Types of thinking
Philosophers and psychologists alike have long realized that thinking is not of a “single piece.” There are many different kinds of thinking, and there are various means of categorizing them into a “taxonomy” of thinking skills, but there is no single universally accepted taxonomy. One common approach divides the types of thinking into problem solving and reasoning, but other kinds of thinking, such as judgment and decision making, have been suggested as well.
Problem solving is a systematic search through a range of possible actions in order to reach a predefined goal. It involves two main types of thinking: divergent, in which one tries to generate a diverse assortment of possible alternative solutions to a problem, and convergent, in which one tries to narrow down multiple possibilities to find a single, best answer to a problem. Multiple-choice tests, for example, tend to involve convergent thinking, whereas essay tests typically engage divergent thinking.
The problem-solving cycle in thinking
Many researchers regard the thinking that is done in problem solving as cyclical, in the sense that the output of one set of processes—the solution to a problem—often serves as the input of another—a new problem to be solved. The American psychologist Robert J. Sternberg identified seven steps in problem solving, each of which may be illustrated in the simple example of choosing a restaurant:
Problem identification. In this step, the individual recognizes the existence of a problem to be solved: he recognizes that he is hungry, that it is dinnertime, and hence that he will need to take some sort of action.
Problem definition. In this step, the individual determines the nature of the problem that confronts him. He may define the problem as that of preparing food, of finding a friend to prepare food, of ordering food to be delivered, or of choosing a restaurant.
Resource allocation. Having defined the problem as that of choosing a restaurant, the individual determines the kind and extent of resources to devote to the choice. He may consider how much time to spend in choosing a restaurant, whether to seek suggestions from friends, and whether to consult a restaurant guide.
Problem representation. In this step, the individual mentally organizes the information needed to solve the problem. He may decide that he wants a restaurant that meets certain criteria, such as close proximity, reasonable price, a certain cuisine, and good service.
Strategy construction. Having decided what criteria to use, the individual must now decide how to combine or prioritize them. If his funds are limited, he might decide that reasonable price is a more important criterion than close proximity, a certain cuisine, or good service.
Monitoring. In this step, the individual assesses whether the problem solving is proceeding according to his intentions. If the possible solutions produced by his criteria do not appeal to him, he may decide that the criteria or their relative importance needs to be changed.
Evaluation. In this step, the individual evaluates whether the problem solving was successful. Having chosen a restaurant, he may decide after eating whether the meal was acceptable.
This example also illustrates how problem solving can be cyclical rather than linear. For example, once one has chosen a restaurant, one must determine how to get there, how much to tip, and so on.
Structures of problems
Psychologists often distinguish between “well-structured” and “ill-structured” problems. Well-structured problems (also called well-defined problems) have clear solution paths: the problem solver is usually able to specify, with relative ease, all the steps that must be taken to reach a solution. The difficulty in such cases, if any, has to do with executing the steps. Most mathematics problems, for example, are well-structured, in the sense that determining what needs to be done is easy, though carrying out the computations needed to reach the solution may be difficult. The problem represented by the question, “What is the shortest driving route from New York City to Boston?” is also well-structured, because anyone seeking a solution can consult a map to answer the question with reasonable accuracy.
Ill-structured problems (also called ill-defined problems) do not have clear solution paths, and in such cases the problem solver usually cannot specify the steps needed to reach a solution. An example of an ill-structured problem is, “How can a lasting peace be achieved between country A and country B?” It is hard to know precisely (or, perhaps, even imprecisely) what steps one would take to solve this problem. Another example is the problem of writing a best-selling novel. No single formula seems to work for everyone. Indeed, if there were such a formula, and if it became widely known, it probably would cease to work (because the efficacy of the formula would be destroyed by its widespread use).
The solution of ill-structured problems often requires insight, which is a distinctive and seemingly sudden understanding of a problem or strategy that contributes toward a solution. Often an insight involves conceptualizing a problem or a strategy in a totally new way. Although insights sometimes seem to arise suddenly, they are usually the necessary result of much prior thought and hard work. Sometimes, when one is attempting to gain an insight but is unsuccessful, the most effective approach is that of “incubation”—laying the problem aside for a while and processing it unconsciously. Psychologists have found that unconscious incubation often facilitates solutions to problems.
