Proceedings of the Day Conference held at Durham University on 06 Jun 2015
Philip Borga and Dave Hewittb
aUniversity of Malta; bLoughborough University
Through examples from the early stages of a study with Grade 7 low-attaining learners from Malta using Grid Algebra, we argue for the significance of actions, pictures and symbols in learners developing concepts for formal expressions. The interrelationship between these forms the basis of the CAPS (Concept, Action, Picture and Symbol) framework as an analytical tool, which is presented in this paper.
University of Reading
The importance of providing students with challenge has become entrenched in our understanding of learning, set down as the first teaching standard and sought by Ofsted. But what do we mean by challenge? Challenge implies a testing task, a result of struggle. While struggle may be a path to learning for some, reproducing Piaget’s idea of cognitive conflict as the precursor of change, I would argue that for many children mathematical struggle is not stimulating but threatening, and leads to the phenomenon of mathematics anxiety. This paper uses my doctoral research of six intervention sessions with each of four small groups to illustrate the reaction of low-attaining students to challenge. I find that the learning of algebraic concepts is hampered by feelings of panic and low self-esteem, and that the more challenging the material, the less appropriate the response. Improved results were achieved by reinforcing and developing students’ understanding of unchallenging material, corresponding to Bryant’s belief that confirming evidence is better for learning. The significance of this for teachers is to recognize that challenge is not universally positive, but developing unchallenging material by stealth can be preferable.
03 Students’ perceptions of A-level Further Mathematics as preparation for undergraduate Mathematics
As part of a large project involving over 4,000 Science and Social Science undergraduates, 928 undergraduate mathematicians took part in an online questionnaire. Participants were surveyed regarding their experiences of studying Further Mathematics, motivations for doing so, and the extent to which A-level study had prepared them for their undergraduate course. Participants were positive about Further Mathematics, describing it more favourably as preparation for undergraduate study than the single A-level Mathematics. This research suggests that university admissions tutors and schools should consider at least encouraging prospective undergraduate mathematicians to take Further Mathematics – even if it is not a requirement for entry to their chosen universities – in order that they can be better-prepared for future study.
Sue Gifford1, Jenni Back2 and Rose Griffiths2
1University of Roehampton, 2University of Leicester
This paper summarises the initial findings of the Nuffield funded project ‘Making numbers’, which aims to develop guidance for teachers of children from age three to nine on the use of manipulatives to support the learning of arithmetic. A survey of teachers found they used manipulatives more with younger children and lower attainers of all ages. The literature review considers the history of manipulatives and suggests that a fruitful way of using them is to exploit their ambiguity by relating alternative representations. Key pedagogical factors are also identified.
Karadeniz, Mihriban1; Baran, Tuğba2; Gökçek, Tuba3 and Aydin Güç, Funda1
1Giresun University (Turkey); 2Kirikkale University (Turkey); 3Karadeniz Technical University (Turkey)
The current study aims to present the distribution of the middle school mathematics Turkish teachers’ exam questions in terms of Bloom’s cognitive process and knowledge dimension as well as the question types. Additionally, it will prove if there is statistically difference on the questions’ placement in the Revised Bloom’s taxonomy with the question types. In the study, 10 middle school mathematics teachers’ exam questions posed during the first semester of the 2013-2014 academic year were analysed. A total of 77 exam papers were reviewed in the study and the total of 1152 questions from these papers were examined separately. A chi-square test was used to determine whether the cognitive process and knowledge dimensions of the questions were statistically different by question types. The results gained from the study reveal that mathematics teachers usually prepare questions at the lower cognitive dimensions of the Bloom Taxonomy. According to chi-square test results, there was a significant difference between knowledge dimensions of the questions as well as the question types. Besides, there was also a significant difference between cognitive process dimensions of the questions and the question types.
06 The transition from High School to University Mathematics: Messages interpreted by first year mathematics students
Loughborough University, Mathematics Education Centre
This paper reports on a pilot study of a project that seeks to investigate the different discourses that surround teaching and learning interactions during the transition to university mathematics. The focus is to study the different messages that first-year mathematics undergraduates receive within the university community, how they interpret these messages according to their individual backgrounds and previous experiences and how this facilitates or hinders their transition.
