Obituaries: Professor Richard Skemp

The development of mathematics education as an academic discipline owes much to 40 years of pioneering work by Richard Skemp. When he achieved his PhD from Manchester University in 1959, he was one of a handful of junior lecturers researching in that field. Now there are 15 Professors of Mathematics Education in the UK, and every one of them would attest to the influence of Skemp's work in stimulating their interest in the subject.

His book The Psychology of Learning Mathematics (1971) is among the best- selling books on school mathematics; it has been translated into more than 10 languages and, 25 years on, still appears on booklists. The book was unashamedly written for teachers, yet was academically rigorous, unpatronising, and a fascinating read.

Richard Skemp's lifelong mission was to improve the teaching of mathematics in classrooms. This was to be achieved by educating teachers about the nature of learning and by providing them with high-quality teaching materials, generated collaboratively and based on his theories. He was determined to replace ''instrumental understanding'' (knowing how) of mathematics, which was and still is the aim of much classroom teaching, with ''relational understanding'' (knowing both how and why). Instrumental understanding leaves the learner dependent on memorising arbitrary teacher-given instructions, whereas relational understanding endows the power to reconstruct, relate, apply and transfer knowledge.

It is not so much that his ideas were novel - he acknowledged his debt to Jean Piaget and others - rather that they were expressed in speech and in writing with an exemplary clarity and elegance, and a creative deployment of metaphor, which made them accessible to students, teachers and academics world-wide. Who can forget his analogy between learning a particular bit of mathematics and finding the route from Cambridge Circus to Leicester Square? How much more effective to use a mental street-map pieced together from the experiences of many previous trips (relational understanding) than easily forgotten verbal instructions (instrumental understanding)?

But in all his writing, and especially in a later academic book, Intelligence, Learning and Action (1979), published after his appointments as Professor and Director of the Mathematics Education Research Centre at Warwick University, he incorporated his own research results and adapted and extended existing theory.

The immediate result of his publications was many weekends spent debating with groups of mathematics teachers from Inner London and elsewhere, the publication of a set of secondary textbooks, and a rich source of material for primary schools. In the longer term, his ideas permeated into mathematics teaching both in Britain and overseas, helped by many invitations to give lectures and seminars.

It seems likely that it was his strong sense of humanity that first led Skemp to reject the then prevailing psychological paradigms of behaviourism and psychometrics. Although he possessed an Oxford degree in mathematics as well as in psychology, his regard for the value of individuals never allowed him to reduce their abilities to strings of numbers, or their minds to those of automatons. To Skemp the mathematical thinking of each child was important, rational and fascinating. He had no discernible vestige of self-importance or pretension, and gave as much patient attention to the views of an overseas primary teacher or a five-year-old as to those of learned scholars.

My personal memories of his kindness include an invitation to an unhurried and delightful afternoon tea at his London club in response to a mere tentative written request for a reference. After proffering what turned out to be extremely shrewd career advice, he escorted me to a shop on Piccadilly and earnestly sought, and took, my advice on the selection of a suitable woollen checked tie.

With similar generosity, Richard Skemp gave his time to countless individuals and many good causes, both private and professional. In particular he initiated, with support from others, two flourishing organisations, the British Society for Research in the Learning of Mathematics, and the International Group for the Psychology of Mathematics Education.

Margaret Brown

Richard R. Skemp, psychologist, mathematician: born Bristol 10 March 1919; Lecturer in Psychology, Manchester University, 1955-52, Senior Lecturer 1962-73; Professor of Educational Theory, Warwick University, 1973-86; Director of the Mathematics Education Research Centre, Warwick 1978-86; Visiting Professor, University of Calgary 1987-94; married 1961 Valerie Watts (one son); died Coventry 22 June 1995.