Spatial Abilities

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There is a broad range of materials on Spatial Abilities. Some overall conclusions are

 that these are not uniform across people; 
 that these are learnable;
 that these matter in fields like geometry, engineering, biochemistry;
 there are tests for each of these abilities; 
 young children learn / are born with some of these abilities.

These abilities were first identified in the work of Thurstone (see for example)

  • Thurstone, L. L. (1950). Some primary abilities in visual thinking (Rep. no. 59). Chicago, IL: Psychometric Laboratory, University of Chicago.

A recent description (cited in an article about Air Traffic Controllers) says:

spatial abilities "have to do with individuals' abilities in searching the visual field, apprehending the forms, shapes, and positions of objects as visually perceived, forming mental representations of those forms, shapes and positions, and manipulating such representations mentally"

  • Carroll, J. B. (1993). Human cognitive abilities: A survey of factor analytic studies. Cambridge, England: Cambridge University Press, p. 304)

Here is a review article by Alan Bishop:

  • Alan J. Bishop (1980) Spatial abilities and mathematics education—A review, Educational Studies in Mathematics Volume 11, Number 3 / August, 1980, Pages 257-269
  • Some interesting connections (among many in this article)are the positive connection between the use of manipulatives in early schooling and the development of better spatial reasoning, as well as the negative findings that taking a geometry course (even one called solid geometry) can have no impact on spatial reasoning.

One area that I need to clarify, for this exploration, is whether there are two distinct processes for each of these abilities, depending on whether the exploration of space is body centered (how does this relate to my position and body) or is relative to an external coordinate system. There is a literature here, but I have not processed it. I recall (but need to verify) that children are more likely to use body centered coordinates.

3D and 2D

There is a key issue of which dimensions are being tested.

So, for example, consider the quote (taken from Bishop): " low-level spatial abilities were defined as requiring the visualization of two-dimensional configurations, but no mental transformations of those visual images. High-level spatial abilities were characterized as requiring the visualization of three-dimensional configurations, and the mental manipulation of these visual images."

  • Guay, R. B. and McDaniel, E. D.: 1977, 'The relationship between mathematics achievement and spatial abilities among elementary school children', Journal for Research in Mathematics Education 8, 211-215.

Spatial Relations

To a geometer, these involve working with the isometries of space: translation, rotation, reflection, and combinations (e.g. inversion in a point, screw motions). The current studies seem to focus on mental rotation, and comparison of 'left right' (mirror image) versions of a fixed object.

These are not just done 'visually'. There is substantial evidence that blind people have these spatial reasoning abilities (though theymay have different strategies in some details).

There is also substantial evidence that pre-motor planning is part of our investigation of some of these which do involve motion: specifically mental rotation.

A very nice article about human cognition of all of these transformations, and more, is found in:

  • Roger Shepard: The role of transformations in spatial cognition, in Spatial Cognition: Brain Bases and Developement, J. Stiles=Davis, M. Kritchevsky, and U. Bellugi (eds) Lawrence Erlbaum, 1988, pages 81-110.

This article surveys a large body of research, as well as arguments for why these abilities should be part of our brain structure and cognition from birth, and across species. There is an emphasis on motion and our capacity to recognize the 'same' object in multiple positions. The article goes further, and suggests that the more motions under which an object or pattern is unchanged (invariant) the easier it is for us to 'recognize' it.

Interestingly, recent work on 'mirror neurons' (see the October 2006 Scientific American) actually seems to involve pre-motion planning, in the context of a mentally rotated image, not an actual mirroring effect. See, for example: and Note that they are active in infants, and may be more active in women than in men.

The use of the word 'mirror' is yet another case of possible confusion because terms are used in different ways in different fields.

There is a probability that tests of spatial ability with static images and tests with dynamic images are also testing distinct abilities. A review, and some recent tests (in the context of Air Traffic Controllers) is found in

  • Contreras, Ma Jose; Colom, Roberto; Hernandez, Jose M.; Santacreu, Jose (2003) Is static spatial performance distinguishable from

dynamic spatial performance? A latent-variable analysis. The Journal of General Psychology Retrieved from: on June 30, 2007.

