Compartmentalization of representation in tasks related to addition and subtraction using the number line

Abstract

The present paper aims at identifying the difficulties that arise in the conversion from one mode of representation of the concepts of addition and subtraction to another, and examining the phenomenon of compartmentalization, i.e. deficiency in the coordination of at least two modes of representation of a concept. Three tests were administered to 231 first and 241 second grade students. All the tests consisted of the same addition and subtraction tasks, but differed in the types of conversions that they involved. Data analysis showed lack of connections among the tasks of the three tests for both age groups. This finding reveals that different types of conversions among representations of the same mathematical content were approached in a distinct way,indicating the existence of the phenomenon of compartmentalization.