Mental rotation: the one cognitive skill that reliably improves with practice
Here is a task with one rule. You are shown a figure. You are then shown four more, and one of them is that figure turned. The other three have been flipped. Which is the turn?
It sounds like a spot-the-difference. It is not, and the reason is a piece of timing data from 1971 that is still one of the tidiest results in cognitive psychology.
The line that made this famous
Roger Shepard and Jacqueline Metzler showed people pairs of block figures and asked whether the second was the same object or its mirror image. People were accurate. What mattered was how long they took.
The time rose in a straight line with the angle. A figure turned 60 degrees took reliably longer than one turned 30, and 120 longer again, right out to 180.
Think about why that is strange. If you were recognising the shape, or ticking off features against a checklist, there is no obvious reason a bigger angle should cost more. A list is a list. The straight line suggests something continuous is going on: a representation being turned at a roughly steady rate, more like handling an object than like consulting a memory. People were, in some functional sense, rotating a picture.
The accuracy tells you whether someone can do it. The slope tells you how they are doing it.
Why the flipped ones are the whole task
The distractors are mirror images rather than different shapes, and that is deliberate. A mirror image of a chiral figure cannot be produced by rotating it, no matter how far you turn it. So if you are genuinely rotating the thing in your head, the reflections fall away on their own. If you are matching features (there is a blob on the left, there is a blob on the left), a reflection passes the check and you get it wrong.
That is why our own rotation test puts two reflections in every set of four, and why every figure in it is asymmetric in both axes. A symmetrical figure would have several correct answers and nobody would notice.
The part that makes it worth practising
Most of what these tests measure is fairly stubborn. You can be better rested, better fed and less distracted, and that is roughly the extent of it. Spatial skills are the conspicuous exception. Mental rotation responds to practice more reliably than almost anything else on this site, and it responds quickly: people typically get faster within a few sessions, and the gains hold up better than the "brain training" literature would lead you to expect.
What is genuinely contested is how far it transfers. Getting quicker at rotating block figures makes you quicker at rotating block figures. Whether that carries into reading a map, packing a boot, or a technical drawing is a live argument with results on both sides, and anyone who tells you it definitely does is ahead of the evidence.
Two strategies, and one is faster
People solve these in one of two ways, and you can usually feel which one you are using.
Holistic rotation turns the whole figure at once. It is what the Shepard result describes, and it is the faster route once you trust it.
Feature matching picks a landmark, finds it in the candidate, and works outward. It feels safer and it is slower, and on reflections it is actively dangerous, because a landmark survives a flip perfectly well.
If you find yourself hunting for the dot on the end, you are doing the second one. Trying to turn the whole shape in one go feels worse at first and is worth persisting with.
What it is not
Mental rotation is one narrow spatial ability. It is not general intelligence, it is not a measure of how visual you are as a person, and it is not an aptitude that decides what you are suited to. Differences between groups get reported in this area more than most, and they shrink substantially with practice and vary a lot with how the task is set, which is worth knowing before treating any single score as a fact about a person.
Ours is fourteen figures and takes about five minutes. If you want the number, take the test. If you want to get better at it, take it twice a week for a fortnight, and watch the second number rather than the first.