The International Community of Teachers of Mathematical Modelling and Applications
The First Twenty-five Years
- The Beginning
- The Exeter Conferences (1983 and 1985)
- Further afield in Europe - Kassel ((1987), Roskilde (1989) and Noordwijkerhout (1991)
- Across the Atlantic (1993) and back again (1995)
- Travels to Brisbane (1997), Lisbon (1999) and Beijing (2001)
- Criss-Crossing the Atlantic: Milwaukee (2003), London (2005), Bloomington (2007), Hamburg (2009)
- The International Executive Committee
- Application and modelling and ICME and ICMI
- Where to now
School of Computing and Mathematics
University of Ulster
School of Education
University of Queensland
Faculty of Education
University of Hamburg
It all began with the McLone Report (McLone, 1973). This work surveyed what recent mathematics graduates were doing in their employment, how relevant their education was to their work, and how satisfied their employers were with their performance. McLone described the average mathematics graduate as:
Good at solving problems, not so good at formulating them, the graduate has a reasonable knowledge of mathematical literature and technique; he has some ingenuity and is capable of seeking out further knowledge. On the other hand the graduate is not particularly good at planning his work, nor at making a critical evaluation of it when completed; and in any event he has to keep his work to himself as he has apparently little idea of how to communicate it to others (p. 33).
Twelve years on this was still a problem with Challis, Gretton, Houston and Neill (2002) observing:
The SIAM (Society for Industrial and Applied Mathematics) report on Mathematics in Industry (SIAM, 1995) contained data from a survey of PhD graduates working in industry. The report indicated that modelling, communication and teamwork skills together with a willingness to be flexible are important traits in employees. However the PhD graduates themselves indicated that they felt inadequately prepared to tackle diverse problems, to use communication effectively and at a variety of levels, or to work in teams.
The reason for this maybe that too few universities have as yet embraced the mathematical modelling ideal, or even the mathematical modelling idea!
There were other influences. The UK-based Association of Teachers of Mathematics was advocating courses for sixth formers (UK years 12 and 13; US grades 11 and 12) which included "some general awareness about the nature of mathematical activity and the kinds of situations in which it may be usefully applied" and which would develop "the ability to make effective use of both individual study and of working in a group" (ATM, 1978, p. 31). The Cockcroft Report (Cockcroft, 1982) said that it was important for sixth formers to "pursue independent investigations and to discuss and communicate their ideas." [Cockcroft was the Chair of the Committee of Enquiry into the teaching of mathematics in schools in the UK. The Report had a long lasting influence on mathematics education, initiating the development of the National Curricula in the countries of the UK but also impacting on curricula in other countries such as Australia.] In the USA, the Mathematical Association of America through its Committee on the Undergraduate Program in Mathematics, recommended that "Students should have an opportunity to undertake 'real world' mathematical modelling projects, either as term projects, in an operations research course, as independent study, or as an internship in industry" (Mathematical Association of America, 1981, p. 13). That report goes on to add that all mathematical sciences majors should experience mathematical modelling early in their studies.
There were many influences from many directions, and things began to happen. In the UK David Burghes, who could well be described as the Father of ICTMA, decided to try to enliven the school mathematics curriculum by working with teachers to produce interesting modelling investigations for pupils at secondary level. In 1978, while at Cranfield University, he started publishing the Journal of Mathematical Modelling for Teachers, which in 1981 became Teaching Mathematics and its Applications, a journal of the UK-based Institute of Mathematics and its Applications. Burghes continued to edit this journal until 2000. He held modelling workshops for teachers up and down the country, and he formed the Spode Group, so called because it met in the Spode Conference Centre in Staffordshire. His co-conspirators in this venture were John Berry (then at the Open University) and Ian Huntley (then at Paisley College in Scotland). The Spode Group published three books on the theme of solving real problems with mathematics (Spode, 1981, 1982, 1983). The articles in the Spode publications all followed a similar format: a problem statement, followed by teaching notes, possible solutions and related problems. More publications by this group followed later.
