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Students beliefs and attitudes towards risk taking can impact on their mathematics learning and performance. However, at present, risk is not established in the field of mathematics education. The challenge for mathematics teachers in developing their students’ risk taking dispositions is to choose appropriate activities and tools that match this concept and the learning needs of the students. This paper describes some research-based ideas for promoting risk taking behaviours in a mathematics classroom. It presents interactional pedagogical strategies from a design collaborative research conducted at one secondary school. As part of the learning activities, students critically evaluated statistical investigations undertaken by others. Students had to take risks: ask critical questions, construct statistical arguments and respond to others’ arguments in face of criticisms. The findings are interpreted in relation to recent writing about students’ abilities to take risks in mathematics classrooms. The final section considers the issues arising out of the paper and offers suggestions for meeting these challenges. [ABSTRACT FROM AUTHOR]

This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students' autonomous problem-solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among teams composition, and content foci. [ABSTRACT FROM AUTHOR]

The article focuses on the art of seeing in mathematical problem solving. It states that easy things in solving mathematical problems is often difficult to determine that those complex things. It also relates that problem solving can be used as a powerful tool in learning mathematical procedures and concepts.

This article discusses what inquiry conversations could mean when learning mathematics. Referring to Gadamar's distinction of true and apparent questions it is discussed what it takes to be inquiring and if this attitude necessarily includes posing questions. Which qualities are expressed in inquiring questions, and what other ways of communicating may have an inquiring function in learning conversations? The intention is to develop and frame the concept of 'inquiry' in learning conversations, and this is the focus of analysis of an authentic classroom situation, where teacher and pupils are exploring the concept of 'volume'. Further, this analysis informs a discussion of listening as an important element of an inquiring learning conversation. [ABSTRACT FROM AUTHOR]

The theme of this special issue is risk. But risk is not a common topic of investigation in mathematics education, lest it be an occasional interest in “at risk” students, generally defined as those who likely will fail at school. In this study, we are not interested in this rather limited use of the risk concept. Instead, we show that risk not only is a condition of human life generally, but also a necessity for teaching and learning mathematics. To show this, we develop the concept of risk with materials from a second-grade mathematics unit on geometry. Implications are drawn concerning the particular forms of ethics that take into account the risk incurred by teachers and students when doing mathematics in the classroom. [ABSTRACT FROM AUTHOR]