Few studies have a focus on progression in teaching and learning mathematics. An assumption for this study was that progression in teaching between school stages was important. 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 action plans. A second aim was to illuminate what influences progression in their teaching.

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. Wenger’s dimensions of social learning were used as an analytical tool: joint enterprise, mutual engagement and shared repertoire.

Four themes that described teachers’ negotiation of qualities in mathematics instruction were identified: interpreting students’ understandings, basing instruction on students’ understandings, visualizing fractions and ensuring students’ understanding. 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. The team showed a mutual engagement, with students’ learning as their joint enterprise. An implication of the study is that teachers from different educational stages can negotiate progression and improve it.