Takeshi Miyakawa

• Professor (Full) at Waseda University

In this paper, we aim to offer a preliminary analysis of two proof lessons from a comparative perspective. A case study focuses on German and Japanese grade 8 classrooms, where a common topic for a proof in algebra is introduced. Adapting Boero’s (1999) six phases, we discussed how the two lessons are organized differently in ‘pre-activities’, ‘exp...

In this study, we aim to propose a means to explore the nature of theories generated through task design research in mathematics education. To attain this, we offer a combination of two (meta-)theoretical frameworks, 'praxeologies' and 'theory elements', to understand the researchers' work in design research, and then illustrate the results of the...

The aims of this chapter are: (i) to showcase the state-of-the-art for theoretical perspectives for studying mathematics teacher collaboration; (ii) to identify promising theoretical and methodological perspectives for future studies. The ideas that are synthesised in this chapter are based on the presentations, papers, and discussions that occurre...

Lesson study is recognised as a cultural activity and its implementation in a context different from Japan is a complex process. Researchers' role in this process is assumed to be critical, although this has rarely been investigated. In this paper, we analyse a teaching experiment to introduce lesson study into a professional development course for...

The purpose of this study is to reveal the cultural aspects of argumentation and proof in a Japanese classroom introducing Pythagorean theorem to grade 9 students. We delineate a perspective that posits the proof has three aspects, ‘structure’, ‘language’, and ‘function’, to characterise proof and proving in a classroom and better explain its cultu...

The aim of this study is to advance understading of teachers’ and researchers’ work, in particular its cultural specificities, from a resource perspective by exploring the issues and challenges faced during the translation of a theoretical framework, the Documentational Approach to Didactics (DAD), from Western (English and French) to East Asian la...

This paper is one of the contributions to the Research Forum titled "MATHEMATICS TEACHERS’ INTERACTIONS WITH RESOURCES THROUGH A LANGUAGE LENS" which is organized by Jill Adler, Núria Planas, Luc Trouche, and Janine T. Remillard in PME45 (2022).

Mathematics teachers working and learning through collaboration are gaining particular attention today in terms of a form of teacher professional development and an object of mathematics education research. The Japanese lesson study is one of the typical examples often referred to in such a context. In this lecture, focusing on the teachers’ work a...

This is a report of the workshop aiming at investigating teacher learning in a specific collaborative setting of Japanese Open lesson within the Anthropological Theory of the Didactic (ATD). We especially rely on the notion of praxeology to characterize teacher practices and knowledge, and the notions of educational devices and infrastructure to ch...

This theoretical paper proposes a new perspective on identifying and characterizing the cultural specificities of proof and proving in the classrooms of a given country. To this end, based on the related literature, researchers propose "structure", "language", and "function" as a triplet of aspects that constitute proving activities. Researchers th...

The specificities of mathematics teaching in Japanese primary school: a study of the teacher's practices. Mathematics teaching in Japanese primary school presents some specificities: the structured problem solving lessons, the importance of mathematical thinking, and the lesson study tradition. This paper aims to understand ordinary practices of a...

Mathematics teaching in Japanese primary school presents some specificities: the structured problem solving lessons, the importance of mathematical thinking, and the lesson study tradition. This paper aims to understand ordinary practices of a Japanese teacher, especially how these cultural specificities translate into his practices. We analyze tea...

This paper reports on results of teaching experiments with a study and research path carried out in Japanese lower secondary school classrooms. The generating question relates to the change of world population. Based on these results, we discuss the conditions and constraints for implementing inquiry in ordinary teaching in.Keyword: ATD, Study and...

This paper reports the results of an international comparative study conducted in Switzerland and Japan of an elementary school mathematics lesson. The principal aim of the study was to advance understanding of the cultural specificities of a mathematics lesson in its totality using concrete examples of lesson design and implementation and of how c...

This chapter aims to report the results of a comparative study of teachers’ documentation work in China and Japan, as well as to share some East Asian experiences that are less accessible to Western researchers. The Chinese case is gathered from teachers’ collective work carried out inside school, and the Japanese case is taken from the group activ...

In this chapter, we investigate the notion of “teachers as curriculum designers” from the literature and from six international perspectives. This is done in order to (1) develop a deeper understanding of the concept, and (2) provide an international perspective and illustrations of the different facets of teacher design. Based on this investigatio...

This paper investigates the resources the student-teachers used to design and implement grade 4 mathematics lessons in the context of a project-based international exchange programme between Switzerland and Japan. The lesson, initially planned together by nine student-teachers of the two countries, was implemented separately in each country. In spi...

Japanese lesson study was introduced to the West in the late 1990s. Certain widely disseminated publications and classroom videos, and also reports on international surveys of students achievement, led many to consider that Japanese mathematics teaching is highly creative and effective, with lesson study as a main explanatory factor. As a result, s...

There are different meanings of proof-related words and their connotations in different languages. This study aims to reveal issues of the relationship between natural and mathematical language in the teaching of mathematical proof. For this purpose, we examine the grammatical characteristics of language from Japanese and international perspectives...

This paper analyses two grade 4 mathematics lessons given in Switzerland and in Japan by student teachers (pre-service teachers) in the context of a project-based international exchange program. The lesson, initially planned together by the nine student teachers of the two countries, was finally realised in quite different ways in Switzerland and i...

