Teachers’ professional practice conducting mathematical discussions (original) (raw)
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The challenge of mathematical discussions in teachers' professional practice
Didacticae, 2017
We seek to identify patterns of action in mathematics teachers' classroom practice regarding class discussions and to determine how these actions provide learning opportunities for students. The study is based on a framework that focuses on two key elements of teaching practice: 1) the tasks that teachers propose to their students and, 2) the way they handle classroom communication. Qualitative methodology is used with data collected from video recordings of a grade 6 class that is studying rational numbers. We conclude that challenging situations usually require teacher preparation and follow-up with supporting/ guiding and informing/suggesting actions so that the students can learn what is involved in the teacher's motivations.
Mathematical Thinking and Learning, 2008
Teachers who attempt to use inquiry-based, student centered instructional tasks face challenges that go beyond identifying well-designed tasks and setting them up appropriately in the classroom. Because solution paths are usually not specified for these kinds of tasks, students tend to approach them in unique and sometimes unanticipated ways. Teachers must not only strive to understand how students are making sense of the task but also begin to align students' disparate ideas and approaches with canonical understandings about the nature of mathematics. Research suggests that this is difficult for most teachers . In this paper, we present a pedagogical model that specifies five key practices teachers can learn in order to use student responses to such tasks more effectively in discussions: anticipating, monitoring, selecting, sequencing, and making connections between student responses. We first define each practice, showing how a typical discussion based on a cognitively challenging task could be improved through their use. We then explain how the five practices embody current theory about how to support students' productive disciplinary engagement. Finally, we close by discussing how these practices can make discussion-based pedagogy manageable for more teachers.
Students discussing their mathematical ideas: the role of the teacher
Mathematics Education Research Journal, 2011
This article adds to current research on enhancing student discourse in mathematics teaching specifically in secondary schools but with equal relevance to elementary schools. Three mathematics teachers in secondary education were confronted with the question of how to encourage students to discuss their work with each other in the daily practice of their mathematical lessons. In response to this question the teachers devised three different approaches to encourage student discourse. One of the teachers chose to experiment with another setting to perform mathematical tasks that involved students working together on a group test. The second teacher experimented with a new kind of help when students were working on their maths tasks and asked for assistance. The third created a new setting in which the teacher (temporarily) did not provide mathematical hints and the students had to solve their own problems. The three teachers were very motivated, but they all had difficulties in not giving explanations themselves when supporting their students in their collaborative mathematical learning. They found that temporarily diminishing their product help stimulated discussion between students. It also became clear that the process of teacher reflection and follow-up discussions with the researcher/observers promoted changes of practice.
2011
This article adds to current research on enhancing student discourse in mathematics teaching specifically in secondary schools but with equal relevance to elementary schools. Three mathematics teachers in secondary education were confronted with the question of how to encourage students to discuss their work with each other in the daily practice of their mathematical lessons. In response to this question the teachers devised three different approaches to encourage student discourse. One of the teachers chose to experiment with another setting to perform mathematical tasks that involved students working together on a group test. The second teacher experimented with a new kind of help when students were working on their maths tasks and asked for assistance. The third created a new setting in which the teacher (temporarily) did not provide mathematical hints and the students had to solve their own problems. The three teachers were very motivated, but they all had difficulties in not gi...
2019
In this paper we investigate how a group of six mathematics teachers in Greece deals with the need to balance work on mathematically demanding tasks and differentiation in lesson planning and enactment. Videotaped lessons and pre and post reflection interviews were analysed with a specific focus on whole class discussion. The findings show certain teaching practices that appear to promote both mathematical challenge and differentiation and emerging patterns of actions that make the challenge accessible to students.
Teachers' use of productive questions in promoting mathematics classroom discourse
The focus of this study is to investigate how teachers use productive questions to promote discourse in the mathematics classroom. Teachers are faced with a myriad of challenges and make use of productive questions that are geared towards stimulating and promoting mathematics classroom discourses and seeking solutions to problems. Teachers also require a deep understanding of both knowledge of mathematics and how students learn mathematics. The video-recorded footage of one lesson of a high school mathematics teacher was the basis for this study. This video-recorded lesson demonstrating classroom discourse involving student-teacher interactions through questions and answers was transcribed verbatim and analysed interpretively. An analysis of the classroom discourse in the recorded video serves not only as an analytic tool to study classroom interactions, but also as a resource for discussions and reflections on the teacher’s continuous professional development (CPD) activities. The findings of the study show that the teacher made use of a range of productive questions to direct students towards solutions; he also involved students in completing procedural processes, provided opportunities for students to demonstrate solutions to their peers, made visible their thinking processes, and encouraged them to assist one another, through peer-to-peer interaction, to find solutions.
Constructing mathematics in an interactive classroom context
Educational Studies in Mathematics, 2009
This paper investigates the nature of the interaction between the teacher and students as they worked on different mathematics activities in a single classroom over a 10-month period. Sociocultural theories and the Vygotskian zone of proximal development provide the main framework for examining the teaching and learning processes and explaining the incorporation of a four-phase lesson plan as increasing participation of the teacher and students in the teaching and learning process. Drawing on the analyses of discourse from videotaped lessons and the interviews with the teacher and students, five different types of interactions that emphasized mathematical sense-making and justification of ideas and arguments were identified. Excerpts from transcriptions of such interactions are provided to illustrate the learning practices, either academic or non-academic, that students developed in response to these interactions.
Beyond Exhortations Not to Tell: The Teacher's Role in Discussion-Intensive Mathematics Classes
Pressing for more than curricular change, the current mathematics reforms place an unprecedented emphasis on students' mathematical communication and discourse. These visions of mathematics classrooms imply substantial changes for the teacher's role. Unlike much of their own past experience and practice, teachers are urged to open the classroom to student talk. In small and large groups, students are to present their ideas and solutions, explain their reasoning, and question one another. Accustomed to being the source of knowledge, and doing most of the talking, teachers now must refashion their role in ways that responsibly and effectively shift more authority and autonomy to students. The challenge to the teacher has not gone unrecognized by reformers, 1 and yet, we argue, that the teacher's role in this new vision of classroom learning has been underconsidered. Some people seem to believe that teachers should never tell students anything or that students will learn...
Transforming Pedagogical Practice in Mathematics: Moving from Telling to Listening
International Journal for mathematics teaching and learning, 2010
The research reported in this article is part of a larger study that examines an initiative to expand teacher expertise in facilitating mathematical problem solving within the framework of developing and field-testing pedagogical resources. We focus on one year of the study and report on the complex process of professional development as teachers move from traditional pedagogies of teacher explanation of mathematical operations followed by student practice to a pedagogy of teacher and student exploration of number operations within a problem-solving environment. We see that, in this initiative, teachers, consultants, and professional developers explored new mathematical and pedagogical ideas, creating a collective that provided a supportive environment that served as a model for classroom settings where teachers and students, in turn, investigated mathematical ideas. International Journal for Mathematics Teaching and Learning 1 Transforming pedagogical practice in mathematics: Movin...