How teachers handle errors of students in classrooms has been a topic of interest for researchers across disciplines. Mathematics is no exception to this. In this guest blog post, researchers Odd Tore Kaufmann (Østfold University College, Norway), Maria Larsson (MIND & M-TERM Research groups, Mälardalen University, Sweden) and Andreas Ryve (M-TERM Research group, Mälardalen University, Sweden) share their research findings on mathematics teachers’ error handling practices across different lesson phases, drawing on their analysis of lessons from several Swedish municipality schools. The full text of the research article is available open access, and can be downloaded using this link. Please scroll down for a short, accessible summary.
Many studies have been conducted regarding teachers’ error-handling practices and how errors can be treated as opportunities for learning. Most of these studies have been done in the context of whole-class discussions. Therefore, we wanted to investigate teachers’ error-handling practices as they occur in different phases of mathematics lessons: introduction of the task, when students work alone, when students work in pairs, and finally, in whole-class discussions. We aimed to investigate if there are differences in error-handling practices across the lesson phases and what types of error-handling practices dominate the different lesson phases. We collected data from “Matematiklyftet (Boost for Mathematics),” a curriculum-based professional development program launched by the Swedish National Agency for Education. The study included 12 teachers and 51 lessons in grades 4-6 in Sweden. All lessons were video-taped. We categorized teachers’ error handling practices and found eight different types of error-handling.
We found that in the introduction, the most common error handling practice was to ignore the error and give a direct correction (either by saying the correct answer or telling the student that s/he is wrong). We believe the reason for this strategy in the introduction of the lesson is that the teachers want to keep this phase short and avoid too many potentially confusing mathematical discussions.
When students work alone or in pairs, asking students to talk to each other and reflect is the most common error handling practice, in addition to correcting students’ errors by direct or embedded corrections. Embedded correction aims to lead the student towards the correct answer with one or more funnelling questions or comments. The set-up of error-handling practices during these phases is in resonance with the idea that teachers should not disturb students during their mathematical work, hence being somewhat invisible or non-intervening while students are working.
A larger variation of error-handling practices was found in whole-class discussions including discussion and teacher explanation. In a whole-class discussion, often held at the end of the lessons observed, the teacher uses the opportunity to bring up errors that s/he had noticed during individual/group work. In such situations, the teacher involves the students in discussing errors more than s/he does in other lesson phases.
What do these findings tell us?
The study revealed how teachers handle errors within and across lesson phases, and has implications for learning, teaching, and teacher education. We argue that involving students to discuss errors, rather than merely ignoring or correcting them, may enhance learning opportunities. They can give their students time and opportunities to discuss and resolve their errors with their peers in small groups and in whole-class settings. Teachers, however, need to develop awareness of differences between different lesson phases in order to achieve this. This requires that teachers reflect on their lessons to observe these interactional practices, and opportunities for such reflections should be a part of both initial teacher education and continuous professional development.
To read the full text of this research article, please follow this link.
Odd Tore Kaufmann (Østfold University College, Norway)
Maria Larsson (MIND & M-TERM Research groups, Mälardalen University, Sweden)
Andreas Ryve (M-TERM Research group, Mälardalen University, Sweden)