How Domain-general Functions Contribute to the Development of Numerical Competencies – DFCDNC

The project comprised three parts that were supposed to yield a comprehensive assessment of the domain-general and domain-specific factors that contribute to the development of numerical competencies in a key period of child development.

Part 1 was designed as an accelerated longitudinal design to test the contribution of different facets of domain-general (i.e. inhibitory control and attention) and domain-specific factors to the development of mathematical competencies in children in the age range between 3 and 9 years of age.

Part 2 was designed as a longitudinal study of fMRI study exploring the neural correlates of approximate arithmetic, spatial attention, and inhibition in two groups of children (group 1: 5-year-olds; group 2: 7-year-olds) and following these children over the period of two years.

Part 3 was designed as a cross-sectional study to explore the role of inhibition to the development of numerical abilities in two groups of infants (9- and 12-month-old infants).

Deviations from the initially planned study design.

Part 2. The entire project was heavily jeopardized by the COVID-19 epidemic. In 2020, data collection for cohorts 2-4 had started (January to March 2020) when schools were closed for about 6 weeks in France. Even after schools going back to invite children on site, researchers would not be granted access to continue data collection for another 2-3 months – essentially preventing us to enter schools until summer vacation 2020. All data reported for part 2 have been collected in schools. Therefore, COVID-19 interfered substantially with data collection. Even after going “back to normal”, we could not simply re-start data collection since children within a given cohort who were tested after the COVID-19 crisis were were not comparable to those tested before the crisis ( in terms of age and school experience). We hence had to start data collection from scratch in 2021.

This also had consequences for part 2 that was supposed to begin in 2021. Additionally, we faced technical issues due to the delivery and installation of a new MR scanner at the imaging center. We had to reduce the longitudinal study plan to a cross-sectional assessment of two groups of students (5- and 7-year-olds).

Only a small section of the entire and rich data set has been analysed so far.

A cross-sectional study in children aged 3, 5, and 7 years aims at identifying the differential contribution of domain-specific and domain-general contributors to mathematics and delineating their developmental dynamics. Our results reveal a consistent role for non-symbolic magnitude comparison across all age groups, non-symbolic arithmetic starting from the age of 5 years and visuospatial memory only in 5-year-olds. These findings support the notion that mathematics cannot be conceived as a unitary cognitive skill and provide a fine-grained analysis of the cognitive requirements of mathematical skills at different ages. On a more general note, they are in line with the idea that the ANS provides a critical scaffold for the development of mathematical skills but challenge the view that all ANS measures tap into the same underlying process.

Inhibition has been suggested to contribute to symbolic and non-symbolic quantity processing, but conclusions remain inconsistent. Using Structural Equation Modelling in predominantly White French 5- and 7-year-olds (N= 331, 169 females), we found a lack of support for a unitary or binary (Response Inhibition and Distractor Suppression) inhibition construct. Results suggest a link in both age groups between the Stop-Signal Task and symbolic arithmetic, and a link between the Flanker task and non-symbolic arithmetic only in 7-year-olds.

The findings of this study challenge the existence of a unified inhibition construct in both 5- and 7-year-olds, as none of the inhibition measures loaded well unto a single inhibition factor or correlated with each other, except for a small positive correlation observed between both Distractor Suppression tasks in the older cohort. Based on these results, we can conclude that 1) the role of inhibition varies depending on the mathematical format tested, 2) the contributions of inhibition change depending on the ages tested, and 3) they are highly depending on the inhibition measure.

The operational momentum effect (OME) describes the tendency to overestimate outcomes of addition problems while underestimating the outcome of subtraction problems. It has been taken as an index of involvement of spatial attention in mental arithmetic and the association of space with numbers. To explore the developmental trajectory of the OME, we administered non-symbolic addition and subtraction problems to 3-, 5-, and 7-year-old children (N = 387, 199 females, French sample, mixed ethnicities, data collected from January 2020 through June 2022). Results revealed no consistent OME for any age group. This suggests that OME emerges later in childhood, putatively driven by formal mathematical training or spatialization of the numerical magnitude representation.

The richness of the dataset will allow for further analysis, which is currently underway but depends on available resources. Current results show that the role of inhibition in the acquisition of arithmetic skills is more complex than previously thought. They depend on the facet of inhibition that is measured, the arithmetic skill, and the age of the children. Defining the regularities of this developmental trajectory remains an important element that can inform teachers and educators. We have also observed that OME seems to develop late in schooling. This indicates a late recruitment of attentional processes during mental calculation, which somewhat contradicts the idea that OME is related to innate approximate arithmetic abilities. Discovering the mechanisms underlying this cognitive bias will be an interesting area of research for the future.