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W. W. Sawyer Quotes

In mathematics, if a pattern occurs, we can go on to ask, Why does it occur? What does it signify? And we can find answers to these questions. In fact, for every pattern that appears, a mathematician feels he ought to

In mathematics, if a pattern occurs, we can go on to ask, Why does it occur? What does it signify? And we can find answers to these questions. In fact, for every pattern that appears, a mathematician feels he ought to know why it appears.

W. W. Sawyer
Teaching, Math, Answers
W. W. Sawyer (2012). “Prelude to Mathematics”, p.23, Courier Corporation

When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touched. One can begin to reason only when a clear picture has been formed in the imagination. Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination.

W. W. Sawyer
Education, Teaching, Imagination
W. W. Sawyer (2012). “Mathematician's Delight”, p.32, Courier Corporation

Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination.

W. W. Sawyer
Education, Teaching, Imagination
W. W. Sawyer (2012). “Mathematician's Delight”, p.32, Courier Corporation

The present syllabus in our high schools corresponds almost exactly to what was known in 1640.

W. W. Sawyer
School, Syllabus, Formal Education

The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge.

W. W. Sawyer
Education, Math, Growth

Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying 'No, that's wrong.' Rather, he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole of the art of teaching.

W. W. Sawyer
Education, Teacher, Art
W. W. Sawyer (2012). “Vision in Elementary Mathematics”, Courier Corporation

Very few people realize the enormous bulk of contemporary mathematics. Probably it would be easier to learn all the languanges of the world than to master all mathematics at present known.

W. W. Sawyer
Math, People, Would Be

You know what speed is. You would not believe a man who claimed to walk at 5 miles an hour, but took 3 hours to walk 6 miles. You have only to apply the same common sense to stones rolling down hillsides, and the calculus is at your command.

W. W. Sawyer
Education, Believe, Math
W. W. Sawyer (2012). “Mathematician's Delight”, p.137, Courier Corporation

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