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Spatial skills

By Steve Draper,   Department of Psychology,   University of Glasgow.

Different senses of "spatial" skills:
Spatial, visual, geometric, navigation, mental rotation, or Piagetian milk bottle.


They, following Piaget, use the term "spatial" skills but in a very different sense from mental rotation, or the exercises Jack gave Quintin to do. (Their/ Piaget's usage revolves around the test of giving the learners an outline of a tilted milk bottle and asking them to draw in the line representing the surface of the liquid when it is half full. Many draw the line perpendicular to the bottle's sides, not parallel to the ground.) [See Shayer,M., Kuchemann,D.E. and Whylam,H. (1976) for the description of the tests, taken directly from Piaget's "The child's conception of space"]

Crude personal notes

Basic idea: prologue

Spatial skills, using existing tests, seem to be correlated with L success in STEM subjects generally.

2D vs. 2.5D vs. 3   and/or   

     viewer-centric vs. abstract, indep.      and/or   

     schemas (learned, multiple) vs. fingerprints (AI)     and/or   

     metric vs. connection (topography)


James Flynn's speculation about what bits of IQ have recently grown, and are called for in post-industrial-rev. society.

Lots of learning involved in acquring these skills BUT typically when you have them, you think you didn't learn but just had them.  But really lots of work, esp. time and practice, in acquiring them.

Besides spatial and visualisation skills, is it important to have (but takes time to learn) symbolic skills e.g. the diff. between using natLang and a formal lang.;  a lang about effort after meaning and with redundancy, vs. a lang. where every char and its sequence order and its vertical position and ... makes a difference.  Dyslexia – any connection, even harder for learning maths?

Field in/dependence.

Quintin email 5 Nov 17 opening qu. to Jack

Hi Jack (and Lovisa and Steve, for comment),

I read the paper that you recommended to the students as the most influential paper ...


"Spatial Ability for STEM Domains: Aligning Over 50 Years of Cumulative Psychological Knowledge Solidifies Its Importance", Wai, Lubinski, Benbow (2009),

Journal of Educational Psychology, Vol. 101, No. 4,  pp.817-835


and attached here.


Three things struck me:


1.  Is this the best paper for the students?  What about a paper that demonstrates one can get better at SS?


I was struck by the choice.  It demonstrates that spatial skills as measured in early adolescents (around age 13, I think) relate very strongly to later achievement in STEM subjects / careers - via a number of studies of different kinds.  But it makes no mention of being able to get any better at spatial skills with training - just that we should explore this aspect.  Its stronger recommendation is that we should be using spatial skills tests, just as we do maths and verbal/language skills, early on to identify folk for the STEM talent pool that we would otherwise miss.


A student who reads this paper carefully might assume that if they have low skills now, then they're stuffed.  That is very much not the message we aim to convey!!


Which paper should we read to most strongly encourage us/students that we can get better at these skills with training?


2.  Definition of spatial ability in this paper


I also noted that the paper used a definition of spatial ability given by Lohman (1994a,  p.1000) as "the ability to generate, retain, retrieve, and transform well-structured visual images".


The trigger here for me was "visual images" - and I'm thinking of the comments Lovisa has made in passing to the difference between visual ability and spatial ability.  She has referred to this as a recent finding - realising that there are two different, but related presumably - kind of skills - and I wondered how recent?  More recently than 1994?


I'm not sure if this matters - but it struck me.  


3.  The particular tests used in this paper - and how it relates to CS / our study


Further on in the paper, we get the particular kind of tests of spatial ability that the studies depend on - these are reproduced in the screenshot below/attached.


Our particular test is out like the first of these - three dimensional spatial visualisation.


I can see why this and the third one would be of particular value in Engineering education - where I imagine they do a lot of this kind of consideration of physical objects and their properties.  Also in applied areas in Physics and Maths.  


This comes back to the difference between visual and spatial.  These tests do seem quite visual.  But what we do in CS doesn't seem that visual.


