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The world witnessed a growing interest in inquiry-based learning in the past decade. Study and research path (SRP) is a model of such learning based on the anthropological theory of the didactic (ATD). This paper discusses the following... more
The world witnessed a growing interest in inquiry-based learning in the past decade. Study and research path (SRP) is a model of such learning based on the anthropological theory of the didactic (ATD). This paper discusses the following research questions through [Formula: see text] maps of the SRPs of university freshmen using the notion of praxeology: (RQ1) how do students/pre-service teachers create SRPs in an online environment in terms of group work? (RQ2) How are the institutional conditions and constraints of each group characterized? In conclusions, the differences in media searches of the student groups lead to differences in final answers to the inquiry. Additionally, the media-milieu dialectic is closely related to the question–answer dialectic.
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I-3-2. Activities in the Tentative Suggested Course of Study and Mathematical Ways of Thinking(I-3. Mathematical Activities,Part I. The Theory of Problem Solving Approach, Mathematics Education Theories for Lesson Study: Problem Solving Approach and the Curriculum through Extension and Integration)more
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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... more
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, as well as linguistics issues associated with statements with quantifications. A pilot study shows that natural language may influence how statements are formulated by students in mathematical discourse.
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Within the Japanese mathematics education community, we use two terms for proof: shōmei (証明) and ronshō (論証). Both terms share the same Chinese character, shō証. Literally, shō 証 means ‘evidence’ or ‘proof’, mei明 means ‘clarity’ or... more
Within the Japanese mathematics education community, we use two terms for proof: shōmei (証明) and ronshō (論証). Both terms share the same Chinese character, shō証. Literally, shō 証 means ‘evidence’ or ‘proof’, mei明 means ‘clarity’ or ‘shining’, and ron論means ‘argument’ or ‘logic’ [1]. Sometimes ronshō is seen as a special type of shōmei. For example, the current categories of research presentations at the annual conference of the Japan Society of Mathematical Education (JSME) include the category “shōmei, including ronshō and setsumei” (setsumei means ‘explanation’) [2]. Starting from this distinction, we explore cultural and linguistic issues related to teaching proof in Japan and an epistemological perspective on what constitutes proof. The difference between shōmei and ronshō is similar, but not identical to the distinction between preuve and démonstration in French. Balacheff uses preuve and démonstration in the following way:
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In this paper, we explore theoretical approaches to Japanese teachers’ lesson designs involving the adaptation of mathematics textbooks for instructional change. In Japan, although most teachers use textbooks as the main resource for... more
In this paper, we explore theoretical approaches to Japanese teachers’ lesson designs involving the adaptation of mathematics textbooks for instructional change. In Japan, although most teachers use textbooks as the main resource for lesson planning, called kyouzai kenkyuu, the ways in which they use textbooks can differ. In a kyouzai kenkyuu practice, Japanese teachers sometimes attempt to design innovative tasks and/or learning trajectories beyond or parallel to the textbooks and curriculum guidelines. Such practice is often invisible to international researchers, since it is culturally situated in the local context. To make it more visible, in this study we address and advance theoretical approaches using two frameworks which are well-established for research in mathematics education, namely, Anthropological Theory of the Didactic (ATD) and Documentational Approach to Didactics (DAD). Two cases of lesson design regarding fractions using the same textbook chapter for 3rd graders i...