Editors
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PROFESSOR
S K HOUSTON, The University of Ulster, Northern Ireland (sk.houston@ulst.ac.uk)
PROFESSOR W
BLUM, The University of Kassel, Germany (blum@did.mathematik.uni-kassel.de)
DR I D HUNTLEY,
The University of Bristol, England (i.d.huntley@bristol.ac.uk)
DR
N T NEILL, The University of Ulster, Northern Ireland (nt.neill@ulst.ac.uk)
Albion Publishing Ltd, Coll House, Westergate, Chichester, England, PO20 6QL.
Fax and Phone +44-1243-542285
ISBN- 1-898563-29-2 : 410 pages, February1997, £35.00.
This book contributes to mathematical modelling teaching and learning in high (secondary) schools, and in universities throughout degree study. It is sponsored by the organising committee of the series of International Conferences on the Teaching of Mathematical Modelling and Applications (ICTMA). The members of this committee are dedicated to monitoring and developing the teaching of modelling and applications. The contributing authors from many countries reflect a modern and international interpretation of the current state of knowledge and development. The book is both philosophical and creative, and includes innovation in assessment, and evaluation of assessment. Teaching and study at all levels is discussed, and the pervasive and interdisciplinary nature of the applications which are described reflects the use and value of mathematical modelling in mechanics, medicine, patient flow through hospitals, computing science, traffic control, business studies, and areas of mathematics, eg. fractals and analysis.
It is now widely accepted, both by practitioners and educationalists, that mathematical modelling is ‘the way of life of an applied mathematician’. There is a recognition that undergraduate university students, if they are to earn a living as mathematicians of one sort or another, should have opportunities to learn mathematical modelling during their studies - ‘mathematical modelling is a must!’ There is a recognition that pupils in schools should learn about applications of mathematics through engagement in modelling, and have their knowledge and skills assessed. There is the belief that much of mathematics is learnt best when it is situated in the context of a pupil’s everyday experience, that is, through applications.
Nevertheless, despite this widespread recognition and practice, there are still needs to be met. There is still the need to convert some hearts and minds to the belief that modelling and applications are essential components of mathematics learning. There is the need to devise, implement and evaluate new methods of teaching and assessing. There is the need to conduct research on the teaching and learning of modelling and applications, and there is the need to disseminate examples of good practice and the fruits of research into student learning.
This book attempts to meet these needs, at least to some extent. It contains 32 articles on the teaching, learning and assessment of mathematical modelling and applications which were originally presented as papers at the 7th International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA-7) which was held on the Jordanstown campus of the University of Ulster in Northern Ireland in July 1995. (The ICTMA Conferences are held biennially and the next conference is planned for Brisbane, Australia, in August 1997.) There are contributions by authors from 12 different countries, with 16 of the articles coming from authors in the United Kingdom. This reflects the truly international dimension of the subject matter of this book, and provides valuable insights into practices worldwide.
The book is divided into five sections. Section A contains four articles on Reflections and Investigations and includes an article which gives an account of recent educational developments in Northern Ireland. Assessment of student learning is an essential part of the education system and is currently an active research field. Section B contains five articles which deal with assessment, particularly at undergraduate level. Section C contains seven articles dealing with secondary education and contains both case studies of good practice and examples of courses and how they are taught in a variety of countries including Russia, the Netherlands, the USA and the UK. Section D presents seven case studies suitable for use in university teaching and Section E concludes the book with descriptions of five ideas relating to undergraduate modelling courses.
The book as a whole complements the series of books emanating from the ICTMA conference series (see below) and should prove to be a useful source of information and ideas for those engaged in the teaching, learning and assessment of mathematical modelling and applications.
This is now the age of electronic communication and publication. Email addresses of most of the authors are included in the chapter headings, while the Preface, Table of Contents and publishing details of the book are available at the internet address http://www.infj.ulst.ac.uk/~cdmx23/ictma7.html (i.e. the page you are currently reading!).
The IRA cease-fire of October 1994, which held through 1995, provided a window of opportunity for tourists and conference delegates to come to a relatively trouble free Northern Ireland, and we are grateful to all those who attended the conference, either to present a paper or just to listen. It is rumoured that they had an enjoyable and profitable time! See the review by Duncan et al., Zentralblatt fur Didaktik der Mathematik (ZDM), 28 (2), pp 67 - 69, 1996, or the internet page http://www.infj.ulst.ac.uk/~cdmx23/report.html.
