Different intuitive rules in mathematical thinking

Abstract

This study examines the behavior of individuals when two intuitive rules in their minds lead to two different outcomes concerning a problem. In the absence of the formal knowledge, intuitive rules can affect the mathematical thinking. Hence, studies have usually compared the correct answer of the related formal knowledge with the incorrect one obtained from one intuitive rule. What has been rather less explored is the situation where both correct and incorrect answers are obtained from intuitive rules. In so doing, comparing infinite sets as a challenging issue for learning was selected as the theme of the study. Two specific geometric representations regarding the comparison of two intervals were employed, one in line with the intuitive rule ‘More A - More B’ and the other in line with the ‘Same A - Same B’ rule, so that two different results are produced by each of the rules. 85 first grader high school students who had no formal knowledge about comparing infinite sets were participated in the study, and the data were collected through interview. Analysis of the data showed that when the two intended different intuitive rules can be activated in mind and, in turn, create a cognitive conflict, individuals rank intuitive rules based on the degree of transparency of the concepts they have already known.