Other people were becoming involved in the movement to enhance the teaching of mathematical modelling in schools and universities. These included John McDonald, (Paisley) and Glynn James (Coventry Polytechnic). James organised a workshop for lecturers in higher education and published the proceedings (James & McDonald, 1981). Others were Hugh Burkhardt, for many years Director of the Shell Centre for Mathematical Education at Nottingham University, George Hall, also at Nottingham, and Dick Clements at Bristol. In Northern Ireland the Further Mathematics Project was getting under way. Working on the principle WYAIWYG (what you assess is what you get), this project launched an unprecedented effort to introduce an A-Level examination in modelling and investigations (Fitzpatrick & Houston, 1987). Furthermore, the Council for National Academic Awards encouraged mathematics departments in the polytechnic sector of UK higher education to include mathematical modelling in their courses. This resulted in a marked difference between the polytechnics and the universities in teaching applied mathematics. The universities tended to deliver traditional lecture courses on mechanics, fluid dynamics, etc, while the polytechnics students were doing some modelling, writing reports and giving presentations. [The polytechnics in the UK came into existence in the 1970s to further the government's plan to expand opportunities for tertiary level education. They were elevated to university status, each with its own charter to award degrees, in 1992. The Ulster Polytechnic was an exception. It became a constituent part of the University of Ulster in 1984, through a merger with the New University of Ulster.]
In all of the above initiatives, the emphasis was on the teaching of mathematical modelling. For many years there had been conferences at which various mathematical models were discussed, but there had not been any special attention to teaching modelling. The time was ripe for such a conference.
The Exeter Conferences (1983 and 1985)
John Berry (Open University), Burghes (who moved to Exeter University), Huntley (who moved to Sheffield City Polytechnic), Glynn James (Coventry Polytechnic), and Alfredo Moscardini (Sunderland Polytechnic) organised the first "International Conference on the Teaching of Mathematical Modelling." The aspiration that "this will become a bi-annual event" [they meant biennial - every two years, not twice a year] was expressed in the conference literature. And it did so become! [The words "and Applications" were not added to the title until ICTMA 3]. The conference was held at Exeter University in July 1983. ICTMA 1 attracted 125 delegates from 23 different countries. Not unexpectedly, the majority of the delegates (76) were from the UK. There were two plenary lectures and 39 lectures in the parallel sessions. These are reported in the first of the books in the ICTMA series (Berry, Burghes, Huntley, James, & Moscardini, 1984). The majority of the presentations addressed higher education, with only five reporting on developments in schools. This imbalance is understandable given that it was much easier to change the curriculum in a polytechnic than in a school (or even in a university!).
At this first conference people were thinking and talking about issues that are still very pertinent, issues such as assessment and group work. Many of the talks (and the papers in the resulting book) were of the war story variety: "This is how we teach modelling" or "This is our curriculum," and many were useful descriptions of models that the author(s) had used in their teaching. There were a few papers describing research or presenting philosophical perspectives. Five of the people who would organise subsequent ICTMA conferences were present: Werner Blum, Jan de Lange, Chris Haines, Ken Houston and Gabriele Kaiser. The tradition of publishing a book of selected papers from the conference began with ICTMA 1, and at the same time, a long association with Ellis Horwood and the publishing companies he managed. He has published the books resulting from all the ICTMA conferences except one. A complete list of the ICTMA books is given in the ICTMA website
ICTMA returned to Exeter in 1985 as ICTMA 2. Again it was well attended. There were 73 presentations, including two plenaries, by delegates from ten different countries, with the majority again from the UK. It was decided to publish 48 of the papers and, for the only time in ICTMA history, two volumes were produced. The first dealt with "Modelling Methodology, Models and Micros" (Berry, Burghes, Huntley, James, & Moscardini, 1986) while the second was titled "Mathematical Modelling Courses." The preface to the second volume opens thus: "Courses in mathematical modelling in higher education are now quite commonplace, especially in polytechnics." There was a feeling abroad that the battle was being won, at least in that sector of higher education. There was a great variety in the courses being offered, and the volume containing descriptions of courses was written in the hope that "this text will help both newcomers and experienced teachers to learn from others." (Berry, Burghes, Huntley, James, & Moscardini, 1987). Ten of the 25 papers were relevant to school mathematics-a considerably greater number than at ICTMA I. There were descriptions of innovative attempts to enhance and change what were seen as conservative national curricula.
