Proceedings of the Day Conference held at the University of Sussex on 09 Jun 2012
Contents
01 Pushing the boundaries: women teachers’ experiences of learning mathematics
Gill Adams
Liverpool John Moores University (Sheffield Hallam University from September 2012)
This paper reports on a research project exploring women mathematics teachers’ experiences of professional learning. Adopting a life history approach, data was gathered in semi-structured interview-conversations. Initial meetings focused on teachers’ experiences of learning mathematics and of learning to teach. The views and practices of their own secondary mathematics teachers emerge as significant both in terms of informing their A-level and career choice and acting as an important frame of reference when analysing their current teaching practice.
02 Students’ perceptions of assessment practices used in a Business and Industrial Mathematics module
Edmund Chadwick1 and Oana Radu2
1School of Computing, Science and Engineering, University of Salford
2School of Education and Lifelong Learning, University of East Anglia
Business and Industrial Mathematics at the University of Salford is a 20- credit second-year module in the mathematics undergraduate degree. It spans two semesters. Its novelty lies in the diversity of assessments and delivery modes used, such as open-ended problems, problem solving, group work, presentations, report writing, employer seminars and professional studies. This study aims to explore and present students’ perceptions of these various assessments and assessment practices.
03 How frequent are your eureka moments? A discussion of pace in mathematics education
Richard Cowley
Institute of Education, London
The research focused specifically on pace is scarce. The pace is raised in a range of literature in various ways as something for teachers to be concerned about yet it is an ill-defined quality. In this session, I presented texts for discussion with the aim of considering these questions: How is the term ‘pace’ used in representations of school classroom practice found in educational literature? What ways of representing school classroom practices are evident in the way the term ‘pace’ is used? What are the implications for continuing engagement with the notion of pace in mathematics education? Texts were drawn from inspection reports, historical reports and research.
04 Influences of friendship groupings on motivation for mathematics learning in secondary classrooms
Debra Deacon and Julie-Ann Edwards
University of Southampton, Southampton Education School
This small scale study examines the influence of friendship groupings in key stage 4 mathematics classrooms on students’ motivations to engage with mathematics. We use evidence from questionnaires and individual interviews to describe the motivational factors identified in two key stage 4 mathematics classes, and the influence of environmental factors on students’ understandings of their motivation to learn and their knowledge construction. Findings confirm the multi-faceted nature of motivation and suggest some gender differences in interpreting classroom relationships and differences between groups of close friends and those of friends by association. Our findings are interpreted in the context of mathematics classrooms organised by student levels of attainment.
05 Nurturing Possibility Thinking (PT) in mathematics education courses through experiential learning and the use of pedagogical constructs, and beyond
Els De Geest
The Open University
This paper reports on the Creative Thinking in Mathematics Education Enquiry (CTMEE) at The Open University. The study investigates whether the pedagogical approaches of experiential learning and the use of pedagogical constructs in an undergraduate distance learning mathematics education course can lead to creativity seen as ‘possibility thinking’ (Grainger, Craft and Burnard 2007). Data consist of 23 quantitative and qualitative responses from students to an on-line questionnaire. Findings suggest that such pedagogical approaches can indeed contribute to developing possibility thinking. However, it seems the more subtle task design within such approaches is equally crucial, which is reported in this paper.
06 What happens when you divide by 5? Divide what by 5?
Michael Hall
The Open University
This article developed through working with KS2 teachers from a primary school that had expressed a concern about mathematical attainment in KS2 classrooms. The article aims to explore the use of constructs, as labels, to identify and evaluate decisions, actions and events and the challenges involved in the process of developing powers of analysis and self-awareness to enhance teaching and learning. The wider perspective for this is the discussion of the impact of research on practice and of practice on research (Watson 2010), (Hoyles, Joubert and Pope 2012), (Advisory Committee on Mathematics Education 2006). This article is essentially an enquiry into the interplay between research and practice and informal action research, in the sense that some change in practice was considered desirable.
07 Teaching Assistants and intervention programmes in primary mathematics
Jenny Houssart
Institute of Education, London
This paper explores the experiences and views of Teaching Assistants in mainstream primary schools who are assigned to work with individuals or small groups using structured mathematics interventions. The use of such programmes is seen here as an aspect of curriculum implementation and comparison is made with literature concerning implementation of curriculum materials by teachers. The focus is mainly on whether assistants report the need to adapt the programmes, using the notion of fidelity and the categories of offloading, adapting and improvising (Brown 2009). The key finding is that most assistants can be seen as adapters, with variation in the type and extent of adaptation.
08 Measuring fidelity of mathematics intervention programme implementations in primary school settings
Fiona Jackson
University of Cambridge
This paper reports on selected findings of a doctoral study exploring varying implementations of a mathematics intervention programme. Most importantly, the research develops methods for measuring fidelity of implementation and identifying instances of positive infidelity.
