Proceedings of the Day Conference held at Loughborough University, Saturday 11th June 2016
01 Tools, conceptions of mathematics and goals in undergraduate engineering courses: An Activity Theory approach
Marinos Anastasakis, Carol Robinson and Stephen Lerman
Mathematics Education Centre, Loughborough University, UK
In this paper we present and discuss the results of a survey from our investigations into the kind of resources that engineering undergraduates use, their conceptions of mathematics and their goals when studying mathematics. By adopting an Activity Theory perspective, we performed correlational analysis between the components of the basic mediational triangle: the subject (conceptions of mathematics), tools (resources) and the object (goals). We found that most of the students in our sample hold a cohesive conception of mathematics, that institutionally-led resources dominate students’ practice and that getting a high mark is the most popular goal among students. Correlations between the components of the mediational triangle were weak but yielded interesting relationships between the kind of resources that students use and the goals they set when studying mathematics.
02 Working atmosphere in the secondary mathematics classroom: When things do not work according to the lesson plan
Irene Biza, Elena Nardi, Athina Thoma, Lina Kayali, Tom Cook, Ed Hughes, Rebecca Wolsey, Gareth Joel and Manjinder Jagdev
School of Education and Lifelong Learning, University of East Anglia, Norwich
In this paper we focus on a collaborative research and development project in which a team consisting of secondary mathematics teachers (newly qualified and experienced), researchers in mathematics education (faculty and doctoral students) and mathematics teacher educators work together on how to achieve balance between creating opportunities for high quality mathematical thinking and attending to classroom management and behaviour issues. To this aim we deploy Haydn’s 10-point scale on the working atmosphere in the classroom. This construct was not devised specifically for the mathematics classroom and our study explores its potentialities for it: we ask whether a scale (Haydn-M) with mathematics specificity can provide meaningful insight into the working atmosphere in the secondary mathematics classroom. In this paper we provide examples suggested by newly qualified teachers in our team of such a mathematically specific use of the scale.
03 Developing frameworks for evaluating and researching the Shanghai mathematics teacher exchange: practices or assemblage
Sheffield Hallam University
There is currently much interest in ‘mastery’ pedagogies in mathematics in England. To promote teaching for mastery the government has funded an exchangeprogrammewith primary teachers and headteachers from 48 schools visiting Shanghai and/or hosting Shanghai teachers in 2014/15. Schools have, to varying extents, continued to both adopt and implement Shanghai practices. To support the longitudinal evaluation of the exchange a conceptual framework categorises aspects of practice in terms of systemic, school and classroom practices. This allows for change in specific practices in different schools to be compared and evaluation of the extent of implementation of Shanghai informed approaches. However, such an approach has limitations in understanding how different practices interrelate and the relational effects of changes. An alternative is to consider primary mathematics education as an assemblage.
04 Beginner mathematics teachers assessing advanced problem solving: what do they bring, what do they need, and how can the gap be bridged?
Jennie Golding and Cathy Smith
University College London Institute of Education
Secondary mathematics teachers in England are expected to develop teaching and assessment of problem solving in ways which have not been common in schools or initial teacher education in recent years. This study asked what beginner teachers bring to this process, including knowledge, skills and beliefs, and what should be further developed, in the specific context of problem solving for advanced school mathematics. It suggests that the intentions of the change are well-aligned with the professional beliefs of many both beginner and experienced teachers, and that carefully structured workshops can enable beginner teachers to re-envision practice, as well as to acquire specific assessment-related skills. However, acquiring deep expertise in the area is demanding, and perceived to be daunting for both beginner and experienced teachers.
Helen Harth1, Ian Jones2 and Irene Biza1
1Mathematics Education Centre, Loughborough University; 2University of East Anglia
This paper focuses on university lecturers’ planning of undergraduate statistics education. In particular, this study explored aspects of lecturers’ intended curricula such as how lecturers interpret the learning outcomes of statistics courses, their beliefs about specific topics, about teaching approaches and students’ learning of statistics at university. Interview data from interviews with twenty statistical methods lecturers using the repertory grid interviewing technique was used to identify the participants’ curricular goals and beliefs when planning their teaching practices. This data suggested a statistical reasoning curriculum that emphasised ‘basic’ statistical techniques and non-statistical skills, with an emphasis on content rather than intended learning outcomes. This paper discusses implications of the methodological approach and findings.