The first volume was arranged in three sections with the first section reviewing methodology in the process of problem solving and proposing new ideas in formulating models. Research reported at ICTMA 11 (Izard, Haines, Crouch, Houston, & Neill, 2003) continued to identify model formulation as a crucial skill, but one at which students do not do very well. This problem in the teaching of modelling has not yet been solved. The second section of the volume contained a selection of models, which had already been used in teaching to serve as a resource for teachers. The third section was innovative for its time. It described teachers' successes using microcomputers to explore and evaluate models, and to do simulation modelling.
Further afield in Europe - Kassel ((1987), Roskilde (1989) and Noordwijkerhout (1991)
The next three ICTMA conferences were held in continental Europe, in Germany in 1987, in Denmark in 1989 and in the Netherlands in 1991. The chairs of the organising committees were, respectively, Werner Blum (Kassel University), Mogens Niss (Roskilde University) and Jan de Lange (Freudenthal Institute, Utrecht University). Given the wide mathematical education interests of these three and the institutions where they work, it will be no surprise to learn that discussion of teaching at secondary school level was much more prominent than before. This is highlighted particularly in the structure of the books from the Kassel and Roskilde conferences, in which distinct sections addressed the lower secondary, upper secondary and tertiary sectors.
The name of a conference was now the Nth International Conference on the Teaching of Mathematical Modelling and Applications. The phrase applications and modelling now occurs very frequently in conversation and literature. This was a desirable development because it highlights the subtle but significant differences between a study of mathematical models and the process of mathematical modelling. In his plenary lecture at ICTMA 3, Mogens Niss (Roskilde University) said that an application of mathematics was the result of the process of applying mathematics to any area of extra-mathematical reality-a mathematical model-whereas mathematical modelling is the process (Niss, 1989). Another term entered the modelling scene at this time - mathematisation. This is defined by Niss to be the translation stage of the modelling process, when the modeller moves from the physical model created through the making of simplifying assumptions to the mathematical model created by the introduction of variables and their mathematical relationships to one another.
Probably due to the fact that conference venues were invited outside the UK, these three had more participants than the Exeter conferences. In Kassel, for example, there were five plenary lectures, 83 other presentations ran in 7 or 8 parallel sessions and a choice of five workshops. There were 70 papers in the book (Blum, Berry, Biehler, Huntley, Kaiser-Messmer, & Profke, 1989). The introduction of workshops was a very welcome innovation. We all knew that group work was important for the learning of modelling, and we practised it with our students, but so far we had not engaged in group work ourselves at the ICTMAs.
Philip Davis (Brown University) gave a plenary at Roskilde on "Applied Mathematics as a Social Instrument" (Davis, 1991). The goals of applied mathematics include "description, prediction and prescription - tell me what is, tell me what will be, tell me what to do about it." In social and economic modelling he warned that we should beware, because "mathematical descriptions tend to drive out all others," and we all know that models are only as good as their assumptions.
At ICTMA 5, Christine Keitel (Berlin Technical University) observed that while society was becoming more and more mathematised through intelligent technology, individuals were becoming de-mathematised. Mathematics at work was becoming implicit in the machinery and we no longer saw it. School education was the time to make the implicit explicit (Keitel, 1993). At the same conference Cyril Julie (Western Cape University) described how he saw mathematics education as an agent for emancipation and empowerment. "Peoples' mathematics" is not just about mathematical empowerment but also about political and intellectual empowerment (Julie, 1993).
