Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data

Abstract

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.

Keywords: arithmetic; developmental dyscalculia; fact retrieval; finger counting.

Figure A1

Regions of significant BOLD signal change for the control group (sagittal, coronal and axial view from left to right). (a) multiplication > subtraction (cluster threshold Z = 2.3), (b) subtraction > multiplication (cluster threshold Z = 3.1).

Figure 1

Examples of (a) a subtraction trial, (b) a multiplication trial, with the corresponding control trials (panels (c,d)).

Figure 2

Overlay of regions of significant BOLD signal change for the control group in dark color and for RM in light color (sagittal, coronal and axial view from left to right). (a) Multiplication versus control (cluster threshold Z = 2.3) (RM in light red, control group in dark red), (b) subtraction versus control (cluster threshold Z = 2.3) (RM in light blue, control group in dark blue).

Figure 3

(A) Mean percentage signal change in six ROIs (left and right IPS, left and right AG, and left and right posterior superior parietal lobule) by task (multiplication in red, subtraction in blue) for the control group, (B) Mean percentage signal change during multiplication in the left IPS and the left AG for RM (in green) and the control group (in gray).

Figure 4

Regions of significant differences in BOLD signal change between RM and the control group (sagittal, coronal and axial view from left to right). (a) Higher activation for RM than the control group in multiplication versus control (cluster threshold Z = 2.3), (b) Lower activation for RM than the control group in subtraction versus control (cluster threshold Z = 3.1).

Figure 5

(A) Cortical networks and processing pathways for magnitude processing (left panel, red) and arithmetic fact retrieval (right panel, dark blue) in adults with and without DD (developed based on [6,49]). The color-changing arrow between the two panels reflects that these two anatomically separate networks operate together as functionally integrated circuits in numerical cognition. (B) Interplay between magnitude processing and arithmetic fact retrieval. A certain amount of fact retrieval is assumed to be involved in arithmetic independent of the difficulty of the task, depicted as the blue rectangle at the bottom. However, the harder a task becomes, the less fact retrieval (blue triangle, variable fact retrieval component) and the more magnitude processing has been assumed (red triangle, variable magnitude processing component). On the other side, an invariant component of mandatorily involved magnitude processing is assumed as well, depicted as the red rectangle at the top of the figure. Abbreviations: AG—angular gyrus; BG—basal ganglia; EC—entorhinal cortex; EC/EmC—external/extreme capsule system; HC—hippocampus; IFG—inferior frontal gyrus; IPS—intraparietal sulcus; LH—left hemisphere; Medial FG—medial frontal gyrus; MTG—middle temporal gyrus; PSPL—posterior superior parietal lobule; SLF—superior longitudinal fascicle; SMA—supplementary motor area; RC—retrospenial cortex; RH—right hemisphere; TH—thalamus; V1—primary visual cortex; VNF—visual number form.