PurposeThis study explored how teachers change, what teachers learn and how they learn during the implementation of project-based learning through lesson study.Design/methodology/approachIn this study, three university researchers, one doctoral student and six mathematics school teachers formed a lesson study team. Using a qualitative research method, this study employed a locally integrating networking strategy to combine the modified Interconnected Model of Teacher Professional Growth (IMTPG) and Bannister's framework to describe the teachers' knowledge change when participating in a lesson study on project-based learning.FindingsThe research revealed that the school teachers' knowledge about authenticity and assessment in the context of project-based learning was changed after the lesson study and how the changes were triggered.Originality/valueThe study demonstrates how the networking of two different theories—modified IMTPG and Bannister's framework—contributes to a better understanding of the process of teachers' collective practice, as well as the knowledge change in PjBL. This networking was done by combining the two theories, which were superimposed at the domain of practice.

Teacher noticing of student mathematics thinking, an essential professional competency, has not been sufficiently investigated in China. In this paper, based on four video clips, we combined the frameworks of Stockero et al. and Jacobs to analyze the characteristics and changes of 19 prospective teachers’ (PTs) noticing under the intervention of the course “Mathematics Teaching Theory in Middle School.” The results showed that (1) the agent of noticing shifted from teachers and mathematical content to students; (2) the percentage of noticing to content with mathematical characteristics remained high, and that of noticing to general math increased significantly after the intervention; and (3) the percentages of noticing to analyzing student math learning and math interaction noticeably increased. Moreover, from select PT interviews (four in total) and facilitator reflections, we concluded four potential strategies for improving interventions to enhance PT noticing: enriching video resources, refining the task requirements, specifying teaching evaluations, and optimizing course implementation.

Teacher education should foster teachers’ competencies in teaching mathematical modelling since it is a demanding task. Mathematical modelling requires spontaneous reactions, which are related to the core of teachers’ competencies — teacher noticing. The study designed a video-based course to develop these competencies in the context of mathematical modelling. The findings revealed a noticeable improvement in their noticing competencies after participating in the semester-long course. In particular, the Preservice Teachers’ topical foci shifted towards modelling thinking and pedagogy. They made significantly more interpretive comments and used significantly more task-dimensional knowledge for teaching mathematical modelling to reason about events. These results appear to support the viability of using video for this purpose.