Proceedings of the Day Conference held at University of Bristol, November 1997
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1 Mathematics as Social Practice: An Investigation into Primary Student Teachers’ Responses to Mathematics
University of Brighton
“Public” concerns about standards of attainment in mathematics in UK primary schools have led to the development of a National Curriculum for ITT. Such a curriculum is founded on the belief that teachers’ subject knowledge is an essential ingredient for successful teaching. Simplistic responses to teachers perceived lack of mathematical knowledge include provision of more inputs of the same kind. This article questions whether the adoption of a social practice model with its explicit acceptance of maths education as a socio-cultural, ideologically constructed process and acknowledging the complexities of learning, teaching and schooling is an attractive alternative worthy of further exploration with potentially significant pedagogical implications both for student teachers and their future classroom practices.
Ruth Barrington, Cathy Hamilton, Tony Harries
Bath Spa University College
The teaching and learning of Mathematics (and in particular number) has been afocus over a long period of time. This matter has been highlighted in a number of recent reports (Ofsted, 1993,1994, Burghes 1996, and Bierhoff 1996), which have suggested that there are a large number of low attainers in Mathematics. During the last year we have worked with Key Stage 2 teachers as they focus on developing the numerical capability of pupils who they deem to be lowattainers. Much _research has concentrated on the errors that these children make as they perform operations. With these teachers we have been working on the meaning that pupils bring with them instead of using an error analysis approach. In this paper we discuss the way in which pupils work with numbers while performing addition and subtraction calculations.
Sheffield Hallam University
This paper sets out to describe a background in socio-cultural theory and ideas of conviction and proof which can be used both to analyse and inform the classroom use of dynamic geometry. The particular context is the use of the TI92 hand-held computer with 12 year old children in comprehensive schools in the UK Conclusions are drawn about the dialectic in which conviction/proof is reached, and the role of mediation by teacher and software in that dialectic.
Bath Spa University College
Various studies have indicated the difficulty that low attaining pupils have with the object/process nature of mathematical entities. It is further suggested that their ”process focus” hinders mathematical development. Using a case study approach I have bee” working with 13/14 year old pupils and probing the way that they operate in both a number environment and a Logo environment. For both of these environments I will share/discuss some pupil episodes and draw some conclusions about the way in which they work with the object/process duality.
5 Does ‘CAME’ Work? Summary Report on Phase 2 of the Cognitive Acceleration in Mathematics Education (CAME) Project
David Johnson, Mundher Adharni, Michael Shayer
King’s College, University of London
The CAME project aims to contribute to pupils’ achievements and teachers’ professional development by basing classroom practice on research and theory – applicable research. Three major sources are drawn upon: a) research on levels of achievement in mathematics; b) Vygotskian psychology and social constructivism as exemplified in the recent literature on classroom cultures; and c) Piagetian/neo-Piagetian theories on levels of reasoning. These sources have been integrated to provide a theoretical foundation for teacher intervention and pupil-pupil interaction in the early years of secondary school mathematics aimed at increasing pupils’ intellectual development. Findings from the research indicate that the intermediate aims have been achieved – an increase in classroom interactions and significant improvements in pupils’ attainments.
University of Bristol
The present study seeks to explore the complex relationship between teaching and learning that takes place in Malaysian mathematical classroom settings. Specifically, the study investigates the relationship between teachers’ pedagogical content knowledge, instructional classroom practice and students’ learning with a particular focus on the teaching and learning of ratio and proportion. The research is still on going and this paper briefly. outlines some of the findings. The preliminary results indicate that in Malaysian classroom settings, students’ approaches to solving ratio problems varied considerably from formal to informal strategies. This finding highlights the need for wariness when interpreting the relationship between teaching and learning as teachers and students are complex human beings in a classroom setting that carries many different aspects.
Oxford Brookes University
An understanding of how children learn the very early stages of mathematics requires us not just to look at the children’s understanding but also the interaction that happens in the classroom as they learn. This paper discusses a single teaching session in a Reception classroom and analyses it from a social constructivist theoretical framework. In it I argue that the children can be seen to construct their own mathematical understanding and that knowledge of the social context in which they do so is crucial to our understanding of how they learn.
Roehampton Institute, London
Reference to the historical development of mathematics has been widely used in discussions of the problems students have in learning mathematics and the devlopment of concepts in the individual. This paper examines the basis for these claims in the interpretations of the history of mathematics that are current in the literature, the universality of the supposed concepts, and the use of the “principle of parallelism ” where indivudual development is claimed to mirror the historical development of the subject matter. The conclusion is that the majority of these claims are basically unsound, and that what we learn from the history of mathematics is that the richness, complexity and variety of human endeavour in this field is much greater than hitherto supposed. Consequences are drawn which challenge some of the fundamental tenets of Piagetian epistemology.
9 The Socratic Method of Strategic Questioning to Facilitate the Construction of the Target-Concept within the Students Zone of Proximal Development
University of Plymouth
Many A-level examination boards have included a modelling approach in mechanics that demands a qualitative treatment of physical phenomena. The majority of students, however, have ‘misconceptions’ of force and motion that are resilient to change. It has become clear that if students are to develop a qualitative understanding of force and motion that is Newtonian, then a massive cognitive reorganisation is required. This paper will report on the Socratic method as a teaching strategy that challenges ‘misconceptions’ and facilitates the construction of the Newtonian system within the students zone of proximal development.
University of Bristol
A group discussion was conducted with four teachers and excerpts from the transcripts of the discussion were presented in this session. The aim of the discussion was to draw out certain aspects of their assessment practices and for the researcher to consider how the teachers were using intuition in these practices. The excerpts were discussed in the session and participants’ views on the important points made will be used in the researcher’s continuing work on this subject. The session also considered points from writers on intuition to illuminate our understanding of intuition in this context.
11 The Rhetoric and the Reality Behind the Standards Debate: How Progressive or Traditional are Mathematics Lessons?
Ian Wood, Mike Ollerton
University College of St. Martin, Lancaster
The debate on the ‘Standards of Mathematics Teaching’, the methods teachers deploy and the re!>ulting affect upon childrem’ learning of mathematics is omnipresent. Much rhetoric is written about progressive and traditional approaches and how one or the other fails to help children leam mathematics effectively. Headline!> regularly appear, in the press and in international reports about the standards of mathematics teaching in this country, and teachers are left with the task of trying to unravel why it i!> that children are, seemingly, less skilled in comparison with children from past generations and from other countries
In this paper we set out to explore the reality of some aspects of this debate. We also consider the feasibility and desirability of engaging in debate which labels and polarises methods of teaching and seeks to simplify highly complex issues related to the teaching of mathematics. In particular we looked at the organisation of classes into mixed-ability or setted groupings, the types of resource used and, the proportion of lesson time used for whole class, teacher exposition and for students to work individually.
Convenor: Keith Jones
University of Southampton
The release of a videotape of typical geometry teaching in Japan and the US allows a comparison to be made of the teaching methods typically employed. While the typical US lesson emphasised skill acquisition, the typical Japanese lesson focused on the solving of complex problems through pupil exploration and presentation.