Topic, aim and framework

Progression in mathematics instruction can be seen as a quality in teaching that entails gradually increased demands on the student (Säfström, 2017). If there is a lack of progression in teaching or the demands increase too much, this can reduce students’ opportunities to learn. An assumption for this study was that progression in teaching between school stages was important. Furthermore, teachers should take joint responsibility for learning within their teams to develop the quality in teaching (cf. Wennergren, 2016).

The approach of the study was based on action research. Four teachers from preschool to 9th grade (age 1-16) were invited to a temporary team, a community of practice. The overall aim of the study was to develop knowledge about teaching fractions when teachers used students’ understandings as a point of departure for their actions plans. A second aim was to illuminate what influences progression in their teaching. In addition, I intend to highlight the importance of the team’s negotiation of teaching fractions. Wenger’s dimensions of social learning were used as an analytical tool: joint enterprise, mutual engagement and shared repertoire.

Methodology/research design

The team of teachers used the four phases of action research: plan, act, observe and reflect, during their learning processes. The teachers’ learning sessions were videotaped and transcribed and this provided the main data that formed the basis of the results.

Findings

Four themes that described teachers’ negotiation of qualities in mathematics instruction were identified.

Interpreting students’ understandings: By analysing students’ understandings through videotaped instruction, the teachers interpreted students’ understandings and observed which kind of instruction enabled learning.

Basing instruction on students’ understandings: The teachers reified mathematical instructions based on students’ understandings, which entailed an expanded content.

Visualizing fractions: There was not always an automatic correspondence between visualizing fractions with everyday materials or manipulative materials and the conventions regarding fractions within mathematics, which affected students’ learning opportunities.

Ensuring students’ understanding: Even if the students seemed to be united about fractions, the teachers were uncertain how to ensure students’ understanding. The teachers were uncertain whether every student had an understanding of the concept and whether they were able to use their knowledge in another context.

Conclusions

When teachers, regardless of what stage was involved, reified similar instructions, it did not benefit students’ learning opportunities. In order to improve progression in teaching fractions, it was important that teachers succeeded in identifying students’ understandings and that the team negotiated different qualities in their community of practice. The shared repertoire (the pre-tests and the video recordings) formed the core of negotiating progression based on students’ understandings.

Relevance to Nordic educational research

This study contributes knowledge about diverse qualities in analysing students’ understandings by means of pre-tests or video recordings. The study also contributes knowledge about professional learning when participants have diverse experience.