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Clarity is Not Enough
Published online by Cambridge University Press: 03 November 2016
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A Striking thing about contemporary education is the increasing demand for mathematical training. In the eighteenth century the only departments of science which conspicuously called for it were astronomy and such branches of mechanics and optics as had arisen in connection with astronomical pursuits. Navigation was perhaps the only important profession for which any mathematical equipment was an indispensable prerequisite. Though an eighteenth century H. G. Wells might have anticipated minor avenues of future employment for professional mathematicians as teachers attached to artillery or actuarial work, he would scarcely have foreseen that chemistry, power production, genetics, psychology and social statistics would severally enlist the services of the mathematician. The educational problem which arises from the rapid mathematisation of science during the past half-century has found us unprepared, and is largely an unsolved one.
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- Copyright © Mathematical Association 1938
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page note 119 * There is a further source of psychological resistance to this. Young students and pupils are used to the degree as the unit of angular measurement, and the first reaction to a “small angle” is to identify it with something less than one degree. it is very easy for a beginner to forget that even 5° is a relatively small fraction of a radian.
page note 122 * Published by Allen and Unwin.
page note † I sent this in proof to Professor Levy, to whose friendship I owe more intellectual stimulus than I can ever repay. He calls my attention to a serious omission, and I cannot resist the temptation to quote his words : “There is too much teaching of the pupils by the teacher. It is possible so to arrange matters that the pupils can teach the teacher. As you know, I have since I began teaching always encouraged my class to bring stuff to me to tackle in front of the class without any previous preparation on my part, so that the students can see how I flounder about until I get to the answer, or can see me being stumped. We then make a joint study of why I floundered or why I was stumped. They enjoy that, and they learn a tremendous amount in the process.”