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The purpose of this paper is to report a case study of how learning study was incorporated in teacher education programs in Hong Kong. It aims to share the success of the program and to disseminate how pre‐service teachers enhanced their mathematical content knowledge and pedagogical content knowledge by practising learning study. Building on the work, this paper suggests incorporating the framework of learning study, a theory‐guided pedagogical principle, as an integrated subject of mathematics pedagogy and teaching practice in teacher education programs.

In total 32 pre‐service teachers’ learning journals of their reflections of learning processes were analyzed. The analysis of data and reporting of findings are linked tightly to how pre‐service teachers enhanced their mathematical content knowledge and pedagogical content knowledge by practising learning study.

The 32 pre‐service teachers noted that the learning study subject fostered their understanding of relationship between theory and practice and their understanding of transforming knowledge into action. In particular, they came to understand that knowledge of pupils and content involves a particular mathematical idea or procedure and familiarity with students’ prior knowledge and misconceptions. They also reported that they understood better what mathematics pedagogy content knowledge means and what components it includes.

The suggestions of incorporating the framework of learning study in teacher education programs is supported and manifested by the positive feedback and comments of the 32 pre‐service teachers who underwent the entire learning process of learning study in Hong Kong. The findings demonstrate how pre‐service teachers’ mathematical content knowledge and pedagogical content knowledge were enhanced by practising learning study.

This chapter outlines the importance of enhancement courses, particularly in mathematics, to the preservice landscape in England. These programs occur after an individual has completed a degree but before admittance to preservice teacher education. The pedagogies used in these programs are characterized as both pedagogies of teacher preparation and of selection for preservice. The learning that takes place in these programs is an under-researched area. The chapter addresses that issue by specifying, analyzing, and justifying the pedagogies of teacher preparation deployed in the context of one mathematics enhancement course (MEC). We draw on international research to argue that there is a specific body of knowledge for teaching their subject area, which all teachers need to generate. In terms of empirical work and personal scholarship, the chapter is based primarily on the scholarship and practice of the first author, Clarke, between 2008 and 2014. We present an exemplar of teaching, following the principles of the pedagogies of preparation in place for the MEC. These pedagogies aim to develop for student teachers a profound or “relational understanding” of fundamental mathematics, aiming for the re-experiencing and re-construction of an aspect of mathematics, which they first learned as young grade school students. We argue that a distinctive form of mathematical knowledge is thus produced in and through the teaching processes. In the final part of the chapter, we outline the conditions in which these pedagogies might be adopted in other contexts, arguing that they represent good practice in teaching subject knowledge in all teacher education programs.

The purpose of this paper is to examine how lesson study can lead to teacher learning and improvement of instruction by developing teachers’ mathematical-task knowledge and by supporting teachers’ selection, modification, and implementation of mathematical tasks. Mathematical-task knowledge includes knowledge needed to use tasks that require a high level of thinking and reasoning.

A qualitative case study design was used to explore the learning and instruction of three teachers as they went through the process of lesson study, developed knowledge around mathematics tasks, and made changes to their instruction. Methods included direct observation of lessons, semi-structured interviews, and participant observation.

This lesson study project supported teachers in developing mathematical-task knowledge and in making change to instructional practice. The teachers discussed in this paper added to their understanding of mathematical tasks and changed how they implemented tasks after lesson study. The teachers began to challenge students to go beyond memorizing or executing procedures to deepen the students’ understanding of mathematical concepts. Teachers developed key insights and understandings of mathematical tasks, triggering shifts in their thinking, and changes to instruction. Collaboration and reflection altered the selection, modification, and implementation of mathematical tasks.

This study reveals the connections between features of lesson study and the pathways that lead to learning and improvements to instruction. Limitations included the demands of the school district’s pacing guide and curriculum, and a limited number of interviews and observations were conducted after lesson study.

There are many different ways lesson study has been implemented in the USA, yet the effectiveness of many lesson study projects is still unclear. This study reveals more about the lesson study process, what features are important, and how these features lead to development of knowledge and practice. This study examines how teachers within the same lesson study group added to their knowledge and practice and how different features of lesson study prompt them to make changes.

