Frontal and parietal contributions to arithmetic fact retrieval: A parametric analysis of the problem‐size effect

Abstract

The goal of the present study was to investigate the neuroanatomical basis of arithmetic fact retrieval. The rationale was that areas playing a crucial role in arithmetic fact retrieval should show a systematic increase of activation with increasing retrieval effort. To achieve this goal, we utilized the problem-size effect as this is known to be systematically related to retrieval effort. In contrast to many previous studies, we here took a parametric approach to account for the continuous increase of retrieval effort with problem size. BOLD signals were modeled with problem size as parametric regressor and negative slow waves of the EEG were categorized into six levels of problem size. The fMRI data showed that activation in the angular gyrus and ACC/SMA increased parametrically with problem size. The ERP data showed a systematic amplitude increase with increasing problem size, especially at fronto-central electrodes. Consistent with the fMRI data, source modeling localized this effect to the ACC. While these findings support previous notions about the crucial role of the angular gyrus during fact retrieval, they also provide evidence that the medial frontal cortex is involved when single-digit multiplications are solved. Thus, both parietal and frontal structures seem to be integral parts of a system that enables and controls arithmetic fact retrieval.

Neural correlates of numbers and mathematical terms

“…Andres et al (2011) also found no activation in the angular gyrus for multiplication relative to subtraction, letter reading or even fixation. This region has also been found to be susceptible to task difficulty, that is, easy arithmetic problems consistently elicit greater activation than difficult arithmetic problems (e.g., Grabner et al, 2009;Jost et al, 2011;Stanescu-Cosson et al, 2000;Zhou et al, 2007).…”

Individual differences in mathematical competence modulate brain responses to arithmetic errors: An fMRI study

“…Although activation in frontal areas of the brain is frequently observed during calculation, these have been shown to be related to general task demands, such as working memory and attention, instead of being specifically related to the neurocognitive processes underlying calculation (Menon, Rivera, White, Glover, & Reiss, 2000). Moreover, it has been shown that brain activation during calculation is modulated by specific factors such as the size of the arithmetic problems (Jost, Khader, Burke, Bien, & Rosler;Stanescu-Cosson et al, 2000) which is often defined as the product of the operands. Other factors that have been revealed to modulate the brain responses measured during calculation are the type of operations, such as the difference between addition and subtraction (Ischebeck et al, 2006;Kong et al, 2005), and the strategies used to solve arithmetic problems (Grabner et al, 2009).…”

Balancing the 2 Hemispheres in Simple Calculation: Evidence From Direct Cortical Electrostimulation

“…This view has been completed by further studies suggesting the additional involvement, closely related to the demands imposed by arithmetic fact retrieval, of the medial frontal cortex (e.g. Jost et al, 2011).…”