The Second Irish Symposium for

Undergraduate Mathematics Education


10-11 December, 2004

University College Dublin

Kindly sponsored by:

UCD's Academic Conference Support Scheme

The Irish Universities Quality Board

The Irish Mathematical Society

Introduction: The second Irish Symposium for Undergraduate Mathematics Education is being held in University College Dublin from 10 - 11 December, 2004.

The symposium aims are:

The following information can be found below:

Programme: The following is a provisional programme for ISUME2

Friday, 10 December

9.00-9.30 Registration
9.30-9.45 Opening Address
9.45-11.00 What Makes an Example Exemplary

Professor John Mason, Open University



11.30-12.45 Students’ Experiences of Undergraduate Mathematics: Some Findings From Our Research

Dr Melissa Rodd, University of London



1.30-2.00 First Year Calculus for Non-Mathematics Majors

Professor Sean Dineen, University College Dublin

2.00-2.30 Problem Solving in Cork

Dr Tom Carroll, University College Cork

2.30-3.00 Where we Need Technology in Mathematics

Dr Richard Timoney, Trinity College, Dublin



3.30-5.00 Discussion Groups

Conference Dinner

Saturday, 11 December

9.30-10.30 An Irish Perspective on the "Mathematics Problem"

Professor John O'Donoghue



11.00-12.00 The Culture of Mathematics Teaching and Learning

Professor Kathleen Lynch and Dr Maureen Lyons (University College Dublin)

12.00-12.30 OECD PISA Mathematics Survey & Mathematics Education in Ireland

Dr Sean Close (St Patrick's College, Drumcondra) and Ms Elizabeth Oldham (Trinity College, Dublin)

12.30-1.00 Math Thru Edutainment

Dr Micheal Mac An Archinnigh, Trinity College, Dublin

1.00 Symposium Closes


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Plenary Speakers: We are delighted to announce the following plenary speakers for ISUME2:


Professor Kathleen Lynch is co-ordinator of the Equality Studies Centre in University College Dublin and has published widely on education. Dr Maureen Lyons is a research manager in the Equality Studies Centre. In 2003, they completed a study which was initiated and funded by the Gender Equality Committee of the Department of Education and Science. The main findings were published in the book Inside Classrooms - the teaching and learning of mathematics in social context. For further information on Professor Lynch's and Dr Lyons's research interests and publications please see their homepage.

Professor Lynch and Dr Lyons will present on: The Culture of Mathematics Teaching and Learning

‘Just say with an equation, I think if you knew why you were doing it that way you would probably remember it better' (Joe,  2nd year mathematics class)

‘I’d say people are slow to ask a question or ask for help because you wouldn’t want to be seen to be the one who would ask' (Vincent, 2nd year mathematics class)

‘I think mathematical ability and I think ability to a greater extent is inherited. But you can improve with a lot of extra help and one-to-one tuition’ (Ms. Brennan , teacher of top stream in 2nd year)

‘Anyone I have ever discussed mathematics with, we tend to come to the view that mathematics is a peculiar subject, you were either good at it or  you weren’t.. But maybe there is a better way of teaching it..’ (Mr. O’Brien Parent)

The Inside Classrooms (2003) study on which this paper is based was the first video study of Irish mathematics classrooms. Twenty second-year mathematics classes were studied intensely (six English classes were also videoed for comparative purposes). The main objective of the research was to provide greater understanding of the pedagogical practices employed in the teaching of mathematics in single sex and co-educational settings. It also examined the way different pedagogical styles impacted on students’ attitudes to, and experience of, learning mathematics.

To provide a context for the video studies, intensive interviews about mathematics education were undertaken with students, teachers and parents of the observed classes. The study also explored the impact that students’ social class, gender and track position (stream or band), had on their experience of learning mathematics.

