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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.

This study aimed to explore how a group of Chinese primary mathematics teachers learned through conducting an online cross-cultural lesson study between China and Australia.

An expansive learning theory was adopted to examine teachers' learning through collective activities across different activity systems. Multiple data sets including videos of research lessons, debriefings and audios of interviews were collected. From the expansive learning perspective, based on a fine-grained qualitative data analysis, various contradictions (as driving forces of learning) were identified and the ways of resolving the contradictions (as enactment of learning) were located to feature teacher learning throughout the online lesson study process.

Teachers' expansive learning includes enhancing teachers' MKT and Mathematics TPACK, developing instructional design skills and capabilities in addressing challenges occurring in the virtual environment were identified.

Theoretically, the study illustrated how expansive learning theory could be utilized to examine teacher collaborative learning in the online cross-cultural lesson study. Practically, this study showed that reiterative cycles and experts' facilitation are crucial to expansive learning for linking research to classroom practice. However, this study did not focus on student learning in the virtual environment. Australian teachers' reciprocal learning through the online lesson study also requires further exploration.

Both online lesson study and cross-cultural collaboration are innovative. The expansive learning lens are creatively used to examine the complexity of teacher learning in such a novel environment.

The purpose of this paper is threefold. First, the authors set out to advance the thesis that lesson study should be considered as the signature pedagogy of teachers. Second, the authors want to argue that combining the core attributes of Chinese lesson study and Learning study will improve the practice of lesson study. Third, the authors attempt to demonstrate how teachers discover necessary aspects of the object of learning (here called “keys to learning”) through their engagement in Learning studies.

The paper conducted a contrastive analysis of two varieties of lesson studies: the Chinese lesson study and the Learning study.

Lesson studies form a field of varieties, but the commonality among them (i.e. the focus on the lesson) makes the lesson study a strong candidate for being “the signature pedagogy” of teachers. The most important attribute of the Chinese lesson study is its close connection to the daily work of teachers through its embeddedness in teacher research group (arguably the core organisational principle of the Chinese educational system). The most important attribute of the Learning study is its theoretical grounding which helps teachers create an environment for the students to discern and appropriate necessary aspects of the object of learning.

Different varieties may be enriched by including the two core attributes found in the Chinese lesson study and the Learning study.

Two empirical studies are used to exemplify how teacher might discover previously unknown necessary aspects of the object of learning (here called “keys to leaning”).

This study aims to explore how a Chinese lesson study (LS) supports a teacher's learning of transforming curriculum reform ideas into classroom practices.

Data analyzed in this study included lesson plans, three videotaped research lessons, three audio-taped group meetings, interviews, the teacher's reflection journals and other related materials. Clarke and Hollingsworth's interconnected model of professional growth (IMPG) was adopted as the theoretical and analytical framework for examining the teacher's learning process.

This study found that teachers can deepen their understanding of innovative curriculum ideas and implement them through an iterative cycle of planning, enactment and reflection in LS. Involving knowledgeable others in the process and reflecting on evidence-based evaluation of students' learning outcomes is crucial for changing the teacher's knowledge, beliefs, attitudes and teaching practices. Theoretical tools, such as learning trajectory, are useful for transforming curriculum reform ideas that teachers find abstract and overly broad into concrete and actionable lesson designs.

Theoretically, this study can broaden our knowledge about how the under-studied mechanism of Chinese LS can contribute to helping teachers to transform reform ideas into classroom practices. Practically, this study provides suggestions for researchers and educators to reflect on and improve the effectiveness of teachers' professional development programs in a reform context.

The urgency of improving the schools call for a distributed instructional leadership model where teachers are not just recipients of professional development, but also active leaders who are coaches and mentors for their peers. The purpose of this paper is to examine the teacher leadership development system in Shanghai, and identify pathways to constructing actionable models that develop and maximize instructional expertise.

This is a qualitative study. Purposive sampling was conducted to select four teaching-study groups from a frame that included all certified “expert teachers” from a large Shanghai district with about 9,000 teachers. Grounded theory approaches were used to understand “what actually happens in the teachers’ world.” Participative observations (of lesson delivering and collaborative decoding), semi-structured interviews, teachers’ reflective journal entries, and video recording of group work and lessons were the main measures of data collection.

Three key features of expertise infusion were identified: recognizing, differentiating, and labeling teacher expertise at multiple mastery levels; providing expert teachers with support and leadership responsibilities to lead practice-embedded and cross-school peer learning; and creating a roadmap for teachers to chart continuous learning pathways individually and build an enhanced content pedagogical knowledgebase collectively.

Results from this study provide the impetus for further exploration in how Shanghai continuously share and improve good teaching systemically, which could be informative to US schools and districts in their effort of redesigning professional development that maximizes available expertise among teachers and stimulates teacher-led action research for student learning.

The purpose of this paper is to document a three-year international project aimed to improve the capacity of participating schools and districts in implementing and scaling Teacher Peer Excellence Groups (TPEGs). The TPEG model involves teams of teachers organized by subject matter or grade levels, deeply engaged in communities of practice for instructional improvement. It facilitates the professionalization of teaching through the de-privatization of teacher practice, collaborative planning, giving and receiving actionable feedback, and holding one another accountable for implementing improvement measures.

