Some Experiments on Structured Learning

When an experimental psychologist accepts an invitation to share in a conference of distinguished mathematicians and mathematical educators it is most important that when he speaks he makes clear his standpoint and presuppositions and the limitations of what he has to say. With the widespread interest in and enthusiasm for ‘new mathematics’ of one sort or another, it is inevitable, and indeed highly desirable, that educational psychologists should be closely involved in attempts to evaluate the efforts and results of the different innovators in this field. In general, the educational psychologists’ concern tends to be with the gross or overall effects of what the different materials and methods achieve. They therefore tend to be concerned with things like success and failure rates, and rates of progress in developing various mathematical skills. To put it another way, they tend to be more concerned with what is achieved than with how and why it is achieved. By comparison, and from the standpoint of an experimental psychologist interested in understanding more about complex learning and thinking, my primary interest is in understanding the processes whereby the end products are achieved and only secondarily in success or failure rates. To put it another way I want to know what factors are responsible for success or failure not just how many subjects succeed or fail. Perhaps by way of illustration I may compare an approach used extensively by the late Sir Frederic Bartlett and his students.