The study offers many insights into students’ experiences of mathematics classrooms, not only in terms of the pedagogical practices and attitude of teachers, but also in terms of how parents’ resources, school grouping procedures, gender and social class impact on their learning. The findings provide evidence of a strong procedural rather than conceptual, and teacher-led rather than student-led, approach to the teaching mathematics. They also demonstrate the crucial role that emotions play in learning, especially emotions such as fear and anxiety about ‘being wrong’ in a mathematics class. Whether girls or boys like mathematics, or whether they wish to pursue the subject at more advanced levels, is as much about the sense of identity that the subject offers them, as it is about the pedagogy that is employed in the classroom.


Professor John Mason is Professor of Mathematics Education at The Open University, where he was, for some 15 years, Director of the Centre for Mathematics Education. He is a highly respected figure in the field of mathematics education research and is the author of several books on teaching mathematics: Thinking Mathematically and Learning and Doing Mathematics - to name a few. For information on Professor Mason's research interests and publications see his homepage.

Professor Mason will present on: What makes an example exemplary?

Abstract: Mathematics teachers have always provided learners with examples. But what makes an example useful and effective? What must a learner do to
locate what is exemplary about an example? I will offer some ways of making examples maximally effective and for working with learners so that they get the most out of examples.


Professor John O'Donoghue is Associate Professor of Mathematical Education at the University of Limerick. He is responsible for the establishment of the first Mathematics Support Centre in Ireland. The transition of students from secondary to third level mathematics is an area of research in which he has particular interest. For information on Professor O'Donoghue's research interests and publications see his homepage.

Professor O'Donoghue will present on: An Irish Perspective on the ‘Mathematics Problem’

Abstract: The ‘Mathematics problem’ defined in the UK report Tackling the Mathematics Problem (1995) is instantly recognisable in Irish Universities. Indeed many Irish Universities and Institutes of Technology have been grappling with this ‘problem’ for several years with variable success as measured by student data such as progression and retention data and graduate throughput.

A variety of measures and approaches have been deployed in mathematics departments throughout the Irish Higher Education sector to address the problem as it manifests itself in Ireland. However, recent efforts have been characterised by a degree of urgency that was absent in previous work as the importance and scale of the problem impact on policy makers.

In the circumstances the University of Limerick’s response has both practical and research dimensions. It is argued that both dimensions are needed for a successful attack on the problem, and while the practical developmental work gains ready acceptance the necessity for research- based initiatives is less well understood. Consequently, on-going research at UL’s Department of Mathematics and Statistics is reported in more detail here. The presentation concludes with some thoughts on a possible research programme that could be tackled collaboratively by the institutions affected.          


Dr Melissa Rodd has recently taken up a position at the Institute of Education in the University of London. She previously held a position in the School of Education at the University of Leeds. Along with colleagues from King's College London, she has just completed a three-year, longitudinal project on Students' Experience of Undergraduate Mathematics.  This project examined the progress and attitudes of a cohort of undergraduate mathematics students at two English universities. For information on Dr Rodd's research interests and publications see her homepage.

Dr Rodd will present on: Students’ Experiences of Undergraduate Mathematics: Some Findings From Our Research

Abstract: Some undergraduate maths students have a wonderful time at university and achieve splendid results. Others do not fare as well: some get poor results; others don’t enjoy their studies. In this presentation I shall report some details from the three-year project I was involved with: tell you something about students ‘at risk’ and about those that were successful. I shall also indicate how different aspects of ‘culture’ can affect a student’s experience – positively as well as negatively.  I shall also consider how the community established by a university mathematics department implicitly supports some students yet (unwittingly) can alienate others.


I hope to generate a discussion with you concerning your own observations of students’ experiences and to develop ideas for improving the quality of student experience at the undergraduate level.

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Presentations: There will be five 25-minute presentations during the symposium. These are as follows:


Problem Solving in Cork

Speaker: Dr Tom Carroll, School of Mathematics, Applied Mathematics and Statistics, University College Cork

Abstract: I will describe an Honours Mathematics course that has been taught at Cork for several years now on 'Mathematical Experimentation and Problem Solving'. The course team members are Donal Hurley, Des MacHale and myself. I will concentrate on the aims and structure of the course, and on our experience of 'teaching' it.


