Brain areas associated with numbers and calculations in children: Meta-analyses of fMRI studies

Abstract

Children use numbers every day and typically receive formal mathematical training from an early age, as it is a main subject in school curricula. Despite an increase in children neuroimaging studies, a comprehensive neuropsychological model of mathematical functions in children is lacking. Using quantitative meta-analyses of functional magnetic resonance imaging (fMRI) studies, we identify concordant brain areas across articles that adhere to a set of selection criteria (e.g., whole-brain analysis, coordinate reports) and report brain activity to tasks that involve processing symbolic and non-symbolic numbers with and without formal mathematical operations, which we called respectively number tasks and calculation tasks. We present data on children 14 years and younger, who solved these tasks. Results show activity in parietal (e.g., inferior parietal lobule and precuneus) and frontal (e.g., superior and medial frontal gyri) cortices, core areas related to mental-arithmetic, as well as brain regions such as the insula and claustrum, which are not typically discussed as part of mathematical problem solving models. We propose a topographical atlas of mathematical processes in children, discuss findings within a developmental constructivist theoretical model, and suggest practical methodological considerations for future studies.

Keywords: Children; Development; Insula; Mathematical cognition; Meta-analyses; fMRI.

Fig. 1

PRISMA flowchart for identification and eligibility of articles (template by Moher et al., 2009). n = number of papers.

Fig. 2

3D rendered ALE activation maps superimposed on an anatomical brain. All regions survived cluster level correction p = 0.05 for multiple comparison control at an uncorrected p = 0.001. All coordinates are listed in Table 2.

Fig. 3

Mapping results on children meta-analyses (in red), on triple-code model (green), and adult meta-analyses (orange). We illustrate in green the schematized cortical locations of the triple-code model proposed by Dehaene and Cohen, 1995, Dehaene and Cohen, 1997: (1) Inferior parietal cortex: quantity representation, (2) Temporal cortex: visual-computational number symbols, (3) Articulatory loop, (4) Verbal system, (5) Basal ganglia: arithmetic facts, (6) Thalamus: arithmetic facts, and (7) Prefrontal cortex: strategy choice and planning. In orange are additional schematic locations of areas concordant among adult studies, as demonstrated by meta-analyses (Arsalidou and Taylor, 2011): (a) Superior frontal BA 10: formulates complex goals, sub-goal creation, (b) Middle frontal BA 46: in more or less misleading situations it monitors more than a few items, (c) Inferior frontal BA 9: monitor simple rules or a few items, (d) Precentral gyrus: eye movements, (e) Insula: interoceptive motivation of goal-directed and default-mode processes, (f) Cingulate gyrus: converts affective goals into cognitive goals to be implemented, (g) Right angular gyrus: visual-spatial fact retrieval (i.e., spatial-temporal schemes with non-verbalizable configural relations), and (h) Cerebellum: goal directed, visual motor sequencing. Sub-cortical regions specific to meta-analyses of number or calculation tasks were not depicted. Here we added the (i) right basal ganglia: coordination of top-down and bottom-up operative/motor processes. In red are schematic locations of areas concordant among children studies, as demonstrated by the current meta-analyses. (j) Claustrum: integration of motivated top-down and bottom-up processes.

Fig. 4

A simplified illustration of the Theory of Constructive Operators (TCO): Operators (in green; operator definitions are listed in Table 3), schemes (in blue), and the principle of schematic over-determination of performance − or SOP (in red).