Cognitive computational neuroscience approach to the development of mathematical competence

Introduction

Learning the association between numerals (symbolic numbers) and quantity (nonsymbolic numbers) is the initial step toward comprehending symbolic mathematics. According to the symbolic estrangement hypothesis, extensive experience of exposure to numerals and their manipulation may significantly weaken any preexisting relation between symbolic and nonsymbolic numbers.

Background

Previous studies have independently reported representational shifts of brain activity patterns in young children and simulation of number processing systems using artificial neural networks (ANNs). Nonetheless, it has remained largely unclear how such brain representations and ANN features are related to each other in terms of development.

Project Objectives

The current project aims to address these issues by constructing computational models that integrate multimodal neuroimaging data of young children and ANN models for symbolic and nonsymbolic numbers.

Methodology

1. Data Collection:

   • Functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG) data will be collected while children engage in number perception tasks at the outset (5-year-olds) and after two years (7-year-olds) of formal education.

2. ANN Implementation:

   • In parallel with the neuroimaging experiments, I will implement ANNs that learn the association between symbolic and nonsymbolic numbers.

3. Developmental Trajectory Analysis:

   • To determine whether ANNs exhibit a similar developmental trajectory as the human brain, I will construct voxel-wise encoding models based on the latent ANN features.

4. Integration of Data:

   • Encoding models based on the fMRI and EEG data will be further integrated into fine-scale spatiotemporal data showing functional dynamics across multiple brain regions.

5. Comparison of Dynamics:

   • Finally, I will investigate how these dynamics change with formal education by comparing data from 5- and 7-year-olds.

Conclusion

This project integrates interdisciplinary knowledge from cognitive neuroscience, developmental psychology, and artificial intelligence to establish a novel computational approach to understanding the development of mathematical abilities.