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British Society for Research into Learning Mathematics

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BSRLM Proceedings: Vol 32 No 1 Manchester University, Mar 2012

Proceedings of the Day Conference held at Oxford University on 03 Mar 2012

Contents

01 Problem-Solving in Undergraduate Mathematics

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.

03 Report from the Sustainability Working Group: Developing a Research Agenda

Nichola Clarke
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

Danyal Farsani
School of Education, University of Birmingham

 

05 ‘You weren’t expected to be creative’: policy-practice tensions in GCSE Mathematics

Jennie Golding
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.

06 The Mathematics in Children’s Out-of-School Economic Activity

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.

07 Modelling as a driver for the Level-3 curriculum

Peter Osmon
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.

08 The rise and fall of an investigative approach to mathematics in primary education

Margaret Sangster
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?

09 ‘Going it alone’ within further mathematics?

Cathy Smith
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’

Rebecca Warburton
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 – 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.

Our Aim

BSRLM is for people interested in research in mathematics education and provides a supportive and inclusive environment for both new and experienced researchers to develop their ideas.

Become a Member

Members of BSRLM can attend and present at our termly Day Conferences. You will also receive the three annual issues of Research in Mathematics Education published for BSRLM by Taylor and Francis.
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BSRLM is a national organisation for people who are passionate about mathematics education research. RTs are not endorsements. Posts by K Skilling

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bsrlm_maths BSRLM @bsrlm_maths ·
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Looking forward to the next BSRLM day conference at the University of Southampton- November 2nd 📢

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Save the date for the next BSRLM conference - Sat 2nd November at the University of Southampton 📢

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6 Jun

Only one more sleep until @BSRLM_maths conference at @LboroDME 🏫👩‍🏫

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Interesting and stimulating discussion at the Mathematics Education and Policy Working Group @BSRLM_maths - summer conference @SmartJacques @MarkBoylanEd @GillRAdams @AlfColes

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26 May

Don't forget to register for the BSRLM summer conference and New Researchers' Day taking place 7th and 8th June - registration closes 31st May. (Committee @AlfColes @CristinaMio11 @MandyLLiu1 @OuhaoC @SmartJacques @karen_skilling)

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oxunimaths Oxford Mathematics @oxunimaths ·
10 May 2024

The newly created UK-wide Academy for the Mathematical Sciences today appointed Oxford Mathematician Alison Etheridge as its first President.

The Academy's focus will be on mathematical sciences everywhere: in teaching & education, academic research, & business & government.

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bsrlm_maths BSRLM @bsrlm_maths ·
22 Apr 2024

The next BSRLM conference will be our Summer conference on the 7th and 8th June at Loughborough University. Please use this link to find out about registration and the call for session proposals. https://www.bsrlm-members.org.uk/pages/15-conferences

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scottishmaths SMC @scottishmaths ·
10 Mar 2024

CALL for PRESENTERS: SMC Stirling Maths Conference Saturday 18th May 2024. Open to all from across early years, primary, secondary and tertiary education. Fill in this form by **14 March 2024** https://forms.office.com/e/iPHkKqME0E

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28 Feb 2024

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1 Mar 2024

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Article online now 📷 “The impact of realistic mathematics education on secondary school students’ problem-solving skills: a comparative evaluation study” by Georgios Ventistas, Ourania Maria Ventista & Paraskevi Tsani
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bsrlm_maths BSRLM @bsrlm_maths ·
1 Mar 2024

Looking forward to meeting up online tomorrow at our Spring Conference...choose your sessions

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bsrlm_maths BSRLM @bsrlm_maths ·
5 Feb 2024

Professor Jodie Hunter will be the plenary speaker at our online conference on Saturday 3rd March. Please use this link to register and submit a proposal https://www.bsrlm-members.org.uk/pages/15-conferences

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bsrlm_maths BSRLM @bsrlm_maths ·
16 Jan 2024

Happy New Year to all members. Please note that our next conference will take place via zoom on Saturday 2nd March. Registration for session proposals are open - click here for more details https://bsrlm-members.org.uk/pages/15-conferences…@BSRLM_maths

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londmathsoc London Mathematical Society @londmathsoc ·
8 Dec 2023

The 2023-24 Round of LMS Early Career Fellowships are live, open to early career mathematicians in the transition between PhD and a postdoctoral position.

For further details ➡️ https://www.lms.ac.uk/grants/lms-early-career-fellowships

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bsrlm_maths BSRLM @bsrlm_maths ·
8 Dec 2023

We already have some interest for this Special Issue @RME_ResMathEd and the call for abstracts is open for another week so please consider making a submission Call for Special Issue 2025 Abstracts💡 https://bsrlm.org.uk/call-for-papers-for-the-2025-special-issue-of-research-in-mathematics-education-rme-contemporary-issues-in-mathematics-education-within-a-stem-climate/… Send an Abstract to rme@bsrlm.org.uk by 15th Dec 2023

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