Across the Atlantic (1993) and back again (1995)
I suppose no conference series could claim to be truly international until there had been at least one meeting in the United States of America. And so the Executive Committee of ICTMA accepted Cliff Sloyer's offer to organise ICTMA 6 and to host it at his institution, the University of Delaware - Newark in the summer of 1993. That was the tenth anniversary of ICTMA.
The conference was organised along familiar lines with three plenary lectures, 28 parallel presentations and 13 workshops of varying length organised in series or in parallel depending on the length of each. The book (Sloyer, Blum, & Huntley, 1995) has 24 chapters and, in a break with tradition, was published by an American publisher. The three plenaries were in the nature of survey papers. Werner Blum (Kassel University) looked at important aspects of practice and research. He gave examples to illustrate what exactly is meant by "applications and modelling", and answered the question: "What is the use of A&M in mathematics teaching?" by giving five arguments. He wrote "A&M is one way to make the learning and teaching of mathematics more meaningful and to supply students with orientational knowledge as well." He proposed practical measures to promote the teaching of A&M and listed several, as yet unanswered research questions (Blum, 1995). While the community has wrestled with these questions now for fifteen more years, and while we have found out much and understand more than we did in 1993, we have not yet cracked the problem!
Peter Galbraith (University of Queensland), soon to be the chief organiser of ICTMA 8, spoke on "What I have learned." His summary notes that he felt that, even after ten years, "questions and needs continue to emerge." There was a continuing need for case studies, right through from primary to tertiary, to minimise re-invention of wheels. There was a need to design, implement and study experiments located in a system of institutions. Much remained to be learned about ways to make group learning more effective, and here the mathematics community could learn from other communities. Assessment was also seen as persisting as an issue of importance and controversy (Galbraith, 1995).
Ian Huntley (Sheffield Hallam University) gave a "state of the (UK) nation" report, telling of the move in the UK towards a mass higher education system that would bring many problems in its wake (which today are still rumbling), and he described the initiatives in technology-based training that were then being funded. He spoke of the initiative to embed information technology in the whole school system. He noted that ICTMA should have been ICTMMA - there are, after all, two words beginning with M in our title-and he asked if we should consider becoming the International Conference on Modelling and Applications, thus broadening the scope beyond mathematics, and letting the teaching develop the acquisition of key personal skills and competencies (Huntley, 1995). This is an interesting proposition, but this community has continued to concentrate on mathematical modelling. We are all aware that our students develop other key skills in the process of mathematical modelling activity, thus giving them a double endowment. After all, "mathematical modelling is a way of life!"
A fourth plenary was given on Comprehension Tests by Ken Houston, the organiser of ICTMA 7, at the University of Ulster.
The conference accommodation on the Jordanstown Campus of the University of Ulster was brand new, there was an IRA cease-fire throughout 1995, and over 100 delegates came. The conference themes were not dissimilar from the past. In the preface the editors wrote, "It is now widely accepted that mathematical modelling is 'the way of life' of an applied mathematician." "Nevertheless, despite this widespread recognition and practice, there are still needs to be met." We listed these as the need to convert some hearts and minds, the need to devise, implement and evaluate new methods of teaching and learning, the need to conduct research and the need to disseminate (Houston, Blum, Huntley, & Neill, 1997). At one level, nothing changes, but at another as a community we become wiser and more aware of how to do this great task of educating the world's young people. In the plenaries, Sue Lamon (Marquette University) talked about modelling and what is known about the way our minds work (Lamon, 1997), Leone Burton (University of Birmingham) about assessment (Burton, 1997), Mark Cross (University of Greenwich) about industrial modelling, Catherine Coxhead (Northern Ireland Council for the Curriculum, Examinations and Assessment) about the Northern Ireland schools' curriculum (Coxhead, 1997), and Sally McClean (University of Ulster) about statistical modelling (McClean, 1997).
