The process of selecting the right elements and attaching proper weight to them may be illustrated by the following problem:--"Which of these offers would you take, supposing that you wish a D.C.K. upright piano, have $50 saved, can save a little over $20 per month, and can borrow from your father at 6% interest?"
A Reliable Piano. The Famous D.C.K. Upright. You pay $50 cash down and $21 a month for only a year and a half. _No interest_ to pay. We ask you to pay only for the piano and allow you plenty of time.
We offer the well-known D.C.K. Piano for $390. $50 cash and $20 a month thereafter. Regular interest at 6%. The interest soon is reduced to less than $1 a month.
The D.C.K. Piano. Special Offer, $375, cash. Compare our prices with those of any reliable firm.
If you consider chiefly the "only," "No interest to pay," "only," and "plenty of time" in offer A, attaching much weight to them and little to the thought, "How much will $50 plus (18 × $21) be?", you will probably decide wrongly.
The situations of life are often complicated by many elements of little or even of no relevance to the correct solution. The offerer of A may belong to your church; your dearest friend may urge you to accept offer B; you may dislike to talk with the dealer who makes offer C; you may have a prejudice against owing money to a relative; that prejudice may be wise or foolish; you may have a suspicion that the B piano is shopworn; that suspicion may be well-founded or groundless; the salesman for C says, "You don't want your friends to say that you bought on the installment plan. Only low-class persons do that," etc. The statement of arithmetical problems in school usually assists the pupil to the extent of ruling out all save definitely quantitative elements, and of ruling out all quantitative elements except those which should be considered. The first of the two simplifications is very beneficial, on the whole, since otherwise there might be different correct solutions to a problem according to the nature and circumstances of the persons involved. The second simplification is often desirable, since it will often produce greater improvement in the pupils, per hour of time spent, than would be produced by the problems requiring more selection. It should not, however, be a universal custom; for in that case the pupils are tempted to think that in every problem they must use all the quantities given, as one must use all the pieces in a puzzle picture.