Proceedings of the Day Conference held at University of London, Saturday 4th March 2017
01 Why do few children at rural secondary madrasas in Bangladesh choose to study an optional course in Higher Mathematics?
K. M. Nabiul Alam and Candia Morgan
UCL Institute of Education, University of London
In Bangladesh, children of the science stream education at secondary level may choose to study ‘Higher Mathematics’ as an optional course. This paper reports a preliminary analysis of six focus group discussions (FGDs) with some children of grades 9 and 10 across three rural secondary madrasas (Islamic schools) in Bangladesh. The analysis suggests that shortage of good higher math teachers and a private tuition centered math education have negative effects on children’s participation in an optional course in Higher Mathematics.
02 Implications of Giaquinto’s epistemology of visual thinking for teaching and learning of fractions
University of Nottingham
In this paper, I will present some implications of Marcus Giaquinto’s ideas about visual thinking and its epistemology when combined with Toulmin’s layout of an argument. My claim is that visual representations can be effective for low achieving students when teaching is focused on a carefully chosen model and time is given to students to fully use it.
03 Forced GCSE mathematics resits: Students’ voices
Sheffield Hallam University
Since the introduction of forced resits in Further Education (FE) colleges, current policy-informing research and reports have been centered on employers, teachers and colleges. In this paper, I will present some initial findings, gathered in 30 student interviews at three FE Colleges. Personal mathematical histories have been examined, alongside the effects that forced GCSE resits have had on the students and their lives, in the context of – but not limited to – mathematics education.
04 Using video cases to encourage participants’ engagement with research and theory: Emergent pedagogies from an online course on digital technologies for mathematical learning
Cosette Crisan and Eirini Geraniou
UCL Institute of Education, University College London
In this paper we present the model behind our on-line master level module Digital Technologies for Mathematical Learning, which focuses on the teaching and learning supported by digital technologies. In our evaluation of the delivery of this module over two years, we reflect here on the emergence of two pedagogies: the online pedagogy of the tutors, ensuring that online teaching and learning is effective and the participants’ developing RiTPACK (Research Informed Technological Pedagogical Content Knowledge – our own acronym for this concept) as they start experimenting with using the digital technology in their classroom practice and linking it with the research knowledge base of the module.
05 Development of components of mathematics in 7-to-11-year-old children: A study using Dynamo Assessment
Ann Dowker1 and Karima Esmail2
1Department of Experimental Psychology, Oxford University, 2JellyJames Publishing
Dynamo Assessment is a computerized assessment that tests children’s performance on 14 mathematical components. This study aimed to find out more about typically developing children’s performance. Key findings are that all tests correlate significantly with one another, and that performance on all tests improves with age.
06 Working group on “Using statistics in mathematics education research”: Have statistics lost their power in public policy discussions? (The crisis of statistics – ‘Post-truth’ and Big Data)
Statistics is one of the important branches of mathematics taught in schools, colleges and universities. It is also an important tool in public policy discussions. This session was focused on the use of statistics in society in general, rather than in mathematics education research. Participants had been encouraged to read an article by Will Davies in The Guardian, in which antipathy to statistics is suggested as one of the hallmarks of the populist right, with statisticians and economists chief among the various ‘experts’ ostensibly rejected by voters in 2016. The discussion went on to consider the meaning and consequences of ‘big data’, as well as the results of trends towards ‘identity politics’ and globalisation.
07 Salient moments: The potential for using multiple perspectives in mathematics teacher educator learning
University of Bristol, Graduate School of Education
What might be involved in making the change from teacher to teacher educator? While transcribing the reflective discussion of a group of secondary school mathematics teachers, I was struck by a number of occasions where, as I listened, something stirred in me. I use the Discipline of Noticing to frame the process of identifying particular salient moments from the teacher discussion. These initial noticings form one of a series of multiple perspectives that assist me in learning what it might mean to be a mathematics teacher educator and to bring to conviction future ways of being. One aim of this paper is to further develop thinking within the domain of mathematics teacher educator learning as well as to develop my own personal learning.
