INTRODUCTION

Logical thinking is simply a matter of organizing and manipulat­ing information. Problems or situations that involve logical thinking call for structure, for relationships between facts, and for chains of reasoning that “make sense.” When faced with a problem or decision that requires some kind of logical analysis, how do you react? To what extent do you think of yourself as a logical person?

Research into practical thinking processes has shown that there are two contrasting types of reactions that many people have, with relatively few folks falling in the middle.

At the other extreme, there is the avoidance reaction. This person sees the situation as threatening, uncomfortable, and involving an unpleasant and defeating experience. He or she experiences what might be called the failure reflex, a snap­reaction feeling of dread, which originates in ancient experi­ences of having been defeated by situations similar to the one presenting itself. Just as the person who is in very poor physical condition tends to get negative feelings at the prospect of playing a round of tennis, so the person who has trouble with logical thinking tends to shudder at the anticipation of a round of logical thought.

Why the difference? Why is it that some people are skilled at logical thinking and enjoy it so much, while others nearly break out in hives at the mere prospect? Why have some people imprisoned themselves within a self-definition as basically scatter-brained, using the disclaimer “I’m basically intuitive” as a cop-out? Why shouldn’t they be able to use their intuitive pro­cesses together with their logical processes, rather than instead of them?

The answer, for the most part, is fairly simple: experience.

This explains why so many adults suffer from mathe- phobia in varying degrees. Learning mathematics is a highly sequential process. If you don’t fully grasp a certain concept, fact, or procedure, you can never hope to grasp others that come later, which depend upon it. For example, to understand fractions you must first understand division. To understand simple equations in algebra requires that you understand frac­tions. Solving “word problems” depends on knowing how to set up and manipulate equations, and so on. A person who has trouble with mathematics as an adult must have been, at one time, a child who understood everything that had been pre­sented up to that point.

But sooner or later, the child stumbled over some concept that didn’t make sense. This created a blank spot in his or her learning, and as a result certain concepts that came thereafter never quite made sense either. As the child’s confusion increased and feelings of inadequacy set in, he or she sooner or later concluded “I’m no good at math.” For all practical pur­poses, this was the end of the learning process. Many people, during their adolescent years, give up on math in this way, and extend their aversive feelings to just about all situations involving the intricate mental processes of logic, sequential thinking, and organizing information. Mathephobia is a learned mental process, just as logical thinking is a learned mental process.

If you suffer from some degree of mathephobia, or from the more general problem of “logicophobia,” you can begin to erase this self-defeating reaction in two ways. First, stop avoid­ing or copping out of problem-solving situations that call for logical thinking. Facing up to an uncomfortable situation, and being determined not to feel worthless if you can’t solve it, goes a long way to eliminating the failure reflex. Second, you can study the specific mental techniques used by effective problem solvers, master them, and put them to use on a daily basis in a wide range of experiences. The first of these options is your responsibility. This book can help you with the second.

People with logicophobia seem to think the effective problem solver simply looks at a situation, and by some magical act just solves it. They don’t quite realize that the logical thinker has certain fairly specific procedures at his or her dis­posal, which have the effect of organizing the information, reducing ambiguity, eliminating extraneous factors, zeroing in on key variables and relationships, and extracting certain find­ings. This is not done in one fell swoop. It is a succession of mental actions—a sequence of individual steps that leads to a solution, not a giant leap.

It has been proven that specific training in logical thinking processes can make people “smarter.” Professors in the physics department at the University of Massachusetts created a tutorial program for physics students who were having trouble with their courses. The most common complaint these students registered was “I can do the math okay, but I have a lot of trouble with the word problems.” From this, the professors concluded that the problem students were deficient in a key mental skill they called sequential thought. This type of thought is the ability to take a poorly organized statement of the solution. By studying the comments these students made as they attempted to solve physics problems, and by studying the comments made by graduate students who were expert problem solvers, researchers were able to develop teaching techniques to help students increase their skills at sequential thought.

In a similar vein, I have been analyzing both logical and creative thinking processes as part of my research for courses in thinking at the University of California extension, and for “Brain Power” seminars in corporations.'I have found that being able to apply a simple label to a certain thought process equips a person to develop it and to put it to use on a con­sistent basis. The more you think about thinking, the more clearly you learn to think.