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A embodied-extended approach to the acquisition of numerical skills. (English) Zbl 1430.97001

Felline, Laura (ed.) et al., New directions in logic and the philosophy of science. Selected papers from the triennial international conference (SILFS 14), University of Roma TRE, Rome, Italy, June 18–20, 2014. London: College Publications. SILFS Ser. 3, 111-123 (2016).
Summary: An embodied-extended approach to cognition may be useful for the study of some cognitive activities, like arithmetical skills, which are generally thought as involving only internal resources. In this article, after discussing the theoretical assumptions and scopes of such an approach, I will specify its usefulness for an explanation of some specific arithmetic capacities, i.e. algorithmic skills. I will, then, formalize a finger counting like procedure for single-digit additions by using a bidimensional-Turing machine, which is a computational model specifically designed for the formal description of human algorithmic skills. The formal model analysis suggests an hypothesis on numerical facts learning which will be tested through a neural net model.
For the entire collection see [Zbl 1379.03001].

MSC:

97C30 Cognitive processes, learning theories (aspects of mathematics education)
97F20 Pre-numerical stage, concept of numbers
91E40 Memory and learning in psychology
68Q99 Theory of computing
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