Relational and instrumental understanding

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In 1976 Richard Skemp, a professor of mathematics at Warwick University in the UK, wrote an article on what he called rational and instrumental understanding. He was referring to how we teach mathematics but his ideas have repercussions that extend into how we teach generally and how we understand.

When I was managing a part of a large computer project, I would often employ contractors who had no specific experience in what we were working on. If they were intelligent and had worked on many different systems it was apparent to me that they would pick up what were doing, and generally they proved their abilities. They had a relational understanding of these systems. On the other hand, some other managers only employed people who had specific experience in the actual applications they were using. Often these people proved to be useless and were unable to adapt to a system that they hadn’t been specifically trained in. They had an instrumental understanding in that they knew how to use a particular application but they had no overall understanding of the systems they were working on

Unfortunately, instrumental understanding (what Richard Skemp referred to as ‘not real understanding’) is what passes as understanding at most schools, colleges and universities.

I heard a woman on the radio talking about her experiences at university in Australia and she said that when she left school many years ago and went to university it was a place of discussion and students were encouraged to question through seminars and tutorials. When she returned to university as a mature student she found that all that had gone. It was a production line where students were expected to answer the questions as prescribed, there were only lectures and group sessions for discussion only existed to fill in the gaps in knowledge so students could pass the exams.

We are producing a generation who are unable to really think in the true sense of the word. Instead they seek more and more information because they are unable to use discernment with the information they already have.

It’s worth noting that as a general rule you will find that people with a relational understanding love discussing and dissent as it stretches the mind. People with instrumental understanding refuse to discuss ideas that they don’t agree with because they lack the ability to question the processes that they have been programmed with. It is endemic in our society to suppress ideas that don’t go along with the mainstream of opinion and Universities that should be in forefront of discussion of ideas instead suppress ideas that are not approved of.

Philip Braham is a writer. My podcast is

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