Proceedings of the Day Conference held at the University of Bristol in June 2009
Contents
Research reports
01 Teachers’ use of language in teaching mathematics in Basic Schools in Cape Coast, Ghana
Alfred Ampah – Mensah
University of Bristol
In this paper, I present the initial analysis of data collected on how teachers in two basic schools in Cape Coast use language in teaching mathematics to classes four and six pupils and why they use language the way they do. I present an overview of initial findings from classroom observations, semi formal interviews and stimulated recall interviews with three teachers. The data revealed that English is the preferred choice of language for classroom interaction despite pupils’ limited proficiency in the language. This was largely due to teachers’ perception that English was the language of mathematics and schooling in general.
02 Researching Effective Continuing professional development in Mathematics Education (RECME) Findings: professional development and student change
Jenni Back and Marie Joubert
University of Plymouth and University of Bristol
This paper presents some of the findings of the Researching Effective Continuing professional development in Mathematics Education (RECME) Project which was set up to investigate, amongst other things, the role of research in ‘effective’ CPD for teachers of mathematics. It is generally agreed that changed student behaviour and more particularly improved student learning is the ultimate goal of professional development for teachers of mathematics. The focus of this paper is on some of the findings of the RECME project in relation to student learning. The paper gives examples of the ways in which involvement in the professional development initiatives encouraged teachers to talk about student learning. The implications of these findings for designers of professional development opportunities for teachers are discussed.
03 Generalisation and perceptual agility: How did teachers fare in a quadratic generalising problem?
Boon Liang Chua and Celia Hoyles
Institute of Education, University of London
This study examines the perceptual agility and strategy use of 27 prospective secondary school teachers in Singapore when solving a quadratic generalising problem. The data showed that the teachers were very capable of employing a variety of strategies to visualise the same pattern in different ways, resulting in not only a diverse range of equivalent rules but also some creative visual representations of the pattern structure.
04 The ethics of learning within the research process
Alf Coles
Graduate School of Education, University of Bristol, UK and Kingsfield School, South Gloucestershire, UK
In this paper I explore some implications of taking a virtue theory approach to ethics within classroom-based research. I argue that an ethical dilemma arises around the gaining of informed consent at the very beginning of a relationship with a new class; to the extent that it is not ethical to engage in such research until a classroom culture is established. I argue, secondly, that ethical behaviour as a practitioner-researcher in the classroom is an issue pertinent to every decision, not just something to address at the start of a project. I draw conclusions about ways of developing ethical expertise.
05 A study of primary student teachers’ mental calculation strategies
Sue Davis
University of Leicester
Ten years after the introduction of the National Numeracy Strategy, in a major review of the teaching of mathematics in Early Years settings and primary schools, Williams has called for a refocusing on oral and mental maths in order to particularly benefit under-attaining groups of children (DCSF 2008). One major aspect of this ‘oral and mental’ area of mathematics is for children to know a range of mental calculation strategies and be able to choose and use the most effective method for any given calculation (DfEE 1999). In this paper I discuss the findings of an initial pilot study into the strategies used by five student teachers, and the impact of my intervention on their practice in school.
06 Representational strategies of students with difficulties in mathematics: responses to a ‘Cartesian product’ problem
Carla Finesilver
Institute of Education, University of London
This paper explores aspects of representation in students’ responses to a ‘Cartesian product’ problem presented in story form (Nunes and Bryant, 1996), and is based around multimodal data taken from my current doctoral research project, including scans, photographs and transcriptions. Twelve students were in KS3 mainstream education, one in KS4, and had been identified by their mathematics teachers as the lowest-attaining in their respective year groups, displaying significant difficulties with mathematics. No task-specific materials were provided, but paper, coloured pens and multilink cubes were available for students to use if they wished. Representational strategies included colourful pictorial depictions of the items, physical models both with and without movement into different configurations, and some abstract notations. I am currently developing a framework for analysis, with aspects to be addressed including the level of abstraction found in each of the representations, the ease with which students chose or created strategies, identification of any changes in representational strategy that took place during the task, and the types of support that students required for successful task completion.
07 Engagement, abstraction and visualisation: Cognitive and emotional aspects of Year 2 mathematics undergraduates’ learning experience in Abstract Algebra
Marios Ioannou and Elena Nardi
University of East Anglia, Norwich
Abstract Algebra is considered by students as one of the most challenging topics of their university studies. Our study is an examination of the cognitive, social and emotional aspects of mathematics undergraduates’ learning experience in Abstract Algebra. Our data consists of: observation notes and audio-recordings of lectures and group seminars of a Year 2 course; student and lecturer interviews; and, coursework and exam papers. Here we offer some observations on the students’ apparently diminishing engagement over the ten weeks of the course. Particularly we exemplify from their comments on the effect that the abstract, not easily visualisable nature of Abstract Algebra has on their relationship with the topic.
08 The influence of parental aspirations on students’ dispositions to study further mathematics in Higher Education
Irene Kleanthous and Julian Williams
University of Manchester
The influence of parental aspirations on adolescent students’ dispositions to study further mathematics in Higher Education (HE) has not been investigated thoroughly. The aim of this PhD study is to investigate students’ perceptions of parental influence on their dispositions to study further maths both quantitatively and qualitatively. A scale was designed to measure students’ perceived parental aspirations, motivation to learn mathematics and maths self-efficacy. The questionnaire was distributed to 300 students in Cyprus and the statistical results indicated that parental influence was not statistically significant (p=0.98). Moreover 22 students’ perceptions of parental influence were examined through individual interviews. We argue that parental influence is subconscious and we draw on Bourdieu’s concepts of habitus and capital to discuss the findings.
