Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving.
Following Marr's famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that th...
| Publicado en: | Erkenntnis Vol. 86; no. 4; pp. 961 - 998 |
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| Formato: | Artículo |
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Springer Nature
Aug2021
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=151759792&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 151759792 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 01650106 5KZ jtl: Erkenntnis issn: 01650106 maglogo: N pubinfo: dt: Aug2021 vid: 86 iid: 4 pid: 237 pub: Springer Nature artinfo: ui: 151759792 10.1007/s10670-019-00140-3 ppf: 961 ppct: 37 formats: fmt: @attributes: type: P size: 975KB tig: atl: Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving. aug: au: Pantsar, Markus affil: Department of Philosophy, History and Art, University of Helsinki, Unioninkatu 40A, 00014, Helsinki, Finland su: Computational complexity Problem solving Cognitive science Socialization sug: subj: Computational complexity Problem solving Cognitive science Socialization ab: Following Marr's famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus engage in cognitive processes that make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Therefore, in order to accurately model the human cognitive tasks involved in mathematical problem solving, we need to expand our methodology to also include aspects relevant to the algorithmic level. This allows us to study algorithms that are cognitively optimal for human problem solvers. Since problem solving methods are not universal, I propose that they should be studied in the framework of enculturation, which can explain the expected cultural variance in the humanly optimal algorithms. While mathematical problem solving is used as the case study, the considerations in this paper concern modeling of cognitive tasks in general. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Erkenntnis is a copyright of Springer, 2021. All Rights Reserved. item: Erkenntnis holder: Springer Nature dt: @attributes: year: 2021 holdings: @attributes: islocal: N |
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