Proceedings of the Day Conference in November 1999
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University of Bristol
The learning of mathematics by additional language learners is an underresearched area withIn mathematics education. In this paper, an initial exploratory study of an additional language learner 1!1 the UK is described. Consideration of the learner’s vocabulary of addition shows that during the study, he relies almost exclusively on the word “plus”. This raises important questions regarding the learning of mathematics by such students.
Katrina Daskalogianni and Adrian Simpson
Mathematics Education Research Centre, University of Warwick
This study concerns upper sixth-form students’ attitudes towards mathematics and the influence these attitudes have on their mathematical behaviour. Interviews with A-level students, conducted before their final exams, explored their belief;, previous experiences and, in solving a general problem, their initial mathematical behaviours. The analysis suggests thar attitudes towards mathematics are the product of students’ beliefs about mathematics and of their previous experiences with it and that this attitude has a strong influence on their behaviour.
Sheffield Hallam University
Audio-taped discussions between three students have been examined to shed light on the way in which the behaviour of individual students may affect the shared construction of meaning. These discussions revealed a complex pattern of interaction between the students. Each student was responsible for defining his or her own role within the discourse and these roles appeared to change as the discussion progressed with reference to the framework offered by Winbourne and Watson (1998), it is proposed that local communities of practice have been established and that the individual student’s positioning within the community of practice determines their success as a learner and contributes towards the creation of shared knowledge.
University of Edinburgh
The value practical work has long been recognised at the primary level. Many teachers acknowledge the value of learning by ‘doing’ rather than just being shown or told. There is also evidence to suggest that studying mathematics in context helps to increase motivation and develops modelling and problem solving skills. Despite these benefits, practical activities are rarely used in secondary mathematics classrooms. Most teachers attribute this to time constraints. An investigation into the role and implementation of practical work for older pupils has been initiated in co-operation with the Centre for Mathematics Teaching at Plymouth University. We have gathered a number of practical activities on a theme of parabolas for use with secondary school pupils. We are studying pupil and teacher attitudes and comparing male/female, urban/rural and Scottish/English responses. The ethnographic/illuminative evaluation methodology will be used.
University of Warwick
This paper is a description of the methodology used for my research in the context of science education, in particular the way that science PGCE students develop understanding about science teaching. The set of basic beliefs that guides the research is the Phenomenographic approach. This paper will give a review of literature about Phenomenography. It will consider the origins, the form and the nature of reality, the relationship between the knower and what can be known, and the characteristics of the research process. The approach is applicable in many fields, including science and mathematics education, where it is required to study phenomena and how they are experienced, conceptualised or understood. Phenomenography also defines new problems for enquiry in educational settings.
London University Institute of Education
This paper provides evidence of a long-standing shortfall in the supply of fully qualified mathematics teachers in English secondary schools and suggests that the situation is deteriorating. The selection of applicants for courses leading to Qualified Teacher Status (QTS) is discussed with particular reference to one secondary mathematics PGCE course. Rates of achievement of QTS among those accepted for initial teacher education (ITE) in secondary mathematics are examined in the light of small scale qualitative research among the same groups of PGCE students. The concluding discussion highlights issues for consideration by mathematics educators.
Mundher Adhami, David C. Johnson and Michael Shayer
School of Education, Kings College London
Lessons with written guidance are planned according to generalised empirical or theoretical typical expectations in the target age group. In practice the teacher must always make adjustments according to the particular responses of their own pupils. In CAME lessons success in topic work is not an objective in its own right but rather the context for reasoning activity. Hence the adjustments to lesson plans often involve resolving tensions, at various levels, between misconceptions in the topic agenda on the one hand and related unplanned deeper reasoning activity on the other. In this paper scenes of interactions of a group of Y5 pupils around a mathematical reasoning task involving tessellation concepts are discussed with the aim of eliciting possible teaching strategies that responsively accommodate pupils’ difficulties through pupil-pupil and teacher-pupil interactions, while optimising their progress towards handling the main challenges.
University of Bristol
There seems to have been little work aimed at understanding the process of learning mathematics when the predominant classroom language is not the learner’s first language. This paper reports an exploratory study using the concepts of paradigmatic and syntagmatic axes of language to analyse interaction recorded while two English Additional Language learners sorted mathematical words. There is evidence that these learners may learn mathematical language in syntagms.
9 The anatomy of a bid: from TTA to ESRC – looking at the developing algebraic activity in 4 year 7 classrooms
Laurinda Brown and Alf Coles
University of Bristol, Graduate School of Education
The starting date of our ESRC small grant project was 1st October, 1999 and is titled: Developing algebraic activity in a ‘community of inquirers’. The successful ESRC bid uses an enactivist theoretical framework and methodology. The enactivist framework is discussed, particularly illustrating how our ideas have developed over time. especially from a TTA Teacher Research Grant, and how the theoretical frame links to the methods used. We are developing methodologies for describing the complexity of teaching and consider the research to be transformative for the researchers, but continue to ask ourselves what are the research products for such a framework?
