Making mistakes is part of learning mathematics but these mistakes can be handled in many differe... more Making mistakes is part of learning mathematics but these mistakes can be handled in many different ways which in turn can lead to the process of making mistakes and learning from them very different. Using the conversation analytic idea of repair, and the associated preference organisation of repair, the implicit messages that the handling of mistakes can give is revealed. This structure around the preference organisation of repair is used by many teachers to encourage students to offer explanations and justifications that are a fundamental part of learning and doing mathematics.
The Interactional Treatment of Mathematical Mistakes
In this paper we will explore the role of errors in both the teaching and the learning of mathema... more In this paper we will explore the role of errors in both the teaching and the learning of mathematics. Analysis of classroom interactions show that mathematics teachers are implicitly treating errors as something to avoid despite commenting on the positive role they have in the learning of mathematics. Similarly, the students themselves treat errors as something to be avoided. This leads us to consider, and therefore explore, what possible roles errors may have in the learning and teaching of mathematics.
Conversation analysis offers an inductive approach to the analysis of classroom interaction. With... more Conversation analysis offers an inductive approach to the analysis of classroom interaction. With its roots in ethnomethodology, conversation analysis is underpinned by some key principles that focus on how the learning of mathematics is made visible through teachers’ and students’ interactions. Using the tools developed by conversation analysts, the structures and patterns of interaction within mathematics classrooms can be described to reveal what it means to learn, and what it means to do, mathematics in school classrooms. This approach foregrounds what teachers and students themselves treat as learning and doing mathematics and reveals the multifaceted role of interaction in these processes.
Opportunities and challenges of classroom- based research on mathematics and language
This report is a summary of the questions, comments and issues brought up in the ETC4 panel of th... more This report is a summary of the questions, comments and issues brought up in the ETC4 panel of three expert researchers on mathematics and language. The purpose of this panel was to discuss: (1) What do we mean by the language of the learner, of the teacher and of mathematics? (2) What are today the opportunities and challenges of classroom-based research on mathematics and language? The major recommendations and position statements included: (i) Develop more nuanced theoretical frameworks for the understanding of the politics of language use in the mathematics classroom (ii) Re-evaluate conceptualizations of languages and speakers in terms of distinctions, differences, dichotomies and difficulties (iii) Conduct more language-related design research for teaching and learning of specific mathematical content areas.
The achievement gap between disadvantaged students and others has received considerable attention... more The achievement gap between disadvantaged students and others has received considerable attention from politicians and the press. School performance tables, which are used to rank schools, now include measures of this gap. Results from this study show that using alternative measures of the achievement gap would have a considerable impact on the position schools hold in these tables. Combining measures has allowed schools to be identified that are differentially effective for disadvantaged students in mathematics.
Trying to improve communication skills: the challenge of joint sense making in classroom interactions
In this paper we examine the efforts of one teacher working to improve her students' communic... more In this paper we examine the efforts of one teacher working to improve her students' communication skills as part of a collaborative project with teachers and teacher educators/researchers. The paper reports on a project meeting where the teacher presents a short video clip featuring two student explanations. Yet only one explanation is treated in the lesson as an example of good communication. Following discussion and multiple re-viewings of the video clip in the meeting, what counts as good communication is critiqued by the teachers. Driven by an emphasis on the two-way nature of communication, the need for joint sense-making between teacher and students, and privileging explanations that communicate mathematical understanding, alternative teacher actions are suggested during the meeting that are related to how different teachers interpreted the students' explanation.
Classrooms are all about thinking, knowing, and understanding. Epistemic issues are at the core o... more Classrooms are all about thinking, knowing, and understanding. Epistemic issues are at the core of classroom interactions, yet teachers and students, as well as researchers, can treat knowing, thinking, and understanding in very different ways. Claims and demonstrations of knowing or understanding can achieve different actions in classroom interaction, which result in different meanings for what it means to know mathematics or understand mathematics in different classrooms. This negotiation of mathematical knowing or understanding is a theme of classroom interaction that needs further exploration.
Classroom interaction has a significant influence on teaching and learning mathematics. It is thr... more Classroom interaction has a significant influence on teaching and learning mathematics. It is through interaction that we solve problems, build ideas, make connections, and develop our understanding. This book aims to describe, exemplify, and consider the implications of patterns and structures of mathematics classroom interaction. Drawing on a Conversation Analytic approach, the book examines how the structures of interactions between teachers and students influence, enable, and constrain the mathematics that students are experiencing and learning in school. In particular, the book considers the handling of difficulties or errors and the consequences on both the mathematics students are learning, and the learning of this mathematics. The various roles of silence and the treatment of knowledge and understanding within everyday classroom interactions also reveal the nature of mathematics as it is taught in different classrooms. The book also draws on examples of students explaining, ...
Revisiting the roles of interactional patterns in mathematics classroom interaction
[email protected] The ways in which teachers and students interact about mathematic... more [email protected] The ways in which teachers and students interact about mathematics in lessons can be more powerful in influencing learning than the materials and resources that teachers use. Interactional patterns structure all interactions and there are many such patterns that occur frequently in mathematics lessons. This paper focuses on one such pattern, the funneling pattern, which is widely discussed in the literature. Three distinct examples described in the literature as a funneling pattern are examined in order to examine the different roles sequences of closed questions can have and the opportunities these patterns can provide or constrains to students in the learning of mathematics.
In pursuing the writing and presenting of ‘autonomous’ conference texts –i.e., conference texts f... more In pursuing the writing and presenting of ‘autonomous’ conference texts –i.e., conference texts functioning in terms of meaning making on their own–, all authors deal with issues of reduction, transformation and representation of the concepts and contexts of initiation and development of their research. In this introduction, we point to challenges tied to the writing and presenting of language-sensitive mathematics education research for communication in conference formats. We discuss some ideas for the improvement of current guidelines and standardised decisions relative to processes and texts produced within the CERME culture. Drawing on experiences provided through our roles as co-leaders of the ‘Mathematics and Language’ thematic working group (TWG09), along with the insights gained from the TWG09 set of papers and posters on the occasion of CERME11, each of us brings a focus to the discussion of challenges and changes that might be feasible and worthwhile.
The nature of mathematics, the nature of beliefs about mathematics and what it means to learn mat... more The nature of mathematics, the nature of beliefs about mathematics and what it means to learn mathematics have long been discussion points in mathematics education (Thompson 1984; Boaler, Wiliam and Zevenbergen 2000). The research discussed in this paper focuses on what is said in the classroom during whole class teaching episodes. Using transcripts from two secondary mathematics teachers, we examine how the learning of mathematics is discursively constructed by the teacher and his/her pupils. This conversation analytic approach uses only the content of the interaction to describe the nature of mathematical activity in that interaction. We cannot directly access the beliefs of teachers and pupils, but an examination of how they talk about mathematics reveals how the learning of mathematics and classroom mathematics can be jointly constructed by a teacher and his/her class in quite different ways.
Making mistakes is an essential aspect of learning mathematics, both for the teacher and for lear... more Making mistakes is an essential aspect of learning mathematics, both for the teacher and for learners. Teachers are generally encouraged to use students’ mistakes as teaching points particularly in order to expose common misconceptions. However, teachers use a wide variety of interactional techniques to avoid directly and explicitly negatively evaluating a student’s mistake during whole class interactions. This gives the implicit message that mistakes are embarrassing and problematic (Seedhouse, 2001). So, whilst teachers may explicitly state that making mistakes is part of learning mathematics, interactionally they are saying that they are problems and are to be avoided.
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