Proceedings of the Day Conference held at the University of Southampton on 14 Jun 2014
Ayalon, Michal1; Watson, Anne1 and Lerman, Stephen2
1University of Oxford, 2London South Bank University
Little is known about the overall growth of students’ understanding of functions throughout schooling. We have been identifying the development of students’ understanding of concepts which contribute to understanding functions throughout the school in two different curriculum systems: in the UK and in Israel. In this paper we shall present some of the comparative findings and make conjectures about differences.
02 An intervention programme using fingers and games in primary classrooms to improve mathematical achievement
University of Bristol
In recent years studies have demonstrated the positive association between mathematics achievement and finger-based numerical representations of number where training in finger gnosis has led to gains in mathematical skills. An association between mathematics achievement and numerical magnitude processing has also been established and playing mathematical games has proved beneficial. The aim of the current study was to evaluate the effectiveness of an intervention combining finger gnosis training with games to see if it is more effective than either part alone. 133 children aged 6 – 7 years from five classes took part in the pre-test, intervention, post-test study. The classes were randomly assigned to different conditions: finger gnosis only, games only, full intervention and no intervention control. Results demonstrated that the pupils in the two full intervention groups made significantly more increases in mathematics achievement tests than those in the other groups. This suggests that the combined intervention using the visual representation of fingers and dot patterns acting as mediators could help children of this age to make connections between symbolic and non-symbolic representations of number and raise mathematical achievements.
03 What are prospective teachers’ considerations regarding their intended practice when management interferes with mathematical learning?
Biza, Irene; Nardi, Elena and Joel, Gareth
University of East Anglia, UK
What are prospective teachers’ considerations when they make decisions in situations where classroom management interferes with mathematical learning? In this paper, we present research that explores prospective teachers’ pedagogical and epistemological considerations in intended actions through their written responses to situation-specific tasks. Specifically, we introduce a type of task that addresses both mathematical learning and classroom management issues; and, we discuss the written responses of 21 prospective mathematics teachers to one of these tasks in which a student’s unease with Algebra is met with another student’s dismissive and offensive response. The analysis we present here observes a lack of balance in the participants’ responses in favour of behavioural issues and at the expense of epistemological issues.
Feng, Wai Yi and Kimber, Elizabeth
University of Cambridge
The Cambridge Mathematics Education Project (CMEP) aims to support and enhance A-level mathematics education. Funded by a grant from the UK Department for Education, the project began in October 2012 and is run by members of the University of Cambridge Faculty of Mathematics and of NRICH. The project is developing resources for teachers and students. Partner schools from across England have been recruited to work closely with the project team, trialling resources and giving feedback, and taking part in the internal evaluation of the project. We describe the CMEP pilot site and discuss some of the thinking behind the research and evaluation of the project, including the development of the evaluation questionnaire.
Hernandez-Martinez, Paul and Goos, Merrilyn
Loughborough University, UK and The University of Queensland, Australia
In this paper we report on a developmental design research study in an engineering mathematics undergraduate course, where previous attempts to increase participation had failed. We take ideas from socio-political theories to frame the teaching (re-)design and use a socio-cultural theoretical framework – where learning is seen as participation – to evaluate its impact. We collected data from students’ written feedback and used peer observation to reflect on and refine the teaching strategy and to analyse the students’ learning. Results showed a positive participation (although not all students engaged or liked the approach) and we discuss the implications of our results for Mathematics Education.
06 The views of pre-service teachers on the school-based learning component of their mathematics teacher preparation programme
University of Southampton
Teacher preparation is a highly contested area in England with a range of epistemological approaches potentially being promoted through the availability of a range of preparation routes. The dominant model of teacher preparation used by programmes led by university education departments is that of developing reflective practitioners. However, other models, including those coined as ‘craftworker’ and ‘executive technician’ in Winch, Oancea, and Orchard (2013), are increasingly promoted by government policy. Aspects of professional training such as learning from a more experienced mentor, learning as part of a ‘community of practice’ (Lave and Wenger, 1991) and the need for practical experiences are all characteristics that parts of teacher preparation share with models of vocational learning and with those in other professions. This paper seeks to explore some of the views of those on secondary mathematics teacher preparation programmes with regard to the characteristics of their school-based learning and their experiences on school placement. Data collected from those on a well-established university-led Postgraduate Certificate of Education programme is compared with that from those on a new school-led School Direct programme indicates some commonality of experiences and suggests possibilities for future work.
University of Oxford
Identity is becoming an increasingly important focus of mathematics education research. Most studies to date have focused on narrative accounts of students and have explored relationships between these and the learning of or engagement with mathematics. In this paper, I examine identity on a more micro scale through the in-depth analysis of classroom interaction. Drawing from ethnomethodology, discursive psychology and positioning theory I use a conversation analytic approach to explore how the identities of mathematics teacher and mathematics student are co-constructed in interaction, and how these identities evolve in the interaction.
