Abstract
Some individuals experience more difficulties with math than others, in particular when arithmetic problems get more complex. Math ability, on one hand, and arithmetic complexity, on the other hand, seem to partly share neural underpinnings. This study addresses the question of whether this leads to an interaction of math ability and arithmetic complexity for multiplication and division on behavioral and neural levels. Previously screened individuals with high and low math ability solved multiplication and division problems in a written production paradigm while brain activation was assessed by combined functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). Arithmetic complexity was manipulated by using single-digit operands for simple multiplication problems and operands between 2 and 19 for complex multiplication problems and the corresponding division problems. On the behavioral level, individuals with low math ability needed more time for calculation, especially for complex arithmetic. On the neural level, fNIRS results revealed that these individuals showed less activation in the left supramarginal gyrus (SMG), superior temporal gyrus (STG) and inferior frontal gyrus (IFG) than individuals with high math ability when solving complex compared to simple arithmetic. This reflects the greater use of arithmetic fact retrieval and also the more efficient processing of arithmetic complexity by individuals with high math ability. Oscillatory EEG analysis generally revealed theta and alpha desynchronization with increasing arithmetic complexity but showed no interaction with math ability. Because of the discovered interaction for behavior and brain activation, we conclude that the consideration of individual differences is essential when investigating the neurocognitive processing of arithmetic.
Highlights
IntroductionIndividual differences in math ability matter when arithmetic problems get increasingly complex
In the analysis of response time (RT), significant main effects were observed for complexity (F1,32 = 1341.99, p < 0.001, ηp2 = 0.977) and math ability (F1,32 = 38.09, p < 0.001, ηp2 = 0.543), indicating that participants were faster at solving simple rather than complex arithmetic problems and individuals with high math ability were faster than individuals with low math ability
In the analysis of ER, significant main effects were observed for complexity (F1,29 = 241.31, p < 0.001, ηp2 = 0.893), math ability (F1,29 = 14.06, p = 0.001, ηp2 = 0.327) and operation (F1,29 = 7.01, p = 0.013, ηp2 = 0.195), indicating higher ER for complex compared to simple arithmetic problems, for individuals with low compared to high math ability, and for division compared to multiplication
Summary
Individual differences in math ability matter when arithmetic problems get increasingly complex. Because with higher arithmetic complexity the difficulty level increases, individuals with low math ability, who might already struggle with simple arithmetic, experience even more difficulties when solving complex arithmetic problems (e.g., Artemenko et al, 2018b). The most frequently studied arithmetic operation in the context of arithmetic complexity and math ability is multiplication (e.g., Grabner et al, 2007; Soltanlou et al, 2018; for a review, see Zamarian et al, 2009). The aim of the current study is to replicate the findings regarding arithmetic complexity and math ability for multiplication and further explore the interaction of these factors in both multiplication and division, which is the inverse operation of multiplication and largely understudied. Studying division provides the chance to examine to what extent the findings from multiplication can be generalized
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