Algorithms and heuristics
Other means of solving problems incorporate procedures associated with mathematics, such as algorithms and heuristics, for both well- and ill-structured problems. Research in problem solving commonly distinguishes between algorithms and heuristics, because each approach solves problems in different ways and with different assurances of success.
A problem-solving algorithm is a procedure that is guaranteed to produce a solution if it is followed strictly. In a well-known example, the “British Museum technique,” a person wishes to find an object on display among the vast collections of the British Museum but does not know where the object is located. By pursuing a sequential examination of every object displayed in every room of the museum, the person will eventually find the object, but the approach is likely to consume a considerable amount of time. Thus, the algorithmic approach, though certain to succeed, is often slow.
A problem-solving heuristic is an informal, intuitive, speculative procedure that leads to a solution in some cases but not in others. The fact that the outcome of applying a heuristic is unpredictable means that the strategy can be either more or less effective than using an algorithm. Thus, if one had an idea of where to look for the sought-after object in the British Museum, a great deal of time could be saved by searching heuristically rather than algorithmically. But if one happened to be wrong about the location of the object, one would have to try another heuristic or resort to an algorithm.
Although there are several problem-solving heuristics, a small number tend to be used frequently. They are known as means-ends analysis, working forward, working backward, and generate-and-test.
In means-ends analysis, the problem solver begins by envisioning the end, or ultimate goal, and then determines the best strategy for attaining the goal in his current situation. If, for example, one wished to drive from New York to Boston in the minimum time possible, then, at any given point during the drive, one would choose the route that minimized the time it would take to cover the remaining distance, given traffic conditions, weather conditions, and so on.
In the working-forward approach, as the name implies, the problem solver tries to solve the problem from beginning to end. A trip from New York City to Boston might be planned simply by consulting a map and establishing the shortest route that originates in New York City and ends in Boston. In the working-backward approach, the problem solver starts at the end and works toward the beginning. For example, suppose one is planning a trip from New York City to Paris. One wishes to arrive at one’s Parisian hotel. To arrive, one needs to take a taxi from Orly Airport. To arrive at the airport, one needs to fly on an airplane; and so on, back to one’s point of origin.
Often the least systematic of the problem-solving heuristics, the generate-and-test method involves generating alternative courses of action, often in a random fashion, and then determining for each course whether it will solve the problem. In plotting the route from New York City to Boston, one might generate a possible route and see whether it can get one expeditiously from New York to Boston; if so, one sticks with that route. If not, one generates another route and evaluates it. Eventually, one chooses the route that seems to work best, or at least a route that works. As this example suggests, it is possible to distinguish between an optimizing strategy, which gives one the best path to a solution, and a satisficing strategy, which is the first acceptable solution one generates. The advantage of optimizing is that it yields the best possible strategy; the advantage of satisficing is that it reduces the amount of time and energy involved in planning.
Obstacles to effective thinking
A better understanding of the processes of thought and problem solving can be gained by identifying factors that tend to prevent effective thinking. Some of the more common obstacles, or blocks, are mental set, functional fixedness, stereotypes, and negative transfer.
A mental set, or “entrenchment,” is a frame of mind involving a model that represents a problem, a problem context, or a procedure for problem solving. When problem solvers have an entrenched mental set, they fixate on a strategy that normally works well but does not provide an effective solution to the particular problem at hand. A person can become so used to doing things in a certain way that, when the approach stops working, it is difficult for him to switch to a more effective way of doing things.
Functional fixedness is the inability to realize that something known to have a particular use may also be used to perform other functions. When one is faced with a new problem, functional fixedness blocks one’s ability to use old tools in novel ways. Overcoming functional fixedness first allowed people to use reshaped coat hangers to get into locked cars, and it is what first allowed thieves to pick simple spring door locks with credit cards.
Another block involves stereotypes. The most common kinds of stereotypes are rationally unsupported generalizations about the putative characteristics of all, or nearly all, members of a given social group. Most people learn many stereotypes during childhood. Once they become accustomed to stereotypical thinking, they may not be able to see individuals or situations for what they are.
Negative transfer occurs when the process of solving an earlier problem makes later problems harder to solve. It is contrasted with positive transfer, which occurs when solving an earlier problem makes it easier to solve a later problem. Learning a foreign language, for example, can either hinder or help the subsequent learning of another language.
Expert thinking and novice thinking
Research by the American psychologists Herbert A. Simon, Robert Glaser, and Micheline Chi, among others, has shown that experts and novices think and solve problems in somewhat different ways. These differences explain why experts are more effective than novices in a variety of problem-solving endeavours.