Teachers in the USA have been conducting lesson study for more than ten years since it was introduced from Japan in the late 1990s. Although interest in conducting lesson study in the USA is still strong and greater numbers of teachers have become involved in this professional learning, there are significant obstacles to conducting high quality and effective lesson study that enhances teachers’ content and pedagogical knowledge, as well as improving their instruction and student learning in classrooms. Because of the needs of improvement in lesson study in the USA, so it can be administered effectively and sustained, the purpose of this paper is to discuss the current status of lesson study in the USA, what high quality and effective lesson study is, and what ideas might be help to improve lesson study in the USA.

In this paper, issues that are common barriers to conducting effective lesson study, such as: US teachers’ misunderstanding or lack of understanding of lesson study; teachers’ insufficient knowledge of content, pedagogical content, curriculum knowledge; lack of support from administrators for lesson study; non‐systematic approach to implement lesson study; and having short‐sighted vision to conduct lesson study will be discussed. The discussions are based on the author's 12 years of experience working with teachers, schools, and school districts in the USA, interactions and information exchanges with other lesson study educators and researchers and professional development coordinators in schools and districts in the USA, and existing research documents in the USA. Through this discussion, the author attempts to provide suggestions for improving lesson study in the USA.

In order for lesson study to be successful, teachers need to think of lesson study as a way to improve their own learning as well as student learning. Spending more time studying mathematical content and curriculum, developing a strong pedagogical content knowledge with colleagues, and establishing a professional community of learning through lesson study will help it to be effective for improving classroom teaching and learning.

The paper provides some helpful suggestions for improving quality and effectiveness of lesson study in order to improve: classroom teaching – teacher's content, pedagogical content and curriculum knowledge; and student learning. The paper is particularly valuable for lesson study practitioners, and administrators and staff developers who are implementing lesson study in schools.

The article presents the construction of a conceptual framework, which is rooted in mathematics education and in dialogic analysis. It aims to analyse how dialogic interactions contribute to constructing teachers' mathematical problem-solving knowledge. The article provides one example of this analysis.

The networking between a content analysis framework (Mathematical Knowledge for Teaching Problem-Solving) and a dialogic analysis framework (Lesson Study Dialogue Analysis) is presented. This leads to the construction of indicators to quantitatively and qualitatively code our data: five meetings during one lesson study cycle of a group of eight Swiss primary teachers, working on the teaching of problem-solving.

This article does not present empirical findings. The developed conceptual framework is the result presented.

The presented framework allows modelling, on the one hand, the knowledge relating to the teaching and learning of problem-solving and, on the other hand, the analysis of interactions during a lesson study. The article does not contain the results of the research.

The use of our framework can contribute to teacher educators' and facilitators' training by highlighting which types of intervention are favourable to the development of knowledge.

Our analysis involves a “systematic coding” approach. It allows a fine-grained analysis of the interactions in relation to the evolution of knowledge. Such a systematic approach offers the possibility of questioning the coded data in various ways.

Lesson Study is a model for advancing knowledge about how teachers can enhance teaching through collaboration in schools. This study aims to focus on two learning situations for students in Grades 1–3: elementary school (the first years of school) and school-age educare (activities for students before and after school while their parents are working or studying). The case study aims to describe how teachers use Lesson Study to enhance students' mathematical learning in the two learning situations. The objectives were to describe teachers' perceptions of Lesson Study activities and collaboration and students' knowledge before and after lessons.

Data were collected as a narrative case study using audio-recorded conversations between researchers and teachers in the different learning contexts. A questionnaire comprising five open-ended questions was used to map students' knowledge of the subject.

Teachers found it advantageous to cooperate with each other across the different learning situations. Mapping students' knowledge before and after a teaching session helped them understand how to create a teaching situation that benefits their students. They saw the value of continued collaboration and called for implementation of the Lesson Study method throughout the school.