Carol Knights and Stephen Lee
Mathematics in Education and Industry
An innovative course focusing on extension and enrichment for Key Stage 4 teachers in England was conceived and created by Mathematics in Education and Industry (MEI). This was made possible by a successful bid for funding from the Department for Education (DfE) following a tender for a more far-ranging Further Mathematics Support Programme (FMSP). The initial creation and implementation of the national programme utilised existing research findings to inform the structure and design of the course. This resulted in a two-day course, with the two days separated by a gap of 8-12 weeks, where opportunity was given to use skills and materials from the course. This paper outlines the processes involved in setting up the programme in 2012 and reports on the evaluation of it over 3 years.
08 Developing instructional and pedagogical design for the Cambridge Mathematics Education Project: A Design-based research approach
Louis Major, Steve Watson and Elizabeth Kimber
University of Cambridge
This paper details how the Design-based research (DBR) methodology is being used to support a sub-component of the Cambridge Mathematics Education Project (CMEP). It is set in the context of on-going research taking place at the University of Cambridge’s Faculty of Education. This involves the development of instructional and pedagogical design to support and enhance mathematics education. An introduction to both DBR and CMEP is provided while details of the developed research strategy are outlined. This is followed by an overview of data collection activities completed to-date and planned activities.
09 Constructing a dialogic teacher’s identity: a case study exploring the impact of community of practice.
University of Manchester
Drawing on recent developments in dialogic approaches to learning and teaching mathematics, my PhD study investigates how Saudi mathematics teachers develop their understanding of classroom dialogue through a professional development process in mathematics teaching. The nature of this study is qualitative. It involved an embedded case study focusing on a teacher development programme (TDP) for three Saudi primary mathematics teachers in relation to their use of dialogic teaching. This research draws upon the community of practice theory (Wenger, 1998). The analysis of data shows how the three math teachers’ identities have been developed through their participations within the emergent community of practice. This paper will show evidence of the emergence of a new professional identity for one teacher Zayed as one case study.
10 The CAPTeaM Project (Challenging Ableist Perspectives on the Teaching of Mathematics): A preliminary report
Elena Nardi1, Lulu Healy2 and Irene Biza1
1University of East Anglia, UK; 2Universidade Anhanguera de São Paulo, Brazil
According to the ableist world-view, the able-bodied are the norm in society, and disability is an unfortunate failing, a disadvantage that must be overcome. Within education, ableism results in institutional and personal prejudice against learners with disabilities and has a drastic effect on approaches to teaching. Our project investigates how ableist perspectives impact on the teaching of mathematics, a quintessential part of the curriculum, and a discipline where public perceptions of ability as innate often shape pedagogical perspectives and practice. Our focus is on mathematical faculties typically associated with visual and auditory perception. In this one-year project, we are establishing a partnership which combines Nardi and Biza’s Task design approaches to investigating and transforming teachers’ beliefs about mathematics and about teaching in the UK and Healy’s research with mathematics learners with disabilities. We are developing and trialling tasks that invite teachers to reflect upon the challenges of mathematics teaching in inclusive classrooms. In this paper we focus on one task; and, discuss emerging analyses of the data we have just completed collecting.
Manchester Institute of Education, University of Manchester
This paper presents a joint early stage analysis of data from a doctoral pilot study and the Mathematics for Education and Industry (MEI) funded ‘core maths’ project, which explored the contextualization of real-life problems in the teaching and learning of mathematics in post-16 core maths classrooms. The study considers the ‘criticality’ or ‘criticalness’ of students’ intuitive mathematical reasoning on problem-solving real-life problems through dialogue generated between students, and teachers during lesson study sessions. Bakhtin’s philosophical orientation concerning dialogue and difference, captured in a methodological application called ‘dialogism’, offers significant insights to classroom discourse. To Bakhtin, dialogue, as an antidote to monologism, generates a difference and, as a consequence has the potential to expand students’ capacity to cross individual borders. Case study data was collected from two sixth form schools and an FE college, with real-life context mediated pedagogy as the overarching research theme. Initial findings suggest that dialogism and dialogical pedagogical practices in this context have the potential to develop students’ critical mathematical thinking (CMT).
Sheffield Hallam University
Beliefs that students hold towards their intelligence have been shown to affect their orientation towards learning. In situations considered challenging, those with incremental views have been shown to exhibit adaptive motivational patterns whereas those with entity views have been shown to exhibit maladaptive motivational patterns. This qualitative exploratory study focuses on the extent of incremental and entity beliefs amongst a group of 26 Kenya secondary school students. Analogical diagrams by students, written protocols and participant observations were used to provide a contextualised perspective on predominant intelligence beliefs amongst the students as postulated by Dweck’s theory of intelligence. This research suggests that most of the students held the theory that their intelligence for mathematics is innate and fixed.