Travels to Brisbane (1997), Lisbon (1999) and Beijing (2001)
The preface to the book of the Brisbane conference draws attention to the truly international nature of ICTMA in 1997 (Galbraith, Blum, Booker, & Huntley, 1998). All continents of the earth except Antarctica were represented. Furthermore, for the first time the word "technology" appeared in the title, acknowledging the fact that the use of technology is highly desirable in the teaching of applications and modelling. The preface continues:
The vertical scope of the content extends from secondary school mathematics through tertiary undergraduate levels, so recognising that the ability to apply mathematics is important whatever the level of techniques available. The horizontal scope of the book reflects issues that are currently challenging existing theory and practice in the teaching of application and modelling skills.
Beside the use of technology, assessment was still a major issue as was the development of students' communication skills. In his cryptically titled plenary Claudi Alsina (1997) invited us to bring the joy of learning into our lives and our classrooms. Anne Street (1997) showed how discrete mathematics can be used in modelling discrete problems in agriculture and questionnaire design. In the final plenary, João Filipe Matos discussed the need of theory to better understand students' mathematical learning processes in relation to mathematical modelling activity. He explored the possibilities and benefits of taking into account concepts from a socio-cultural approach, situated learning, an embodied view of the mind, meaning making in mathematics and its relations to mathematical thinking and learning in a socio-culturally organised space. The post conference book contains a good collection of models for use in teaching, and accounts from several countries of national developments in the teaching of modelling. The world was now getting the message!
Two years later, in 1999, the conference was back in Europe, in Lisbon, Portugal. The chair of the organising committee was João Filipe Matos of the University of Lisbon. There was a greater philosophical air about the conference this time as his Brisbane plenary foreshadowed. There were the customary selections of papers describing innovative uses of technology, innovative uses of mathematical methods, innovative curricula, and pedagogical issues, but three of the plenaries opened up new directions.
Stephen Campbell (University of California-Irvine) gave his audience a lively introduction to his philosophy of mathematical modelling. He proposed a radical enactivist view of life in general and modelling in particular (Campbell, 2001). Susana Carreira (New University of Lisbon) spoke on the metaphorical nature of mathematical models (Carreira, 2001) and developed the "psychological argument" for learning applications and modelling proposed by Blum (1991). She argued that "mathematical models and applied problems are a powerful context for the emergence of metaphorical thinking." And John Mason (Open University, UK) did some meta-modelling (Mason, 2001). He used the mechanical idea of centre of gravity as a metaphor for the focus of attention when modelling is performed. Where is the student's centre of gravity or focus of serious attention when he or she is modelling? He wrote, "exposing students to mathematical modelling is not just a form of teaching applications of mathematics, nor of illuminating the mathematics being applied. It is equipping students with the power to exercise a fundamental duty." The way of life idea again!
And so to China in 2001! Particularly during the 1990s, China had opened up to the West. There was much more coming and going, and Chinese colleagues interested in teaching modelling had been attending recent ICTMAs. These included Qi-Xiao Ye (Beijing Institute of Technology) who was appointed to organise ICTMA 10 and Qi-Yuan Jiang (Tsinghua University, Beijing) who was also on the local organising committee for ICTMA 10. There were over 150 participants, with the vast majority from the host nation, but only about 40 or so of the "regulars" attending. But it was a wonderful experience to meet so many new teachers of modelling, so eager to tell the world what they were doing. And there is much going on in China. Both secondary and tertiary institutions were teaching modelling, and a number of case studies are included in the book of the conference (Ye, Blum, Houston, & Jiang, 2003).