OECD PISA Mathematics Survey and Mathematics Education in Ireland

Speakers: Dr Sean Close, Senior Lecturer in Mathematics Education, St. Patrick’s College, Drumcondra, Dublin 9

Ms Elizabeth Oldham, Senior Lecturer in Education, Trinity College, Dublin 2

Abstract: The OECD set up the PISA Project to assess, at three-year intervals,  the mathematical knowledge of students at the end of the period of compulsory schooling (15 year-olds). A brief description of the OECD PISA mathematics framework will be provided along with an indication of how it relates to the Irish second-level mathematics curriculum. Some general results from PISA Mathematics 2000 and 2003 will be outlined followed by some comments on Irish mathematics education in the light of PISA.


First Year Calculus for Non-Mathematics Majors

Speaker: Professor Sean Dineen, Department of Mathematics, University College Dublin

Abstract: This talk describes the speaker's experience of teaching first year Calculus to students from different faculties and how he arrived at an alternative approach.


Math Thru Edutainment

Speaker: Dr Micheal Mac An Archinnigh, Trinity College, Dublin

Abstract: Culture and civilization arises pre-eminently out of playing. Math, like Arts and Science, is a cultural artefact and consequently the heritage of all. In this paper I explore the use of Edutainment (education thru entertainment), in the senses both of live performance (the play[ing]) and thru digital media (especially the WWW), by which the learning of math can be fun and serious.
    The Math thru Edutainment research is part of a long-term project on the Digital re-Discovery of Culture [DrDC] being undertaken within the framework of the KT-DigiCult-BG project of the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences partially funded by the EU.
    This paper addresses math at University level and three specific areas of application are illustrated:
a) skirted males and topos logic,
b) Goethe's Farbenlehre and linear algebra,
c) board games and the math of computing.
Where the playing is digital across the WWW and constructed as multi-player game then the electronic publication of game transcripts is an essential part of the introduction to and repeatability of the learning experience.


Where we Need Technology in Mathematics

Speaker: Dr Richard Timoney, Trinity College, Dublin

Abstract: Althought technology in the form of simple calculators and more complicated use of computing to perform numerical calculations has been with us for some decades, the fact that symbolic computation is now practical on modest machines seems not to have influenced the way we instruct our students very much. I will describe my own experience in this direction and how far I think one should be influenced by this technology.

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Discussion Groups: On the afternoon of December 10, there will be parallel discussion group sessions. Discussion Group Topics which have been suggested are:

Discussion Group A: Supporting Mathematics Teaching: Mathematics Learning Centres

    Group Leaders: Mr Donal Dowling (DCU) and Mr Ronan Flatley (UCD)

Room: Q004 in Quinn School

A course in mathematics forms a part of many third-level qualifications. Students studying science, accountancy, business, engineering and computing are likely to have to take a maths courses in their first (and subsequent) years. Such students have often struggled to get to grips with elementary mathematics, and so inevitably, problems manifest themselves. The problems can be exacerbated by the nature of third-level institutions, with their emphasis on self-study and independent learning. Students can drift farther and farther behind, with maths either neglected entirely or taking up a disproportionate amount of time.
    An additional problem encountered is that classes are typically much larger than in second-level, and mathematical ability accordingly is diverse in the extreme. Thus many third-level institutions have started to address this problem by setting up special centres where students can receive extra tuition in maths. This discussion group will focus on the various ways that this support is provided across different institutions. We will discuss the experiences of recently established learning centres (for example, DCU and UCD) and we hope to gain from the experience of more well-established centres (for example, IT Tallaght and UL).

The question of how to measure the success of these centres will be addressed.