09 The effect of real world contextual framing in A-level sequence questions
Chris Little
University of Southampton
This paper provides a preliminary analysis of data from a study into the effect of real-world contextual framing in A-level sequence questions. Alternative versions of the same questions were presented in explicit, algebraic, word and pattern contexts, and set to a sample of 594 Year 13 students (aged 17-18) in a one-hour test. Facility levels of the questions were then compared. In addition, the paper presents results of a student questionnaire on real-world context which accompanied the test.
10 Activity theory in mathematics education
Iskra Nunez
Institute of Education, University of London
Cultural-Historical Activity Theory (CHAT) has been described as a ‘psychological and multidisciplinary theory with a naturalistic emphasis that offers a framework for describing activity and provides a set of perspectives on practice that interlink individual and social levels’ (Barab, Evans and Beak, 2004, 199-200). In this report, I argue that CHAT provides a set of assumptions by which to understand and explain learning processes that occur for example in the mathematics classroom. This argument hinders on a review of the historical development of this framework. I close this report by bringing together some of the assumptions that underlie my future research in mathematics education.
11 The maths A-level curriculum from a university viewpoint
Peter Osmon
Department of Education and Professional Studies, King’s College London
It is proposed that the purpose of mathematics at A-level is to lay down a mathematical foundation for quantitative degree courses. From this viewpoint the consequence for universities of the present modest numbers of students taking maths at A-level is described and options for increasing these numbers are considered. Also from this viewpoint, the ACME and QCA proposals for reforming maths A-level curricula are reviewed. Adoption of a Free Standing Maths Qualification in statistics as an entry qualification for quantitative degree courses unable to demand A-level is identified as a priority.
12 Analysing the relationship between teacher’s cognitions: differences and similarities in the teaching modes of two primary teachers
Carlos Miguel Ribeiro
University of Algarve, Portugal
The teacher’s cognitions (goals, beliefs and knowledge) have a major role in their practice. Through the exteriorization of those cognitions – in action – teachers reveal their perspective and how they envisage the teaching process. To study these cognitions, the relations between them and the way they are exteriorized (type of communication, resources and pupils way of work) a model has been elaborated. For such teaching process I focused on the practice of two primary teachers and, from the analysis of that practice, using the model, it is possible to frame the teaching modes of each teacher. In this paper I will present, briefly, the modelling process and discuss the teachers cognitions (focusing in goals and beliefs) identified in the cluster of episodes presenting the content. I will make a first approach to the discussion of the similarities and differences in the teaching modes of the two teachers in that specific cluster.
13 Why do parents help their children with maths?
Rosemary Russell
St. Peter’s Comprehensive School, Bournemouth
My PhD research, ‘Parents Helping Their Children With Mathematics’, (Russell 2002), illuminated the hitherto unresearched ‘hidden’ help that parents give their children with maths – in other words, help that is initiated by parents themselves, without prompting from school or researchers. Help of this kind is behind closed doors, in the privacy of the home, away from the view of schools and researchers. The research established that the practice exists; that without prompting from school or researchers, parents do help their children with maths, and the practice is more widespread than had previously been acknowledged. It identified new aspects of why and how parents help with maths. In this paper, I shall discuss the methods I used to research this topic. I shall be reporting on some of my findings by focusing on answering the question: Why do parents help their children with maths?
14 Contrasting pre-service teacher education and school practice in two countries
Sunderlik, J.
Constantine the Philosopher University in Nitra, Slovakia
In this article, I will present two contrasting mentor meetings and some approaches to exploring the development of mathematics pre-service teachers during their student teaching. I am trying to identify themes for both countries, Slovakia and UK and discuss the influence of pre-service teacher development in different cultural settings.
15 Paired ITE teaching placements: Implications for partnership development
Paul Wilson; Julie-Ann Edwards
University College Plymouth; University of Southampton
This paper describes outcomes from a project designed to maximise the potential of paired placements for secondary mathematics ITE students We explore the development of models for effective pairings and provide the rationale for these models. Evidence is offered from interview data from paired students, analysed against Maslow’s hierarchy of needs, from one of the institutions and from evaluations from paired students from the other institution. Practical implications of managing paired placements are identified and discussed.
16 BSRLM Geometry working group: Geometrical reasoning in the primary school, the case of parallel lines
Nathalie Sinclair and Keith Jones
Simon Fraser University, Canada; University of Southampton, UK
During the primary school years, children are typically expected to develop ways of explaining their mathematical reasoning. This paper reports on ideas developed during an analysis of data from a project which involved young children (aged 5-7 years old) in a whole-class situation using dynamic geometry software (specifically Sketchpad). The focus is a classroom episode in which the children try to decide whether two lines that they know continue (but cannot see all of the continuation) will intersect, or not. The analysis illustrates how the children can move from an empirical, visual description of spatial relations to a more theoretical, abstract one. The arguments used by the children during the lesson transcend empirical arguments, providing evidence of how young children can be capable of engaging in aspects of deductive argumentation.
17 Working group on trigonometry: meeting 2 (Cambridge, February 2009)
Notes by Anne Watson
Department of Education, University of Oxford
These notes record the discussion at the second meeting of this working group. The focus was on the fundamental ideas involved in trigonometry and a programme of work was devised.
18 Working group on trigonometry: meeting 3
Notes by Anne Watson
Department of Education, University of Oxford
These notes record the discussion at the third meeting of this working group. The focus was on feedback from tasks undertaken since the last meeting.