10 An investigation on the effect of homework on pupil gains in an assessment of numeracy in the first year of the Leverhulme Numeracy Research programme
Hazel Denvir, Valerie Rhodes, Margaret Brown
Mike Askew, Dylan Wiliam and Esther Ranson
School of Education, King’s College London
A range of data was collected from the 73 Y4 classes which participated in the first year of the Leverhulme study (1997-1998). This included teacher questionnaire, pupil data, classroom observation and teacher interview. These data are being matched to the mean class gains which pupils made between October and June in an assessment of numeracy. In this paper we report our findings relating to one aspect, homework, explored in the Teacher Questionnaire and match these to class mean gains in the assessment.
11 Being a teacher and doing research: reflections on the primary Cognitive Acceleration in Mathematics Education (CAME) project
Sally Dubben, Croydon LEA
Jeremy Hodgen, King’s College London
Ann Longfield, Croydon LEA
In this paper we will explore the development of two Thinking Maths lessons as part of the primary Cognitive Acceleration in Mathematics Education (CAME) project. The focus of this paper is on the experiences of two of the authors, Sally Dubben and Ann Longfield, as teacher-researchers. We explore the lesson development as a collaborative process between university researchers and teacher researchers both in the classroom and in research team seminars. We believe this collaboration between academics and teachers to be a crucial element in linking theory and practice. In addition we seek to convey the excitement that teachers and children feel about the lessons.
As an aim for the classroom, raising self-esteem is a noble one, although difficult to quantify. What are identifiable are those activities that help children feel good about themselves and their mathematical activity. Within the context of a secondary school for boys with emotional and behavioural difficulties, some mathematical activities will be discussed from the perspective of the teacher/researcher and the pupils. The aim of this session is to explore the link between mathematical activity and selfesteem.
This work arises from interviews with key stage two teachers who were shown a task based on the Fibonacci sequence and asked ‘whether they would use it’ with their current class or mathematics set. Mentions of the word ‘pattern’ and related ideas were extracted from the resulting discussions and considered in more detail. The word ‘pattern’ was used fairly frequently, though with differing degrees of enthusiasm. There were also differences in whether teachers felt all children could be helped to see patterns, with a tendency to regard pattern spotting as a top set activity.
Peter Huckstep and Tim Rowland
Homerton College, University of Cambridge
In this paper, we examine notions of ‘creative’ that might apply to mathematics and to mathematical activity. Our motivation to do so has been our discussion of the meanings of ‘creative’ which seem to be applied or implied in Upitis, Phillips and Higginson (1997). Our general approach is philosophical, drawing on literature which considers creativity in the arts, in mathematics and in educational settings. We question the tendency of some promoters o0f mathematics to justify mathematics by annexing it to the arts, and examine whether different kinds of criteria for creativity apply to mathematics.
15 Maths knowledge and understanding of primary student teachers: initial findings from a 2 year study
Adrian Pinel Jeni Pinel
University College Chichester Independent Researcher
This is an initial report about a project that arose from the recognition that the mathematics knowledge and understanding of some trainee primary teachers did not match up to the 4/98 requirements. The key areas and the nature of the challenges faced were identified through preliminary research, portfolio trialling, operating a ‘drop-in’ numeracy support centre, and feedback from current year 3/4 students. The project, run by AP [with JP’s support] is linked to a ‘parent’ project group. It is based upon students using the project and its materials to categorise their needs in each content section according to 3 levels of support. Strategies employed are face to face workshops and input sessions, through to multiple choice, self-assessment and distance study materials. The results to date have been very encouraging in certain respects, though the ‘electronification’ and ‘distancing’ of relevant study materials remains a challenge. The researchers are currently involved in further developments.
Stephanie Prestage and Pat Perks
School of Education, University of Birmingham
In this paper we offer a brief discussion of a model created for considering aspects of subject matter knowledge necessary for teaching mathematics where personal subject matter knowledge and professional content knowledge of teachers are mediated by deliberate reflection in order to create a more fluid and connected personal understanding of mathematics needed for the classroom (Prestage and Perks, 1999a and 1999b) . These ideas are further developed to show how they might be used for analysing the pedagogy of teacher educators.
Convenor: Keith Jones, University of Southampton, UK
A report based on the meeting at the University of Warwick, 13th November 1999 by
Catia Mogetta, University of Bristol
Federica Olivero, University of Bristol
Keith Jones, University of Southampton
A major challenge for mathematics education is to find ways in which proof in geometry has communicatory, exploratory, and explanatory functions alongside those of justification and verification. Ongoing research is suggesting that providing students with tasks which state “prove that…” might actually inhibit students’ capacity for proving. In contrast, open tasks which favour a dynamic exploration of a statement and encourage the use of transformational reasoning may allow students to reconstruct, in terms of properties and relationships, all the elements needed in the proof. In this report we consider the transforming of closed problem into open ones and discuss the use of dynamic geometry software, such as Cabri, in such a process.