Discussion Group B: Mathematics for Mathematicians

    Group Leader: Dr Rachel Quinlan (UCD)

Room: Q005 in Quinn School

This group will consider suitable objectives for mathematics degree programmes and discuss questions along the following lines : what can we expect a mathematics graduate to know and what skills should we expect a mathematics graduate to have? If these questions can be answered, how does one acquire these skills? Is there a conflict between content and process and if so, how should it be managed? How do mathematics students and graduates perceive the subject?The discussion will begin with some short presentations, including

What mathematics should a mathematician know? - Dr Niall Madden, NUI, Galway

To be Announced - Dr Maria Meehan, University College Dublin

Other participants are welcome to give short presentations and are invited to submit suggestions to Intending participants might be interested in looking at the document, entitled "Towards a common framework for Mathematics degrees in Europe", which was produced by the mathematics group of the project "Tuning Educational Structures in Europe" and may form a basis for some of the discussion.


Discussion Group C: The Transition from Second to Third Level Mathematics

    Group Leader: Dr Ann O'Shea (NUI Maynooth)

Room: Q006 in Quinn

Many students find the transition from second to third level Mathematics difficult. In this discussion group we will explore the reasons for these
difficulties. We will talk about ways of identifying the students who are most likely to find the transition traumatic and we will look at strategies
to help students with the problems they encounter. The discussion group will begin with some short presentations including:

Beginning Engineering Mathematics at IT Tralee - Joan Cleary (IT Tralee)

Analysis of Leaving Certificate as preparation for service Mathematics courses in UL - Olivia Gill (UL)

Computer assisted learning of Mathematics for first Engineering students - Paul Robinson (IT Tallaght)

Helping students to make the transition from school to university - David Wraith (NUI Maynooth)


Discussion Group E: Overcoming Math Anxiety

    Group Leader: Ms Fiona Watson (GMIT)

Room: Q007 in Quinn

Many students find mathematics a difficult subject. This group will discuss why this is so, how fears and anxieties manifest themselves and
how these can be overcome. We will also discuss some alternative teaching styles and approaches which we have found useful and the
creation of a forum for sharing our experiences. The session will start with some short presentations on:

Causes of math anxiety and using technology to overcome it - Fiona Watson (Galway-Mayo IT)

A confidence building strategy for adults learning vectors with math anxiety - Gerry Golding (University of Limerick)


A suggested format for each discussion group is to have three to four 10-minute presentations by interested participants, followed by general discussion and debate. The leader and participants of each group will be invited to compile a short summary, highlighting the main points discussed. These will be posted here when complete.

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Conference Dinner: The conference dinner will be held in Ouzos of Baggot Street at 8pm on Friday, 10 December, 2004. The price of the conference dinner is 35 euro. The Number 10 bus, whose route starts in UCD, goes past Ouzos - just get off the bus outside the Spar/Weir's on Baggot Street.

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Registration and Directions:

Registration: To register, please complete the following Registration Form. The conference fee is 25 euro and the conference dinner is 35 euro. Both are payable by cheque or bank draft. (Cheques and bank drafts should be made payable to ISUME-UCD.) The completed registration form and cheque/bank draft should be sent to:

Dr Maria Meehan, Department of Mathematics, Science Lecture Building, University College Dublin, Belfield, Dublin 4, Ireland.

To ensure that ISUME2 is appropriately catered for, you are kindly requested to register before Friday, 3 December, 2004.

There is a limited amounted of funding to cover the registration fee for students interested in attending. Please indicate on the Registration Form whether you wish to apply for this.

Location and Directions: The conference will take place in the

Quinn School of Business

on the Belfield Campus in Room Q015. For the location of this building, please consult the map of the Belfield campus. The Quinn School of Business is number 59 on this map and is labelled Undergraduate School of Business. For information on getting to UCD Belfield Campus please read the following directions.

For further information on ISUME2 you can contact one of the organisers:

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Page Maintained by Maria Meehan.

Last Updated: Tuesday, 8 December, 2004.