Dantzig, T. (1954). (2003). On our view, the way in which physical notations are perceived is at least as important as the way in which they are actively manipulated. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. Quantitative & Symbolic Reasoning Center Psychology Schedule Psychology Schedule. (Accessed April 9, 2014), Anderson, J. R. (2007). People can be taught to manipulate symbols according to formal mathematical and logical rules. Substantial evidence suggests that this prediction holds. Preprint: arXiv:1304.5257v2. How the Body Shapes The Mind. How do people reason arithmetically, algebraically, and logically? Like many other kinds of problem solving, the process of symbolic reasoning can be seen as a chain of transformations that links input and output representations, each of which changes its format and/or semantic structure. Barsalou, L. W. (1999). doi: 10.1016/j.cognition.2010.11.001. Like interlocking puzzle pieces that together form a larger image, sensorimotor mechanisms and physical notations “interlock” to produce sophisticated mathematical behaviors. Mathematical reasoning enjoys a property called monotonic. Trends Cogn. Therefore, although it seems likely that abstract mathematical ability relies heavily on personal histories of active engagement with notational formalisms, this is unlikely to be the story as a whole. “Exograms and interdisciplinarity: history, the extended mind, and the civilizing process,” in The Extended Mind, ed R. Menary (Cambridge, MA: MIT Press), 189–226. CallUrl('psychology>wikia>com African Sumac Dropping Leaves,
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