Representational Structures of Arithmetical Thinking: Part I

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• 作者：Wojciech Krysztofiak
• 关键词：Cognitive arithmetic ; Mental number line ; Subitizing ; SNARC effect ; Distance effect ; Size effect ; Summation mental number axes ; Point ; place mental number axes
• 刊名：Axiomathes
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：26
• 期：1
• 页码：1-40
• 全文大小：689 KB
• 刊物类别：Humanities, Social Sciences and Law
• 刊物主题：Philosophy
  Philosophy
  Ontology
  Linguistics
  Cognitive Psychology
  Logic
  
• 出版者：Springer Netherlands
• ISSN：1572-8390

文摘

In this paper, representational structures of arithmetical thinking, encoded in human minds, are described. On the basis of empirical research, it is possible to distinguish four types of mental number lines: the shortest mental number line, summation mental number lines, point-place mental number lines and mental lines of exact numbers. These structures may be treated as generative mechanisms of forming arithmetical representations underlying our numerical acts of reference towards cardinalities, ordinals and magnitudes. In the paper, the theoretical framework for a formal model of mental arithmetical representations is constructed. Many competitive conceptions of the mental system responsible for our arithmetical thinking may be unified within the presented framework. The paradigm underlying our research may be interpreted philosophically as a neo-Kantian approach to modeling the mind’s representational structures.