W. W. Sawyer (1911-2008)

Mathematics is commonly believed to be a difficult and esoteric subject, a holy temple situated at high altitude accessible only to a select and privileged few. The life and work of W.W. Sawyer, who passed away at the ripe age of 97, was dedicated to disproving the above thesis by demonstrating the converse proposition: that ordinary people can be taught to understand, learn and enjoy important, non trivial mathematics.

Born in 1911, W. W. Sawyer graduated from Cambridge University with specialization in the applied mathematics of quantum mechanics and relativity. Immediately thereafter, he began his long career dedicated to teaching and learning math.

His first book "Mathematician´s Delight" (1943) (MD), was written with the aim "to dispel the fear of mathematics". It is probably the most successful math book ever written, going through numerous editions, translations into 10 languages, and selling more than 5,00,000 copies.

In MD Sawyer criticizes the teaching of math without context:
"Nearly every subject has a shadow, or imitation. It would, I suppose, be quite possible to teach a deaf and dumb child to play the piano. When it played a wrong note, it would see the frown of its teacher, and try again. But it would obviously have no idea of what it was doing, or why anyone should devote hours to such an extraordinary exercise. It would have learnt an imitation of music, and it would fear the piano exactly as most students fear what is supposed to be mathematics."

In the Sawyerian alternative:
"Education consists in co-operating with what is already inside a child's mind. The best way to learn geometry is to follow the road which the human race originally followed: Do things, make things, notice things, arrange things, and only then reason about things."

Sawyer consistently argued that a rigorous approach to the problem of mathematics teaching and learning is conceptually distinct from and should not be confused with the problem of rigour in mathematics.

For example, in "A Concrete Approach to Abstract Algebra" he writes about how not to teach :
"In planning such a course, a professor must make a choice. His aim may be to produce a perfect mathematical work of art, having every axiom stated, every conclusion drawn with flawless logic, the whole syllabus covered. This sounds excellent, but in practice the result is often that the class does not have the faintest idea of what is going on. Certain axioms are stated. How are these axioms chosen? Why do we consider these axioms rather than others? What is the subject about? What is its purpose? If these questions are left unanswered, students feel frustrated. Even though they follow every individual deduction, they cannot think effectively about the subject. The framework is lacking; students do not know where the subject fits in, and this has a paralyzing effect on the mind."

Is there an alternative ?
"On the other hand, the professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. The work may not proceed so quickly; all topics may not be covered; the final outline may be jagged. But the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own."

Sawyer´s writings cover a broad spectrum from primary math to ´advanced´ math. In "Vision in Elementary Mathematics", he shows how a simple game "Think of a number", can be translated into an introduction to algebra- how unknown numbers can also be represented by things, and can be added and subtracted much like pebbles. This writer has used this approach to introduce algebra to hundreds of primary school teachers. The universal response is "I never realized algebra is this simple."

 

Places lived:

New Zealand	1911-1914	Tottenham, London, England	Gold Coast - Ghana
	1914-1918	Harrow-on the Hill, near London, England
	1918-1923	Sunderland, County Durham, England
	1924-1930	Highgate, London, England
	1930-1935	Cambridge, England -studying at Cambridge University
	1935-1937	Dundee, county Angus, Scotland -first academic position
	1937-1944	Manchester, Lancashire, England -Lecturer at University of Manchester
	1945-1947	Leicester, Leicestershire, England-Lecturer, then Head of Math department at Leicester University
	1948-1950	Achimota, near Accra, Gold Coast (now Ghana) - Head of Math.
	1951-1956	Christchurch, New Zealand- Professor at Canterbury University
	1957-1958	Urbana, Illinois, U.S.A.- University of Illinois- invited during U.S.A./Russia space race period
	1958-1964	Middletown, Connecticut, U.S.A. Professor at Wesleyan University
	1964-1965	summer in Cambridge, England
	1965-1976	Toronto, Ontario, Canada- Joint appointment, Math. And Education, University of Toronto. Retired Professor Emeritus
	1976-2003	Cambridge, England- for retirement until wife died
	2003-2008	Toronto, Ontario, Canada-lived with daughter and her husband, then in a nearby nursing home. Lived to be 96 and 5/6's years old!