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A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving

  • Regina E. FabryEmail author
  • Markus Pantsar
Article

Abstract

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way.

Keywords

Mathematical problem solving Levels of analysis Computational modelling Competence Performance Computational complexity Enculturation Neural plasticity Embodied cognition 

Notes

Acknowledgements

We would like to thank an anonymous reviewer for very helpful comments. M.P. would like to thank the Academy of Finland and professor Gabriel Sandu for making this reseach possible as part of the project “Dependence and Independence in Logic”.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Philosophy IIRuhr University BochumBochumGermany
  2. 2.Department of Philosophy, History, and Art StudiesUniversity of HelsinkiHelsinkiFinland

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