06 Prompting for progress: Using teacher voice for the implementation of Realistic Mathematics Education with low achieving mathematics students
University of Bristol
In teaching a group of low-achieving 14 and 15 year old students, I struggled to motivate them because they could not see the point of doing their General Certificate of Secondary Education examinations (GCSEs, taken at the end of compulsory education aged 16) when theywere only going to get the lowest grades. The work of Freudenthal and the Realistic Mathematics Education Group (RME) at the Freudenthal Institute provided an alternative way of doing things, allowing students to take away more flexible mathematical ideasto use beyond the classroom. My research question was, ‘How can we promote the use of more sophisticated methods by students?’ 4 teachers taught a series of lessons to their classes using the idea of realistic situations. From our group ‘teacher voice’ discussions a common theme was when to intervene to take conceptual thinking on, what we called ‘prompting for progress’.
Dietmar Küchemann1, Jeremy Hodgen1and Helen Konstantine2
1University of Nottingham; 2Barking Abbey School, London
Our current work with ‘low attaining’ Year 7 (age 11-12) and Year 8 (age 12-13) students suggests they tend to see multiplication in terms of procedures rather than structure. On the other hand, we have found that they can sometimes make insightful use of models of multiplication once they have become familiar with them. In this paper we report on interviews undertaken by the authors with students from a Year 7 ‘nurture group’, using various patterns. The students showed evidence of being able to construe the multiplicative nature of the patterns. Moreover, in comparing two blocks of 20 dots, they showed evidence of being able to see how the structure of one 20-block is embedded in the other.
Stephen Lee1, Anna Stevens2 Mark Boylan2, Sean Demack2
1Mathematics in Education and Industry, 2Sheffield Hallam University
Over the last decade there has been a marked increase in the number of students studying, and schools/colleges offering, A level Further Mathematics in England –14,298 entries across 1428 state institutions in 2015, compared to 5,627 entries across 762 state institutions in 2005. Mathematics in Education and Industry’s government funded Further Mathematics Support Programme (FMSP) has been influential in stimulating the increase. This paper draws on FMSP analysis and aspects of an independent evaluation (2014-16) by Sheffield Hallam University, including the creation of an ‘FM Security’ construct derived from School Census data1(2013-2015). Findings show a third of schools or colleges change status over this period. Concepts of organisational Further Mathematics capital are used to interpret the analysis. We reflect on reasons for these patterns in relation to the wider Further Mathematics education landscape, including recent policy/budgetary changes that threaten to reverse the positive trends in Further Mathematics.
Jinhua Mathias and Douglas Newton
From time to time, students are characterised as having a deep or shallow approach to learning. A deep approach to learning tends to attract more approval than a shallow approach, at least in the West. Students on a university-based Foundation course to prepare them for undergraduate studies were divided into those likely to have a deep approach (26) and those likely to have a shallow approach (18). Their performance in a test of problem solving in an aspect of applied mathematics was compared. Contrary to expectations, the test scores and interviews with the students indicated that those with a deep approach did not benefit when asked to apply their learning in new contexts, and those with a shallow approach were not markedly disadvantaged. It is suggested that, at least amongst learners, neither approach is likely to be entirely self-sufficient, but should be seen as acceptable starting points of potential routes to success. Although a small scale study, mathematics tutors should be able to relate the findings and suggestions to their own experiences and practices.
Manchester Metropolitan University
Education discourses and regulatory teaching standards governing pre-service teachers’ entry into the profession produce ambivalent conditions for how student teachers conceptualise the curriculum. The notion of mathematics mastery has been reactivated as a nodal orientation of collectively articulated ambitions in some quarters. I start from the premise that these motives are located within particular discourses: the need to comply with new directives, to achieve outstanding status, educate or get educated, and so forth. In this paper, I explore the discursive construction of the mastery curriculum with reference to Lacan’s notion of the master signifier. This analytical tool provides a framework for addressing the multifaceted discursive encounters towards disrupting habitual thinking patterns and opening alternative interpretations.