The project is a collaborative partnership between US and Chinese universities and school districts in Tennessee and Shanghai. Mixed-method approaches were used to track the development and implementation of the TPEG model in 27 pilot schools in six Tennessee districts from 2013 to 2016. Data were collected through school site visits, lesson-planning documents, classroom observations, focus groups, interviews, and teacher and principal surveys.

This paper compiles the key findings from multiple research studies and program reports about the TPEG project. Findings provide encouraging evidence that, given sufficient support and guidance, teachers can construct productive learning communities. The results show consistent positive and statistically significant result across all three key signposts for effective communities of practice – increases in instructional collaboration, comfort with deprivatized teaching practice, and engagement in deprivatized teaching practice. These findings hold after controlling for key enabling conditions and school characteristics. Qualitative analyses provide a rich and nuanced picture of how TPEGs were doing after the implementation grants. Participating schools reported a full range of engagements in TPEGs, and emphasized the role of school leadership in facilitating and supporting teachers to lead and participate in TPEGs.

The TPEG project provides a valuable case study to address the benefits, concerns, and potential risks associated with cross-cultural learning of effective instructional practices. Findings from the three-year process highlight the key steps of cultivating the necessary culture and expertise to support, implement, and sustain effective TPEGs school-wide and district-wide. It also underscores the necessity of developing and customizing tools and resource kit for supporting this work such as observation protocols, feedback guides, and examples of timetables to conduct TPEG activities.

Are education systems converging toward a global model of teacher education or do local models tend to predominate in spite of attempts to reform them? How much do global, national, and local cultures shape and condition future teachers’ opportunities to learn to teach? How do these opportunities influence teachers’ pedagogical content knowledge? In this chapter we use data from the IEA’s first study of the effectiveness of pre-service teacher education in order to investigate teacher education policy, program structure, and outcomes. Using multilevel modeling we found that across countries individual characteristics have a similar and powerful influence on what future teachers come to know at the end of their pre-service programs. The effects of teacher education curriculum on future teachers’ mathematics pedagogical content knowledge reaffirm the prevalence of local cultures on the implementation of an increasingly globalized ideal. We conclude that while the provision of teacher education shares many common features in goals and structure across countries, it is strongly influenced by local conditions and norms, and by cultural notions of the knowledge that is considered essential – framing how quality is to be defined and operationalized – when learning to teach.

The purpose of this paper is to reflect on the experiences and challenges brought about by subject-specific mentoring within a distinctive learning environment, namely, mathematics for English as a second language (ESL) classes for 16-18-year-olds. The reflection is carried out over the stages of the mentoring process during an academic year within a college of further education in England with the purpose of adding to the store of knowledge on mentoring mentees who are specialists in mathematics.

The author employs an auto-ethnographic methodology.

Amongst its conclusions, the author argues that through a mentor demonstrating specific numeracy methods and techniques to mentees, and making them aware of language issues facing ESL learners relating to terminology used in mathematics, mentees are more able to develop their learners’ numeracy skills and relevant language skills, hence facilitating their adaption and integration into the English education system.

Research on the pedagogy of mathematics teaching, as well as language issues relating to terminology used in mathematics, needs to be considered during the mentoring of teacher trainees who are specialists in mathematics. In addition, specific language issues need to be considered for those mentees who are likely to have ESL learners in their classes.

In challenging some of the conventions of mathematics teaching, the paper addresses issues of inequality through identifying strategies designed to improve the educational opportunities of 16-18-year-old ESL learners.

The originality of the paper lies not only in its focus on the nuances of subject-specific mentoring, within the context of a particular target group, namely, 16-18-year-old ESL learners studying functional skills mathematics in a college of further education, but in its attempts to address the challenges that can arise when contesting, through theory and practice, education conventions.

In this chapter, the interplay between the development of the discipline, the development of the field of study, and the emergence of professional fields is examined using the example of mathematics. In connection with the formation of the modern research university, mathematics has emerged as an independent scientific discipline and as an independent field of study. In the process, mathematics attains a high degree of formalization and internal coherence. This is the basis for the penetration of mathematicians into more and more professional fields, even outside science. Real problems or real facts are reduced to aspects that are amenable to mathematical modeling by treating them as quantifiable parameters. As mathematics expands as a field of study, more and more professional sectors become applications of mathematical models. As a consequence, more mathematical fields of study are differentiating themselves, specializing in these application fields. This chapter analyzes this dynamic and its preconditions.

The focus of this chapter is on the effective and inclusive classroom practices for the teaching and learning of mathematics at the primary and early secondary levels. The research literature and major national and international reports on effective and inclusive mathematics teaching at the primary and secondary levels of schooling are examined. Some of the challenges to inclusive mathematics teaching are explored. Based in Florian’s (2014) inclusive pedagogical approach in action framework, a research-based exemplar of effective and inclusive primary mathematics teaching is described. The elements of effective and inclusive practices at the secondary level are outlined and a sample lesson presented. Potential impediments to inclusivity are examined.