Richard Barwell

Patterns of attention in the interaction of a primary school mathematics student with English as an additional language

This paper presents a preliminary analysis from a study designed to investigate the participation of students learning English as an additional language(EAL) in primary school mathematics. A key question for the study concerns how such students make sense of mathematics classroom interaction. Primary data consists of two transcripts in which a 9-year-old EAL student works on a word problem task with a monolingual peer. The discursive analysis explores the two students use of patterns of attention in their interaction. The analysis describes three patterns of attention: attention to narrative experience, to the genre of word problems and to the mathematical structure of their problems. These patterns of attention are used in the process of the two students sense-making together in ways which support the participation of the EAL student.

Ambiguity in the mathematics classroom

Mathematics is commonly seen as a discipline with no place for linguistic ambiguity. In this paper, the treatment of ambiguity in two data extracts is critically examined. Analysis draws on two contrasting models of the nature of mathematics and mathematical language. The formal model sees meaning as fixed and relating to language relatively unproblematically. The discursive model sees meaning as situated in and by interaction, and so as shifting and changing as interaction unfolds. Analysis of the extract from the National Numeracy Strategy suggests that it is based on the formal model. This analysis is contrasted with analysis of classroom interaction which reveals how, from a discursive perspective, ambiguity can be seen as a resource for doing mathematics and for learning the language of mathematics.

Working on arithmetic word problems when English is an additional language

There has been little research in the UK into how students learning English as an additional language (EAL) learn mathematics. This article reports results from a three-year study of the participation of learners of EAL in Year 5 in an arithmetic word problem task. The research, drawing on ideas from discursive psychology, used discourse analysis to explore patterns of attention in students interaction as they worked in pairs or threes. The article briefly describes four patterns of attention: to genre, to mathematical structure, to narrative experience and to written form. Further analysis explored how students used attention as part of the social activity involved in working on the task. The rest of the article illustrates how students used attention to narrative experience to make links between word problems and their own experience, as well as to negotiate their relationships with each other.

Discursive Psychology and Mathematics education: Possibilities and challenges

This paper provides an overview of some of the key ideas of discursive psychology and its theoretical and methodological approach to the analysis of interaction. These ideas include a view of interaction as discusive practice, primarily structured by the social action it performs, rather than by its content. The relevance of this approach to research in mathematics education is demonstrated, drawing on extracts from transcripts of mathematics classroom talk. The paper concludes by considering how discursive psychology may be developed within research mathematics education.

Language in the Mathematics Classroom.

Mathematics is a central part of school curricula around the world. There has been much interest in linguistic aspects of the teaching and learning of mathematics, both from mathematics educators and from applied linguists. This short paper introduces a set of five articles exploring the intersection between these two communities. The articles all discuss two texts: an extract from the guidance issued to primary school mathematics teachers in the UK; and an extract from a primary school mathematics lesson. This paper begins by summarising some of the research on language in the mathematics classroom, before introducing the two texts.

Empowerment, EAL and the National Numeracy Strategy

This paper concerns the relationship between learning English as an additional language (EAL) and school mathematics. In bilingual education, Cummins has proposed a distinction between coercive and collaborative power-relations as an important consideration in the education of such students, advocating collaboration as a means to empower such students, and so enable more effective learning. In this paper, I explore these ideas through a discursive examination of two texts: extracts from the National Numeracy Strategy (NNS) concerning EAL; and extracts from a transcript of two EAL students working on a mathematics classroom task. My analysis highlights the multilayered nature of collaborative and coercive powerrelations within mathematics classrooms.

Mathematics education in culturally diverse classrooms

. Monologism is associated with a formalist perspective on social interaction, with communication seen as a kind of exchange that takes place between individuals. Dialogism, by contrast, is practice-oriented, and sees communication as an ongoing process of negotiation between people and contexts (see Linell 1998, p. 6-8). The roots of dialogism can be traced back to Bakhtin (e.g. 1986), for whom meaning emerged from the interplay of voices. Alro and Skovsmose (2002) apply the distinction between monologism and dialogism to different perspectives on learning. For example, they associate monologism with Piaget’s learning theory, by which they mean:

A DISCURSIVE PSYCHOLOGY APPROACH TO THE ANALYSIS OF ATTENTION IN MATHEMATICS CLASSROOM INTERACTION

The notion of attention as a discursive practice has emerged as a key element of my approach to the analysis of students participation in mathematics classroom interaction. The principal purpose of this paper is to describe and illustrate this approach, which draws on ideas from discursive psychology and conversation analysis and sees talk primarily as a form of social action. It is a principle of conversation analysis that what we say indicates something that we are attending to in that moment. Discursive psychology suggests that the way we use words, reflects the social actions in which we are engaged. By looking at what students attend to, and then at how this attention is rhetorically deployed, insights emerge into how students think together.