Two thoughts:

a. Are these four all really measuring the same underlying ability, or are we missing something by only really using exercises of the first kind?


b.  I'm still looking for that coherent argument as to why ability at these kinds of exercises should help with CS.  What is it we do in CS that relates to these kinds of exercises?  

Steve, that's the sort of thought-experiment that I'd think appeals to you - red rag to a bull?


Cheers, Quintin.


My email 5 Nov 17 Re: spatial skills and our intervention.

Quintin and others: here are some remarks of mine.


The convincing way of showing that spatial ability helped STEM learning would be to take a learner (L), measure their spatial ability (SA) and STEM knowledge; train them to improve their SA; then teach them more STEM and show that sped up their learning.  Cooper & Sorby (2015) tried this, but failed to improve their SA so they failed.


Wai et al. discuss longitudinal studies, showing that SA when young "predicted", i.e. was correlated with, STEM performance later.  A  minute's thought shows that this is no proof.  If it is possible to improve your SA by practice at all, then just taking more STEM courses would improve it too, so the early measure isn't the cause so much as just doing more STEM makes you better at learning STEM.

            Could a longitudinal study be convincing?  If Ls were sorted by SA score, and their STEM test scores after some STEM courses showed they were still sorted in that order, perhaps.  Especially if this was done before they had any choice about whether they were taking STEM subjects.


But things are probably worse than that.  Alec Johnstone (sorry, I don't have a ref. for this) showed in a study using GU chemistry finals exam questions, that many questions produced student marks correlated with the size of the student's working memory.  In other words, from a psychometric (i.e. scientific) point of view, the questions were not measuring chemistry knowledge as they should have been, but the size of a student's working memory.  So it is entirely possible that STEM performance = STEM exam scores = spatial ability if questions unintentionally presuppose spatial ability e.g. use diagrams, require you to imagine spatial layouts from descriptions, .....  I.e. the correlation may well be produced by poor unconscious practice by academics.

I am in fact pretty sure that some small areas of science end up teaching their students spatial abilities the rest of us don't have.  Crystollography (part of inorganic chemistry; and also of Materials Science) is like this: people who have done a serious course on this can think spatially about non-rectangular space in the way the rest of us can't.  Yet crystals are VERY simple: often just a pattern of 5 or so atoms (points) in a particular spatial relationship which repeats.  (E.g. "face centered cubic"  vs.  "body centered cubic".)  My conclusion is that humans CAN learn more about spatial relations, but we are VERY VERY bad at it without special practice.  And by "we" I include most people with several STEM university degrees like me.


Here is a demo thought experiment that Geoff Hinton taught me, and which shows that most people, and probably you, are embarrasingly incompetent at visualisation / spatial reasoning.  Imagine a wire-frame cube.  Just about the most simple and familiar 3D shape to everyone.  There it is (in your imagination) on a table in front of you: one square flat on the table top, 4 vertical edges, a second square forming the top and parallel to the one on the table.  Easy.

        Now imagine taking one corner in your fingers and raising it so that the cube is now standing on one corner, with the opposite (diagonal) corner held by you directly vertically above it.  Do this now using your physical hand, but with an imaginery wire frame cube.  Now with your spare hand, point to where the other corners are in space.


[Go on: do it right now.]


When people do this, many just indicate 4 other corners. (But with the cube flat on the table, you can easily see in your mind 4 corners on the table; 4 more on the top face = 8 altogether = 6 other than the two corners held by you and the table top in the exercise.)  Furthermore, they indicate the remaining corners as more or less in a plane.  Actually the 6 remaining zig up and down alternately.

            I know this because I was taught it by Geoff.   Generally, it shows what rubbish we are at this kind of thing.  (It must also cast doubt on the importance of the test items generally used.)


Now for some points that are, in a way, the opposite of this.

Is being rubbish at these rotation skills actually good?


