town. He always leaves a twenty-five-cent tip even though 15 percent of his breakfast check comes to about one dollar. Ogden is also a regular customer for breakfast. He always leaves a three-dollar tip. Both Nolan and Ogden are success- ful businessmen. The servers in the restaurant refer to Nolan as a “cheapskate” and to Ogden as a “big spender.” The two concepts are relational because they arise from the fact that Ogden’s tip is more than Nolan’s.
(a) A disjunctive concept treats perceived attributes in terms.
(b) What kind of a concept treats perceived attributes in terms of some connection between object or ideas such as “more than,” or “less than”?
Answers: (a) either-or; (b) Relational.
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.
What kind of heuristic approach is characterized by identifying a goal and then finding a way in which the goal can be obtained?
Answer: A means-end analysis.
If possible, it is desirable to be systematic when there is a problem to be solved. This is particularly true if the problem involves a project that will require a span of time involving days or even weeks. When an orderly approach to solv- ing a problem is taken, psychologists have identified five important steps. These are (1) definition of the problem, (2) preparation, (3) incubation, (4) illumina- tion, (5) and verification. This general approach can be applied to many prob- lems. Usually a problem can be stated in question form. Examples include:
“How do I get a weed-free lawn?” “How do you raise a child to have high self- esteem?” “How do you study effectively for examinations?” and “How do you lose weight?”
Assume that Laura, a thirty-three-year-old engineer, wife, and mother of two children, wants to lose some weight. It’s a problem because she’s been trying to lose weight off and on for a couple of years without much success. She decides to use her training as an engineer to solve her problem. So she takes a systematic approach. First, she defines the problemin a precise way. She decides that she will stop vaguely saying, “I want to lose some weight.” Instead she asks the ques- tion, “How can I lose ten pounds in the next five weeks?”
What is the first step in systematic problem solving?
Answer: Defining the problem.
Second, she prepares to lose weight by gathering information. She obtains two books on nutrition, a third book on the psychology of weight control, and a fourth book on breaking habits. She takes notes on key points in the books.
Third, she lets the information incubate before she takes action. She reflects on what she has learned. She feels a little bit overwhelmed and confused by contradictory information in the books she has read. She thinks, “I’ll just sleep on all of this stuff for a while and let my subconscious mind bring things together.”
Fourth, illumination arrives in about a week. She feels she has new insights about weight control. She sees that she needs to stay away from fad diets. She decides that she has been eating too many refined carbohydrates and excessive amounts of saturated fat. She writes an eating plan for herself, one that she believes she can follow.
Fifth, Laura begins to eat in accordance with her plan. She verifies that the plan is working—or not working—by weighing herself in the morning every other day.
(a) What step in systematic problem solving involves reflection on what one has learned?
(b) What step in systematic problem solving is associated with insight?
Answers: (a) Incubation; (b) Illumination.