MATHEMATICS LEARNING AND ASSESSMENT: SHARING INNOVATIVE PRACTICES

University of Birmingham, University of Brighton, Brunel University, City University (lead site), University of Hertfordshire, Kingston University, University of Leeds, University of Manchester, Napier University, Open University, University of Plymouth, Robert Gordon University, University of Southampton, University of Teesside, University of Ulster

Project Director: Dr Chris Haines, City University

The challenge addressed by the project is the creation of an environment within which university teachers can enhance their teaching and assessment skills to meet the demands of society at the same time as they are faced with resource constraints, diversity in entrance standards and assessment of teaching quality. Teaching quality assessment forces them to consider the positive relationships between teaching and research. The delight which the researcher has in exploring mathematical structures can be extended to the teaching mode. Engendering this delight for mathematics in students, not only amongst those on single honours courses but also amongst those for whom mathematics plays a supporting role in other disciplines as a guiding principle has shaped the work of the project.

The Mathematics Learning and Assessment: Sharing Innovative Practices project has developed and disseminated innovative approaches to the teaching, learning and assessment of mathematics with aims of offering solutions which can be utilised by universities in their own contexts and encouraging individual mathematicians to take on board ideas and practices which are known to be successful elsewhere. The consortium has addressed teaching problems facing departments at the present time.

The range of responses developed by consortium members includes exemplar case studies published in 1996 by Arnold in five booklets with an accompanying video. The distinctive approach, of first sharing experiences within the consortium and then constituting teams to write up these exemplars with collective responsibility is unique for mathematics in the UK.

To help share best practice and to promote the development of exemplar material, university staff throughout the UK were invited to join regional workshops and a national symposium. 139 academic staff from 49 universities participated in six workshops held, in January 1994 at the University of Ulster, City University and the University of Manchester and in March 1994 at Napier University, the Open University and at the University of Hertfordshire. A national symposium was held at the University of Birmingham in June 1994, involving 105 participants from 47 universities. Over 200 staff from 69 institutions joined these regional workshops and the symposium.

Meeting the problems from a different point of view, a vigorous debate has been initiated during the course of the project by the London Mathematical Society, the Institute for Mathematics and its Applications and the Royal Statistical Society in Tackling the Mathematics Problem. Within ETAP, the Mathematics Learning and Assessment project has addressed some of these issues to help staff to manage these changes and to breathe new life into courses. Indeed, in May 1996 at The Royal Society, a further national meeting was held as part of the dissemination process. A news release of that that meeting is provided below. 110 academics from 60 universities attended the meeting, participated in the discussion and took part in the interactive workshops on groupwork, rating student achievement, comprehension, assessing assessments and reflection in mathematics which were the focus of keen debate. These themes mirrored exemplar material gathered by the consortium members during the course of the project,

The consortium will continue to offer consultancy advice, workshops and seminars. It has produced a display showing the work of the consortium, which has been used at several universities and is available for use throughout the HE sector.

Don't blame the students - Proper mechanisms for change the responsibility of universities

Universities have a responsibility to construct mechanisms which encourage change for teaching and learning. Speaking at a meeting on Mathematics Learning and Assessment, held at The Royal Society on 17 May 1996, Professor Norman Gowar, the Principal of Royal Holloway, maintained that in this context effective examples of change are often those which take place slowly. In some respects, mathematics is not different from other subjects, there is a responsibility placed on academics to make their subject more attractive, to use the new technologies to reinforce independent learning in the face of declining resources and to face up to the challenges of information systems which will place a premium on higher order skills in the learning environment. Professor Gowar suggested that these specific challenges need to be addressed at departmental level and that whilst staff naturally feel threatened by change they should resist the 'not invented here' syndrome as a reason for not tackling innovation. Strong staff can cope with change very effectively and innovation places a premium on the best staff.

For their part, the funding councils had attempted to promote innovation through the Effective Teaching and Assessment Programme. Cliff Allan, HEFCE Policy Division said that the twin aims of identifying and disseminating best practice had been achieved by ETAP but it should be recognised that funding was restricted and that the short duration of the programme had not helped. Within this discussion major questions of quality enhancement were also raised by Dr Norman Jackson (HEQC). This meeting was itself part of a major project involving a consortium of 15 universities, led from City University, seeking to promote the sharing of innovative practices in mathematics.

Opening the first panel discussion on managing change, Dr Chris Haines (City) welcomed 110 academics, from 60 universities and colleges, on behalf of the consortium. They shared a deep concern over the teaching and learning of mathematics in universities, voiced some of those concerns, particularly regarding training for undergraduate teaching, the interaction between teaching and research assessment and poor government funding. During the afternoon, interactive workshops on groupwork, rating student achievement, comprehension, assessing assessments and reflection in mathematics were the focus of keen debate.

