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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 proposes an exercise of problematization and denaturalization of a math classroom that is born from research carried out with a cartographic approach, in which, when occupying the elementary school math classroom, questions are asked: what happens in a math classroom? Which mathematics happens in a classroom? The event is here in affinity with the philosophy of the event of Gilles Deleuze, in which event is that which cuts time off, drags it, breaks it. Events are possible worlds that erupt in the things that happen. To do so, the writing of this paper takes place in relation to an episode in a classroom, evoking events that involve mathematical production, "mistakes" and learning, experiencing engendering of learning in the learning process. This writing involves two problematizing movements: the first one unfolds the problem of connection between learning and teaching in mathematical education; the second one in which, by the force of the event in the math classroom, the connection between learning and teaching as something necessary is under suspicion since it suffers an inflection in tradition in and of a mathematical education. [ABSTRACT FROM AUTHOR]

In the present article, we undertook a systematic study of bibliographic review based on the discussions, in the academic scope, about the contribution of the Anthropological Theory of Didactic - ATD (Chevallard, 1992) linked to Mathematics teaching and learning processes. The purpose was to investigate the current appropriation of ATD in Stricto sensu researches in Brazil. It is worth mentioning that the present study refers to a part of a PhD thesis. Thus, we aim to present an overview of thesis and dissertations answering the following question: "What are the main programs, institutions and researchers in Brazil that have been working on ATD?" In addition, we developed a study on the investigation axes of the researches, classified as: I) Teaching: focusing on the teacher, II) Learning: the object being the student's learning and III) Analysis of documents: books, lesson plans, course projects. For this purpose, we selected as a corpus 69 dissertations and 37 thesis defended in the period from 2005 to 2017. [ABSTRACT FROM AUTHOR]

It is necessary to expand the analysis about affective processes in mathematic learning in different contexts. In Brazil this research area is still in the embryonic phase, but it is a space that has strong potential to respond the gaps that still exist in the field, leading to the understanding affective processes in mathematic learning. It is in this way that the present research aims to analyze how the mathematic learning difficulty is produced in the subjectivity of a child from the elementary school in Brazil. To understand how the student's development occurs in the school space, and how the difficulty is build, we took as a theoretical basis the Theory of Subjectivity by Fernando González Rey. The case study was a resource used in the constructive-interpretative process. The research was carried out in a public school in the Distrito Federal, Brazil. The mathematic learn difficulty, in this work, was produced by the research participant in different contexts, including, family, school and friendships. Several experiences and influences of the person generate subjective senses that will emerge in subjective configurations in often school activities, regardless if these subjective senses were produced in school or outside it. [ABSTRACT FROM AUTHOR]

In this paper, we highlight one whole-class discussion that took place in a middle school mathematics Rational Number and Proportional Reasoning course, one of the six mathematics courses teachers take to complete our state-wide middle school mathematics specialist program. Statistical measures indicate that teachers made gains in their understanding of concepts and substantial gains in their views of teaching and preparedness. We provide a microanalysis of one of the lessons, to explain, in part, how they might have made this progress. To develop our argument, we coordinate a social analysis with an analysis of the types of specialized mathematical knowledge that teachers might have considered as they engaged in these discussions. As we will illustrate, these types of classroom discussions provided teachers opportunities to consider new visions for mathematics learning and teaching. [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]

This study aims to characterise the pedagogical practices of 45 observed primary mathematics lessons taught by 24 mathematics teachers in six national primary schools (SK) and six Chinese vernacular primary schools (SJKC). The data were collected using two video cameras, one focused on the teacher while the other camera focused on the pupils' activities. The qualitative data were analysed based on two main activities in the classroom, which are teacher's activities and pupils' activities. The findings show that mathematics lessons conducted by SK teachers tended to engage the pupils in individual seatwork so as to assess pupils' understanding. Conversely, SJKC teachers were focused more on explaining mathematical concepts to help the pupils build up their conceptual understanding. By characterising the pedagogical practices of mathematics lessons in various schools, the researcher hopes that the findings of this study will contribute to better understanding of the teaching and learning process in SK and SJKC mathematics classrooms. The results serve as a documentation of pedagogical practices in Malaysia to enable implementation of suitable programmes to help in improving teachers' pedagogical practices from different types of primary schools. While the results are interesting and provide some directions, a much larger study would be needed to determine if the results are due to the teachers' enthusiasm, geographical differences, cultural or social differences, or what is known as the Hawthorne Effect. [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]