Method is more than the sum of its parts

Nigel Steele recalls a guru who calculated a route to learning success

Everyone remembers a good teacher. If you asked a meeting of the institutes of electrical or mechanical engineers how many people remembered Ken Stroud, the chances are most hands would go up.

Very few would have met him and almost none would have been taught by him. But they would all remember Engineering Mathematics, Programmes and Problems, one of the most successful mathematics textbooks ever published.

The book grew out of Stroud's approach to teaching, which was that of a student guide who made mathematics accessible and understandable. Stroud, who died last month aged 91, was interested in the difficulties students faced in the transition from school to university and in the psychology of their learning. He developed the idea of "programmed" learning in the 1960s.

At the time it was expected that he would produce an inexpensive Dalek-like teaching machine for general class use, but instead he produced a more subtle learning aid.

Stroud's target audience was first-year mechanical and production engineering students. He broke the syllabus down into sections or programmes, each requiring about the same amount of effort and each scheduled for a week of study. There was both a continual review of the material in each programme and a (published) statistical analysis of results comparing those of the programme group with those of a control group. By 1968, the material had settled to more or less its final form, as it was later to appear in the book.

The class met for three hours a week. In the first hour each student read the programme at his or her own pace, asking questions if necessary. The next two hours were for further problems, presented by the lecturer with a stress on the application of the material, and for surgery-style tutorial help. It is likely that the success of this surgery-style activity formed the basis for many of the drop-in maths support centres in existence. The idea was not to save staff time or resources, but rather to show how to do a job better. There may also be a lesson here for today's "techies" in appreciating the difference between learning and enhancing learning.

It would be false to give the impression that Stroud's ideas were always received with enthusiasm, breaking as they did with the traditional approach. When he first proposed his method, there was concern that students would be left too much on their own, with the absence of formal "developmental" lectures. It is now seen as desirable for students to take responsibility for their own learning.

Stroud was ahead of his time in identifying precise learning objectives, and then helping the student to achieve these by small, closely guided steps. This is particularly appropriate, and indeed often necessary, for first-year students who have just made the transition from school or college to university. Such students may not have developed the necessary study skills, including note-taking and reflection, to cope immediately with a full set of lecture courses.

Many universities are still devising interesting and novel approaches to deal with this problem, which is by no means restricted to mathematics. The challenge is not just to get the students to make a successful start but also to equip them to take, with less direct guidance, the larger steps necessary to understand the material that will come later in a degree course.

As well as being a mathematician, Stroud was interested in electronics and analogue computing. His family watched the 1953 coronation on a television he had built from scratch. Being assigned to stand in for Stroud in the analogue computing class was fine when the (then) modern electronic analogue computers were being used.

However, when it came to demonstrating the electro-mechanical simulator that Stroud had built, there was trouble. Mis-setting the parameters, that is not tightening the damping screw enough, could mean yards of steel strip on the floor, distressed motors and a wrecked apparatus.

Stroud's book, now in its fourth edition, has become a legend. Sales of this and its partner volume, Further Engineering Mathematics, are still high. Even when lecturers choose a different textbook as their set text, word gets round that Stroud's is the book you need if you want to be able to master the mathematics, and piles of it sit in book shops right next to the recommended text.

Nigel Steele is head of mathematics at the University of Coventry.