As you probably know, if you are shown a photograph of a face upside down you immediately know it is a face but you can't recognise who it is -- no-one can.  That means not only that we encode faces in one 2D orientation only, but that no-one can do 2D rotation of the face (picture) in front of them so that they can compare the face against our memory of faces.

        Irvin Rock showed that it isn't just faces that are strongly affected by orientation.  If I do a fairly accurate tracing of the outline of Africa and show it to you as a shape without in any way making you expect something from a map, you will spontaneously recognise it as Africa; but if I present it rotated at right angles you will probably never notice that it is Africa-shaped.


One thing all STEM subjects have in common is a lot of symbolic notation.  In such notation, things (characters, symbols) mean different things depending on their orientation.  Not just in English (in some fonts) 'u' vs. 'n' but say 'T' vs. the T upside down which is a symbol from ?logic? set theory?  So in STEM it is important NOT to do even 2D rotation automatically, but to turn it on and off according to context and normally off. Some accounts of dyslexia suggest it is not turned off so reliably in dyslexics.


This illustrates how the things often tested as spatial ability are in fact NOT generally useful in either life or STEM, only in special contexts.  And must make us also wonder about what tests WOULD be appropriate.


It is possible that spatial tests are one kind of test for abstraction (an object regardless of its orientation ...): and that that is both unnatural and what is specifically useful in STEM as opposed to humanities, where human meaning and connotation are what is absolutely central.  Testing, in fact, for being able to learn abstract meaningless stuff.


Quintin's reply to my email 6 Nov 17

Hi Steve,

First thoughts on your email.


I fell straight into your trap and did exactly what you predicted, on the cube exercise.


And I completely appreciate that teachers may ask questions that require a skill that is not necessarily their own discipline's.


But I'm not totally sure about that for CS, and CS is one of those subjects where the SA has been shown to correlate.  I don't think we have that many exercises at all that obviously depend on overtly visualisation ability.  Whereas, I can imagine that engineering would do that.  I think the visualisation aspects that much of your mail concerns may be a red herring -- it's spatial ability we're talking about &  but I don't know enough about this &  Lovisa does...


Lovisa, we need a paper on the separation between visual and spatial skills that you were talking about!!  Please send one along!


It seems to me that juggling information at the limit of working memory space - not just single items - but a collection of items that are related - seems to be what we are getting at here.  So not as simple as remembering 7 digits, or something like that, but remembering a number of bits from different but related contexts.


I don't think the face-upside-down is a good example, as the information is much more continuous than either the spatial skills tasks, or what one does in programming - much more discrete in the latter two.  There's just too much information to juggle in one's head at the same time to do the face rotation.


And with the Africa example - pretty much the same, I think.  In any case, I'm not sure how visual and spatial are related in these two examples - Lovisa, we need you!.


There is something that is being tested in these exercises that is about relationships between things, and being able to make the mapping.  It's not about visualisation, per se, that is just one context for it.  It's about a number of models of the same thing, and being able to make the mapping from aspects in one model to aspects in another.  So, yes, it's abstract, because it's any kind of model that I'm trying to hold in my head.  And it needs to be reasonably simple models too, otherwise I just cannot hold it all - hence why faces and Africa might not work the same way.


Steve, this relates to what you have often told me about Chemistry, I think - three models that a chemist must keep together - the equation, the molecular model and the atomic model.

Roy Tasker's (Alex Johnstone's) 3 representations in Chemistry.

a)    Roy Tasker is the key man.  Looks as if he is now semi-retired.  I met him years ago while he was visiting here, and he left a deep impression.

b)  Johnstone, A. H. (1991) "Why is science difficult to learn? Things are seldom what they seem" Journal of Computer Assisted Learning vol.7 no.2 pp.75-83 doi:10.1111/j.1365-2729.1991.tb00230.x


I tried some of Jack's sketching exercises - they hurt my head in a very similar way to trying to hand execute a piece of code with just too many variables to comfortably hold onto - just one or two too many pieces of information to hold for comfort.  I did get into the swing of it a bit - but after a while I definitely felt mentally tired and my success flagged a little.


