Abstract

It has been established that many children perceive the equal sign as an operational symbol rather than a relational one, and as a result, they have trouble solving non-canonical equations. In the present study, I investigated whether exposure to non-canonical equations would result in students’ ability to solve such equations and acquire a relational view of the equal sign. Fifty three (N = 53) second- and third-grade students were tested for their ability to solve non-canonical problems and whether they viewed the equal sign as a relational symbol before and after an exposure intervention, during which students practiced solving different types of equations. In one condition, the students practiced solving canonical equations; in a second condition, the students practiced solving non-canonical part-whole equations; and in a third condition, they practiced solving non-canonical identity equations. The students were required to solve the problems in their condition without receiving any type of feedback on their work or any explanations on the meaning of the equal sign. All the students improved significantly on their ability to solve non-canonical problems regardless of the type of problem to which they were exposed during the intervention. The students did not, however, improve on their ability to generate relational definitions of the equal sign. The analysis also revealed a significant effect of problem type. Students were more successful on canonical problems than non-canonical ones. As well, students were more successful at solving identity problems than part-whole problems. The study’s limitations and pedagogical implications are discussed.