Psychology: A Self-Teaching Guide

Thinking: Exploring Mental Life 125

were taught in school. They might apply it and obtain the square root. Others

might say, “I forgot the formula. I can’t get the answer.” This response betrays an

excessive reliance on algorithms to solve math problems. Even if the formula is

forgotten, the problem can be solved.

Solving a problem without a formula involves the use of heuristic

approaches. Heuristic approaches employ principles, rules-of-thumb, and

insights to solve problems. A heuristic approach is based on the attitude “I can

solve this problem even if I can’t solve it in an elegant way.” Returning to the

search for the square root of 12, it is necessary to ask oneself this question:

“What isa square root?” As most adults know, it is the number that when mul-

tiplied by itself will generate the squared number. For example, 3 × 3 =9; the

square root of 9 is 3. Once this is clearly seen, it should be possible to discover

the square root of 12 without an algorithm. One can do it by trial and error. Try

multiplying 4 ×4. The product is 16. Obviously the square root of 12 must be

between 3 and 4. It has to be a decimal fraction. Try multiplying 3.5 ×3.5. The

product is 12.25. The answer isn’t 12, but it’s close. One can close in on the

answer by multiplying numbers somewhat smaller than 3.5. As already noted, a

heuristic approach is not an elegant, efficient way to solve a problem. But it will

get the job done, and should not be scorned. On the contrary, it is often essen-

tial to use heuristic approaches to solve problems when formulas are either not

available or forgotten.

(a) Solving a problem without a formula involves the use of approaches.

(b) Heuristic approaches employ principles, , and insights to solve prob-
lems.
Answers: (a) heuristic; (b) rules-of-thumb.

A particular kind of heuristic approach is a means-end analysis. A means-end

analysisis characterized by identifying a goal and then finding a way in which the

goal can be obtained. Questions such as: “Where is this going?” and “How will I

get there?” are associated with a means-end analysis.

For example, let’s say that you are buying a home and are told by a broker

that the payments are only $1,200 a month. This sounds good, and you might

sign on the dotted line. Or, you might make a means-end analysis. You ask the

broker, “How long will it take to pay off the house if I stick to the payment

schedule?” You are told it will take thirty years. You reply that you have a goal.

You want to pay off the house in twenty years. The broker explains that if you

will pay $1,400 a month, following a different payment schedule, you can

accomplish your goal. You have now been provided with the means—the

way—to obtain your goal. It is up to you to decide if you can afford the larger

payments.