round or re-checking too often.
• Pathfinder reports the share of routes you connected and the share of route tiles you had correctly oriented. If the second is high and the first is low, you were nearly there and one tile broke the chain; check the tile next to where the lit path stops.
• Penguin Escape reports the share of steps you took cleanly, collisions per hundred steps, and the share of runs you finished without a single bump. Collisions bunched just after a narrow column mean you saw the bottleneck too late.

Change one habit at a time, and judge it over several sessions rather than one.

A four-week plan with our games

Each session below is about ten minutes. Spread them across the week rather than stacking them on one day.

1. Week 1: learn the formats
   • ShapeDance, 3 sessions: use anchor and flag on every card, even easy ones
   • Pathfinder, 2 sessions: trace from the start port and watch the lit tiles
   • Penguin Escape, 2 sessions: look for bottlenecks before they reach you
   • Try five mirror and water image items and five paper-folding items on paper
2. Week 2: accuracy first
   • ShapeDance, 3 sessions: note after each session whether your misses were mirrors or moved cells
   • Pathfinder, 3 sessions: plan the whole route before the first tap
   • Penguin Escape, 2 sessions: aim for clean runs, not fast reactions
   • Ten cube and net items: find opposite pairs first
3. Week 3: add pace
   • ShapeDance, 3 sessions: time yourself turning the short way round
   • Pathfinder, 2 sessions: fewer wasted taps by counting turns before tapping
   • Penguin Escape, 3 sessions at your current level
   • Puzzle Reconstruction, 2 sessions: corners and edges first
4. Week 4: test conditions
   • One mixed session a day across all four spatial games
   • A timed set of 20 mixed visual reasoning items in 20 minutes
   • Review your profile: which facet is lowest, and which error type repeats
   • Keep the weakest game in your daily rotation after the plan ends

What to remember

• Across 217 studies, spatial training beat control conditions by about half a standard deviation, lasted, and transferred to untrained spatial tasks.
• Control groups also improved by retesting alone, so early gains are partly format familiarity.
• Transfer to maths exists but is small (g = 0.28) and strongest when the maths is spatial.
• For rotation: anchor, flag, confirm, and turn the short way.
• For routes: find the bottleneck and plan back from it.

Sources

1. Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402. PDF
2. Wright, R., Thompson, W. L., Ganis, G., Newcombe, N. S., & Kosslyn, S. M. (2008). Training generalized spatial skills. Psychonomic Bulletin & Review, 15(4), 763–771. doi.org/10.3758/pbr.15.4.763
3. Hawes, Z. C. K., Gilligan-Lee, K. A., & Mix, K. S. (2022). Effects of spatial training on mathematics performance: A meta-analysis. Developmental Psychology, 58(1), 112–137. doi.org/10.1037/dev0001281
4. Sorby, S. A. (2009). Educational research in developing 3-D spatial skills for engineering students. International Journal of Science Education, 31(3), 459–480. ERIC EJ828856
5. Sorby, S. A., et al. (2020). A tale of two universities: Developing spatial skills of engineering students during a global pandemic. Engineering Design Graphics Journal. ERIC EJ1345131
6. Feng, J., Spence, I., & Pratt, J. (2007). Action video game training and gender differences in spatial attention and mental rotation (title paraphrased). Psychological Science, 18(10), 850–855. doi.org/10.1111/j.1467-9280.2007.01990.x
7. Khooshabeh, P., Hegarty, M., & Shipley, T. F. (2013). Individual differences in mental rotation: Piecemeal versus holistic processing. Experimental Psychology, 60(3), 164–171. doi.org/10.1027/1618-3169/a000184