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The purpose of this paper is to explore what professional knowledge and competence (PKC) that knowledgeable others, namely, mathematics teaching research specialists (MTRS) in China, need to know, and how they may develop their PKC.

This study adopts mixed methods. A survey on PKC with 549 MTRS is utilized to examine MTRS’ perceived held and ideal PKC and perceived effective ways of developing their PKC. The responses to the open-ended questions on the survey were used to identify additional dimensions of PKC and ways of developing PKC. Multiple techniques of quantitative data analysis were employed to feature the characteristics of PKC and structure of the survey, and the relationship between background variables and perception of PKC. Collectively, this study paints a rich and comprehensive picture about Chinese knowledgeable others’ knowledge and competence, and its development.

The data analysis reveals that the participants appreciated the six-dimension model of MTRS’ PKC. They were confident with their PKC in general, but varied in different aspects. The factor analysis showed the six-dimension model could be further clustered into two components: knowledge about mathematics teaching and learning and competence in mentoring and educational leadership, and knowledge about content, assessing student learning, and use of technology. The participants perceived their learning through multiple ways including: learning through reading, attending specific training programs, attending and mentoring teaching research activities both school-based and across regions, observing and debriefing lessons, sharing within online learning communities. All these venues jointly contribute to developing MTRS’ PKC.

This is the first empirical study on MTRS’ PKC and its development in China based on such a large sample. The findings of this study not only contribute to an understanding of knowledgeable others in Chinese lesson study and providing suggestions for support of their development, but also provide implications for studies of practice-based mathematics teacher-educators globally.

When designing learning environments in primary teacher education, there is an attempt to represent real teaching practice in an authentic way to prospective teachers. When constructing these environments, teacher educators have to consider how to best motivate the student teacher, identifying the most relevant practice-based principles and the ways in which the theory and practice can be bridged. There are other considerations as well. For example, in the Netherlands, as in some other countries, teacher education is changing drastically. Controversial teacher education curricula, consisting of primary school subjects originated after more than one hundred years of reflection on the subject matter of primary education and the ways teachers have taught, have been replaced by curricula merely intended to improve the general professionalization of the prospective teacher, neglecting the school subjects. More specifically, the new objective is to adequately prepare students to become competent beginning teachers.

The purpose of this study was to explore middle and secondary mathematics preservice teachers' (PST) perceptions of the benefits, challenges and impacts of implementing lesson study.

This paper presents a single case study in the university context. Embedded units of analysis included a group of middle and a group of secondary mathematics PSTs, who were in the internship year of a teacher preparation program.

This paper presents several perceived benefits, challenges and impacts according to PSTs. PSTs indicated benefits included their focused student observations and their collaboration in lesson design. Perceived challenges included observing as a nonparticipant observer and aspects of planning. The different impacts occurred in three phases: planning, observing during teaching and reflection.

First, the study participants included a small group of middle and secondary mathematics PSTs from one university in central Texas. Second, the PSTs in this study were not able to reteach the lesson, which may have influenced their perceptions.

Mathematics teacher educators could use insights from this study as they implement lesson study or other field experiences to support PSTs in their growth as mathematics teachers.

This paper examines PSTs' perceptions, which could benefit mathematics teacher educators as they consider how to introduce or implement lesson study with PSTs.

This paper examines how mathematics teacher educators (MTEs) learn to enact equitable mathematics instruction using technology through lesson study (LS).

A LS team with three MTEs conducted three iterations of LS on teaching the Pythagorean Theorem in an in-person, technology-mediated environment. Many forms of data were collected: Desmos activities, videos of research lessons (RLs), videos of MTE RL debriefings, artifacts of student learning in the Desmos Dashboard, and MTEs' written self-reflection. The authors investigate the teacher educators' learning through LS by analyzing the MTE debriefings of the RLs using Bannister’s (2015) framework for teacher learning in communities of practice.

The MTEs learned to enact equitable mathematics instruction using technology through addressing emerging issues related to intellectual authority and use of student thinking. Throughout the LS, the MTEs sought ways of promoting students' mathematical authority and using student thinking through features of the Desmos platform.

This study focuses on MTEs' learning without examining participating preservice teachers' learning. It demonstrates the benefits of LS for MTEs' professional learning.

This study showcases how a research-based Desmos activity is used and refined to promote MTE learning how to implement equitable mathematics instruction.

The study contributes to better understanding of how LS could be used to develop MTEs' professional learning. Moreover, the dual process of participation and reification was concretized through diagnostic and prognostic frames in the LS context, which enriches the concept of community of practice.

Elementary teachers' understanding of mathematics is a significant contributor to student success with mathematics. Consequently, teacher educators are frequently charged with the responsibility of supporting the development of prospective elementary teachers' mathematics content knowledge as they re‐learn concepts in ways they are required to teach. The purpose of this paper is to describe one teacher educator's efforts to support prospective elementary teachers' tenuous understanding of rational numbers.

