Learning how to guess
Should students be encouraged to guess, in the interest of learning eventually how to make intelligent conjectures? Possibly there are certain kinds of situations where guessing is desirable and where it may facilitate the development of intuitive thinking to some reasonable degree. There may, indeed, be a kind of guessing that requires careful cultivation. Yet in many classes in school, guessing is heavily penalized and is associated somehow with laziness. Certainly one would not like to educate students to do nothing but guess, for guessing should always be followed up with as much verification and confirmation as necessary; but too stringent a penalty on guessing may restrain thinking of any sort and keep it plodding rather than permitting it to make occasional leaps.
May it not be better for students to guess than to be struck dumb when they cannot immediately give the right answer? It is plain that a student should be given some training in recognizing the plausibility of guessing. Very often we are forced, in science and in life generally, to act on the basis of incomplete knowledge; we are forced to guess. According to statistical decision theory, actions based on inadequate date must take account of both probability and costs. What we should teach students to recognize, probably, is when the cost of guessing is too high, as well as when guessing itself is too costly.