What are standard tests for mental visualization (image, representation) for kids? So far I know about mental arithmetics and spatial rotation tests. Is there any other way to check mental vision ability?

As an example, here's a test I've created. One has to imagine and do manipulation over the mental image:

  • imagine a white square with clearly visible white borders on a black background
  • now draw white vertical line in the middle of the square. What do you see now?
  • now draw white horizontal line in the middle of the square. What do you see now? Which and how many parts do you see?
  • now clear up the two lines you draw. Instead, draw two vertical lines which divide square vertically on equal parts, and draw two horizontal lines which divide square horizontally on equal parts. What do you see? How many parts are there?
  • now use lines as guides and cut out corners of the resulting figure and remove those from pictures. What do you see? How many parts does it have?
  • now attach red squares to the corners (instead of previously cut ones)
  • now split the figure into 3 parts using vertical lines you've imagined before. Let the side parts glide in opposite directions and rotate 90 degrees clockwise. After rotation, merge the the parts back into one figure
  • now imagine two transformations: 1) rotate resulting figure 180 degrees and 2) mirror the figure. Are the two transformations equal (do they produce same image)?
  • now name colors of parts of the image after 180 degrees rotation

Here's how I'd like to interpret results:

  • correct answers to all questions: child is capable for mental vis
  • in the middle of test says "this is boring" or distracts: child has reduced capability for mental vis
  • has problems with answering 3rd questions: child isn't capable of mental vis. This is a real problem for further education

I haven't yet tried to run this test, but I'd like to know if there are other such, which can verify a child is doing mental visualization.

  • $\begingroup$ My mother did her PhD thesis on this sort of stuff and used me as a test subject when I was a kid. One of the tests I recall was drawing a drinking glass with water in it, when the glass is tilted. Visualizing rotations is AFAIK one of the only mathematical skills where there are strong sex-linked differences. (My mother tried to determine whether this sort of thing was linked to a gene on the Y chromosome, but she didn't have enough data to reach a definite conclusion.) $\endgroup$ – Ben Crowell Oct 4 '20 at 19:10
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    $\begingroup$ Are the kids supposed to understand these verbal descriptions? And to guess their intention? That seems more difficult than the visualization. For example, if the first bullet item means (as it seems to) that the whole square is white, not only its boundary, then adding (as in the second bullet item) a white line will make no visible difference, since white on white isn't visible. $\endgroup$ – Andreas Blass Oct 4 '20 at 22:25
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    $\begingroup$ Looks like I have reduced capacity! In addition to what Andreas Blass mentioned, after cutting off the corners, I see a figure with 12 corners and thus many ways to attach the red squares (which I chose to be all different sizes, naturally). I could also think of many ways to merge my resulting pieces (and this is the only part where I'm genuinely not sure what you mean, unlike the rest where I'm being intentionally obtuse). If you allow for such variations and aren't locked into one "correct" answer, I think this is a great question to give to children. $\endgroup$ – Thierry Oct 5 '20 at 3:10
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    $\begingroup$ I've never managed to get my head around the intuition of algebraic geometry (and that's despite some of my work being cited by algebraic geometers!). I'm not sure if it's related, though. $\endgroup$ – user3482749 Nov 9 '20 at 21:23
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    $\begingroup$ The difficulty is essentially that you have to come up with problems which are (a) sufficiently complex to work with non-visually that I can't just solve them by non-visual means, and (b) sufficiently simple that you can explain them to children and those with strong visualisation abilities will be able to visualise them. I'm not convinced there's an overlap, in general, so you'd have to tune your test pretty narrowly to the target population, and even then, I'm not sure how you could tell the difference between visualisation abilities and artifacts of one of the above two problems. $\endgroup$ – user3482749 Nov 9 '20 at 21:23

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