The pseudo-conceptual and the pseudo-analytical thought processes in mathematics learning

This paper suggests a theoretical framework to deal with some well known phenomena in mathematical behavior. Assuming that the notions 'conceptual' and 'analytical' are clear enough in the domain of mathematical thinking, the notions 'pseudo-conceptual' and 'pseudo-analytical' are proposed and explained. Examples from mathematics classrooms, mathematics exams, and homework assignments are analyzed and discussed within the proposed theoretical framework. The notions 'pseudo-conceptual' and 'pseudo-analytical' proposed in this paper, actually narrow the extension of the notion 'cognitive' by restricting it to the domain of meaningful contexts. Analysis of meaningless behaviors, it is claimed, requires a different theoretical framework. The attempt to analyze meaningless behaviors in the same way as meaningful behaviors is called here 'the cognitive approach fallacy'. © 1997 Kluwer Academic Publishers.