Schemata and Intuitions in Combinatorial Reasoning

Fischbein, Efraim; Grossman, Aline
October 1997
Educational Studies in Mathematics;Oct97, Vol. 34 Issue 1, p27
Academic Journal
The problem that inspired the present research refers to the relationships between schemata and intuitions. These two mental categories share a number of common properties: ontogenetic stability, adaptive flexibility, internal consistency, coerciveness and generality. Schemata are defined following the Piagetian line of thought, either as programs for processing and interpreting information or as programs for designing and performing adaptive reactions. Intuitions are defined in the present article as global, immediate cognitions. On the basis of previous findings (Fischbein et al., 1996; Siegler, 1979; Wilkening, 1980; Wilkening & Anderson, 1982), our main hypothesis was that intuitions are always based on certain structural schemata. In the present research this hypothesis was checked with regard to combinatorial problems (permutations, arrangements with and without replacement, combinations). It was found that intuitions, even when expressed as instantaneous guesses, are; in fact, manipulated �behind the scenes� (correctly or incorrectly) by schemata. This implies that, in order to influence, didactically, students� intuitions, those schemata on which these intuitions are based should be identified and acted upon.


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