11 Factors affecting teachers’ participation in continuing professional development (CPD): the perspectives of secondary school mathematics teachers in Zambia
Maureen Kanchebele Sinyangwe, Berry Billingsley and Yota Dimitriadi
University of Reading
This paper focuses on secondary school mathematics teachers’ perspectives of factors affecting their participation in Continuing Professional Development (CPD). It makes use of findings from multiple data collection methods including questionnaire, face-to-face in-depth interviews and focus group discussions. The study was conducted in a selected district of Central Zambia. The factors affecting the teachers’ participation in CPD are discussed, along with the implications for CPD provision.
12 Not everyone talked about cats: learning from Year 5 learners’ responses to lessons using Numicon (a visual concept manipulative)
UCL Institute of Education, London and Firs Farm Primary School, Enfield
In upper Key Stage 2 (KS2) English mathematics classrooms, written work produced in response to questions in textbooks features prominently. Individual output,, is emphasized and mathematical artefacts, present in earlier school life, are absent . Through a piece of action research, the responses of 90 Year 5 children to one such artefact, Numicon, during and after 3 lessons about number, were considered. Though quantitative data was collected from the children, this paper focuses on conclusions drawn from the verbal responses of individuals, articulated immediately after each lesson, in semi-structured small-group interviews: these show Numicon use could still benefit Year 5 children. Crucially, its limited availability necessitates sharing of equipment thereby stimulating partnership and talk. Here, there is the potential for verbal thought exchange about mathematics which can enhance learners’ understanding. The complexity of enabling this to occur between pairs of learners in upper KS2 mathematics classrooms is discussed.
13 Could an iterative approach to relational and procedural tasks aid depth of understanding Mathematics?
Tupton Hall School
This paper provides an account of ongoing research undertaken as part of my Teaching A-Level Maths course run through Leeds University and Mathematics in Education and Industry (MEI). I chose to research a sequence of A-Level lessons (16-18 year olds) where I was re-teaching the topic of transformations of graphs as my students did not have a deep understanding of the concepts involved. Whilst undertaking the researchforthis topic, a supplementary question arose which is ‘When presenting tasks to learners designed to increase procedural skills and/or conceptual understanding, does the order in which they are taught matter?’ The research shows the students in question had a perceptible growth in their procedural and conceptual understanding of the topic. The ongoing aim of the research is to see how iteratively presenting tasks could aid cognition of mathematics at all ages and attainment levels.
14 Working Group report: Building and sustaining active research collaborations with teachers of mathematics
Alison Clark-Wilson and Geoff Wake
UCL Institute of Education and University of Nottingham
This BSRLM working group met for the second time to explore collaborations between teacher and researchers in the processes of doing, reflecting upon and engaging with the findings, of mathematics education research. This theme is considered within the current English educational context where Teaching Schools and DfE-funded Maths Hubs are being encouraged to participate in ‘research-informed’ practice.
Leo Rogers and Sue Pope
British Society for the History ofMathematics (BSHM); Manchester Metropolitan University
Despite the words: ‘Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems.’ in the Purpose of Study section, the new English mathematics curriculum alludes only to Roman Numerals in the primary programme of study, and there is no further mention of historical or cultural roots of mathematics in the aims, or in the programmes of study. In contrast, the increased expectations for lower and middle attainers in the new curriculum challenge teachers to make more mathematics accessible and memorable to more learners. The history of mathematics can provide an engaging way to do this. There arealsomanyopportunities in post-16 mathematics. Further to our recent articles on quadratic equations and trigonometry, we use functions to illustrate some of the ways that history of mathematics can enrich teaching of this topic.
Gill Adams and Hilary Povey
Sheffield Hallam University
In England, the neoliberal political agenda has created an environment in which teachers are constantly subjected to a discourse of marketisation, managerialism and performativity. It is also part of the neoliberal project to cut us adrift from our past and to de-historicise our lived experience of the present. We are suffering from what John Berger has called a sense of ‘historic loneliness’. Many teachers are engaged in re-storying themselves against this audit culture. We are currently exploring using stories from the past – in this case, recollections of Smile, a teacher-led mathematics curriculum project with roots in inner London in the 1970s – to combat this ‘historic loneliness’ and to create a space in which to understand, interrogate and oppose the dominant discourses. We have conducted extended interviews with groups of Smile teachers from an earlier era and are now looking at ways to make these data perform this potentially transformative function. In this workshop, we presented a small part of the data in three different ways – as edited transcript, as story and as aphoristic fragment – and invited participants to compare and contrast the effectiveness or otherwise of these forms of presentation.