The academic programme included five plenaries. Gabriele Kaiser (University of Hamburg) spoke on "The Role of Figurative Context in Realistic Tasks" (Busse & Kaiser, 2003). Zhang Jingzhong (Chinese Academy of Sciences) spoke on "How to Teach Mathematics by Using the 'Intelligent Platform for Education.'" Bai Fengshan (Tsinghua University, Beijing) spoke on "Reforming University Mathematics Education." Avner Friedman (University of Minnesota) spoke on "Industrial Mathematics: Course Development" and Sue Lamon (Marquette University) spoke on "Modelling Rates of Change: Assessing Student Progress in Differential Calculus".
Criss-Crossing the Atlantic: Milwaukee (2003), London (2005), Bloomington (2007), Hamburg (2009)
In 2003 ICTMA returned to the United States after a 10-year period with a very small conference in Milwaukee. Susan Lamon was the chief organiser of ICTMA 11 which was held at Marquette University. The low attendance was mainly due to a disappointing level of involvement by participants from the host country. There was, however, a good breath of international representation, and high quality presentations across every level of education from primary to undergraduate. Lyn English of Queensland University of Technology "argue[d] for the implementation of mathematical modelling activities within the elementary and middle school years" (English, 2003, p. 3) in her plenary entitled "Mathematical Modelling with Young Learners". Ken Houston gave us all an historical tour in his plenary, "ICTMA: The First 20 Years" (Houston, 2003), parts of which have formed the basis of this chapter. Stephen Merrill (2003) reminded us that "Those who teach MM (or even general PS involving "story problems") universally recognise the difficulty in teaching the subject. Part of the difficulty is that students have no idea how difficult problems are actually solved. Instead, they are given procedures to follow, techniques to apply, and reports to be written. With hard problems, however, defined as those for which common procedures and techniques do not work, creative exploration is required - and the avenue to creative thought and unpredictable insight often takes an unanticipated path through dreams." Richard Lesh spoke on "How mathematising reality is different from realising mathematics" introducing many of us to his notion of model-eliciting activities.
ICTMA12 saw the conference return to Europe. The conference was held at City University in London in July of 2005, at the time of the London bombings. Chris Haines of CITY University London was Conference Chair and first editor of the Proceedings and took leading responsibility for both the organizational and academic commitments of the conference. Despite the disruption caused by the bombings many members attended as can be see by the official photograph in Figure 1. The resultant book (Haines, Galbraith, Blum & Khan, 2007) contains 49 chapters from a wide cross-section of countries as participants came from more than 30 countries. In his preface to the book, Chris points out "The effective practice, teaching and learning of mathematical modelling and applications play major roles in enabling successful activity within industry, business and commerce, and education. Mathematical modelling permeates society and so it is very appropriate that ICTMA contributions cover the whole spectrum of mathematicians, engineers and scientists, modellers in industry, government and finance, and teachers and researchers in schools and universities" (Haines, 2007, p. v). Models, modelling and applications for education, business and the professions featured strongly in the conference academic programme. Julian Hunt FRS gave a comprehensive overview of some of the big problems faced by modellers in applied mathematics (Hunt, 2007) whilst Kate Barker (2007), a member of the monetary policy committee of the Bank of England, discussed the range of issues that arise from the use of economic models and the importance of recognising the context when selling particular models to the bank's clients. Peter Galbraith (2007) pointed out that there are yet "more windmills to conquer" in the area of mathematical modelling and applications to the real world taking a stronghold in classrooms but we can dream a 'possible dream'. Katja Maaß (2007) added to previous attempts to flesh out the concept of "modelling competencies" by giving participants a window into what students in her research classrooms learnt from engaging in modelling. Celia Hoyles and Richard Noss (2007) reported on the design of a programming environment for students to build models of their mathematical and scientific knowledge and a set of web-based collaboration tools to share ideas and programmed models. It was hoped that by constructing and sharing models students would develop deeper understanding of concepts and the relationships betweeen them.
