This study aims to explore an early career teacher’s noticing within a school-based lesson study (LS) in mathematics at a primary school, focusing on the transformation and its characteristics. The study describes how the teacher, who had no prior experience of teaching a “research lesson,” learned during LS to transition from being an observer to becoming a research lesson teacher. Data analysis draws upon participant observation, recorded meetings, interviews, and written comments collected from a public primary school-based LS in Japan. Through a case study approach, the study uncovers the transformation of the teacher’s noticing and its characteristics, highlighting a goal-oriented review of research lessons, attention to the sequence of mathematics content, and openness to challenges enhancing understanding of task design and students’ ideas. Furthermore, the study reaffirms the importance of shared goal-setting and research themes in lesson study, offering implications for supporting early career teachers and professional development.

Our study investigates the potential of inquiry-based learning for teaching definite integrals in Japanese senior high schools. We developed a sequence of lessons based on the Reference Epistemological-Didactic Model (REDM) of definite integrals, which illustrates how this mathematical concept can be studied and taught. The lesson sequence was designed and implemented at a senior high school, with data systematically collected and analyzed using the tools proposed by the Anthropological Theory of the Didactic. The analysis revealed substantial insights: Firstly, students encountered different kinds of the mathematical knowledge pertaining to definite integrals that they were supposed to learn in the curriculum within a meaningful context highlighting their practical and theoretical importance. Furthermore, the inquiry process expanded as students explored various quadrature methods, enhancing their understanding and appreciation of the subject matter. Second, the inquiry process was further enriched by active student interactions with their milieus, promoting deeper engagement with the mathematical concepts. These findings affirm that inquiry-based learning is a viable and effective approach for teaching definite integrals, providing students with a robust framework to actively explore and understand complex mathematical concepts.

Given the difficulties pupils encounter with analogies that require adaptation, the purpose of this study was to clarify some aspects of adaptation by re-representation in junior high school students. The research framework by Yan et al. (2003) was adopted for identifying opportunities and methods of re-representation to analyse how junior high school students engage in problem solving by analogy. The analysis examined the transformation of representations yielded by re-representation and its role in facilitating adaptation. The results indicate that, among the opportunities and methods outlined by Yan et al. (2003), the opportunities ‘Gulches’ and ‘Rivals’ emerged, with students employing ‘Decomposition’ and ‘Entity collecting’ as methods to resolve them. As an aspect of this process, we clarified the identity of the elements and relations that map onto each other through re-presentation, and revealed the students’ adaptation to adjust the content of the map to satisfy this identity. Therefore, it is considered that if students are encouraged to reflect on the solution of the base problem and to rethink it from a different point of view, their adaptation through re-representation can be promoted.

Programming and mathematics share fundamental concepts such as algorithms, underscoring the importance of interdisciplinary learning that combines these subjects in Japanese high school education. Despite its significance, this integrated approach is seldom adopted in Japanese high schools. Employing the Anthropological Theory of the Didactic (ATD), this study investigates the following two main questions: (1) What programming praxeologies (practice and knowledge) are depicted in Japanese high school informatics textbooks? (2) What programming praxeologies emerge in interdisciplinary inquiry-based learning, called Study and Research Paths (SRP), that merge programming and mathematics? Our textbook analysis revealed six distinct types of tasks: T₁: Create a program, T₂: Modify a program, T₃: Run a program, T₄: Evaluate a program (algorithm), T₅: Decipher a program, and T₆: Analyze the output of a program. On the other hand, interdisciplinary SRP, which we experimented with in a Japanese high school, showed a significant shift in the distribution of these tasks, suggesting a dynamic interaction between the two fields. The study also explores the pivotal role of mathematical inquiry, highlighting its potential to effectively bridge programming and mathematics in educational settings in Japan.