Proceedings of the Day Conference held at Oxford University on 03 Mar 2012
Matthew Badger and Sue Pope
Coventry University; University of Manchester
This report outlines two projects in problem-solving funded by the National HE STEM programme. The first project is a collaboration between the University of Birmingham and sigma. The Mathematical Problem-Solving Project (MaPS) is led by Trevor Hawkes at Coventry University and Chris Sangwin at Birmingham. Matthew Badger is the project’s full-time research assistant based at Coventry. The second project is a collaboration between Liverpool Hope University and the NRICH Project based at the University of Cambridge. This project, Problem Solving in Undergraduate Mathematics (PSUM), is headed by Sue Pope with Nick Almond and Anesa Hosein at LHU, and Vicky Neale at NRICH. The aim of each of these projects is to satisfy the recommendations of the HE Mathematics Curriculum Summit that pertain to problem-solving. This report gives a brief overview of the aims of the project, its current state and its future direction.
02 ‘The backwards ones?’ — Undergraduate students’ reactions and approaches to example generation exercises
Sinead Breen, Ann O’Shea, Kirsten Pfeiffer
CASTeL, St Patrick’s College, Drumcondra; National University of Ireland, Maynooth; National University of Ireland, Galway
As part of a project exploring the design and use of mathematical tasks to promote conceptual understanding of Calculus concepts, first-year undergraduate students were assigned homework problems which required them to use various processes including generalising, conjecturing, evaluating statements, analysing reasoning and generating examples. In subsequent interviews with five students, a number of them spontaneously referred to the example generation problems posed as being the ‘backwards ones’ or requiring them to work backwards as well as forwards. In this paper, we will report on the students’ reactions to a particular example generation exercise, the strategies they adopted in an effort to solve such problems, and what they feel they learnt in the process.
University of Nottingham
The Sustainability Working Group is being convened to discuss how to integrate sustainability issues with the teaching and learning of mathematics. The aim of the group is to share perspectives on a range of research questions and to develop collaborative research on sustainability in mathematics education. The group is open to all. In this article, I explore some potential issues for a research agenda.
04 Mathematics Education and the Analysis of Language Working Group: Making multimodal mathematical meaning
School of Education, University of Birmingham
King’s College London
This paper reports on an on-going study to illuminate the relationship between policy and implementation of GCSE 2010 by (initially) exploring the beliefs and departmental-level context of two teachers in one department. The analysis draws on both Spillane’s (1999) and Ball et al’s (2011) approach to policy implementation. Both the department and the two teachers are well-placed to implement the reform and believed they were doing so, yet after a year significant deviations from intended enaction were sometimes observed. I will reflect on the constraints and affordances of large-scale policy imposition.
Tim Jay and Ulises Xolocotzin
Graduate School of Education, University of Bristol
We report a study designed to investigate children’s out-of-school economic activities, with a focus on the mathematical thinking that these involve. Children in Year 5 (9-10 years old) and Year 8 (12-13 years old) participated in a series of activities over two weeks, which involved the documentation of out-of-school activities. These included a structured diary, a photo-taking activity, and a questionnaire for parents to complete. Groups of 3-4 children were then interviewed in order to understand and explore the activities represented in these documents. We will present two main findings from our ongoing analysis. The first is that children are engaged in a rich range of mathematical practices. The second is related to differences in the language that children use to talk about out-of-school mathematics and classroom mathematics, and ways in which these differences appear to play a role in inhibiting children’s ability to mathematise aspects of their lives outside of school.
Department of Education and Professional Studies, King’s College London
A previous paper identified the potential learning gains from substituting group-project model-making for traditional applied mathematics at Level-3. In this paper, I investigate the feasibility of this change by considering a set of recently published project proposals. These range over various application domains and mathematics topics. I suggest subjective criteria for evaluating potential projects from the likely viewpoints of learners and teachers and learners’ knowledge of a project’s application domain and the appropriate mathematics as objective success criteria. It follows that, except where the application domain is familiar to mathematics students, projects will have to be interdisciplinary — which generally seems impractical. But in the application domain that is familiar to all students — that of twenty-first century everyday life — the mathematics (IT and probability) is increasingly discrete whereas the curriculum still emphasises the mathematics of the continuum — surely evidence of how out of date it has become. The remedy might be for model-making to determine the pure mathematics in the curriculum.
Canterbury Christ Church University
This paper is based on a discussion session held at the March day conference of BSRLM. The session was an opportunity to share points of view about the role of investigative mathematics in primary mathematics teaching. From 1982 when the Cockcroft report promoted this aspect of mathematics, through the introduction of the National Curriculum and the National Numeracy Strategy, to the latest Ofsted research (2011) on ‘good practice in primary mathematics’, what can we say about the current state and place of investigation in primary schools? In the light of national and international league tables, assessment and the value teachers place on investigations, what is the status of investigations in primary schools?
Institute of Education, London University
In this paper, I examine the idea of choosing further mathematics as positioning oneself/being positioned as belonging to an imagined collective (Anderson 1991). My previous research has analysed students’ accounts as practices of neoliberal self-entrepreneurialism that construct them as individually successful (or not). Here I consider the roles of belonging and not belonging as practices of the self that are produced/reproduced by the collectives to which students belong. I use the examples of two students to show how they negotiate different senses of belonging within their accounts and manage to produce simultaneous discourses of inclusion and going it alone.
10 Continuous and discrete knowledge: analysing trainee teachers’ mathematical content knowledge change through ‘knowledge maps’
University of Leeds
Shulman is renowned for shifting the focus of teacher knowledge research onto content knowledge for teaching with the introduction of his categories of content knowledge. Following Shulman, many researchers have defined further categories of knowledge for teaching or refined his ideas (e.g. Deborah Ball and colleagues). Many accept that there is a specialised knowledge of mathematics for teaching. However, others argue that teaching is simply utilising mathematical content and processes within a different (teaching) context, rendering categories of knowledge types unnecessary (e.g. Anne Watson). Both points of view are taken into account in the introduction of ‘continuous’ and ‘discrete’ knowledge â€“ a proposed metaphor for how mathematical content knowledge is held within teachers’ minds. Not only do these terms aim to reconcile these seemingly opposing perspectives, but they take into account the dynamic nature of knowledge, allowing it to be represented in the form of ‘knowledge maps’ for comparison over time. This paper introduces the proposed metaphor and representation as a means to research trainee teachers’ mathematical content knowledge change.