Mental Translation

One wonders whether there is a difference in ability in 'mental translation' among people, by age and experience (e.g. among the blind, or those with impaired mobility). I have not seen material on this. Here is one study that implicitly involves this:

  • Martin J. Farrell and James A. Thomson (1998) Automatic Spatial Updating During Locomotion Without Vision The Quarterly Journal of Experimental Psychology, 1998, 51A(3), 637-654

In this context, the ability to update 'your position' as you move involves a number of spatial abilities. [Hence the query - does mobility impairment lead to lower spatial abilities in this area?] There is evidence of mental maps and updating of position in these maps, among young children who are born blind. So mobility may be a bigger issue that vision here.

Mental Rotation

This is perhaps the most widely studied visual ability. Sometimes it stands as a proxy for a number of the visual abilities. There is some evidence that mental rotation in 3D is primary, and mental rotation in 2D can be a distinct skill.

The classic study, which convinced people there was mental rotation and even a speed at which we mentally rotate 3D objects, was:

  • Shepard, R.N. & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701-703.

A description of some basic experiments is given on the pages:

Surprisingly, many of these 'tests' even for 3D objects are done with plane pictures of the objects, on the assumption people can construct both objects in 3-space (simultaneously I think) and compare them.

Young children, learning sign language, use 'mental rotation' to compare what they see with their hands when they sign, and what they see when another person signs. There is evidence that their language processing centers have a richer set of connections to mental rotation, and that, on average, they develop stronger abilities at mental rotation.

Recently, people have been able to study these processes using fMRI, to distinguish some variations of mechanisms, depending what is being mentally rotated.

These studies suggest that Piaget was not correct in distinguishing two forms of intellectual space: sensor-motor space and representational space (in which we can imagine movement). Since we engage pre-motor neurons, it is likely that both representations are engaged in mental rotation etc.

The work on Mirror Neurons also suggests a linking of the perceptual space and the sensor-motor space.

Overall, the situations where the brain area associated with eye-hand coordination, and motion planning, lights up when doing mathematics suggests that this set of connections is embedded in how many of us do mathematics.

Mental Reflection

While primary teachers may take a short-cut to learning of plane reflections, by calling them 'flips' and generating them by turning something over around a line in 3-space, we are interested in the distinct skills involved with reflections / left-right comparisons in 3-space.

We are pretty well 'wired' to visually detect that one image is the mirror image of another, if they are aligned with a vertical spatial mirror, and our point of view is on the mirror. One suspects that this same mechanism is used to verify plane mirror symmetries as well.

We can detect mirror symmetries with a horizontal mirror (more slowly) and symmetries with a mirror at another angle, even more slowly. Although one of our 'common' experiences of seeing an object mirrored is a scene (building, animal, trees) in flat water, this does not seem to be a central metaphor for our reasoning.

Of course a blind person is likely to process mirror symmetry from the pieces to the whole, comparing a set of measures (e.g. with the two hands) - towards the whole.

It is likely that the process of creating a mirror image (as opposed to testing a pair of images) is composite, and higher level, with 'checking' done by looking for a symmetry of the combined pair.

Mirror Tracing has been the subject of experiments:


A SIGRAPH White Paper on Visual Reasoning in Science and Engineering from a SIGRAPH workshop:

White Paper


There is controversy about whether this is distinct. A recent paper with a survey of prior work, and discussion of evidence that it is a distinct ability, is:

  • Mary Hegarty, David Waller (2004) A dissociation between mental rotation and perspective-taking spatial abilities, Intelligence 32 (2004) 175 – 191

Learning of Spatial Abilities

I am still looking for additional references on this, but here is one article which discusses learning for engineering students:

  • Manuel Contero, Ferran Naya, Pedro Company,José Luís Saorín Julián Conesa (2005): Improving Visualization Skills in Engineering Education, IEEE Computer Graphics and Applications 25, 24-31.

The article investigates the use of CAD / Sketching type software to bring engineering students up to a basic level of spatial abilities, as they begin engineering studies.

  • Yeung, Yau-Yuen (2004): A Learner-Centered Approach for Training Science Teachers through Virtual Reality and 3D Visualization Technologies: Practical Experience for Sharing, Paper presented at the International Forum on Education Reform (4th, Bangkok, Thailand, Sep 6-10, 2004)

This article presents various VR and 3D visualization technologies designed to help in the training of science teachers. The author asserts that a consequence of this training is the development of visualization skills for student teachers (and students) alike: "Furthermore, those self-learning resources can help students develop their ability to visualize, understand and mentally construct the details of complex scientific data and models which will otherwise be lost, distorted or easily misinterpreted in planar 2D projection (or monoscopic images)" (Yeunt, 2004, Abstract).


Back to Links and Resources for summer Spatial Reasoning projects