We are also grateful to the authors of these articles for their excellent contributions and for their care in presenting material in the form we requested.
We thank the other members of the local team - Derek Curran, Jack Cromie, Norman Smith, Keith Simpson (Catering), Fred Ruck (Premises) and Hazel Alderdice (Accommodation) - for organising the conference and making it run smoothly. The technicians and computing officers of the Faculty of Informatics also receive our thanks. Above all we wish to thank the conference secretary, Sharon Kelly, for all her work, before, during and after the conference, and for preparing this manuscript. Finally we acknowledge the encouragement and interest of our publisher, Ellis Horwood of Albion Publishing Ltd.
S K Houston W Blum I D Huntley N T Neill
January 1997
Preface
Section A Reflections and Investigations
1 Curriculum Development and Assessment in Northern Ireland. Catherine Coxhead
2 Mathematical Modelling and the Way the Mind Works. Susan J Lamon
3 What Makes A Model Effective and Useful (or Not)? Eva Jablonka
4 A Case Study of Instruction and Assessment in Mathematical Modelling - ‘the delivering problem’. T Ikeda
5 The Quest for Meaning in Students' Mathematical Modelling Activity. João Filipe Matos and Susana Carreira
6 Some Mathematical Characteristics of Students entering Applied Mathematics Degree Courses. P L Galbraith and C R Haines
Section B Assessment at Tertiary Level
7 The Assessment Factor - by Whom, for Whom, When and Why. Leone Burton
8 Assessment of Complex Behaviour as Expected in Mathematical Projects and Investigations. John Izard
9 Mathematical Proficiency on Entry to Undergraduate Courses. Peter Edwards
10 Evaluating Rating Scales for the Assessment of Posters. Ken Houston
11 Deriving Learning Outcomes for Mathematical Modelling Units within an Undergraduate Programme. Andrew Battye and Maggie Challis
Section C Secondary Courses and Case Studies
12 An Operative Approach to Formal Reasoning. Paola Forcheri and Maria Teresa Molfino
13 The Application of Mathematics - an Essential Component of New Vocational Qualifications in the UK. John Gillespie
14 Mathematics as Orientation in a Complex World. Hans-Wolfgang Henn
15 The ‘Mathematical Modelling’ Course for Russia's Schools: its Aims, Methods and Content. EK Henner and AP Shestakov
16 On the Use of Open-ended, Real-world Problems. Ted Hodgson
17 Slow Learners, Mathematics and Future Profession: the search for mathematics on the shop floor of the future. Pieter van der Zwaart,
18 Mathematical Modelling for 16-19 Vocational Courses. Julian Williams and Geoff Wake
19 Mathematical Modelling and Children's Development of Science Concepts. Brian Doig, Susie Groves and Julian Williams
20 The Development of a Secondary-School Course in Probability, Statistics and Modelling that Attracts and Empowers Students. Thomas L Schroeder and Barry E Shealy
Section D Tertiary Case Studies
21 A Unified Approach to the Mathematical Modelling of Mechanical Systems. Krzysztof Arczewski and Wojciech Blajer
22 Performance Modelling of Parallel Algorithms. D B Clegg
23 Modelling Cancer Chemotherapy. JR Usher and D Henderson
24 Motoring - Modelling in the Fast Lane.M J Herring
25 Computer-based Experiments in Mechanics. D A Lawson and J H Tabor
26 Modelling Patient Flow through Hospitals. Sally McClean
27 Lagging a Pipe or Bandaging a Limb. A J I Riede
Section E Tertiary Courses
28 The Relevance of Research in the Development of Undergraduate Courses in Mathematical Modelling. Angela Botham and Jean Crowe
29 An Introductory Course on Mathematical Models and Modelling: A Constructivist Approach for Middle School Teachers. Don Cathcart and Tom Horseman
30 Simulation Modelling for Undergraduate Mathematicians. Andrew Fitzharris
31 Experiences With System Modelling in a Social and Business Context. MJ Hamson and MAM Lynch
32 Using Critical Reviews in Mathematical Modelling Courses. Bryan A Orman
Mathematics libraries and teachers in schools, sixth form colleges, universities, technical colleges, polytechnics, and teachers' training colleges. Inspectors of Schools, Local and government departments of education.
