When math operations have visuospatial meanings versus purely symbolic definitions: Which solving stages and brain regions are affected?

Abstract

How does processing differ during purely symbolic problem solving versus when mathematical operations can be mentally associated with meaningful (here, visuospatial) referents? Learners were trained on novel math operations (↓, ↑), that were defined strictly symbolically or in terms of a visuospatial interpretation (operands mapped to dimensions of shaded areas, answer = total area). During testing (scanner session), no visuospatial representations were displayed. However, we expected visuospatially-trained learners to form mental visuospatial representations for problems, and exhibit distinct activations. Since some solution intervals were long (~10s) and visuospatial representations might only be instantiated in some stages during solving, group differences were difficult to detect when treating the solving interval as a whole. However, an HSMM-MVPA process (Anderson and Fincham, 2014a) to parse fMRI data identified four distinct problem-solving stages in each group, dubbed: 1) encode; 2) plan; 3) compute; and 4) respond. We assessed stage-specific differences across groups. During encoding, several regions implicated in general semantic processing and/or mental imagery were more active in visuospatially-trained learners, including: bilateral supramarginal, precuneus, cuneus, parahippocampus, and left middle temporal regions. Four of these regions again emerged in the computation stage: precuneus, right supramarginal/angular, left supramarginal/inferior parietal, and left parahippocampal gyrus. Thus, mental visuospatial representations may not just inform initial problem interpretation (followed by symbolic computation), but may scaffold on-going computation. In the second stage, higher activations were found among symbolically-trained solvers in frontal regions (R. medial and inferior and L. superior) and the right angular and middle temporal gyrus. Activations in contrasting regions may shed light on solvers' degree of use of symbolic versus mental visuospatial strategies, even in absence of behavioral differences.

Keywords: Graphs; Math problem solving; Mental stages; Symbolic; Visuospatial representation.