The componential nature of arithmetical cognition: some important questions

Dowker, Ann · 2023 · Crossref

DOI: 10.3389/fpsyg.2023.1188271

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Summary

This review article argues that arithmetical cognition is not a unitary ability but consists of multiple, functionally independent components. The author synthesizes evidence from developmental psychology, neuropsychology, and neuroscience to demonstrate that arithmetic involves distinct processes, including non-symbolic and symbolic quantity representation, counting procedures, arithmetic operations, factual and conceptual knowledge, and domain-general abilities like working memory. The paper highlights that these components can dissociate significantly in both typical development and in cases of developmental or acquired dyscalculia, challenging the notion of a single, hierarchical mathematical ability. The review analyzes data from diverse sources, including studies of typically developing children, individuals with mathematical difficulties, and patients with focal brain lesions or neurodegenerative disorders. Developmental studies examined children ranging from preschoolers to primary school students, assessing tasks such as object counting, cardinal word principles, estimation, and derived fact strategies. Neuropsychological evidence draws from case studies of patients with specific impairments in operations like addition, subtraction, or fact retrieval, while preserving other abilities. Neuroscientific evidence includes functional MRI and ERP studies investigating brain activation patterns during exact calculation, approximation, and processing of arithmetical principles. Findings indicate substantial functional independence among arithmetic components. Patients with brain damage often exhibit selective deficits, such as impaired fact retrieval with preserved conceptual knowledge, or specific impairments in subtraction borrowing while maintaining other calculation skills. Similarly, typically developing children and adults show marked discrepancies between tasks like estimation, calculation, and strategy use, with no clear hierarchy of difficulty. Neuroimaging reveals distinct neural networks for different processes: approximation activates parietal and frontal areas, while exact calculation involves the angular gyrus and frontal regions. Furthermore, early numerical foundations, specifically subitizing (exact recognition of small quantities) and the Approximate Number System (ANS), appear to be separate processes that may not strictly predict later arithmetic proficiency, as evidenced by weak correlations and dissociations in brain injury cases. The significance of this work lies in its challenge to unitary models of mathematical ability. It suggests that arithmetic is componential from its earliest foundations, involving both subitizing and approximate magnitude comparison. The review emphasizes the need for further research into the origins of these components, their interactions, and how domain-general abilities contribute to mathematical development. Understanding this componential nature is crucial for identifying specific weaknesses in dyscalculia and for developing targeted educational interventions, rather than treating arithmetic as a single, monolithic skill.

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• individual differences