As compared with novices, experts tend to have larger and richer schemata (organized representations of things or events that guide a person’s thoughts and actions), and they possess far greater knowledge in specific domains. The schemata of experts are also highly interconnected, meaning that retrieving one piece of information easily leads to the retrieval of another piece. Experts devote proportionately more time to determining how to represent a problem, but they spend proportionately less time in executing solutions. In other words, experts tend to allocate more of their time to the early or preparatory stages of problem solving, whereas novices tend to spend relatively more of their time in the later stages. The thought processes of experts also reveal more complex and sophisticated representations of problems. In terms of heuristics, experts are more likely to use a working-forward strategy, whereas novices are more likely to use a working-backward strategy. In addition, experts tend to monitor their problem solving more carefully than do novices, and they are also more successful in reaching appropriate solutions.
Reasoning consists of the derivation of inferences or conclusions from a set of premises by means of the application of logical rules or laws. Psychologists as well as philosophers typically distinguish between two main kinds of reasoning: deduction and induction.
Deductive reasoning, or deduction, involves analyzing valid forms of argument and drawing out the conclusions implicit in their premises. There are several different forms of deductive reasoning, as used in different forms of reasoning problems.
In conditional reasoning the reasoner must draw a conclusion based on a conditional, or “if…then,” proposition. For example, from the conditional proposition “if today is Monday, then I will attend cooking class today” and the categorical (declarative) proposition “today is Monday,” one can infer the conclusion, “I will attend cooking class today.” In fact, two kinds of valid inference can be drawn from a conditional proposition. In the form of argument known as modus ponens, the categorical proposition affirms the antecedent of the conditional, and the conclusion affirms the consequent, as in the example just given. In the form known as modus tollens, the categorical proposition denies the consequent of the conditional, and the conclusion denies the antecedent. Thus:
If today is Monday, then I will attend cooking class today. I will not attend cooking class today. Therefore, today is not Monday.
Two other kinds of inference that are sometimes drawn from conditional propositions are not logically justified. In one such fallacy, “affirming the consequent,” the categorical proposition affirms the consequent of the conditional, and the conclusion affirms the antecedent, as in the example:
If John is a bachelor, then he is male. John is male. Therefore, John is a bachelor.
In another invalid inference form, “denying the antecedent,” the categorical proposition denies the antecedent of the conditional, and the conclusion denies the conclusion of the conditional:
If Othello is a bachelor, then he is male. Othello is not a bachelor. Therefore, Othello is not male.
The invalidity of these inference forms is indicated by the fact that in each case it is possible for the premises of the inference to be true while the conclusion is false.
It is important to realize that in conditional reasoning, and in all forms of deductive reasoning, the validity of an inference does not depend on whether the premises and the conclusion are actually (in the “real world”) true or false. All that matters is whether it is possible to conceive of a situation in which the conclusion would be false and all of the premises would be true. Indeed, there are valid inferences in which one or more of the premises and the conclusion are actually false:
Either the current pope is married or he is a divorcé. The current pope is not a divorcé. Therefore, the current pope is married.
This inference is valid because, although the premises and the conclusion are not all true, it is impossible to conceive of a situation in which all of the premises would be true but the conclusion would be false. Examples such as these demonstrate that the validity of an inference depends upon its form or structure, not on its content.
Reasoning skills are often assessed through problems involving syllogisms, which are deductive arguments consisting of two premises and a conclusion. Two kinds of syllogisms are particularly common.
In a categorical syllogism the premises and the conclusion state that some or all members of one category are or are not members of another category, as in the following examples:
All robins are birds. All birds are animals. Therefore, all robins are animals.
Some bachelors are not astronauts. All bachelors are human beings. Therefore, some human beings are not astronauts.
A linear syllogism involves a quantitative comparison in which each term displays either more of less of a particular attribute or quality, and the reasoner must draw conclusions based on the quantification. An example of a reasoning problem based on a linear syllogism is: “John is taller than Bill, and Bill is taller than Pete. Who is tallest?” Linear syllogisms can also involve negations, as in “Bill is not as tall as John.”