Official photograph of attendees at ICTMA12, London
In 2007 there were two major ICTMA events, the ICTMA 13 Conference at Indiana University in Bloomington, USA, and a formal satellite conference at the University of Nepal, Kathmandu. The satellite conference was hosted by Bhadra Tulhadhar in the last week of June, 2007. Five plenary lectures were given by Harald Krogstad (Norway), Francois-Xavier Le-Dimet (France), Vinod Saxena (India) , Hans-Wolfgang Henn, (Germany) and Daniel Clark Orey (USA). A total of 140 participants from 11 countries attended.
Richard Lesh was the chief organiser of ICTMA 13 which was hosted by Indiana University in collaboration with Purdue University, INSPIRE project, and the United States Air Force Academy at Fort Worth. In addition to the delegates in Bloomington, delegates to the Modelling in Mathematics Learning Workshop at Makerere University in Kampala in Uganda participated in some sessions via internet link. The Plenary lectures were as follows: "Modelling Theory for Math and Science Education" - David Hestenes (USA), "Priorities in a Research Agenda for Engineering Education" - Barbara Olds (USA), "Modelling to Address Techno-Mathematical Literacies in Work" - Richard Noss and Celia Hoyles (UK) and "Modelling a Crucial Aspect of Students' Mathematical Modelling" - Mogens Niss (Denmark). A total of 53 papers were presented at the conference. Several discussion groups operated throughout the conference. There were 157 delegates from 18 countries but the vast majority were from the United States.
Looking to the future, ICTMA14 will be held in 2009 in Hamburg. Gabriele Kaiser is the Chief organiser. There is also the possibility of a North American Chapter of ICTMA having its first conference in 2008, our 25th year.
The International Executive Committee
Before we complete our journey, we should discuss the changes that have occurred in our organisation. In the beginning John Berry, David Burghes, Ian Huntley, Glynn James, and Alfredo Moscardini comprised the organising committee for ICTMA 1 and 2. Then came ICTMA 3 and the tradition began to include the chief organiser of each conference in the executive committee. Thus it grew and grew. Somehow Ian Huntley remained the perpetual chair of the committee. His principal task was to determine the venue and chief organiser of the next conference. At each ICTMA, the venue for the next conference was chosen from the sites that had bid for it. Apart from giving advice to organisers, that was all the committee did. It did not exercise any power to influence the programme at a conference; the design of the programme was entirely at the discretion of the local organising committee.
By 1998 the executive committee was beginning to recognise that it was not a terribly democratic body so a constitution was written with established rules for membership and voting. There was a growing number of women members and the first women to serve on the executive committee were elected at this time when there was elections for President and for the executive committee members. The three conference organisers, those of the last conference, the current one and next one, remained on the committee ex officio. Ken Houston was elected president in 1999 and served in that capacity until 2003. We had moved from a (fairly) benign dictatorship to a democracy! Peter Galbraith served as the next president from 2003-2007. Gabriele Kaiser is the current president, presiding over quite a diverse international executive, where Chris Haines is the one remaining UK connection. Chris is the only ICTMA member to have contributed papers at all ICTMAs since there inception in 1983.
Application and modelling and ICME and ICMI
At ICME-3 in 1976, Henry Pollak, who had been pleading for an integration of applications and modelling into mathematics teaching (e.g., Pollak, 1969) brought applications and modelling to the fore by giving the survey lecture, "The Interaction between Mathematics and Other School Subjects" (Pollak, 1979). Applications and Modelling has been represented on the agenda of the ICME conferences since ICME 5 in Australiain 1984 (e.g., Blum, Galbraith, & Christiansen, 2001; Blum, Niss, & Huntley, 1989; Breiteig, Huntley, & Kaiser-Meßmer, 1993; Galbraith, Blum, & Christiansen, 2002).
In 2003 ICTMA became an affiliated study group of the International Commission on Mathematical Instruction. Many members participated in ICMI Study 14 on "Applications and Modelling in Mathematics Education in February 2004 in Dortmund, Germany. Werner Blum was the chair of the International Programme Committee. The study effectively began in 2002 with the development of the Discussion Document by the International Programme committee (Blum et al., 2002). A pre-conference volume of papers for discussion at the conference were published by Henn and Blum (2004). The study volume (Blum, Galbraith, Henn, & Niss, 2007) that resulted from conference discussions includes plenaries from the conference, working group discussions, selected revised or new papers from conference participants, and additional papers in areas where there were gaps.