08 Student learning through collaborative design and teaching of STEM Foundation Mathematics: Catalyst Project
Barbara Jaworski, Stephanie Treffert-Thomas and Dave Hewitt
We introduce our Catalyst A Project focusing on innovation in teaching of mathematics with university students in a Foundation Studies programme. The innovation involves the inclusion of Student-Partners (SPs), former Foundation students, in design of tasks for their current peers. We study the task design process and the involvement of students, seeking to understand students’ perceptions of tasks that are helpful for conceptual learning. The SPs also join us in tutorials for the current cohort. Our research is developmental in feeding back to current practice from what we learn in studying it.
09 Sharing perspectives on mathematical methods: A dialogic investigation
University of Bristol, Graduate School of Education
Bakhtin’s work on perspectives forms the basis for a dialogic investigation into perspectives on the mathematical methods used by secondary school students and teachers. As part of this PhD project, students from Years 7 (aged 11) to Year 13 (aged 18) in a UK comprehensive school completed questions designed to encourage a range of different methods to be used. The artefacts will form prompts for teacher and student discussion groups which will focus on sharing perspectives on mathematical methods.
10 Collaborative teacher projects in mathematics: Teachers in charge
Seagreen Educational Consultancy
There is some criticism in the mathematics education professional development literature that the majority of studies are designed and run by teacher educators and second that the voice of the teacher is not well represented. This paper aims to address this criticism by reporting on 49 funded research studies, requiring collaboration between at least two schools, but otherwise designed, conducted and reported on by teachers of mathematics. The reports suggest that overall the projects generated enthusiasm, energy and a real sense of having done something worthwhile.
11 Describing the cycles of a modelling activity: The drug concentration in the human body
Education Office, Greek Embassy, London
This study explores the effects of two teaching experiments that focus on exponential modeling activity and collaborative inquiry learning in workplace problem solving. Ten heterogeneous groups of year 11 students took part in this research. Results show that students, while solving the problem, developed mathematical abilities, which are divided in three modelling cycles: arithmetic, geometry and algebra. It is important to note the teachers’ focus on mathematics rather than on realistic situation and the students’ difficulties in the transition from recursive to the general type of geometric series.
12 How much cream for 6 people? Some of the complexities that emerged as three 13 year old students attempted to solve ‘a quarter plus an eighth’
University of Nottingham
In this paper I report on an interview on a fractions task (in the context of a recipe) with three 13 year old (Year 8, grade 7) students, undertaken by their maths teacher and myself. I will argue that the students’ responses fit a socio-constructivist view that mathematical understanding is formed of a complex network of ideas, which are consolidated, developed, challenged and restructured in part through social interactions with others.
13 Patterns of mediation between students and mathematics in secondary school
UCL Institute of Education, London and UEA, Norwich, UK
In this paper, I discuss possible mechanisms involved in classroom mediation. I draw from PhD research that examines the observable positive emotions of experienced teachers in action in the classroom to illustrate three patterns of mediation; flipping, chained and distal. Mediation in this context is taken as how teachers actively reconcile two things; in this case students and mathematics such as through modelling engagement. Drawing from Positioning Theory, I examine positioning a mathematics teacher as mediator, in a triangular relationship bridging between students and mathematics. I explore risks inherent in each pattern of mediation in terms of teacher and student affect, and some implications of mediating through play, or temporal mediation between current state and imagined futures of students, both of which act to align students with positive mathematics positions. Teacher patterns that seem supportive of positive student alignment involve continual, rapid, intense, structured and emotionally driven shifting of positions.
14 A learner’s experience of flow when engaged with mathematics
The Open University & University College London Institute of Education
Learners of mathematics often have great enjoyment when carrying out mathematical tasks, questions or problems. This experience can be labelled as ‘flow’. In this paper, I start from the premise that flow is an essential part of the mathematical learning process. A longitudinal study was carried out with a group of secondary students, anticipating how flow can assist positive relationships with mathematics. Initial findings suggest certain didactics (including task design, delivery methods, and questioning techniques) elicit flow and engender an ‘optimal experience’.
15 The role of defining in pre-proving activity
UCL Institute of Education
In this paper, I present and discuss findings from a research study the aim of which is to investigate the activity of proving as constituted in a Cypriot classroom for 12 year old students. By drawing on Cultural- Historical Activity Theory and collaborative task design, this study explores the way the teacher is working with the students to foreground mathematical argumentation. In this paper, I illustrate how defining, an activity integrated in the activity of explanation, plays a crucial role in regards to pre-proving activity.