Malcolm Bernard Swan, educational designer, born 20 March 1953; died 24 April 2017
Professor Malcolm Swan, who has died at the age of 64, was an international star in the world-wide movement to improve the teaching and learning of mathematics, principally through the research-based design and development of materials that combine educational ambition with robustness in practice. This was the strategic mission of the University of Nottingham’s Shell Centre for Mathematical Education, a research team which, after a few formative years in the classroom, he joined in 1979 and where he played a leading role throughout his career.
A person of many talents, Malcolm’s exceptional skill was in the design of tools that enable typical teachers to make specific research insights on teaching and learning into a happy reality in their classrooms. He did this through a combination of deep understanding, creative ideas and graphical skills. His lessons contain surprise and delight, warmth and humour – qualities that students find too rarely in mathematics classrooms. The huge popularity of his work among teachers is no surprise.
Here I shall focus on the research aspects, outlining examples of his research and the broader issues they illustrate.
Malcolm led the Shell Centre team in a coherent program of studies of “diagnostic teaching”, a specific approach to formative assessment based on eliciting and confronting student thinking and misconceptions, then resolving them through structured discussion. It was design research before Ann Brown coined the term. Working initially with Alan Bell, he and the team first explored in a coherent sequence of small-scale studies the validity of this approach across three key variables: students, mathematical topics, and different designers of the experimental teaching material. Later, the research focused on more typical teachers, showing that collaborative discussion materials can be effective when used appropriately, even with low attaining students. The accompanying research program also offered insights into the ways in which teachers’ beliefs (about mathematics, teaching and learning) affect the ways in which they use teaching materials and, conversely, the ways in which the materials affect beliefs and practices. What was the key finding on student learning? The studies showed that diagnostic teaching, when compared with the standard direct instruction approach of the time, showed a common pattern of much improved long-term learning. This key result was stable across the various “parallel” studies. Malcolm described this insight-focused research in his book Collaborative Learning in Mathematics: A Challenge to our Beliefs and Practices.
This program was a strategic departure from the mainstream of educational research in seeking empirical evidence on the range of applicability of a set of insights – in Alan Schoenfeld’s phrase “warrants for generalizability”. In typical individual studies this generalization from specific treatment to general principles, though frequently suggested in the final section of the paper, is essentially speculative. Of course, a coherent long-term program is much easier to set up in a centre with a team that is funded for research but, as “Big Science” has shown, researchers can tackle important challenges this way through inter-university collaborations.
The second strategic innovation was to focus on research designed to have direct impact on large-scale professional practice – the goal of the mathematicians who founded the Shell Centre – aiming to reflect research like that developing effective treatments in medicine. In our view, the issue of scale required reproducible materials for improving teaching, assessment and professional development. This gave a key role to design that is both research-based and creative – Malcolm epitomised this combination at an exceptional level. However, to develop products that help teachers realise new types of learning in their classrooms, the range of research methods had to be broadened from the insight-focused studies of the ‘science’ paradigm, like design research, to an engineering research approach. In the words of the UK’s Research Assessment Exercise definition of research, moving from “original investigation undertaken in order to gain knowledge and understanding” to include “the use of existing knowledge in experimental development to produce new or substantially improved materials, devices, products and processes”. Development requires an iterative process: classroom trials, for example, with rich and detailed feedback from structured observation to inform revision at each stage.
Malcolm’s skill in leading the revision process, where common factors were distilled from the reports of different observers on different teachers’ realisations of the lesson materials, epitomised his interpersonal skills. Many people have commented on his modest, thoughtful, patient way with those new to design, and the insights this gave into his approach to task and lesson creation. He believed that design could be taught and learned.
Malcolm led the design effort through a series of projects that achieved large-scale impact. This started with work with examination boards in the 1980s. Nearly 30 years later he was awarded the first annual prize “for excellence in design” of the International Society for Design and Development in Education for The Language of Functions and Graphs, an examination module and perhaps his most famous product; it is still influential today. Later the professional development support package, Improving Learning in Mathematics, was developed with the Department for Education; it was sent to all secondary schools, colleges and prisons. For the last 25 years international collaborations with US and EU funding have widened the scope and impact of the Shell Centre’s work. For the US-based Mathematics Assessment Project, Malcolm led the design of 100 formative assessment lessons across the age range 11-17. These built on the previous research-based design on concept development and on problem solving. There have been over 7 million lesson downloads so far from map.mathshell.com alone.
In 2015 this body of work was recognised by the International Commission on Mathematical Instruction when Malcolm and I were chosen as the first recipients of the Emma Castelnuovo Award for “more than 35 years of development and implementation of innovative, influential work in the practice of mathematics education, including the development of curriculum and assessment materials, instructional design concepts, teacher preparation programs, and educational system changes”.
Malcolm was dedicated to the whole field of mathematics education, writing articles, giving talks, and hosting workshops. Since his death the Twitter-sphere has been alive with evidence of the insights, and the pleasure, he has given to so many teachers and others who have come across him and his work.
He was a lovely man with a touch of genius
Note: This obituary was written by Hugh Burkhardt with other colleagues.
The Language of Functions and Graphs
Nothing conveys as clear a sense of Malcolm as his designs, combining serious mathematics with warmth and gentle humour. His lessons contain surprise and delight, humanity and humour – opening up the world of mathematics even to students who struggle with the abstractness of school mathematics. Something of this can be seen in the two tasks shown, from The Language of Functions and Graphs.
The Bus Stop Queue
“You can pick up his The Language of Functions and Graphs, now thirty years old, and wonder, ‘What have we been doing all this time?’ Swan drew math out of the world and thought out of our students in ways that feel challenging and new even today.” Dan Meyer