Teachers’ approaches to handling student errors in mathematics classes

Abstract

Empirical research has demonstrated that mathematical errors originate from various causes that may have different implications for the learning process. Mathematical errors are an international phenomenon as all teachers from different cultural background must handle them every day during teaching-and-learning processes. When errors arise, teachers must determine whether and how to deal with them and whether the error should be corrected. Although errors and how they are addressed by teachers are of high pedagogical importance, teachers’ approaches to handling student errors remain underexplored. The study reported herein examines the ways in which mathematics teachers handle student errors in various situations, and whether any connection between the error type and the manner in which it is corrected may be reconstructed. The study participants comprised 13 secondary mathematics teachers in a large city in northern Germany. Each teacher was video-recorded over two 90-min-lessons, and the data were subsequently evaluated using qualitative content analysis. The results indicate that teachers’ approaches to correcting mathematical student errors diverged considerably depending on the phase of the lesson during which the error occurred. In particular, during the class discussion phase, a high proportion of the corrections were performed by the students’ classmates, whereas corrections executed during the group work, partner work, or individual work phases were primarily performed by students who had made the errors and the teachers. Given that the teacher's approach to handling errors exerts a significant influence on teaching-and-learning processes, further research is required to identify the most prolific approaches to handling errors in order to foster students’ mathematical understanding.