An Introduction to Richard Skemp's

Theory of Intelligent Learning

 

Richard Skemp was an educational theorist of the first order. He was also a very practical man. He developed a very practical and useful theory of intelligent learning while applying it to the problems of teaching mathematics and carefully field-testing it in that context, among others. When asked why he attached so much importance to theory, this is what he replied:

Few thinking persons would question the importance of theory in increasing our understanding and control of the physical world. Electromagnetic theory has given us radio and television, with the Edison telegraph as its forerunner and fax as the latest electrical marvel. Without this theory we would still depend on sending pieces of paper by mail or courier. When Bruce and I talk to each other by transatlantic telephone, we depend on the geo-stationary satellite which hangs motionless above mid-Atlantic sending and receiving our radio messages with the speed of light. This represents highly sophisticated applications of several theories, Newtonian theory of gravitation being one of the most important. In another realm of discourse, the control of diabetes rests on theoretical discoveries in physiology and biochemistry; and when a cure for cancer is discovered, this too will rest on theoretical advances.

It is only by having an appropriate theory that we can understand the invisible causes which lie beyond the visible effects. We need it whenever common sense is not enough. We still hear people, including some who should know better, asserting that we don't need theories in education. Would they entrust their child to a doctor who learnt only by trial and error? Or themselves to an airline whose navigators had no knowledge of navigation, by which to take them safely to their destination when the plane is out of sight of land, and when often the earth's surface itself is hidden by cloud?

A person who intervenes in the workings of the human body needs a mental model beyond common sense, if he is to do more good than harm. (Medieval doctors often did more harm than good.) And if as teachers we intervene in the mental processes of a growing child, which are even more inaccessible to our senses, the same applies.

Until education has a theoretical foundation comparable with those which give such power in the fields of science and technology, teachers' efforts will not meet with the success they deserve.

I should have said 'teachers and children', since children are required by law to attend school for around ten years of their lives. So surely they deserve the best we can give them. And in my view, we can't do this except by the application of appropriate theory. (Richard Skemp, 1992, "Question Time with Richard Skemp," Videocassette Recording, Calgary, AB, Communications Media Department, The University of Calgary.)

In the Prologue to Mathematics in the Primary School, Skemp has described two very different kings of learning and understanding. If one learns with instrumental understanding one learns to use rules without reasons whereas with relational understanding one knows both what to do and why. Without a theory of learning one can only have instrumental understanding. Professional educators need relational understanding of the complex task in which they are engaged.

According to Professor Skemp, intelligent learning involves building networks of "schemas" that enable us to achieve our goals. Our schemas are cognitive or intellectual structures that represent the relationships that we have become aware of between concepts and processes, at one level, and between selected schemas, themselves, at another. (see Mathematics in the Primary School, pp. 32-48) In Mathematics in the Primary School he likened the process of schema construction whereby humans build their concepts and processes to that of building a brick wall while periodically testing its alignment. He described intellectual schema construction in terms of building and testing:

Schema Construction

BUILDING

TESTING

Mode 1
from our own
encounters with the
physical world:
experience
against expectations
of events in the
physical world:
experiment

Mode 2
from the schemas of
others:
communication
comparison with the
schemas of others:
discussion

Mode 3
from within, by
formation of higher-
order concepts: by
extrapolation,
imagination, intuition:
creativity
comparison with one's
own existing knowledge
and beliefs:
 
internal consistency
Skemp, R. R. (1989). Mathematics in the Primary School. London: Routledge. p. 74.

Recognizing the importance of structure and learner awareness of the relationships among the concepts and processes being learned, Richard Skemp and his research associates spent the first year of an eight-year project that was to produce SAIL through Mathematics carrying out a thorough conceptual analysis of elementary school mathematics. The eighteen concept maps found in SAIL through Mathematics were the fruit of that effort and it was these, along with Skemp's theory, that guided the development of the more that 475 learning activities that make up the SAIL through Mathematics program.

Here is a sampling of the ideas that guided Richard Skemp as he developed his theory of intelligent learning and applied it to the needs of the elementary school mathematics curriculum:

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