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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.

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.