Many aspects of problem solving involve inductive reasoning, or induction. Simply put, induction is a means of reasoning from a part to a whole, from particulars to generals, from the past to the future, or from the observed to the unobserved. Whereas valid deductive inferences guarantee the truth of their conclusions, in the sense that it is impossible for the premises to be true and the conclusion false, good inductive inferences guarantee only that, if the premises are true, the conclusion is probable, or likely to be true. There are several major kinds of inductive reasoning, including causal inference, categorical inference, and analogical inference.
In a causal inference, one reasons to the conclusion that something is, or is likely to be, the cause of something else. For example, from the fact that one hears the sound of piano music, one may infer that someone is (or was) playing a piano. But although this conclusion may be likely, it is not certain, since the sounds could have been produced by an electronic synthesizer. (See also induction, problem of.)
In a categorical inference, one makes a judgment about whether something is, or is likely to be, a member of a certain category. For example, upon seeing an animal one has never seen before, a person with a limited knowledge of dogs may be confident that what he is seeing is a dog but less certain about the specific species.
In reasoning by analogy, one applies what one has learned to another domain. Aristotle stated the formulae for two possible analogical inferences: “As A is to B, so C is to D”; and “As A is in B, so C is in D.” Analogical inference involves applying the outcomes of a known situation to a new or unknown situation. A risk in this approach, however, can occur if the two situations are too dissimilar to merit the analogous comparison.Robert J. Sternberg
Other types of thinking
A simple form of realistic thinking—i.e., thinking that is oriented toward the external environment—underlies the ability to discriminate discrete objects or items of information (e.g., distinguishing a lion from a tiger). The outcome is a judgment, and accordingly the process may be called decision making. The availability of information, the rate at which it is presented, the expectations of the person making the judgment, and the number of alternatives available influence the judgment’s accuracy and efficiency. Redundancy (or surplus) of information facilitates judgment. For example, a lion may be identified on the basis of a number of different sensory cues, such as being tan or brown, lacking stripes, having a mane, and so on.
A more complex form of realistic thinking underlies the ability to identify or use a class of items, as in selecting several different kinds of triangle from an array of other geometric figures. In the course of solving the problem, the individual will link together a newly experienced group of objects according to one or more of their common properties. This new grouping is then given a general name (as in first learning the meaning of the word triangle). It might also be determined that a new object fits an existing category. Physical objects are multidimensional; that is, they may vary in shape, size, colour, location (in relation to other objects), emotional significance, or connotative meaning. How a person identifies such dimensions, develops hypotheses (or tentative conclusions) about which of the specific dimensions define a class, arrives at the rules of class membership, and tests various hypotheses all reflect his ability to grasp concepts. Successful performance in all these processes leads to the formulation of pertinent rules based on one’s ability to classify specific items. (See concept formation.)
As discussed above, divergent (or creative) thinking is an activity that leads to new information, or previously undiscovered solutions. Some problems demand flexibility, originality, fluency, and inventiveness, especially those for which the individual must supply a unique solution. (See creativity.)
A number of processes or phases have been identified as typical of creative thinking. According to one well-known theory, in the first phase, preparation, the thinker assembles and explores resources, perhaps making preliminary decisions about their value in solving the problem at hand. Incubation represents the next phase, in which the individual mulls over possibilities and shifts from one to another relatively freely and without any rigid rational or logical preconceptions and constraints. Illumination occurs when resources fall into place and a definite decision is reached about the result or solution. Next is verification (refinement or polishing), the process of making relatively minor modifications in committing ideas to final form. Often enough, objective standards for judging creative activity (e.g., musical composition) are lacking, especially if the emotional satisfaction of the creator is an important criterion. Although the four phases have been ordered in a logical sequence, they often vary widely and proceed in different orders from one person to the next. Many creative people attain their goals by following special strategies that are not neatly describable.
The phases of preparation, incubation, illumination, and verification are characteristic of creative thinkers generally but do not guarantee that a worthwhile product will ensue. Results also depend on whether an individual has the necessary personality characteristics and abilities; in addition, the quality of creative thinking stems from the training of the creator. The artist who produces oil paintings needs to learn the brushing techniques basic to the task; the scientist who creates a new theory does so against a background of previous learning. Furthermore, creativity intimately blends objective and subjective processes; the successful creator learns how to release and to express his feelings and insights.
Creative thinking is a matter of using intrinsic resources to produce tangible results. This process is markedly influenced by early experience and training. Thus, school and work situations that encourage individual expression and that tolerate idiosyncratic or unorthodox thinking seem to foster the development of creativity.W. Edgar Vinacke
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