In 2004, ICTMA participated in ICME as an Affiliated study group for the first time. However, there were other opportunities for members to participate in the topic study group on Applications and Modelling, through the Discussion Group on the same topic and in the report of ICMI Study 14. A selection of papers from ICME's 9 and 10 were published in the journal, Teaching Mathematics and Its Applications (e. g. Houston, 2005).
Where to Now
The history of ICTMA began with concerns about the undergraduate preparation of students who were later required to solve real problems, often collaboratively, when employed as graduates, and the early conferences had a special emphasis on sharing challenges involved in designing and delivering courses to address the identified needs. Were this to have remained the sole focus it might be argued that the field is limited, with the constant revisiting of problems tending towards re-invention of wheels. In fact challenges continue to emerge in this original focus area, but the field of interest has since grown, spurred by the variety of settings and purposes within which applications and modelling are implemented. The emphasis then has expanded to include learning settings that involve all levels of schooling, undergraduate and teacher education, together with professional and workplace environments in which the application of mathematics to real problems is a valued goal. The academic focus encompasses themes such as the design and delivery of programs, analysis of modelling competencies and student performance, development and improvement of effective methods of teaching and assessment, and group and individual problem solving expertise. A focus on research recognises the importance of establishing a robust knowledge base from which to address problems that continue to emerge.
From the outset ICTMA has maintained the integrity of its focus, which has both a mathematical and an educational component. This makes a distinction from a purely mathematical problem focus on the one hand, and a mathematics education context in which the mathematics need have no connection with applications and modelling. Thus a distinctive aspect of ICTMA is the interface it provides for collaboration between those whose main activity lies in applying mathematics, but who have an informed interest in sharing these abilities and developing relevant skills in others (an educational focus), and those whose principal affiliations are within education, but who have a commitment to promoting the effective application of mathematics to problems outside itself.
Much progress has been made on many fronts, not the least of which includes winning over many hearts and minds. But, as the Preacher once said, "What has been will be, what has been done is what will be done; and there is nothing new under the sun." (Ecclesiastes, 1, 9, The Bible, RSV) Our themes recur-curriculum, teaching, learning, group work, assessment, and so on. But they are evolving themes and there are new things under the sun-new ideas, new understanding, new students, new teachers. The quest for understanding and beauty will never be finished, and our community, the Community of Teachers of Mathematical Modelling and Applications, will continue to seek innovative ways of teaching our subject to the next generation and will continue to seek understanding of how our students learn.
- Alsina, C. (1998). Neither a microscope nor a telescope, just a mathescope. In P. Galbraith, W. Blum, G. Booker, & I. Huntley (Eds.), Mathematical modelling: Teaching and assessing in a technology rich world (pp. 3-10). Chichester, UK: Horwood Publishing.
- ATM. (1978). Mathematics for sixth formers. Derby, UK: Association of Teachers of Mathematics.
- Barker, K. Economic modelling: Theory, reality, uncertainty and decision-making. In Haines, C., Galbraith, P., Blum, W. & Khan, S. (2007). (Eds.). Mathematical modelling (ICTMA12): Education, Engineering and economics (pp. 25-42). Chichester, UK: Horwood Publishing.
- Berry, J. S., Burghes, D. N., Huntley, I. D., James, D. J. G., & Moscardini, A. O, (Eds.), (1984), Teaching and applying mathematical modelling. Chichester, UK: Ellis Horwood.
- Berry, J. S., Burghes, D. N., Huntley, I. D., James, D. J. G., & Moscardini, A. O. (Eds.), (1987). Mathematical modelling courses. Chichester, UK: Ellis Horwood.
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