In this study we explore the interactions between teachers and resources during lesson preparation from different perspectives. We ask in which ways the crossing of perspectives help to develop deeper understandings of teacher interactions with curriculum resources. For doing this, we have chosen the following three theoretical frames: (1) Document...

This presentation focuses on the analyses of a grade 4 mathematics lesson (9-10 years old students), which was prepared and implemented in the context of lesson study carried out by a group of Japanese and Swiss student teachers. We will first describe the PEERS (Student and Researcher Social Networks Projects), the main framework of our internatio...

Using the Theory of Instrumental Genesis (TIG) as a theoretical framework, this exploratory study investigates which instrumentation processes are dominant in a GeoGebra-enhanced mathematics-learning environment to support students to develop an understanding of function transformations. Students in a bridging program at a South African university...

The aims of the present study are two-fold. The first aim is to reveal the cultural and linguistic issues that need to be considered in the development of curricular content and sequencing for teaching mathematical proof in secondary schools in Japan. The second aim is to elaborate an epistemological perspective that may allow us to understand what...

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This study discusses the evolution of mathematical proofs in Japanese junior high school geometry textbooks and the conditions and constraints that have shaped them. We analyse the evolution of these proofs from their inception in the Meiji era (1868-1912) to the present. The results imply that features of the Japanese language affected the evoluti...

This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof—statement, proof, and theory—suggested by th...

This paper elucidates the nature of proving activities required in the inquiry-based learning of mathematics using the Internet, wherein the didactic contract is different from that in the ordinary mathematics classroom. Based on the anthropological theory of didactics, proving activities conducted in the study and research paths are explored in th...

The aim of this paper is to construct a theoretical framework for curriculum development in the teaching of mathematical proof at the secondary school level. To accomplish this aim, we first search for, through the review of related literature, the principal aspects of mathematical proof that should be taken into consideration for the framework. In...

This paper explores in-service mathematics teacher learning in a practice-based professional development program. Through an analysis of daily journals written by an in-service teacher during practicum, we try to identify changes in his discourse over the course of a two-year Professional Degree Program newly implemented in Japanese universities. W...

In this paper, we first present a theoretical approach to study mathematics teacher knowledge and the conditions for developing it, which is firmly rooted in a systemic approach to didactic phenomena at large, namely the anthropological theory of the didactic. Then, a case of open lesson is presented and analysed, using this theoretical approach, t...

We consider the functions of proof in mathematics from the perspective of the work of the mathematics teacher. The work of proving and the time spent on proving, what can a teacher account it to? How can he or she justify it? We frame that problem in a descriptive theory of teaching and place within that frame the work of scholars who have inquired...

In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from dif...

Dans cet article nous présentons un dispositif d’origine japonaise pour organiser le travail collectif d’enseignants pour préparer, réaliser et évaluer l’enseignement d’une seule leçon. Ce dispositif est connu dans le monde anglophone sous le nom de « lesson study ». Même si sa genèse et son usage dépend d’un bon nombre de facteur propres au contex...

While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner’s perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology tha...

We research the work of the teacher in the context of proof and proving in secondary school geometry. In this paper we advance understanding of teaching phenomena that result in the fact that theorems are not always proven in US geometry classes, in spite of the fact that for a proposition to be theorem it has to have a proof. Our hypothesis is tha...

In Before It’s Too Late: A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21st Century (2000) in the US, the authors quote from James Stigler’s conclusions from various videotape research studies of mathematics teaching: "The key to long-term improvement [in teaching] is to figure out how to generate,...

Under the Japanese school system, teachers must use textbooks that have been approved by the Ministry of Education, Culture, Sports, Science and Technology. There are six types of mathematics textbooks for elementary and junior high schools and about twenty types, by grade level, for high school. These are published by private publishing companies....

The objective of this presentation is to report our developed contents based on the advantage of leaming with ICT and the potentiality of Macrornedia Flashmx whose way of contents development differs from other prograrnming languages.

This research presents an analysis of the relationship between knowledge and proof through a mathematical concept: reflective symmetry (in a situation of construction of a proof). We propose to clarify the cognitive distance which would exist for the students, between geometrical construction and the theoretical geometry by the specification of kno...

Current Japanese technological innovation in mathematics classroom is illustrated by the following categories of classroom technologies: Computer Supported Collaborative Learning, Free Software, Commercial Software and Free web-based material.

a theorem in terms of abstract concepts (Herbst & Nachlieli, 2007). In this paper, we advance understanding of instructional phenomena by focusing on the norms of those instructional situations as they relate to two different activities which have traditionally been studied in their cognitive and epistemological dimensions: convincing (or

We report preliminary results of research on the underlying rationality of geometry teaching, especially as regards to the role of proof in teaching theorems. Building on prior work on the classroom division of labor in situations of "doing proofs," we propose that the division of labor is different in situations when learning a theorem is at stake...

Ce travail présente une analyse des rapports entre connaissance et preuve à travers une notion mathématique : La symétrie orthogonale (abordée dans une situation de construction d'une preuve). Nous nous proposons d'éclairer la distance cognitive qui puisse exister chez les élèves, entre la construction géométrique et la géométrie théorique à partir...