Categorical and continuous--disentangling the neural correlates of the carry effect in multi-digit addition

Abstract

Background: Recently it was suggested that the carry effect observed in addition involves both categorical and continuous processing characteristics.

Methods: In the present study, we aimed at identifying the specific neural correlates associated with processing either categorical or continuous aspects of the carry effect in an fMRI study on multi-digit addition.

Results: In line with our expectations, we observed two distinct parts of the fronto-parietal network subserving numerical cognition to be associated with either one of these two characteristics. On the one hand, the categorical aspect of the carry effect was associated with left-hemispheric language areas and the basal ganglia probably reflecting increased demands on procedural and problem solving processes. Complementarily, the continuous aspect of the carry effect was associated with increased intraparietal activation indicating increasing demands on magnitude processing as well as place-value integration with increasing unit sum.

Conclusions: In summary, the findings suggest representations and processes underlying the carry effect in multi-digit addition to be more complex and interactive than assumed previously.

Figure 1

ANOVA results. A: Main effect of problem size at an uncorrected voxelwise p-value of < .00001 and cluster size k = 10 voxels: Bilateral intraparietal activation as well as activation of the left angular gyrus and the left retrosplenial cortex. Please note that a stronger p-value of < .00001 had to be used to enable a dissociation of the different maxima of activation (at a p-value of < .005 a cluster of > 10000 voxels covered large parts of bilateral occipital and parietal cortices). B: Main effect of carry at an uncorrected voxelwise p-value of < .005 and cluster size k = 10 voxels: Bilateral intraparietal activation as well as activation of the left angular gyrus and the left retrosplenial cortex. C: Interaction of problem size and carry: In the most difficult condition (i.e., large addition problems with a carry) right intraparietal activation is observed at an uncorrected voxelwise p-value of < .005 and cluster size k = 10 voxels.

Figure 2

Modulation of the fMRI signal by categorical and continuous properties of the carry effect. A: fMRI activation significantly modulated by the requirement of a carry operation at an uncorrected voxelwise p-value of p < .005 and k = 10 voxels: please note the lack of significant magnitude-related activation. B: Cortical regions showing modulation of fMRI signal due to increasing unit sum (uncorrected p-value of < .005, cluster size k = 10 voxels): magnitude-related activation in the bilateral IPS.

Figure 3

Direct comparison of categorical vs. continuous properties of the carry effect. A: Unit sum - carry at an uncorrected voxelwise p-value of p < .005 and k = 10 voxels. Magnitude-related activation in the left IPS, which is explained significantly better by the continuous predictor unit sum than by the categorical predictor carry. B: Carry - unit sum at an uncorrected voxelwise p-value of p < .005 and k = 10 voxels: Activation of the left Broca's Area as well as the right middle temporal gyrus bordering the angular gyrus.

Figure 4

Cortical regions modulated by increasing decade sum. Magnitude-related activation in the bilateral IPS (uncorrected voxelwise p-value of < .00001 and cluster size k = 10 voxels).

Figure 5

fMRI signal modulations reflected by distractor type. A: Cortical regions showing modulation of fMRI signal due to a distractor type of +/- 10 at an uncorrected voxelwise p-value of < .005 and cluster size k = 10 voxels: Magnitude-related activation in the right IPS. B: fMRI activation significantly modulated by the distractor type +/- 2: Activation of the left insula.

Figure 6

Increasing fMRI signal changes with decreasing decade/unit sum. A: fMRI signal change predicted by decreasing decade sum (uncorrected p < .005, k = 10 voxels) comprising the bilateral angular, the right supramarginal gyrus, the right hippocampus as well as the left retrosplenial cortex. B: fMRI activation significantly modulated by decreasing unit sum (uncorrected p-value of < .005, cluster size k = 10 voxels) included the left angular gyrus and the right retrosplenial cortex.