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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.

The purpose of this paper is to review the research concerning the use of lesson studies in the education of secondary school prospective mathematics teachers. It discusses the adaptations made on the designs, the aims and outcomes established, the processes used, and the needed improvements in the experiences reported so far.

The scientific studies reviewed were identified in a Google search, using the key words “lesson study”, “mathematics”, and “secondary.” The identified material was recorded in a database and the themes for the analysis cover the planning, execution, and reflection phases of a formative process.

The paper identifies the several pending issues regarding the use of lesson studies in prospective teacher education such as defining the aims, establishing the relationships among participants, scaling, and adapting lesson studies for the particular purpose of educating future teachers.

At a practical level, this review suggests that lesson studies in pre-service teacher education must have a clear formative aim. It also shows that many formats are possible and must be chosen according to the specific conditions. In addition, it suggests the need for research regarding the definition of the aims, the working relationships established among participants, the problem of scale, and the problem of adaptation or simplification.

The paper identifies the key issues in the design of lesson studies in initial teacher education. It argues that besides signaling the positive outcomes, more critical (or self-critical) investigations are needed, e.g. using external researchers as “critical friends”, which address their difficulties, limitations, and drawbacks in a more thorough way.

This research aims to understand the learning with regard to didactic knowledge of an early childhood teacher who participated in a Lesson Study (LS) on the topic of patterns, as well as her perspective about LS as a teacher education process.

This is a qualitative case study of an early childhood teacher who participated in a LS alongside three other colleagues and a facilitator. Data collection was made by participant observation with elaboration of a research journal, audio recording of sessions and a collective interview. Data analysis was made by content analysis based on the conceptual framework.

This case study shows that early childhood teachers may become aware of the importance of working with their children mathematical ideas. It also shows that they may develop their didactic knowledge in several dimensions such as school mathematics, curriculum, children and their learning, and teaching practice and that they may appreciate LS as a means of professional development.

This study shows the potential of LS for the professional development of early childhood teachers, a scarcely researched area. It also shows that their learning may include dimensions related to specific curricular areas such as mathematics.

This article aims to analyse how a teacher leads whole-class discussions during and after participating in lesson studies and to what extent that participation influences her teaching practice.

This is a qualitative/interpretative research with a case study design, carried out with a secondary school mathematics teacher who participated in two lesson studies. Data were collected from participant observation, audio recording of lesson study (LS) sessions and discussions with the teacher, video recording of lessons and semi-structured interviews. Frameworks regarding the teachers' actions are used in the analysis.

The results suggest that in her teaching practice, the teacher led students to explain their strategies with supporting/guiding actions, but she also challenged the students to justify their productions, ensuring that the students' ideas were clear. Additionally, the teacher explored incorrect strategies and disagreements, inviting and challenging other students to intervene or react and involved students in drawing connections, as discussed in the LS. Therefore, the teacher put into practice several actions teachers can do in leading whole-class discussions to promote students' learning. Participating in LS was an opportunity to rethink her teaching practice, as the teacher pointed out, bringing her a new perspective on leading discussions in which students play an active role in learning mathematics, creating opportunities for the students to explain and react to their colleagues' ideas.

This article examines an under-researched issue: the influence of LS on the way a teacher leads whole-class discussions, during and after participating in lesson studies.

To understand how lesson study (LS) can promote the development of pedagogical content knowledge (PCK) of prospective primary teachers. More specifically, to know what PCK prospective primary teachers develop during LS and how this development occurs.

Following a qualitative approach, this study took place in a teacher education institution where a LS was carried out during the last semester of the academic year with the participation of two prospective teachers, a teacher educator, a cooperating teacher and a researcher.

The results suggest that prospective teachers may develop PCK when they participate in LS, regarding lesson planning (goals and lesson plan), task design, students' difficulties and solving strategies, whole-class discussions and observation of student learning. This development occurs through the engagement in LS activities that allow prospective teachers to deepen their knowledge.

This study investigates how the development of prospective teachers' PCK occurs during LS, providing knowledge about how different activities of the LS help develop different aspects of PCK.

This paper focuses on prospective teachers’ (PTs) participation in a lesson study (LS) that prompted them to research their own practice. We seek to describe the dimensions of PTs’ knowledge of student learning developed during the process and the LS features fostering it.

The participants were two PTs, a teacher educator, a cooperating teacher and a researcher. The LS was integrated into a Portuguese initial elementary teacher education program. Following a qualitative approach, we used participant observation.

The PTs developed their knowledge of students’ learning of the concept of area in four dimensions: theories; students’ interests and expectations; ways students interact with the content and students’ strengths and weaknesses in learning the concept. To support this development, the LS design considered follow-up sessions and emphasised collaborative work.

This study focuses on PTs researching their practice and disseminating the results, which has been overlooked in previous research of LS with PTs. The results highlight the potential of LS to motivate PTs to research their practice and emphasise the importance of involving them in disseminating LS results.

The purpose of this paper is to understand what physics and chemistry preservice teachers learn on the nature of the inquiry tasks and about classroom communication in an inquiry task when they take part in a lesson study.

This is a qualitative and interpretive research which was carried out within a master’s degree course in physics and chemistry teaching with three preservice teachers. Data were collected from participant observation with video recording, interviews, written reflections and group report by the preservice teachers. This two-cycle lesson study was conducted over 12 sessions. The data analysis took place through asking questions and using the constant comparison method, which allowed the identification of the most relevant issues about the preservice teachers learning according to the categories nature of the inquiry tasks and communication promoted by the teacher.

The results show that the preservice teachers learnt to identify the characteristics of inquiry tasks, how to develop an inquiry task when planning the research lesson and acknowledged its potential for student learning. Moreover, the preservice teachers acknowledged the fact that the classroom communication promoted by the teacher fostered student participation, negotiation of meanings about scientific concepts and construction of new learning that can be shared within the class.

Research is needed as regards how initial teacher education providers may contribute to the learning of preservice teachers in lesson study in initial teacher education programmes.

This research contributes to show potentialities of lesson study in the initial teacher education of preservice physics and chemistry teachers.

The purpose of this paper is to illustrate the methodology used by the authors to describe the enacted object of learning, a methodology where data production and analysis is rooted in a theorisation of pedagogy. The authors share how the authors used this methodological approach to provide a comprehensive description of the enacted object of learning and in so doing the authors hope to make a methodological contribution to the field of learning study. The lesson analysis foregrounds the importance of “evaluation” in pedagogic practice, and thus a key element of pedagogy. Tools from variation theory are incorporated into this broader approach that the authors suggest illuminates the enacted object of learning. The authors offer this approach as a methodological contribution to the development of research in and on learning study.

A case study approach was adopted as the key research methodology in this study. The four teachers who participated in this study were purposively identified since in the first instance the design of the study warranted that the teachers who participated were teaching mathematics at grade 10. Second, the need to be purposive in the sampling strategy employed was based on issues around cost, logistics and convenience.

While learning study foregrounds the importance of examining the constitution of the enacted object of learning, the contention is that it is through a focus on evaluation that the authors are able to fully describe what is constituted as mathematics with respect to the enacted object of learning. Analysis of evaluation thus adds to the description of the enacted object in critical ways.

Within the domain of learning study, this paper provides a novel way of engaging with a lesson transcript in an attempt to fully describe what comes to be constituted as the enacted object of learning. This is achieved by combining the notion of evaluative events and authorisation on one hand and variation theory on the other.