作者: 布鲁纳 文/邵瑞珍 译 / 1999次阅读 时间: 2018年7月17日
来源: 《教育过程》 标签: 布鲁纳 分析思维 直觉思维


MUCH has been said in the preceding chapters about the importance of a student's intuitive, in contrast to his formal, understanding of the subjects he encounters. The emphasis in much of school learning and student examining is upon explicit formulations, upon the ability of the student to reproduce verbal or numerical formula. It is not clear, in the absence of research, whether this emphasis is inimical to the later development of good intuitive understanding-indeed, it is even unclear what constitutes intuitive understanding. Yet we can distinguish between inarticulate genius and articulate idiocy-the first represented by the student who, by his operations and conclusions, reveals a deep grasp of a subject but not much ability to "say how it goes," in contrast to the student who is full of seemingly appropriate words but has no matching ability to use the ideas for which the words presumably stand. A careful examination of the nature of intuitive thinking might be of great aid to those charged with curriculum construction and teaching.

Mathematicians, physicists, biologists, and others stress the value of intuitive thinking in their respective areas. In mathematics, for example, intuition is used with two rather different meanings. On the one hand, an individual is said to think intuitively when, having worked for a long time on a problem, he rather suddenly achieves the solution, one for which he has yet to provide a formal proof. On the other hand, an individual is said to be a good intuitive mathematician if, when others come to him with questions, he can make quickly very good guesses whether something is so, or which of several approaches to a problem will prove fruitful.

The development of effectiveness in intuitive thinking is an objective of many of the most highly regarded teachers in mathematics and science. The point has been repeatedly made that in the high school plane geometry is typically taught with excessive emphasis upon techniques, formal proofs, and the like, that much more attention needs to be given to the development of students who have a good intuitive feel for geometry, students who are skillful in discovering proofs, not just in checking the validity of or remembering proofs with which they have been presented. There has been very little done, for example, on the use of diagrams as geometrical experiments as in Hilbert and Cohn's Geometry and the Imagination, in which visual proof substitutes for formal proof where possible. Similarly, in physics, Newtonian mechanics is typically taught deductively and analytically. In the judgment of many physicists, at least, there is too little attention to the development of intuitive understanding. Indeed, some have suggested that improving the use of intuitive thinking by teachers is as much a problem as improving its use by students.

Yet, as one member of the Conference put it, it is wrong to look at intuition as "all ala mode and no pie." The good intuiter may have been born with something special, but his effectiveness rests upon a solid knowledge of the subject, a familiarity that gives intuition something to work with. Certainly there are some experiments on learning that indicate the importance of a high degree of mastery of materials in order to operate effectively with them intuitively.

Those concerned with the improvement of curricula in physics and mathematics particularly have often cited as one of their important aims the use of procedures that will contribute to the improvement of intuitive thinking. In their attempts to design such procedures, there has been a question of the kind of systematic psychological knowledge that would be of help. Unfortunately, little systematic knowledge is available about the nature of intuitive thinking or the variables that influence it. What seems most appropriate at this point, therefore, is an attempt to outline the kinds of research which, if even only partially carried out, would begin to provide information useful to those concerned with the improvement of particular courses or, more generally, of the curriculum as a whole. What kinds of questions do we need the answers to?

Questions about the nature of intuitive thinking seem to center upon two large issues: what intuitive thinking is, and what affects it.
关于直觉思维的性质问题好象集中在两个大的题目上:什么是直觉思维T 影响直觉思维的又是什么?

One can say many more concrete things about analytic thinking than about intuitive thinking. Analytic thinking characteristically proceeds a step at a time. Steps are explicit and usually can be adequately reported by the thinker to another individual. Such thinking proceeds with relatively full awareness of the information and operations involved. It may involve careful and deductive reasoning, often using mathematics or logic and an explicit plan of attack. Or it may involve a stepby- step process of induction and experiment, utilizing principles of research design and statistical analysis.

In contrast to analytic thinking, intuitive thinking characteristically does not advance in careful, welldefined steps. Indeed, it tends to involve maneuvers based seemingly on an implicit perception of the total problem. The thinker arrives at an answer, which may be right or wrong, with little if any awareness of the process by which he reached it. He rarely can provide an adequate account of how he obtained his answer, and he may be unaware of just what aspects of the problem situation he was responding to. Usually intuitive thinking rests on familiarity with the domain of knowledge involved and with its structure, which makes it possible for the thinker to leap about, skipping steps and employing short cuts in a manner that requires a later rechecking of conclusions by more analytic means, whether deductive or inductive.

The complementary nature of intuitive and analytic thinking should, we think, be recognized. Through intuitive thinking the individual may often arrive at solutions to problems which he would not achieve at all, or at best more slowly, through analytic thinking. Once achieved by intuitive methods, they should if possible be checked by analytic methods, while at the same time being respected as worthy hypotheses for such checking. Indeed, the intuitive thinker may even invent or discover problems that the analyst would not. But it may be the analyst who gives these problems the proper formalism. Unfortunately, the formalism of school learning has somehow devalued intuition. It is the very strong conviction of men who have been designing curricula, in mathematics and the sciences particularly, over the last several years that much more work is needed to discover how we may develop the intuitive gifts of our students from the earliest grades onwards. For, as we have seen, it may be of the first importance to establish an intuitive understanding of materials before we expose our students to more traditional and formal methods of deduction and proof.

