Cognitive Foundations of Mathematical Learning
Summary
The cognitive foundations of mathematical learning rest on the interplay between domain-general processes—including working memory, executive function and spatial reasoning—and domain-specific mechanisms such as symbolic number processing and the approximate number system (ANS). Initial numerical intuitions arise from the ANS, which supports non-symbolic quantity discrimination across species and infancy. As formal instruction progresses, language-mediated symbols enable precise arithmetic and the emergence of abstract structures. Neuroimaging has identified the intraparietal sulcus as a key neural substrate for both non-symbolic and symbolic number cognition, while visuospatial working memory underpins geometry and algebraic reasoning. A pivotal milestone is the development of functional thinking, wherein learners understand functions as mappings between varying quantities. Instructional approaches that foster emergent modelling and instrumentation—where dynamic tools prompt learners to appropriate new representations—can catalyse the shift from procedural operations to structural insight. Across development, socio-cultural contexts and personalised pedagogies modulate these core processes, offering avenues for effective interventions and technologies that promote equitable mathematical learning worldwide.
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Cognitive Foundations of Mathematical Learning publication trend
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Technical terms
Approximate Number System (ANS): Innate cognitive system supporting rough estimation of quantities without symbolic notation.
Symbolic number processing: Manipulation and understanding of numerical symbols such as Arabic numerals.
Executive function: Higher-order cognitive processes—including working memory, inhibitory control and cognitive flexibility—required for goal-directed tasks.
Functional thinking: Cognitive approach emphasising the understanding of functions as mathematical objects defined by relationships between varying quantities.
Emergent modelling: Instructional strategy in which mathematical concepts arise through interaction with dynamic representations and tools.
Instrumentation: Process by which learners internalise and integrate technological tools into their cognitive activities.
References
- Learning Difficulties with the Concept of Function in Maths: A Literature Review. Education Sciences (2023).
- TOOL USE AND THE DEVELOPMENT OF THE FUNCTION CONCEPT: FROM REPEATED CALCULATIONS TO FUNCTIONAL THINKING. International Journal of Science and Mathematics Education (2012).
- Designing digital technology tasks for the development of functional thinking. ZDM – Mathematics Education (2020).
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