Mathematical equivalence and grade 6 students’ errors

Previous research has stressed the importance of a good understanding of mathematical equivalence. However, despite decades of research, we still do not know to what degree the theory of operational understanding can explain errors. In this paper, children’s understanding of mathematical equivalence is studied using answers (n = 1608) and written solutions (n = 340) to a large-scale test. We identified tasks within the test designed to assess mathematical equivalence and first studied the consistency. Then, we did a qualitative analysis focused on error characteristics in the students’ answers. The results show that a large portion of the errors can be explained by an operational understanding, interpreted as grave errors. One conclusion is that most errors can be explained by the theoretical concept “operational view”. However, further quantitative analysis shows a considerable variation in the response rate, indicating students have both an operational and a relational understanding.