08 Statistical literacy in subjects other than mathematics: an exploratory case-study with pre-service science teachers
School of Education, University of Sheffield, UK
This article describes part of a PhD study exploring how statistical literacy knowledge and skills may be transferred from mathematics to other domains, investigating the skills and dispositions of pre-service teachers. I report on an observational case-study of science student teachers on a postgraduate Initial Teacher Education (ITE) course, delivering a model lesson involving statistics to their peers. I discuss my initial investigation with reference to recent international research in the field, finding that the participants have a wide range of statistical knowledge and experience leading to mixed views and dispositions towards the application of statistics in science lessons.
09 An investigation of developing teachers’ understanding of using a dialogic approach in Saudi primary mathematics classrooms
University of Manchester
Classroom talk and dialogue is fundamental to students’ learning mathematics. Much research has focused on the ways teachers interact with their students and the quality of dialogue between them. Drawing on recent developments in dialogic approaches to learning and teaching mathematics, this study investigates how Saudi mathematics teachers develop their understanding of classroom dialogue through a professional development process in mathematics teaching. The study involves multiple case studies collecting qualitative data on i) teachers’ espoused beliefs about their teaching practice and dialogic teaching and ii) teachers’ enacted practices using dialogic teaching principles. The participants were three male primary mathematics teachers in third-, fifth- and six-grade classrooms. The paper utilizes an early analysis and discussion about a teacher named Ahmad as one case study.
University of Manchester
If the rhetoric of politicians is to be believed then the mathematical achievement of English school children is dire and declining or at best stagnating. Close scrutiny of the data reveals a complex picture that is not consistent with this simplistic political message. Drawing on England’s outcomes in PISA and TIMSS I attempt to illuminate some of this complexity. International comparisons also reveal interesting differences in practices between primary and secondary phases.
11 “It’s helping your child experience the world.” How parents can use everyday activities to engage their children in mathematical learning
Rose, Jo; Jay, Tim and Simmons, Ben
Graduate School of Education, University of Bristol
This paper presents the content and preliminary findings of the Everyday Maths project workshops for parents. Research suggests that support from parents and/or carers can have a significant impact on children’s mathematics learning. While parents are motivated to help their children learn, they often have little confidence engaging with mathematics as presented in the school curriculum. The Everyday Maths workshops were designed to help parents reflect upon and find the mathematics in their everyday lives, and support parents in developing conversations with their children around everyday mathematics. Workshops were run once a month in four primary schools in the Southwest of England, from November 2013 to February 2014. Preliminary findings suggest that through the workshops some parents were afforded opportunities to develop a ‘mathematical lens’ which led them to identify the mathematical reasoning underpinning decisions and actions in everyday life. This inspired parents to initiate conversations with their children about mathematics and construct activities which engaged children in mathematical thinking.
Bath Spa University and University of Bristol, Graduate School of Education
Having decided to write “Teresa’s Tale”, a narrative case study of one student’s journey through a Mathematics Enhancement Course, it was apparent that it would be impossible to retain anonymity due to the nature of the events to be described. This paper attempts to explore and resolve some of the ethical issues and conflicts encountered. In medical research, there is strict adherence to anonymity and clear guidance as to when this not only could, but also should, be breached. The situation is less clear in qualitative research scenarios, as it is not possible to guarantee anonymity totally in the first place and the situation is more complex as one moves towards narrative research where it is often the case that the research participant wishes to be identified in telling their story.
St. Patrick’s College, Dublin City University
The purpose of my research is to explore to what extent children in Irish primary schools are developing skills in algebraic reasoning. Generalisation has been identified as a highly significant component of algebraic reasoning (Carpenter and Levi, 2000; Kaput, Blanton and Moreno, 2008). Patterning plays a key role in supporting children’s developing skills in generalisation and internationally visual spatial patterns tasks have been utilised in many research projects to investigate children’s success in generalising (Radford, 2011; Rivera and Becker, 2011; Warren, 2005; among others). In this paper I discuss preliminary findings of research into the algebraic reasoning of children in Irish primary schools, focusing on generalisation strategies in response to visual spatial patterns. The research instrument I am using is the clinical interview. In assessing children’s ability to generalise, I am interested in exploring the reasons behind responses they proffer and the clinical interview is a research instrument which offers this facility. Through the method of clinical interviewing I investigate the participants’ responses to the patterns and ask them to consider near and far generalisations of the patterns. In this way I aim to develop “an interpretation or a series of interpretations” that may provide a new perspective on Irish children’s algebraic reasoning and in particular their thinking about generalisation (Ginsburg, 1997, p. 114).