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PurposeThe purpose of this study is to examine what teachers notice in their own enactment of eight high leverage practices as well as the patterns of interactions between the teachers and their peers when participating in video-based lesson study.Design/methodology/approachEach teacher taught and uploaded video from one lesson to a platform, which allowed video annotation, for their lesson study team. There were nine lesson study teams. This study used a qualitative design to examine the teachers' comments on their own videos as well as the patterns in the comments between peers on lesson study teams.FindingsTeachers noticed both positive instantiations as well as opportunities for growth in their enactment of: using and connecting mathematical representations, posing purposeful questions and supporting students' productive struggle. Analysis displayed a pattern of exchanges where peers coached, validated, empathized and pushed each other beyond their comfort zone as critical peers.Research limitations/implicationsAlthough not all lesson study teams were made up of school-based teams and the teachers shared short recordings of their teaching, this research contributes to the understanding of how adapting lesson study by using video can help teachers notice their instantiation of teaching practices and peers can support and push one another towards ambitious instruction. Future research could extend this work by investigating the impact of video-based lesson study on teachers in isolated areas who may not have professional learning networks.Practical implicationsVideo-based LS may help to overcome barriers to the implementation of lesson study, such as the challenge of scheduling a common release time for lesson observation and the financial burden of funding substitute teachers for release time.Originality/valueThe current realities of COVID-19 creates an opportunity for mathematics educators to reimagine teacher professional development (PD) in ways that push the field forward. In light of this disruption, the authors propose an innovative model of utilizing video-based Lesson Study (LS; Lewis, 2002) with peer coaching to offer PD opportunities with methodological considerations for both mathematics researchers and teacher practitioners. The authors document and analyze a collection of online LSs that were taught by a focal teacher and recorded for the peers in the LS group. Video-based LS PD structure allowed the authors to examine how they can leverage this online model of LS to analyze student thinking and learn about teaching rich tasks in an online environment using eight teaching practices. Through their paper the authors will detail the necessary features of online LS specifically using a video annotation tool like Goreact and how video can be used to enhance the professional learning of the mathematics teaching practices (MTPs; NCTM, 2014) and the noticing of student thinking (Jacobs et al., 2010; Sherin and van Es, 2009; van Es and Sherin, 2002, 2008). In addition, the authors will document the norms that were established in the online LS community that impacted collaboration of LS teams and developed strong peer coaching relationships. The online LS PD design also supports collaboration of teachers from varying contexts, promotes professional growth and demonstrates how educators might leverage peer coaches as social capital within their schools to develop teachers along the professional continuum.

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This paper examines the experiences of two elementary teachers' implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1) How can phases of mathematical modeling as a process serve as a venue for exhibiting students' critical 21st century skills? (2) What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students' 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.