09 From research to practice: making an impact?
Marie Joubert, Geoff Wake, Julian Williams, Sue Pope and Celia Hoyles
The University of Bristol, University of Nottingham; University of Manchester; Institute of Education
The working group has met four times at BSRLM to explore the relationships between research, practice and policy. The particular focus is on ‘impact’ – for example, the group is interested in ways in which research might make an impact by informing practice at the classroom, institutional and/or systemic level and influencing policy makers.
10 ‘I get the feeling that it is really unfair’: Educational triage in primary mathematics
Rachel Marks
Department of Education & Professional Studies, King’s College London
Reviews highlight the implications of ability-grouping in secondary mathematics, but knowledge of practices in primary mathematics is limited. My wider study (Marks 2012) suggests ability-grouping practices seen in secondary mathematics are mirrored in primary mathematics. One such practice is educational triage. This involves the direction of resources towards those most likely to benefit. This paper presents the outcomes and experiences of Year 6 (ages 10-11) pupils at ‘Avenue Primary’. It examines how educational triage is enacted and justified. Quantitative data highlights the academic outcomes of educational triage. Qualitative data illustrate the differential experiences of pupils.
11 A response to the JMC Working Group Report: ‘Digital technologies and mathematics education’
Peter Osmon
Department of Education and Professional Studies, King’s College London
A multi-layered model of STEM subjects extending upwards from mathematics to applications, with separate classical and digital branches (classical STEM is underpinned by continuum mathematics, digital STEM by discrete mathematics), is used to interpret the JMC Report. The Report recognises that today’s schoolchildren are wholeheartedly embracing the digital applications with which they are surrounded. But perhaps more significantly they are the first generation to grow up in a society being shaped by digital STEM, whereas their parents and their teachers have lived their lives in a classical STEM world. There is always a generation gap, but for this generation, a widening gulf separates teachers and pupils. The Report recognises a danger that school mathematics will seem like a dead language and suggests three remedial steps: bring digital technologies (such as Dynamic Geometry and Computer Algebra Systems) into mathematics classrooms, emphasise student-led modelling and problem solving, and include a programming language in the curriculum. In other respects, the Report is silent about curriculum content. The traditional mathematics curriculum emphasises continuum mathematics, but future generations will need more emphasis on discrete mathematics if they are to understand their world, model applications in it, and become application innovators.
12 A consideration of familiarity in Irish mathematics examinations.
Brendan O’Sullivan1, Sinead Breen1 and Ann O’Shea2
1St. Patrick’s College, Drumcondra; 2National University of Ireland, Maynooth
In this paper, we focus on the idea of familiarity and the differing levels of it that are apparent in Irish mathematics end of school state examination questions. We provide the results of an analysis of recent Higher Level and Ordinary Level Leaving Certificate mathematics examinations in terms of familiarity. Our findings do not indicate any particular recurring pattern evident in the levels of familiarity measured but generally not more than 20% of marks are allocated to unfamiliar questions.
13 May mathematical thinking type be a reason to decide what representations to use indefinite integral problems?
Eyup Sevimli and Ali Delice
University of Marmara
In this study, we focused on whether mathematical thinking type affects what representations to use indefinite integral problems. The participants were three of thirty-seven first-year undergraduate mathematics students who were selected through a purposeful sampling technique. Data collection techniques were tests and interviews. Tests were used for determining which students going to be selected for interviews and main data were collected by interviews. Results show that students’ mathematical thinking types have some effect on their representation preferences. On the other hand, it seems that students’ problem-solving behaviours are more affected by teaching processes than thinking types.
14 Mathematics teaching in the Seychelles: The challenges of reforming practices in a small developing state
Justin Valentin
Department of Education and Professional Studies, King’s College London
This paper is drawn from my PhD research which aimed at investigating the outcomes of a primary mathematics teaching reform in Seychelles. As part of the research, 4 primary schools were chosen for the fieldwork. In each school the following activities were achieved: (a) samples of mathematics lessons were observed followed by post-lesson interviews with the teachers, (b) a six-teacher focus group interview was held to gauge the teachers’ experiences enacting the reform, and (c) relevant documents were reviewed to acquire background data about the school and the reform. This paper is based on findings from the focus group interviews. The findings revealed that the reform benefited the implementers’ practices, but the schools were challenging sites for pedagogical reform. The results have implications for teacher in-service education and policy making on pedagogical reforms.
15 Observing changes in teachers’ practice as a consequence of taking part in professional development: developing a protocol for the observation of lessons
Steven Watson and Sheila Evans
University of Nottingham
In this paper, we will describe the development of a system for lesson observation. This system has been designed to be used to observe changes in teachers’ practices as a result of taking part in professional development (PD). The PD promotes and supports secondary mathematics teachers’ use of inquiry-based learning and problem-solving. Many approaches to the evaluation of PD rely on the assessment of changes in teachers’ thinking and beliefs, largely because of the complexity and difficulty of analysing practice. As part of a design-based research study, we are developing an observation protocol that allows the rapid analysis of a number of lessons. This involves identifying the lesson structure as an arrangement of episodes. In this way, we are able to code episodes and identify changes in the nature and structure of the lesson. In this paper, we will describe the ongoing development work and the system that has been developed and trialled so far.