University if Bristol and John Cabot Academy
I link the concept of mathematical resilience, as introduced by Johnston-Wilder and Lee (2010), to the emotional and affective issues that a student might have with mathematics. My main research questions are:
- What can we do as teachers to engender the positive emotions associated with mathematical resilience?
- Does having more time explicitly ring-fenced for the development of learning and thinking skills have a positive impact on mathematical resilience?
- Is there a case for making a distinction between long-term and short-term mathematical resilience?
I gained insight into these questions by focusing on a case study of 2 of the classes I taught in an 11-18 school in the UK. I videoed each class looking for evidence of the use of thinking skills and mathematical resilience (or its absence) and then selected 3 students from each class to interview. Thus my research methods fell into the case-study model described by Burgess (1990) as the ‘multi-site case-study’ (p.5), whilst trying to describe some ‘paradigmatic cases’ as described by Freudenthal (1981, p.135).
Faculty of Education, University of Cambridge
Prior research has shown how ideas about ‘rational man’ and media images of male mathematicians can create an environment in which doing mathematics is ‘doing masculinity’ (Mendick, 2006). This report re-visits the intersection of gender and mathematics, highlighting a form of ‘physical’ masculinity that is opposed, rather than aligned, to mathematics. The analysis draws primarily on thematic analysis of interviews with three low socio-economic status (SES), ethnic minority Year Nine (age 13-14) boys in New Zealand. I argue that colonial images of Maori (indigenous) and Pacific men as physically but not academically talented are still evident in these students’ narratives about school mathematics.
15 Does adding Mathematics to English language learners’ timetables improve their acquisition of English?
Chesterfield College/Sheffield Hallam University
This enquiry based project set out to find out if adult English language learners, known as ESOL (English for Speakers of Other Languages) learners in the UK, might benefit, in terms of their acquisition of English, from studying maths. This research has been conducted at a medium sized FE college in the East Midlands where I teach. I evaluate this in two ways, firstly by analysing learners’ results, and secondly by asking experienced ESOL teachers to observe and reflect on an ESOL Maths session. This project found a correlation between attending a maths class and improved English language exam results over 5 cohorts of students. In addition, ESOL teachers noted many and varied opportunities for English language learning in an ESOL Maths class, with higher levels of learner participation and confidence than seen in language classes. I recommend that we offer ESOL maths to ESOL learners, and that we reassess maths teaching for all learners, ESOL and English speakers, as a triad: conceptual understanding, procedural competence and language acquisition.
16 Using a Single-Subject Design to Examine the Effectiveness of a Mathematical Instructional Activity
University of Roehampton
This article examines a single-subject research design as a means to assess the effectiveness of an instructional activity in mathematics. Research from the special educational needs field commonly uses a single-subject research design to examine the effectiveness of instruction because the unique nature of individuals’ special educational needs means that there are a limited number of comparable participants. This article examines the strengths and weaknesses of this research design for use in mathematics education research by referring to a research project in which I used this design to assess the effectiveness of an instructional activity for developing base-ten concepts in students with dyslexia. I then propose additions to this design that make it more explanatory and therefore more useful for examining students’ learning.
Manchester Metropolitan University
The 2014 primary mathematics National Curriculum for England refers to mastery; a nebulous concept. This paper reports on pilot lesson observations to explore whether the Knowledge Quartet is a useful tool for both observing classroom teaching for evidence of mastery and also for understanding the Discourses drawn on by teachers in their interpretations of mastery. It concludes that the KQ is a useful heuristic but that a grounded approach will be more appropriate for this study.
David Wright, Jill Clark and Lucy Tiplady
Research Centre for Learning and Teaching, Newcastle University
This paper will report on the ongoing work and progress of the FaSMEd project, which is a design research project, now in the second year of a three-year programme. FaSMEd aims to develop the use of technology in formative assessment classroom practices in ways that allow teachers to raise achievement in mathematics and science. This international project adapts and develops existing research-informed pedagogical interventions (developed by the partners), suited to implementation at scale, for raising achievement and transforming teaching. The project aims to: foster high-quality interactions in classrooms that are instrumental in raising achievement and expand our knowledge of technologically enhanced teaching and assessment methods addressing achievement in mathematics and science. The project will be producing a toolkit for teachers to support the development of practice and a professional development resource to support it.