Given the variety of factors influencing the development of teacher knowledge, a mixed method research design was utilized. Research participants were prospective elementary teachers enrolled in a nine‐week elective course who agreed to participate in the study (n=40); while the control group were prospective elementary teachers not enrolled in the elective course (n=35).

The results of this study indicate that it may be possible to improve prospective teachers' conceptual understanding of mathematics by providing additional short‐term support, such as an elective course and/or web‐based video clips. However, the program intervention can only build upon the existing knowledge that prospective teachers bring when they begin their Bachelor of Education programs.

For prospective teachers with a limited foundation in mathematics (e.g. less than four secondary school mathematics courses), short‐term support may be insufficient to compensate for their nebulous understanding of rational numbers. Based on this finding, one‐year Bachelor of Education programs might consider, either: including Grade 12 mathematics as a pre‐requisite for elementary teacher applicants; or mandating enrolment in a full‐year math content course similar to the elective course described in this paper.

The purpose of this paper is to describe the design and initial implementation of a lesson study network in the US intended to support implementation of the Common Core State Standards (CCSS).

Participant observation and artifact collection document the development of the teaching through problem solving (TTP) network over a 14-month period.

The TTP network draws heavily on Japanese practices (e.g. lesson study) and Japanese materials (e.g. coherent, focussed mathematics curriculum) to support changes envisioned in the US CCSS related to students’ mathematical practices and dispositions. The reasons for choice of these key Japanese features are explicated, and teachers’ initial reactions described.

The design shows promise for combining teacher “ownership” with implementation of high-quality approaches designed by others; and allowing instructional innovations developed in Japan to flow into US practice. TTP in mathematics has persistently resisted implementation in the US, so the network is designed to target a central problem in implementing the CCSS.

A method for instructional innovations to spread from classrooms in one country to another is suggested.

This paper reports on experiences of university-level mathematics teacher educators (MTEs) from participating in lesson study to improving mathematics teacher preparation. The authors investigate the questions: “What did MTEs report as benefits of participating in cross-departmental lesson study?” and “What considerations did MTEs report for stakeholders interested in lesson study?”

This study employed qualitative methodologies on one cycle of lesson study where the authors served as lesson study participants. Debrief and focus group interview data were analyzed for emergent codes on benefits, supports and challenges from a university-level lesson study.

Engaging in university-level lesson study provided MTEs firsthand professional development, created community, enabled attention to detail, improved knowledge of issues related to teaching mathematics, improved curricular materials and extended beyond one lesson. Institutional support, a natural evolution of the process, alignment of goals among members and support within the group supported their university-level lesson study. Challenges of time and funding, imposition, misalignment of goals and building trust are discussed.

The paper contributes insights about benefits for MTEs who use lesson study to examine their own teaching practice for mathematics teacher preparation. The importance of supports and constraints is highlighted.

The 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.

Each 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.

Teachers 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.

Although 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.

Video-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.

The 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.

The goal of this chapter is to gain a better understanding of the experiences of mathematics anxiety that some women elementary preservice teachers encounter while learning mathematics during their own K-12 years. Specifically, this chapter is an analysis of the personal well-remembered events (WREs) told and recorded by women during their preservice teaching professional sequence. These narrative writings provide a powerful voice for the degree to which mathematics anxiety shape preservice teachers’ beliefs on what it means to learn mathematics. This intersection of teacher knowledge is important, as these are women who are on the professional track to teach mathematics. The focused analysis for this chapter is aimed at ways in which teacher preparation programs could broaden current views of women who have anxiety and confidence issues in mathematics.

This study aims to investigate contemporary mobile learning practices in teacher education, exploring the following research question: how are teacher educators exploiting the pedagogical features of mobile learning?

The study uses data from an online survey that elicited information about how 46 teacher educator participants were using distinctive mobile pedagogical features (Personalisation, Authenticity and Collaboration) in their mobile learning practices. It uses the iPAC theoretical framework to analyse the data collected.

Findings indicated high self-ratings of authenticity, and positive perceptions of collaborative sharing (Collaboration construct), often involving generative tasks that required use of creative, media production mobile applications. There were weaker perceptions of personalisation and online conversation (Collaboration construct). In light of these findings, we discuss implications for teacher education and recommend future directions for research and development.

This study underlines our contention that teacher educators struggle to exploit the entire range of mobile pedagogical approaches. The findings suggest that teacher educators are cautiously exploring the potential for online collaboration mediated through mobile devices, but have not yet fully grasped the opportunities to design tasks which exploit (and model) the personalised nature of m-learning. The limitations of the study include the size of the sample (46), its self-selected nature and its bias towards Australian and the UK respondents.

In response to the issues raised in this paper, the authors are developing a mobile learning toolkit (www.mobilelearningtoolkit.com) for teacher educators.

There is a scarcity of m-learning studies in teacher education exploring pedagogical insights, and the views of teacher educators themselves are often absent.