An important limitation of this case study is that it was conducted in a very specific context, and the findings cannot, therefore, be generalized to other situations. However, there is a need for similar case studies to be conducted in different contexts, both in Sweden and in other countries, to pay attention to ways in which elementary schools and school-age educare can develop supplementary teaching situations.

The originality of this case lies in planning and reporting a Lesson Study in two different learning situations in the same school, and the conclusion that educators identify and develop collaborative links in different subjects.

The purpose of this paper is to investigate the development of mathematics teachers’ pedagogical content knowledge (PCK) over successive cycles of lesson study. Utilising the framework of mathematical knowledge for teaching (MKT) (Ball et al., 2008), this research classifies features of PCK as utilised by post-primary mathematics teachers in their planning and reflection conversations in lesson study. The development of these features of PCK is then traced over successive cycles.

In total, 12 teachers in two Irish post-primary schools participated in this research. Over the course of one academic year, these two groups of teachers completed a number of cycles of lesson study and qualitative data were generated through audio recordings of all lesson study meetings and through individual interviews with participants.

Analysis of teacher dialogue reveals distinct features of knowledge of content and students (KCS) and knowledge of content and teaching (KCT) incorporated by these teachers in their planning and reflection conversations, providing empirical evidence of MKT in lesson study. The occurrence of these features of KCS and KCT in lesson study conversations increased over successive cycles, demonstrating teacher learning.

This research contributes to the literature in expanding the theoretical underpinnings of teacher learning in lesson study. It also provides further empirical evidence of MKT (Ball et al., 2008) in teacher practice, specifically related to post-primary mathematics teachers.

The purpose of this paper is to identify changes in teacher’s pedagogical content knowledge (PCK) as a result of their participation in two learning studies in mathematics.

A group of four mathematics teachers and the researcher of this paper explored two objects of learning related to division with decimal numbers and the straight-line equation in a learning study (LS) project over the course of one year. The data used consist of eight video-recorded lessons, four written student tests, eight student interviews and 14 recorded team meetings. The analysis was based on the variation theory principle about learning (Marton, 2015) and on ontological assumptions within the phenomenographic approach (Marton, 1981).

It was found that teachers’ PCK was changed and refined through the LS process in terms of differences in ways of understanding and discussing critical aspects related to each object of learning. In the paper, the terms “presumed critical aspects” and “explored critical aspects” are used to illustrate this difference. Furthermore, the concepts are viewed in relation to three subdomains of PCK: knowledge of content and curriculum (KCC), knowledge of content and students (KCS) and knowledge of content and teaching (KCT).

Bringing out the difference between “presumed critical aspect” and “explored critical aspects” advances the view that critical aspects are dynamic and emergent in practice – in the interaction between teaching and student learning. The research exposes “explored critical aspects” as a specific form of PCK in which KCC, KCS and KCT are intertwined.

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.

This paper seeks to understand how teachers' mathematical knowledge for teaching (MKT) is developed during a lesson study regarded as a professional development process that places particular emphasis on teachers' knowledge of tasks, representations and students' learning.

This study is based on the networking of two theories, namely the Interconnected Model of Teacher Professional Growth (IMTPG) and MKT. The methodology is qualitative and interpretative. The participants are three primary school teachers and team members involved in a lesson study. Data collection was conducted by means of participant observation, with audio recordings of the sessions and a final individual interview.

The participant teachers developed their knowledge of tasks and representations, which are essential elements of content and teaching knowledge, as well as knowledge of the curriculum, content and students. Additionally, they developed specialized knowledge of mathematics, the meaning of fraction as a measure and its representation on the number line. This development arose from activities conducted in the Domain of Practice, in many cases prompted by the External Domain, and was particularly important when these activities gave rise to unforeseen consequences. Connections among the various domains were established through enactment and reflection processes.

The study shows how the networking of two different theories, in this case the IMTPG and MKT, may enhance further understanding of educational phenomena. This networking involved the coordination of these two theories, which were superimposed in the Group Domain.