Disentangling Neural Sources of Problem Size and Interference Effects in Multiplication

Abstract

Multiplication is thought to be primarily solved via direct retrieval from memory. Two of the main factors known to influence the retrieval of multiplication facts are problem size and interference. Because these factors are often intertwined, we sought to investigate the unique influences of problem size and interference on both performance and neural responses during multiplication fact retrieval in healthy adults. Behavioral results showed that both problem size and interference explained separate unique portions of RT variance, but with significantly stronger contribution from problem size, which contrasts with previous work in children. Whole-brain fMRI results relying on a paradigm that isolated multiplication fact retrieval from response selection showed highly overlapping brain areas parametrically modulated by both problem size and interference in a large network of frontal, parietal, and subcortical brain areas. Subsequent analysis within these regions revealed problem size to be the stronger and more consistent “unique” modulating factor in overlapping regions as well as those that appeared to respond only to problem size or interference at the whole-brain level, thus underscoring the need to look beyond anatomical overlap using arbitrary thresholds. Additional unique contributions of interference (beyond problem size) were identified in right angular gyrus and subcortical regions associated with procedural processing. Together, our results suggest that problem size, relative to interference, tends to be the more dominant factor in driving behavioral and neural responses during multiplication fact retrieval in adults. Nevertheless, unique contributions of both factors demonstrate the importance of considering the overlapping and unique contributions of each in explaining the cognitive and neural bases of mental multiplication.

Individual Differences in Math Ability Determine Neurocognitive Processing of Arithmetic Complexity: A Combined fNIRS-EEG Study

“…The complexity of multiplication depends on several factors (for an overview, see Domahs et al, 2006), for example, the interference effect (De Visscher and Noël, 2014). One other important factor is the effect of problem size (Tiberghien et al, 2018), i.e., multiplication problems with numerically larger operands are more difficult to solve—as reflected by higher reaction times (RT) and error rates (ER)—than multiplication problems with smaller operands (Verguts and Fias, 2005). While this effect can be derived from the neighborhood consistency when smaller single-digit problems (e.g., 3 × 4) are compared to larger single-digit problems (e.g., 8 × 7; Domahs et al, 2006; for the interacting neighbors model see Verguts and Fias, 2005), the problem size effect might be more pronounced when comparing problems with single-digit operands only (e.g., 4 × 6) to problems with at least one two-digit operand (e.g., 16 × 4).…”

“…On the other hand, complex arithmetic, which is typically solved by applying procedural strategies, requires a rather widespread fronto-parietal network, as it was observed in fMRI studies (e.g., Gruber et al, 2001; Fehr et al, 2007; Grabner et al, 2009a). Thereby, higher activation with increasing complexity in multiplication was observed in frontal areas such as the left inferior frontal gyrus (IFG) and left middle frontal gyrus (MFG), reflecting domain-general cognitive task demands (e.g., maintenance of rule-based decomposed calculation steps), and the posterior parietal cortex, reflecting domain-specific numerical task demands (Gruber et al, 2001; Grabner et al, 2007; Jost et al, 2009; De Visscher et al, 2015; see also Menon et al, 2000; Zago et al, 2001; Tiberghien et al, 2018). In EEG studies, more alpha desynchronization (decrease in alpha power) was observed for complex, non-retrieved arithmetic problems (Harmony et al, 1999; Moeller et al, 2010; but see Micheloyannis et al, 2005).…”

Distinguishing between cognitive explanations of the problem size effect in mental arithmetic via representational similarity analysis of fMRI data

“…We should note that the data reported here are part of a larger dataset; all results reported here are unique and address hypotheses that do not overlap with prior publications arising from this dataset (Tiberghien et al, 2019). Both the pre-scan and fMRI arithmetic tasks included three operations: multiplication, addition and subtraction.…”