Video analysis of mathematical practice? Different attempts to ‘open up’ mathematics for sociological investigation

In this article I argue that in contrast to a large number of sociological studies of laboratory practices in the natural sciences, there have been relatively few studies that have investigated professional mathematical practice. I discuss three different methodological attempts to "open up" advanced mathematics for sociological investigation: (1) LIVINGSTON's "demonstrative sociology"; (2) MERZ and KNORR-CETINA's "e-mail ethnography"; and (3) my own "video ethnography.

Visual grammar in practice: negotiating the arrangement of speech bubbles in storyboards

It is generally acknowledged that we live in an increasingly visual culture, populated with a variety of visual objects. Researchers have recently started to investigate the underlying regularities, the "visual grammar," according to which these objects are assembled. While most existing studies base their analysis on products (such as advertisements, movies or pages from newspapers), this paper studies the processes through which such products are assembled, thereby investigating visual grammar in practice. The particular objects analyzed are storyboards that were produced by secondary school pupils using a new computerized storyboarding tool as part of their engagement with Shakespeare's Macbeth. The paper focuses on situations in which pupils explicitly discuss and negotiate the placement of speech bubbles, thereby revealing aspects of the "meaning-effects" of such placements

From traditional blackboards to interactive whiteboards: a pilot study to inform system design

Interactive whiteboards are a new technology that has gradually found its way into classrooms. The aim of this study is to explore the potential of interactive whiteboards for the teaching and learning of mathematics. From field observations, videorecordings and interviews with a teacher this research develops a description of the teacher’s use of a traditional board, and discusses how the teacher perceives the potential of an interactive whiteboard

News interviews: Clayman and Heritage’s ‘The News Interview'

News interviews: Clayman and Heritage’s ‘The News Interview

Conversation analysis

Conversation analysi

The materiality of mathematics: presenting mathematics at the blackboard

Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body.As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of ‘mind’ and ‘body’. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics.The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an ‘architecture’ visualizing the overall structure of the proof). The paper argues that doing mathematics really is ‘thinking with eyes and hands’ (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics

Unpacking tasks: the fusion of new technology with instructional work

This paper discusses how a new technology (designed to help pupils with learning about Shakespeare's Macbeth) is introduced and integrated into existing classroom practices. It reports on the ways through which teachers and pupils figure out how to use the software as part of their classroom work. Since teaching and learning in classrooms are achieved in and through educational tasks (what teachers instruct pupils to do) the analysis explicates some notable features of a particular task (storyboarding one scene from the play). It is shown that both 'setting the task' and 'following the task' have to be locally and practically accomplished and that tasks can operate as a sense-making device for pupils' activities. Furthermore, what the task 'is', is not entirely established through the teacher's initial formulation, but progressively clarified through pupils' subsequent work, and in turn ratified by the teacher

Interactive whiteboards in mathematics education: possibilities and dangers

Interactive whiteboards are a new technology for ‘traditional’ teaching in the whole class. Although they have been installed in educational settings, the emphasis of research has been on their use in office settings. Preliminary findings from a pilot study of a mathematics teacher's use of a ‘traditional’ blackboard suggest that interactive whiteboards should not only be seen as a presentational device for the teacher, but as an interactive and communicative device to enhance the communication with and among students. In this paper, interactive whiteboards are placed within the wider context of Information and Communication Technology (ICT) as a tool for Computer-Supported Collaborative Learning (CSCL). The potential of interactive whiteboard is explored from the perspective of Requirements Engineering, a branch of computer science that aims to determine what properties a system should have in order to succeed. Drawing on this field, four steps for the design of technology in educational settings are specified and illustrated

Making rounds: the routine work of the teacher during collaborative learning with computers

This paper provides a detailed analysis of the work of the teacher during collaborative-learning activities. Whilst the importance of the teacher for the success of collaborative learning has frequently been recognized in the CSCL literature, there is nevertheless a curious absence of detailed studies that describe how the teacher intervenes in pupils' collaborative-learning activities, which may be a reflection of the ambivalent status of teachers within a field that has tried to transfer authority from teachers to pupils. Through a close analysis of different types of teacher interventions into pupils working in pairs with a storyboarding tool, this paper argues, firstly, that concerns of classroom management and pedagogy are typically intertwined and, secondly, that although there may be tensions between the perspectives of teachers and pupils these do not take the form of antagonistic struggles. The paper concludes that it may be time to renew our interest in the work of teachers in the analysis of collaborative-learning activities

Mathematical relativism: logic, grammar, and arithmetic in cultural comparison

Cultural relativism is supposed to be a bold and provocative thesis. In this paper we challenge the idea that it is an empirical thesis, i.e., one that is supported through anthropological and historical examples. We focus on mathematical relativism, the view that a mathematics from another culture or time might be so radically divergent from our mathematics that ‘theirs’ would stand in direct conflict with ‘ours’ (and in that sense constitute an alternative mathematics). We question in what sense the examples given to support the general thesis are relativistic about mathematics and argue that on close inspection they are not, and certainly not in any radical sense. We do not contest the fact that there can be great mathematical diversity between cultures, but wonder whether it makes sense to talk of ‘the same’ mathematical forms in heterogeneous mathematical environments. Finally, while relativists see the later Wittgenstein as providing support for their own thesis, we claim that Wittgenstein argues against both realism and relativism