What a mental rotation item asks
Each item shows two figures built from cubes joined face to face. The right figure has been turned. In the Same or mirror mode of the mental rotation practice, you answer Same, rotated or Mirror image. Exactly half the questions in every round are mirror images, so pressing one answer every time scores half.
In the Turn to match mode, you do the turning. You turn the right figure a quarter turn at a time until it matches the left one, then press Match. When no turn can match it, you press Mirror. With a keyboard, the arrow keys and Page Up and Page Down each make one quarter turn. You can also drag the figure.
Where the task comes from
Roger Shepard and Jacqueline Metzler ran the experiment this task comes from, and published it in Science in 1971. Each of eight adults saw 1,600 pairs of drawings. Every object was ten cubes joined into one arm-like shape with three right-angle bends. In half the pairs, one object could be turned to match the other. In the other half, one object was the mirror image of the other.
For the pairs that matched, the time to answer rose in a straight line with the angle between the two drawings: about 1 second with no turn, and 4 to 6 seconds at 180 degrees, depending on the person. A turn in depth, into the page, took no longer than a flat turn in the picture. From the slope, the authors put the average rate at roughly 60 degrees a second.
In 1978 Steven Vandenberg and Allan Kuse built a paper-and-pencil group test from the same figures, the Mental Rotations Test. Michael Peters and colleagues later redrew it. They found items very hard when the figure had to turn around both the top-to-bottom axis and the left-to-right axis. In the redrawn version as Alvarez-Vargas and colleagues describe it, each item shows a target and four other figures. Two are the target turned and two are turned mirror images, and you mark both matches.
The practice here uses figures of 6 to 9 cubes with two bends, one pair at a time. Spatial tests often mix this task with others, as the spatial reasoning tests guide shows.
How to solve it: match the ends
Shepard and Metzler's subjects described their own method. They turned one end of one object to line up with the matching end of the other. When the two free ends still did not line up, the objects were different. Three steps turn that into a routine.
- Count the arms, but do not stop there. Each figure here is a chain of cubes with two bends, so it has three straight arms. A mirror image has the same arms, so the counts always match.
- Match one end. Pick an end you can name, such as the end of the longest arm. Find the same end on the right figure.
- Follow the bends. From that end, check that each arm turns off the same way on both figures. A mirror image goes wrong at the last bend, however it is turned.
Four worked examples
Each example below is a real question from the mental rotation practice, drawn by the practice itself. Cover the steps below each one and try it first.
Example 1: a turn along an edge (level 4)
Same, rotated or mirror image?
- Both figures have seven cubes in three straight arms of 4, 3 and 2 cubes, counting each bend cube in both arms. The counts match, so they cannot decide.
- Start at the end of the four-cube arm on the left, and find the same end on the right. Then follow the arms from there, bend by bend.
- Every arm lands on its partner. The right figure is the left one turned 60 degrees about an axis that runs along the edges of the blocks, with nothing reflected.
The answer is Same, rotated. The arm that lies along the axis of the turn points the same way in both drawings. That gives you a fixed place to start.
Example 2: a mirror image (level 5)
Same, rotated or mirror image?
- Both figures have eight cubes in three straight arms of 3, 2 and 5 cubes, counting each bend cube in both arms. The counts match, so they cannot decide.
- Start at the end of the five-cube arm on the left, and find the same end on the right. Then follow the arms from there, bend by bend.
- Line up the first two arms, and the last one points the other way. No turn fixes that. The right figure is the mirror image, turned 90 degrees about an axis that runs along the edges of the blocks.
The answer is Mirror image. A quick look at the first two arms says Same. The difference shows only at the free end, as it did for the subjects in 1971.
Example 3: a diagonal axis (level 8)
Same, rotated or mirror image?
- Both figures have nine cubes in three straight arms of 5, 2 and 4 cubes, counting each bend cube in both arms. The counts match, so they cannot decide.
- Start at the end of the five-cube arm on the left, and find the same end on the right. Then follow the arms from there, bend by bend.
- Every arm lands on its partner. The right figure is the left one turned 90 degrees about a diagonal axis, one that runs along no edge, with nothing reflected.
The answer is Same, rotated. Here the axis runs on a slant, along none of the arms, so no arm keeps its direction. Matching the ends still works.
Example 4: Turn to match (level 3)
Turn the right shape to match the left one, or press Mirror.
Match one end first. Find the end of the target's longest arm on your shape, then turn until that arm points the same way. Here the fewest is two quarter turns. One way is the Right arrow, then the Up arrow.
After one turn.
After two turns: a match.
