mathematics

Richard Skemp

Richard Skemp is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Richard Skemp rather than just read about it. In short: Richard Rowland Skemp, (10 March 1919 – 22 June 1995) was a British mathematician, psychologist and academic, who specialised in mathematical education. Having started his career as a school teacher, he became a lecturer in psychology at the University of Manchester in 1955.

Key takeaways

Richard Skemp belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Richard Skemp to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Richard Skemp from memory before moving on to harder problems.

Reference excerpt

Richard Rowland Skemp, (10 March 1919 – 22 June 1995) was a British mathematician, psychologist and academic, who specialised in mathematical education. Having started his career as a school teacher, he became a lecturer in psychology at the University of Manchester in 1955. He was appointed Professor of Educational Theory at Warwick University in 1973 and also served as director of its Mathematics Education Research Centre from 1978 until he retired in 1986.

Biography Skemp was born on 10 March 1919 in Bristol, England. His father, Professor Arthur Rowland Skemp, had been killed in action during the First World War on 1 November 1918. As a foundation scholar, he was educated at Wellington College, then an all-boys independent school in Berkshire which had been set up for the sons of deceased army officers. He won an open scholarship in mathematics at Hertford College, Oxford, matriculating in 1937. His university studies were interrupted by military service during the Second World War. On 24 May 1941, having trained at an Officer Cadet Training Unit, he was commissioned in the British Army as a second lieutenant to serve in the Royal Corps of Signals. He served in India and had reached the rank of captain by the end of the war. After the end of the war, Skemp returned to Oxford to continue his studies. He graduated from the University of Oxford with a Bachelor of Arts (BA) degree in 1947. He then worked as a mathematics teacher at two private schools; first Oundle School and then at Rye St Antony School. After developing an interesting in how children learn, he returned to Oxford to undertake a second undergraduate degree in psychology in 1952. He then moved to the Department of Education, University of Manchester to undertake a Doctor of Philosophy (PhD) degree under the supervision of C. E. M. Hansel and Professor John Cohen. He completed his PhD in 1959 with a doctoral thesis titled "Investigation into difficulties in learning mathematics by children of good general intelligence". Skemp joined the academic staff of the University of Manchester as a lecturer in psychology in 1955. He was promoted to senior lecturer in 1962. In 1973, he joined the University of Warwick as Professor of Educational Theory. He also served as director of the Mathematics Education Research Centre at Warwick from 1978 to 1986. He retired from full-time academia in 1986, but continued to lecture around the world. He was visiting professor at the University of Calgary from 1987 to 1994.

Personal life In 1961, Skemp married Valerie Watts. Together they had one son. In January 1995, Skemp was diagnosed with non-Hodgkin's lymphoma. He died on 22 June 1995, aged 76, in Coventry, England.

Selected works Skemp, Richard R. (February 1961). "Reflective Intelligence and Mathematics". British Journal of Educational Psychology. 31 (P1): 45–55. doi:10.1111/j.2044-8279.1961.tb01701.x. Skemp, Richard R. (1971). The psychology of learning mathematics. Harmondsworth: Penguin Books. ISBN 9780140212105. Skemp, R. R. (1976). "Relational understanding and instrumental understanding" (PDF). Mathematics Teaching. 77 (1): 20–26. Skemp, Richard R. (1979). Intelligence, learning, and action: a foundation for theory and practice in education. Chichester: Wiley. Skemp, Richard R. (1989). Mathematics in the primary school. London: Routledge. ISBN 978-0415025195.

References

Worked examples

Example 1 — a first encounter with Richard Skemp

Start with the simplest possible case. Write down what Richard Skemp claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Richard Skemp before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Richard Skemp ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Richard Skemp

In research: Richard Skemp appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Richard Skemp in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Richard Skemp is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1919 births, 1995 deaths, 20th-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard Skemp outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Richard Skemp in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Richard Skemp means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Richard Skemp out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Richard Skemp in simple terms?

Why does Richard Skemp matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Richard Skemp?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Richard Skemp.