A warm-up phase for the mental rotation task
A term essay: the linear relation between rotation angle and response time may be part practice effect, and a distinctive shape may hint at which axis to turn. A redesign that spends the learning before anything is measured.
Written for a PSY270H1 (Introduction to Cognitive Psychology) assignment, submitted November 22, 2024. Rewritten here from the APA manuscript: the citations became inline links and the register is looser; the argument is unchanged. The manuscript, recompiled as submitted, is available as a PDF.
Shepard and Metzler showed that deciding whether two three-dimensional shapes are the same object takes longer the further apart their orientations are, and that the relationship is linear in the angle. The natural reading is that participants are turning something in their heads at a roughly steady rate. Two things the design does not separate could be producing part of that line on their own.
What practice does to a curve
A participant in a rotation study sees the task many times. Payne records that practice improves both memory performance and the efficiency with which a task is executed, and McCabe and colleagues list where that improvement comes from: deliberate rehearsal, incidental learning, procedural learning, a changed conception of what the task is, and plain familiarity with the testing environment, which they call test-wiseness.
None of that is mental rotation. If a participant quietly picks up a faster strategy over successive trials, response times fall for a reason the experiment is not trying to measure, and the curve is part rotation and part learning.
Morales and Firestone press on the interpretation from another side: manipulating an object in the mind may not simply mirror manipulating one in the world, because it depends heavily on the observer’s point of view.
What the objects give away
The original study drew on one family of shapes, which leaves the attributes of the object uncontrolled: complexity, symmetry, colour. A simple shape may be recognized faster because it demands less. A complex or distinctive one may do the opposite favour and hand the participant a landmark, a feature salient enough to suggest which axis to turn about. Either way, some of the variance in response time belongs to the stimulus rather than to the rotation.
The redesign
Eighty adult participants from a university population, for a spread of spatial reasoning ability.
Sixty three-dimensional objects in three sets of twenty. Simple shapes, cubes and pyramids, in uniform colour. Complex shapes, asymmetrical and intricate, in varied colours. And distinctive shapes, carrying features particular enough to be used as landmarks.
Then a warm-up phase before anything counts: a hundred rotation trials drawn at random across all three sets, timed but excluded from the analysis. The point is to let participants find whatever strategy they are going to find while nobody is recording it.
The main phase runs six hundred pairs, two hundred from each set. Six hundred objects are not needed, since the sixty already built can be presented again at different colours and orientations. Participants judge each pair congruent or incongruent, and response time and accuracy are recorded.
Presentation order is randomized, and so are the angles for the matching pairs, which are never shown in sorted order. Sorted angles would let a participant anticipate the next trial.
What I would expect
Response times and accuracy in the main phase should be better than they would be with no warm-up, because the familiarity has already been paid for.
Complexity should cost time: as a shape gets harder, both recognition and the congruence judgment take longer. Distinctiveness should cut the other way, since a shape with an obvious feature offers a hint about how to rotate it and should be handled faster than a generic one.
The test of whether the warm-up worked is stability. Response times for a given angle should be about the same wherever that trial falls in the sequence. If they still drift downward across the session, learning is still in the measurement.
If the line holds
The redesign asks what is left of the angle-to-time line once the practice has been spent in advance and the stimulus set is varied on purpose. If the line holds, it holds more cleanly. If it flattens, some of what looked like rotation was participants getting better at the test.
The object half has a use outside the lab. If complexity and distinctiveness change how hard a spatial transformation is, that is worth knowing to anyone teaching spatial reasoning.