This article analyzes Malaysian and Japanese educators' reactions to a mathematics lesson observed by a subset of researchers. The main aims are to reveal the cultural scripts about mathematical learning that are held by, but often invisible to, members of a culture; and to address educators' conceptions of teaching mathematics across cultures.…

The present study compared Japanese and U.S. preschool children's knowledge of geometric shapes. The main goal was to explore if differences in shape-naming conventions in Japanese and English could explain differences in children's understanding of geometric shapes. In ancient Chinese-based languages (e.g., Japanese), all standard 2D shapes…

This study aims to elucidate a common professional learning opportunity in Japan, "instructional circles," which has not yet been studied systematically or described in detail. This study uses the mathematical knowledge for teaching (MKT) framework and research on features of professional learning opportunities that facilitate intended…

Persistence represents a crucial trait in learning. A lack of persistence prevents learners from fully mastering their current skills and makes it difficult for them to acquire new skills. It further hinders the administration of effective interventions by learning systems. Although most studies have focused on identifying non-persistence and…

"Assumptions" play a fundamental role in disciplinary mathematical practice, especially concerning the relativity of truth. However, much is still unclear about ways to help students recognize key aspects of this role. In this paper, we propose a set of principles for task design to introduce students to the role of assumptions in…

This research focuses on enhancing critical thinking in secondary mathematics education using carefully constructed teaching materials. Utilizing socially open-ended framework, complemented by perspectives from critical mathematics education, the study aims to promote students' critical thinking skills. The developed materials were implemented in…

In Japan during the 1980s, there was an interesting debate about how to teach the area of a parallelogram effectively to primary school children. Yutaka Saeki criticized the standard method, which relies on a cut-and-paste procedure. He argued that the standard method inevitably failed to convince children because it does not provide any cogent…

Pupils' ability to represent mathematical concepts in multiple ways is a central aspect of mathematical competence and communication. Thus, classroom instructions should be able to support learners in using multiple representations (MRs) to increase the quality and quantity of connections to a network of ideas. Given the importance of bansho…

In conversations about pedagogy, researchers often overlook how physical space and movement shape teacher sensemaking. This article offers a comparative case study of classroom videos using a dynamic visual method to map embodied interaction called "interaction geography." Our analysis proposes an integrative framework to study classroom…

Purpose: This study aims to develop a self-reflection scale useful for teachers to improve their skills and to clarify the Japanese teachers' characteristics during mathematics lesson observation (MLO). In MLO, it is important to understand the lesson plan in advance to clarify observation points, and we aim to develop a scale including these…

This study focused on improving students' learning mathematical of proofs and proving by using combinations of proof strategies that span different levels of understanding of proof structure; we refer to these as 'level-spanning proof-production strategies'. We analysed the level-specific proof-production strategies evident in the lessons and…

To encourage students' self-regulated learning at home, developing skills for textbook use to overcome learning-related impasses is crucial. This study examined the effects of providing mathematics class sessions that combined teacher instruction on appropriate textbook use with peer instruction, aimed at promoting students' spontaneity and…

Probability is a difficult concept, which is not always taught accurately. This study aims to clarify how experimental and theoretical probabilities are taught in Japanese 7th and 8th grades through a textbook analysis. We analyzed seven, government approved Japanese 7th and 8th grade textbooks each. Focusing on the definition and explanation of…

Purpose: This comparative study sought to identify best practices concerning symbolic mathematical communication between primary school teachers and students in Japanese, Laotian, and Thai classrooms. Method: The target groups were 18 teachers and 671 students in Grade 1 to Grade 6 mathematics classrooms in Japan, Lao PDR, and Thailand. A total of…

In this study, we aim to explore the conditions and constraints of implementing a lesson study-based professional development (LSPD) program for Japanese pre-service primary teachers. Based on the anthropological theory of the didactic--a well-established theoretical framework in mathematics education research--it offers three dimensions…