Chairing a major panel discussion, Professor Leone Burton (Birmingham) posed the question 'Why innovate in teaching and learning mathematics?' Professor Norman Biggs (LSE) said that we had come a long way since mathematics was held to be founded upon the twin peaks of real analysis and abstract algebra, innovation is an integral part of higher education essential for its further healthy development. Mathematicians have sometimes been slow to adopt new perspectives in teaching, and recounting 'how it was for him', Professor Peter Saunders (King's) suggested that it is easier to innovate in situations where mathematics is used in other disciplines. Amongst all this, given the changing background of students entering universities, Professor Rosamund Sutherland (Bristol) stressed that we should understand the prior experiences of the students and should not blame the student if they did not have particular key skills.

For further information contact the Project Director, Dr Chris Haines or the Project Officer,

Sylvia Dunthorne in the Department of Mathematics, City University, Northampton Square, London EC1V 0HB. These and other members of the consortium can be contacted by email:

Chris Haines c.r.haines@city.ac.uk

Sylvia Dunthorne s.dunthorne@city.ac.uk

Nigel Atkins n.atkins@kingston.ac.uk

John Berry jberry@plymouth.ac.uk

Leone Burton l.burton@birmingham.ac.uk

Rosalind Crouch r.m.crouch@hertfordshire.ac.uk

Alan Davies a.j.davies@hertfordshire.ac.uk

Judy Goldfinch j.goldfinch@napier.ac.uk

Gerald Goodall gerald.goodall@brunel.ac.uk

Keith Hirst keh@maths.soton.ac.uk

Ken Houston sk.houston@ulst.ac.uk

Peter Hudson p.c.hudson@tees.ac.uk

Ann Kitchen 100271.1404@compuserve.com

Bryan Orman bao@maths.soton.ac.uk

Christine Shiu c.m.shiu@open.ac.uk

John Usher j.usher@scms.rgu.ac.uk

Kevin Lord and David Le Masurier may be contacted via Chris Haines or Sylvia Dunthorne

Mathematics Learning and Assessment Pack: Sharing Innovative Practices

Edited by Chris Haines and Sylvia Dunthorne London: Arnold (1996) ISBN 0340 645 768

Book One: Introduction

Setting the Scene

Leone Burton, University of Birmingham; Chris Haines, City University, London

The Interface Between Mathematics Post 16 and Higher Education

Ann Kitchen, University of Manchester; Kevin Lord, University of Leeds

Working in Groups

Rosalind Crouch and Alan Davies, University of Hertfordshire

John Usher, Iain Mackenzie and Ernest Forrest, The Robert Gordon University, Aberdeen

Book Two: In Course Projects

Introduction

Ann Kitchen, University of Manchester; David Le Masurier, University of Brighton

Statistics Games

Gerald Goodall, Peter Hall and Chris Walker; Brunel University, London

Investigations in Pure Mathematics

Keith Hirst, University of Southampton; Christine Shiu, The Open University

Modelling Approaches with First Year Undergraduates

Peter Hudson, University of Teesside; Kevin Lord, University of Leeds

Real Problems

David Le Masurier, University of Brighton; Ann Kitchen, University of Manchester

Students Writing for Students

Ken Houston, Neville Neill, Bryan Scotney and Norman Smith, University of Ulster

Book Three: Communcation

Introduction

Rosalind Crouch, University of Hertfordshire

Written Reports

John Berry, University of Plymouth; Alan Davies, University of Hertfordshire

Posters

John Berry, University of Plymouth; Ken Houston, University of Ulster

Oral Presentations

David Le Masurier, University of Brighton; Rosalind Crouch, University of Hertfordshire

Book Four: Teaching and Learning

Introduction

Ken Houston, University of Ulster

Mathematics in Other Disciplines

Patricia Egerton, Peter Hudson and Doreen Makin; University of Teesside

Learning Diaries

Mary Briggs and Christine Shiu; The Open University

Comprehension

Ken Houston, University of Ulster; Bryan Orman, University of Southampton

Experimental Workshops

Nigel Atkins, Kingston University, London; Chris Haines, City University, London;

Bryan Orman, University of Southampton

Book Five: Assessment

Overview

Chris Haines, City University, London; David Le Masurier, University of Brighton

Peer- and Self-assessment After Group-work

Judy Goldfinch, Napier University, Edinburgh; Ron Summers, City University, London

Enhancing Takeaway Assignments

Judy Goldfinch, Napier University, Edinburgh

Issues in Teaching Large Classes

Nigel Atkins, Kingston University, London; John Berry, University of Plymouth

VIDEO: Six

Video Excerpts

Sylvia Dunthorne, City University, London