HOW TO SOLVE IT

Routine Problem May be called the problem to solve the equation x^2-3x+2=0 if the solution of the general quadratic equation was explained and illustrated before so that the student has nothing to do but to substitute the numbers -3 and 2 for certain letters which appear in the general solution. even if the quadratic equation was not solved generally in letters but half a dozen similar quadratic equations with numerical coefficients were solved just before, the problem should be called a "routine problem." In general, a problem is a "routine problem" if it can be solved either by substituting special data into a formerly solved general problem or by following step by step, without any trace of originality, some well worn conspicuous example. Setting a routine problem, the teacher thrusts under the nose of the student an immediately and decisive answer to the question Do you know a related problem? Thus the student needs nothing but a little care and patience in following a cut and dried precept, and he has no opportunity to use his judgement or his inventive faculties. Routine problems, even many routine problems, may be necessary in teaching mathematics but to make the students do no other kind is inexcusable. Teaching the mechanical performance of routine mathematical operations and nothing else is well under the level of the cookbook because kitchen recipes do leave something to the imagination and judgement of the cook but mathematical recipes do not.