Differences in Norwegian and Swedish student teachers’ explanations of solutions of linear equations

Resumé

This study draws on data from 146 Norwegian and 161 Swedish student teachers. They were given a correct but short and unannotated solution to the linear equation x + 5 = 4x – 1. The student teachers were invited to explain the solution provided for a fictive friend, who was absent when the teacher introduced this topic. An accurate solution of this equation contains two additive and one multiplicative operation.

There are two main strategies for solving a linear equation, ‘swap sides swap signs’ (SSSS) and ‘do the same to both sides’ (DSBS). Of the Norwegian student teachers, 2/3 explained the additive steps in the solution by SSSS, while only 1/3 of the Swedish student teachers applied SSSS. Consequently, DSBS was more frequent among the Swedish student teachers regarding the additive steps. However, in the final, multiplicative step, 3/4 of the Norwegian student teachers chose to explain by DSBS. On the contrary, among the Swedish student teachers the proportion applying DSBS for the multiplicative step of the solution decreased, and almost as many provided a deficient explanation of the final operation.

We discuss possible reasons for differences between the nations. We also suggest how teacher educators in both countries can use the results of this study to improve student teachers’ explanations of how to solve linear equations.