I found, and am still finding, the up-ended cube hard to imagine/visualise.  I found the shapes that Jack was getting me to sketch to be much simpler to visualise in my head, from right-side, top-side and front-side views - until I got tired.


Whilst I do find the cube hard to visualise, I am finding the MCQ exercises and the sketching, whilst doable, taxing in a rather similar way to remembering a large number, or, as I say, to tracing code.  I also recognise that for the MCQs, I do a lot of checking that I think I probably don't need to do - my first intuitive answer is usually right.  But it seems to me that I'm just not able to hold the mental model for long enough to be quite confident I have the right answer.  I wonder if practice will help here - and will it be because I can hold the model for longer or because I developed some good tricks for those kinds of questions?  Who knows?


Enough for now.


Lovisa, on spatial vs. visualising 7 Nov 17

I think there is some about this in my psychology dissertation. In it, I mention the work of Markus Knauff ("A Space to Reason") and the evidence that the systems for visual and spatial processing are dissociated, perhaps coinciding with the boundaries of the ventral and dorsal pathway in the two-streams hypothesis. The former is concerned with vivid, metric information, while the latter is concerned with topological, spatial information, and can be said to be "amodal". It is also used in logical reasoning.


Because they are dissociated, the systems compete for the same resources, to the effect that a logical riddle told in a visually vivid way takes longer to process (and activates visual cortex more) than a less vivid version with the same amount of detail. Therefore, mental visual imagery is usually not beneficial, and the goal of both internal and external visualisations should be to facilitate the construction of spatial models, by making abstract relations like transitivity more salient, etc.


Can a person have good spatial skills but poor visualisation skills? I suppose studies with blind people could be of interest in figuring out how separable visualisation and spatial skills are. They can reason without visual input, though maybe tactile diagrams serve as a modality-specific analogue that could either help or impede spatial model construction.


Can a person have good visualisation skills but poor spatial skills? Yes, I personally still get lost in the psychology and CS buildings...

(2) Lovisa, on spatial vs. visualising 7 Nov 17

Hi everyone and thank you for all of your insights!


Regarding visuo-spatial skills: there is research dating back from the 1980s that the systems for visual and spatial processing are dissociable. Dissociation means that impairments in one system do not necessarily impact the other, and that activation of one system (e.g. including a vivid visual description of a character in a logical riddle) interferes with the processing of the other (the spatial system's ability to solve the riddle).


The visual system would be concerned with metric information (e.g. exact relative distances between features in a face) textures, and colours, whereas the spatial system would be topological (about the logical relations of entities, like a subway map, or indeed faces in general). They operate semi-independently of each other. Simulating programs would be a case of spatial processing, because it does not depend on visual appearances, though visually processed representations could help highlight spatial relations.


Separating them as skills seems tricky, however. I don't know to what extent blind people are impaired by not having visual aids available (maybe they have tactile equivalents of visualisations), and I am not sure of how pure visual skills could even be measured. Sketching portraits may seem valid, but from personal experience, I'd say that being able to draw accurate portraits does not involve a vivid visual experience, but is simply about iteratively comparing the relationship on the paper to that of reality. It does not subjectively feel like solving a logical problem, rather like perceptually isolating relationships.


(Construct validity measuring what we want to measure - is a problem in working memory research, and it is easy for the cognitive philosophical entities like "systems" and "abilities" to take on a life of their own when there are no strong empirical constraints.)


Manipulating mathematical operators or programming constructs may seem far removed from mental rotation, because it is about following arbitrary formal rules rather than simulating things that could be physically presented before your eyes. There is a parallel difference between simulating algorithms (logical procedures) and mechanical systems of levers and pulleys.  (Mary Hegarty has dedicated her career to studying this).


