W. W. Sawyer (1911-2008)
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.
Betty Crowther and W. W. Sawyer wedding
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."
After school math club
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."
|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!|