The answer is Match, in two turns. Half the targets in this mode are mirror images. For those, no number of turns will do, and the answer is Mirror.
Common mistakes
Counting cubes. In every example above, both figures have the same cubes and the same arms. Counting can only rule a pair out, and in this practice it never does.
Stopping after two arms. In example 2, the first two arms line up. The difference is at the free end, so follow every arm to the end.
Judging by how different the pictures look. A large turn can make a figure look new, as in example 3. The arms and their order stay the same.
Expecting a turn into the page to take longer. In the 1971 experiment it took no longer than a flat turn. Treat both the same way.
Pressing Mirror too soon. In Turn to match, a shape turned the wrong way can look like a mirror image. Before you press Mirror, match one end and follow the arms to the last bend.
How to practice it here
Start with the lesson Turn a shape, don’t flip it. Its example step has a figure you can turn by hand. Then open the mental rotation practice. Its levels change the figure, the angle and the axis:
- Levels 1 and 2: 6 cubes, turns of 90 or 180 degrees. 6 questions.
- Levels 3 and 4: 7 cubes, turns of 60, 90, 120 or 180 degrees. 6 or 8 questions.
- Levels 5 and 6: 8 cubes, turns of 45, 60, 90, 120, 135 or 180 degrees. 8 questions.
- Levels 7 and 8: 9 cubes, turns in 15 degree steps from 30 to 180 degrees, around diagonal axes as well. 8 or 10 questions.
Up to level 6, every turn is around an axis that runs along the edges of the blocks. There is no time limit. The result counts your correct answers, shows your median time per question, and shows turned and mirrored questions separately. In Turn to match it also compares the turns you used with the fewest. The score describes this practice on that day, nothing wider.
Related practices on this site
- Mirror images. Reflection on its own, without the turn.
- Cube nets. Its Match the cube mode also asks you to reject a mirror image.
- Rolling cubes. Follow a marked cube as it turns along a route.
Questions people ask
What is a mental rotation test?
A mental rotation test shows two figures built from cubes and asks whether the second is the first one turned, or its mirror image. Roger Shepard and Jacqueline Metzler ran the experiment the task comes from and published it in Science in 1971. In 1978 Steven Vandenberg and Allan Kuse built a paper-and-pencil group test from the same figures, the Mental Rotations Test.
How are mental rotation test items built?
Each figure is a chain of cubes joined face to face, with right-angle bends. In the 1971 experiment, each item was a pair: in half the pairs one object could be turned to match the other, and in the other half it was a mirror image. In the redrawn Mental Rotations Test as Alvarez-Vargas and colleagues describe it, each item shows a target and four other figures. Two are the target turned and two are turned mirror images.
How do you tell a turned figure from its mirror image?
Match the ends. Pick an end you can name, such as the end of the longest arm, and find the same end on the other figure. Then follow the bends and check that each arm turns off the same way on both. A mirror image has the same cubes and the same arms, but it goes wrong at the last bend, however it is turned.
What are the common mistakes on a mental rotation test?
Counting cubes, stopping after two arms, and judging by how different the pictures look. A mirror image has the same cubes and arms, so counting can only rule a pair out. It can match for two arms and differ only at the free end, so follow every arm to the end. A large turn can make a figure look new, but its arms and their order stay the same.
Does a larger turn take longer to judge?
In Shepard and Metzler's 1971 experiment it did. For pairs that matched, the time to answer rose in a straight line with the angle between the two drawings: about 1 second with no turn, and 4 to 6 seconds at 180 degrees, depending on the person. A turn into the page took no longer than a flat turn in the picture.
How do you practice mental rotation on this site?
Start with the lesson Turn a shape, don’t flip it. Its example step has a figure you can turn by hand. Then open the mental rotation practice, whose figures have 6 to 9 cubes with two bends. In Same or mirror, you answer Same, rotated or Mirror image. In Turn to match, you turn the figure a quarter turn at a time until it matches, or press Mirror. There is no time limit.
Sources
- Shepard, R. N. and Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701 to 703.
- Vandenberg, S. G. and Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47, 599 to 604.
- Peters, M., Laeng, B., Latham, K., Jackson, M., Zaiyouna, R. and Richardson, C. (1995). A redrawn Vandenberg and Kuse mental rotations test: different versions and factors that affect performance. Brain and Cognition, 28, 39 to 58.
- Alvarez-Vargas, D., Abad, C. and Pruden, S. M. (2020). Spatial anxiety mediates the sex difference in adult mental rotation test performance. Cognitive Research: Principles and Implications, 5, 31.