Quintin's idea of mapping as a key predictor of programming ability and Steve's/Jack's mention of abstraction seem to go hand in hand, abstraction being the ability to perceive an invariance across different representations, which no doubt involves performing many conscious comparisons in WM. Much literature related to pattern-oriented instruction is related to this (see Jens Bennedssen's Abstraction ability as an indicator of success for learning computing science?). I will make sure to summarise related studies once I have read them more carefully.


Finally, I thought the point raised by Steve about a possible circularity built into SA research is interesting. If course examinations are unconsciously designed to measure spatial skills, then no wonder that it correlates with spatial skills! However, this does not necessarily diminish the relevance of the research. If the goal is to help people advance in their STEM careers, and course examinations are the gatekeepers, then we can keep them as a fixed benchmark --regardless of how ill-suited they are - and address what leads to success in them.  Otherwise we get a case of moving target --if we don't know our goal, it's hard to know our solution.


Kind regards,



Lovisa Resources / refs

            On spatial/visual divide: My favourite resource for this is:

Markus Knauff's book "Space to Reason", which the university has available as a free e-book.

Farah, Hammond, Levine, & Calvanio (1988): Visual and spatial mental imagery: Dissociable systems of representations

Hecker & Mapperson (1997): Dissociation of visual and spatial processing in working memory

Miyake, Friedman, Rettinger, Shah & Hegarty (2001): How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis.

The issue is far from settled -- in this study, for example, the authors argue that increasing the number of visual components in a WM task does not impede performance if the cognitive load is the same:

Vergauwe, Barrouillet & Camos (2009): Visual and spatial working memory are not dissociated after all: A time-based resource-sharing account.


Jens Bennedssen's Abstraction ability


Mary Hegarty xxx


Main points from the above?


2 brain pathways:  "visual" and "spatial".  They are different, but remember schema-driven recog.


Is it AI/automatic/2D  vs.  conceptual, structural?  Actually finding your way out of the building sounds "spatial" but is connectivity not metric-distance.  While mental rotation is metric.


Working memory making a diff. on tests (and so being about schemas not quantity).


Practice makes a BIG difference, but

     there could also be some general transfer?

     Piaget's "genetic" – dev. pathway that depends on history as well as fn learning.



Consider 2D, vs. 2.5D (viewer-centered) vs. 3D (no viewpoint).  Humans aren't very good at 3D, perhaps because a) gravity makes our world 2.5D, unlike swimming and flying

b) Immediate visual processing has to be 2.5D  at first, and so this rep. persists and is often enough by itself.


Pure spatial, as Jack and Lovisa probably think of, is tested for by mental rotation.



Piagetian (Adey & Shayer) "spatial"

Their view is that effects on STEM learning is about how much each L has advanced from early SensoriMotor to Formal op. thinking.  Their CASE intervention moves Ls onward;  and this then improves their school science learning after that.

This also is in the form that some non-school practices have a sig. effect on sci. learning.


Shayer did papers on surveying relevant ages (and genders) in school for how advanced Ls were in this sense.  And it "predicts" exam results.  It has a large gender effect.  But the intervention works on a useful subset of both genders (but not on everyone).


They used tests taken directly from Piaget books.  3 tests, one of which they call "spatial", following Piaget's book title "The child's conception of space", but it is actually about asking what level water adopts in a tilted bottle.

They also reference papers on well know effects of spatial k. on ....


            The tests are taken from:

Piaget and Inhelder (1952)  The child's conception of space

            and described in:
Shayer,M., Küchemann,D.E. and Whylam,H. (1976) British Journal of Educational Psychology vol.46 no.2 pp.164-173 "The distribution of Piagetian stages of thinking in British middle and secondary school children" doi:10.1111/j.2044-8279.1976.tb02308.x


            The survey results and sex differences are presented in:

Shayer,M. & Whylam,H. (1978) "The distribution of Piagetian stages of thinking in British middle and secondary school children. II - 14- to 16-year olds and sex differentials" British Journal of Educational Psychology vol.48 no.1 pp.62-70 doi:10.1111/j.2044-8279.1978.tb02370.x

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