The Papers of

Richard R. Skemp

March 10, 1919 – June 22, 1995

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Selected research papers of Professor Richard Skemp.

Skemp, Richard R. (1961), Reflective Intelligence and Mathematics, British Journal of Educational Psychology. 31, P1, 45–55.
Abstract: This paper is an attempt to continue into the field of mathematics the kind of psycho-logical analysis which Piaget has made in that of number. Differences between arithmetic and mathematics are related to the difference between sensori-motor intelligence and reflective intelligence. The latter concept is developed further, and an experiment is described to test the hypothesis that the transition from mechanical arithmetic, via problem arithmetic, to mathematics, involves the transition from sensori-motor to reflective intelligence.

Skemp, Richard R. (1962). The Need for a Schematic Learning Theory, British Journal of Educational Psychology, 32, P2, 133–142.
Abstract: Current learning theories have little direct application to problems of teaching and learning school subjects. The development of a schematic learning theory will, it is hoped, help to remedy this deficiency. Such a theory will also have wider applications.

Skemp, Richard R. (1962). The Psychology of Teaching and Learning Mathematics.
An unpublished paper presented to a UNESCO conference in Paris 1962, with the explanation ‘Study No.1: this is one of several studies, on the various aspects of the teaching of mathematics in secondary schools, which are intended to provide an analysis of how this subject is being taught in different parts of the world.’
The paper reviews the literature to report the lack of papers on theories of learning concerning concept formation, schematic learning, mathematical exploration and generalization, problem solving and correction of errors, symbolism, motivation. Skemp produces 33 hypotheses to consider the difference between schematic and rote learning.

Instrumental Understanding and Relational Understanding [PDF]

The Silent Music of Mathematics [PDF]

Theoretical Foundations of Problem-Solving: A Position Paper (1993) [HTML]