Abstract
The present high-density event-related potential (ERP) study on 13 adults aimed to determine whether number conservation relies on the ability to inhibit the overlearned length-equals-number strategy and then imagine the shortening of the row that was lengthened. Participants performed the number-conservation task and, after the EEG session, the mental imagery task. In the number-conservation task, first two rows with the same number of tokens and the same length were presented on a computer screen (COV condition) and then, the tokens in one of the two rows were spread apart (INT condition). Participants were instructed to determine whether the two rows had an identical number of tokens. In the mental imagery task, two rows with different lengths but the same number of tokens were presented and participants were instructed to imagine the tokens in the longer row aligning with the tokens in the shorter row. In the number-conservation task, we found that the amplitudes of the centro-parietal N2 and fronto-central P3 were higher in the INT than in the COV conditions. In addition, the differences in response times between the two conditions were correlated with the differences in the amplitudes of the fronto-central P3. In light of previous results reported on the number-conservation task in adults, the present results suggest that inhibition might be necessary to succeed the number-conservation task in adults even when the transformation of the length of one of the row is displayed. Finally, we also reported correlations between the speed at which participants could imagine the shortening of one of the row in the mental imagery task, the speed at which participants could determine that the two rows had the same number of tokens after the tokens in one of the row were spread apart and the latency of the late positive parietal component in the number-conservation task. Therefore, performing the number-conservation task might involve mental transformation processes in adults.
Highlights
New imaging technologies, such as high-density electroencephalogram (EEG), may help us answer some of the oldest and deepest questions regarding what logicomathematical cognition is and how it works
We analyzed the response times (RTs) in the INT condition for the number-conservation and imagery tasks using a Task × Distance difference between the tokens in the two rows (3 vs. 5 vs. 7 mm) repeated measures analysis of variance (ANOVA) to determine whether the RTs increased linearly with the distance by which the longer row had to be shortened to align with the tokens in a one-to-one correspondence
The event-related potential (ERP) analyses revealed that the N2 and P3 component amplitudes increased in the INT condition
Summary
New imaging technologies, such as high-density electroencephalogram (EEG), may help us answer some of the oldest and deepest questions regarding what logicomathematical cognition is and how it works. In the seminal number-conservation task, two rows with an identical number of objects are initially presented with the objects in the two rows yielding a one-to-one correspondence. When the children acknowledged that the two rows possess the identical number of objects (i.e., initial equivalence), one of the rows is transformed in length but not in number (e.g., the objects are spread apart). To understand that the transformation of the length of the row does not affect the number of objects in that row, children must grasp that operations (such as transformation) are reversible, e.g., the movement from A to B (i.e., the lengthening of the row) can be eliminated by the movement from B to A (i.e., the shortening of the row)
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