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This research aims to understand how prospective teachers develop their knowledge about whole-class discussions during a lesson study. Following a qualitative approach, we focus on the work of three prospective mathematics teachers preparing, leading, and reflecting on wholeclass discussions. Data was collected through participant observation with field notes, audio recordings, and document collection. The results show that a detailed analysis of a lesson plan, previously prepared autonomously by a prospective teacher based on a guide, promotes a focused discussion and a collaborative environment. Additionally, being involved in each other's formative process, through lesson study micro-cycles, created opportunities for prospective teachers to analyze and discuss different classroom situations, which promoted the development of their knowledge. Finally, classroom experiences seemed to be fundamental for the development of prospective teachers' knowledge. They were able to put into practice the work carried out during the lesson study, which allowed them to link theory and practice, and reflect on their own practice. This research also underlines the importance of the teacher educator's role in creating fruitful opportunities for the development of prospective teachers' knowledge.

This investigation adjusted the lesson study (LS) model for the initial teacher education aiming to examine its effect in the development of the pre-service teachers' pedagogical content knowledge (PCK) namely, both their knowledge and understanding on how to transform a science topic to make it more understandable for the students. The LS topic was the speed of sound that is taught in the 8th grade. The PCK construct was evaluated, as well as and in terms of both PCK-topic specific knowledge and PCK-pedagogical knowledge. The participants on this investigation were three pre-service teachers. The data were collected through video recording of LS sessions. The qualitative data collection was combined with quantitative and qualitative analysis procedures. The results showed that the LS promoted an improvement on pre-service teachers' PCK as well as in most of the aspects of both PCK-topic specific knowledge and PCK-pedagogical knowledge. PCK's aspect' 'Strategies for pupil self-evaluation' has not improved satisfactorily. These findings suggest that LS should be carried out during the training programs of the science PSTs.

A teaching practice consistent with the development of students' mathematical reasoning requires teachers to hold a profound understanding of mathematical reasoning. The aim of this research is to study the development of middle and secondary mathematics teachers' understanding about the processes of generalizing and justifying in a professional development course. Data collection included observation of the course sessions, with video recordings, and document collection of teachers' and their students' productions. A qualitative in-depth analysis was carried out focusing on the ways and complexity of generalizing identified by the teachers. The results indicate that teachers progressively focus their attention on these reasoning processes, identifying and characterizing them. The way the course was designed and enacted appears to have contributed to enable the teachers to deepen their understanding of two central mathematical reasoning processes, generalizing and justifying, in addition to their ability to foster and identify such processes in the work with their students.

This article discusses how two beginning mathematics teachers mobilize and develop their didactics knowledge, specifically concerning knowledge of statistical content and teaching practice, during a teacher education experience. This work was developed as part of a specialization course for elementary school mathematics teachers, in the subjects Data Analysis I and II. The teacher education course took place in the West Zone of Rio de Janeiro, Brazil. This is a qualitative study with an interpretive paradigm, based on a case study with two beginning teachers. The data collected was obtained from sessions by a logbook, audio recordings, and interviews with the teachers after the teacher education course. The course was structured to articulate didactics and statistics knowledge from activities directed to teaching practice. Concerning statistical knowledge, the results show the development of knowledge about different concepts associated with carrying out statistical investigations. Regarding teaching practice, teacher's learning is highlighted to carry out statistical activities of exploratory nature and statistical investigations in the school context.

Purpose: 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. Design/methodology/approach: 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. Findings: 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. Originality/value: 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.

Purpose: 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. Design/methodology/approach: 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. Findings: 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. Originality/value: 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.

Purpose: 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. Design/methodology/approach: 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. Findings: 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. Originality/value: 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.

Purpose: 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. Design/methodology/approach: 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. Findings: 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. Originality/value: 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.

In the research reported in this paper, using a modified version of the interconnected model of teacher professional growth (IMTPG) proposed by Clarke and Hollingsworth (Teaching Teacher Educ 18:947-967, 2002), we aimed to understand the learning dynamics in a lesson study of a group of five teachers of grades 5-6, during their work around mathematical tasks and in the elaboration and analysis of a diagnostic test of students' knowledge. We draw on examples from a lesson study that took place in a school in Lisbon, involving five teachers that constituted the whole mathematics group of the school. The main feature of our adaptation is the consideration of a Group Domain instead of the Personal Domain of the original model. In the original model, the Domain of Practice had a broad definition but usually it was restricted to classroom experimentation. In the research reported in this paper, the lesson study sessions were taken as part of the Domain of Practice. For data collection, there was audio and video recording of the lesson study sessions and of the research lesson and the writing of a research journal. Data analysis was done using the modified IMTPG. The results suggest that this model is helpful in understanding the processes that make lesson study a valuable professional development setting, contributing to responding to the question of 'how lesson study works' (Lewis et al., Theory and practices of lesson study in mathematics: an international perspective, Springer, New York, 2019). In addition, the use of this model showed that the lesson study promoted the teachers' development regarding knowledge of didactics, especially knowledge of students and their learning processes and of teaching practice.

We aim to identify what prospective mathematics teachers indicated that they learned regarding mathematics and mathematics teaching as they participated in a lesson study. The theoretical framework is supported by models about teachers' knowledge and prospective teachers learning processes. The methodology is qualitative and interpretative, with data collected by interviews and documents made by participants. The participants indicated to understand the importance of different representations in mathematics. They also indicated to appreciate the value of the detailed planning of the lesson, the careful selection of tasks, the analysis of possible student strategies and difficulties, and the preparation of classroom communication. [ABSTRACT FROM AUTHOR]

The research, guided by the question "What professional knowledge is mobilized in a Calculus lesson study conducted with university instructors?", involved eight instructors from higher education institutions in southern Brazil who are dedicated to the training of prospective mathematics teachers. The lesson study, structured in twelve weekly two-hour meetings, addressed the topic "maxima and minima". The qualitative analysis showed that the approach and dynamics of lesson study mobilized and deepened professional knowledge regarding mathematics, mathematics didactics and the mission of the trainer of future mathematics teachers. [ABSTRACT FROM AUTHOR]