I hope that I shall shock a few people in asserting that the most important single task of mathematical instruction in the secondary schools is to teach the setting up of equations to solve word problems. Yet there is a strong argument in favor of this opinion.
In solving a word problem by setting up equations, the student translates a real situation into mathematical terms: he has an opportunity to experience that mathematical concepts may be related to realities, but such relations must be carefully worked out. Here is the first opportunity afforded by the curriculum for this basic experience. This first opportunity may be also the last for a student who will not use mathematics in his profession. Yet engineers and scientists who will use mathematics professionally, will use it mainly to translate real situations into mathematical concepts. In fact, an engineer makes more money than a mathematician and so he can hire a mathematician to solve his mathematical problems for him; therefore, the future engineer need not study mathematics to solve problems. Yet, there is one task for which the engineer cannot fully rely on the mathematician: the engineer must know enough mathematics to set up his problems in mathematical form. And so the future engineer, when he learns in the secondary school to set up equations to solve “word problems,” has a first taste of, and has an opportunity to acquire the attitude essential to, his principal professional use of mathematics.
Saturday, January 11, 2014
"An engineer,,, can hire a mathematician to solve his mathematical problems for him" -- Pólya on word problems
George Pólya writing in the book Mathematical Discovery: