Cognitive computational neuroscience approach to the development of mathematical competence

Project Information

MathDevCCN

Grant agreement ID: 101161519

DOI

10.3030/101161519

Project terminated on 31 March 2026

EC signature date 4 February 2025

Start date 1 June 2025

End date 31 May 2030

Funded under

• European Research Council (ERC)

Total cost

€ 1 496 500,00

EU contribution

€ 1 496 500,00

Coordinated by

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France

Periodic Reporting for period 1 - MathDevCCN (Cognitive computational neuroscience approach to the development of mathematical competence)

Reporting period: 2025-06-01 to 2027-11-30

Summary of the context and overall objectives of the project

The ability to acquire symbolic mathematical competence is a cornerstone of modern society, underpinning scientific and technological development as well as individual socioeconomic well-being. However, the developmental mechanisms through which humans learn to associate symbolic numbers (e.g. Arabic numerals) with nonsymbolic quantities remain poorly understood, despite evidence that a substantial proportion of the population experiences mathematical learning difficulties (Landerl et al., J Exp Child Psychol 2009). Two competing theoretical frameworks have been proposed to explain this relationship: the approximate number system (ANS) hypothesis, which posits that nonsymbolic quantity processing scaffolds symbolic mathematics (Feigenson et al., Child Dev Perspect 2013), and the symbolic estrangement hypothesis, which suggests that formal education progressively decouples symbolic and nonsymbolic representations (Lyons et al., J Exp Psychol Gen 2012). While behavioral and neuroimaging studies provide partial support for both accounts, the developmental trajectory of the underlying brain representations remains unresolved.

At the same time, advances in artificial intelligence, particularly artificial neural networks (ANNs), have opened new possibilities for modeling cognitive processes (Nakai & Nishimoto, NeuroImage 2023). However, research on brain development and ANN-based modeling has largely progressed independently, and no unified framework has been established to link developmental neuroimaging data with computational models of number processing. To address this gap, the project aimed to establish a cognitive computational neuroscience framework integrating longitudinal neuroimaging data from children with ANN-based modeling. Specifically, it sought to (i) characterize developmental changes in functional brain dynamics underlying number processing, (ii) construct computational models that learn associations between symbolic and nonsymbolic numbers, and (iii) examine whether artificial systems exhibit developmental trajectories comparable to those observed in the human brain.

By achieving these objectives, the project was expected to provide a mechanistic understanding of how symbolic mathematical abilities emerge through learning and education, while bridging neuroscience and artificial intelligence within the emerging field of NeuroAI. The expected impact extends beyond basic science, with potential implications for educational practices, interventions for mathematical learning difficulties, and the development of more human-like artificial intelligence systems. Overall, the project integrates cognitive neuroscience, developmental psychology, and machine learning, combining empirical and computational approaches to address the complexity of mathematical cognition and its development.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

During the reporting period (June 2025 – March 2026), the project focused on establishing the methodological and computational foundations required to investigate the developmental relationship between symbolic and nonsymbolic number processing, while also extending this framework toward a broader understanding of the neural basis of quantitative and mathematical abilities and the development of ANN-based analytical approaches. Given the early stage of the project and the limited duration of participation, the work primarily addressed preparatory and initial implementation phases of the planned research program.

In this context, the project contributed to the identification of intergenerational similarities in neural representations of mental arithmetic (Constant-Varlet et al., PNAS 2025). This work demonstrated that brain activity patterns associated with mathematical processing exhibit familial resemblance across two generations, providing novel insights into the interplay between learning and shared familial factors in the development of mathematical cognition. In parallel, methodological advances were made toward the quantitative analysis of developmental neuroimaging data, including approaches for characterizing representational structure and variability in fMRI data from children.

In addition, the project contributed to investigating the relationship between mathematical abilities and other cognitive functions (Nakai et al., Neurosci Res 2025). This work examined how mathematical processing relates to broader cognitive domains, providing evidence for shared and distinct neural substrates underlying mathematical and non-mathematical functions. These findings support a more integrated understanding of mathematical cognition within the wider architecture of human cognitive functions.

Furthermore, the project contributed to theoretical developments in understanding the brain as a computational system (Baltieri et al., arXiv 2025). This work advanced a formal framework for modeling predictive processing in the brain, providing a principled account of how neural systems can be described in computational terms. In parallel, the project facilitated the strengthening of collaborations and research networks, particularly with theoretical neuroscientists, thereby supporting the integration of computational theory and empirical neuroscience.

At the current stage, the project is advancing the design of experimental paradigms for efficient data collection of symbolic and nonsymbolic number processing in children. In parallel, ANN models based on contrastive learning are being developed to extract shared quantitative latent representations across symbolic and nonsymbolic formats. These ongoing efforts aim to establish a unified framework for linking developmental neuroimaging data with computational models of numerical cognition.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The results obtained during the reporting period extend the state of the art in cognitive computational neuroscience along two main directions: (i) the expansion of developmental neuroimaging toward intergenerational perspectives, and (ii) the advancement of ANN-based approaches for modeling brain activity across cognitive domains.

First, the project contributed to extending developmental studies of mathematical cognition toward an intergenerational framework. In particular, the findings of Constant-Varlet et al. (PNAS, 2025) demonstrate that neural representations of mental arithmetic exhibit familial similarities across two generations. This work goes beyond conventional developmental approaches by suggesting that brain representations of mathematical cognition are shaped not only by individual learning but also by shared familial factors, thereby opening a new research direction that may be described as transgenerational neuroimaging.

Second, the project broadened the scope of ANN-based modeling of brain activity. Recent work (e.g. Denk et al., Nat Commun, 2025; Kubo et al., in revision) demonstrates that advanced machine learning models, including generative models and large language models, can capture high-level neural representations across domains such as music and language. These findings extend previous work on ANN–brain alignment by showing that hierarchical and modality-general representations can be quantitatively linked to brain activity, thereby advancing the methodological frontier of NeuroAI.

Together, these results contribute to a broader conceptual shift from domain-specific and single-generation analyses toward integrated frameworks that link development, intergenerational structure, and machine learning models of cognition. This shift opens new possibilities for understanding human intelligence as an emergent property of both biological and computational systems.