As to the nature of intuitive thinking, what is it? It is quite clear that it is not easy either to recognize a particular problem-solving episode as intuitive or, indeed, to identify intuitive ability as such. Precise definition in terms of observable behavior is not readily within our reach at the present time. Obviously, research on the topic cannot be delayed until such a time as a pure and unambiguous definition of intuitive thinking is possible, along with precise techniques for identifying intuition when it occurs. Such refinement is the goal of research, not its starting place. It suffices as a start to ask whether we are able to identify certain problem-solving episodes as more intuitive than others. Or, alternatively, we may ask if we can learn to agree in classifying a person's style or preferred mode of working as characteristically more analytic or inductive, on the one hand, or more intuitive, and, indeed, if we can find some way to classify tasks as ones that require each of those styles of attack. It is certainly clear that it is important not to confuse intuitive and other kinds of thinking with such evaluative notions as effectiveness and ineffectiveness: the analytic, the inductive, and the intuitive can be either. Nor should we distinguish them in terms of whether they produce novel or familiar outcomes, for again this is not the important distinction.

For a working definition of intuition, we do well to begin with Webster: "immediate apprehension or cognition." "Immediate" in this context is contrasted with "mediated"-apprehension or cognition that depends on the intervention of formal methods of analysis and proof. Intuition implies the act of grasping the meaning, significance, or structure of a problem or situation without explicit reliance on the analytic apparatus of one's craft. The rightness or wrongness of an intuition is finally decided not by intuition itself but by the usual methods of proof. It is the intuitive mode, however, that yields hypotheses quickly, that hits on combinations of ideas before their worth is known. In the end, intuition by itself yields a tentative ordering of a body of knowledge that, while it may generate a feeling that the ordering of facts is self-evident, aids principally by giving us a basis for moving ahead in our testing of reality.

Obviously, some intuitive leaps are "good" and some are "bad" in tenns of how they turn out. Some men are good intuiters, others should be warned off. What the underlying heuristic of the good intuiter is, is not known but is eminently worthy of study. And what is involved in transforming explicit techniques into implicit ones that can be used almost automatically is a subject that is also full of conjecture. Unquestionably, experience and familiarity with a subject help-but the help is only for some. Those of us who teach graduate students making their first assault on a frontier of knowledge are often struck by our immediate reactions to their ideas, sensing that they are good or impossible or trivial before ever we know why we think so. Often we turn out to be right; sometimes we are victims of too much familiarity with past efforts. In either case, the intuition may be weeks or months ahead of the demonstration of our wisdom or foolhardiness. At the University of Buffalo there is a collection of successive drafts of poems written by leading contemporary poets. One is struck in examining them by the immediate sense one gets of the rightness of a revision a poet has made-but it is often difficult or impossible to say why the revision is better than the original, difficult for the reader and the poet alike.

It is certainly clear that procedures or instruments are needed to characterize and measure intuitive thinking, and that the development of such instruments should be pursued vigorously. We cannot foresee at this stage what the research tools will be in this field. Can one rely, for example, upon the subject's willingness to talk as he works, to reveal the nature of the alternatives he is considering, whether he is proceeding by intuitive leaps or by a step-by-step analysis or by empirical induction? Or will smaller-scale experimental approaches be suitable? Can group measurement procedures involving pencil and paper tests be used to provide a measure? All of these deserve a try.
的确很清楚,描绘测量直觉思维需要一定的程序或工具,而且应该大力发展这种工具。我们不能在现阶段预见在这个领域里将要用什么研究工具。例如,我们能否依赖受试者在工作中显出思维选择性时的谈话来判断他到底是靠直觉的跳跃,还是靠一步步的分析,抑或是靠经验的归纳来进行思维的呢?采用小规模的实验方适合适吗? 能否用团体测量程序包括笔和纸的测验来提供某种测度呢?所有这些都值得试一试。

What variables seem to affect intuitive thinking? There must surely be predisposing factors that are correlated with individual differences in the use of intuition, factors, even, that will predispose a person to think intuitively in one area and not in another. With respect to such factors, we can only raise a series of conjectures. Is the development of intuitive thinking in students more likely if their teachers think intuitively? Perhaps simple imitation is involved, or perhaps more complex processes of identification. It seems unlikely that a student would develop or have confidence in his intuitive methods of thinking if he never saw them used effectively by his elders. The teacher who is willing to guess at answers to questions asked by the class and then subject his guesses to critical analysis may be more apt to build those habits into his students than would a teacher who analyzes everything for the class in advance. Does the providing of varied experience in a particular field increase effectiveness in intuitive thinking in that field? Individuals who have extensive familiarity with a subject appear more often to leap intuitively into a decision or to a solution of a problem-one which later proves to be appropriate. The specialist in internal medicine, for example, may, upon seeing a patient for the first time, ask a few questions, examine the patient briefly, and then make an accurate diagnosis. The risk, of course, is that his method may lead to some big errors as well-bigger than those that result from the more painstaking, stepby- step analysis used by the young intern diagnosing the same case. Perhaps under these circumstances intuition consists in using a limited set of cues, because the thinker l{nows what things are structurally related to what other things. This is not to say that "clinical" prediction is better or worse than actuarial prediction, only that it is different and that both are useful.

In this connection we may ask whether, in teaching, emphasis upon the structure or connectedness of knowledge increases facility in intuitive thinking. Those concerned with the improvement of the teaching of mathematics often emphasize the importance of developing in the student an understanding of the structure or order of mathematics. The same is true for physics. Implicit in this emphasis, it appears, is the belief that such understanding of structure enables the student, among other things, to increase his effectiveness in dealing intuitively with problems.

What is the effect on intuitive thinking of teaching various so-called heuristic procedures? A heuristic procedure, as we have noted, is in essence a nonrigorous method of achieving solutions of problems. While heuristic procedure often leads to solution, it offers no guarantee of doing so. An algorithm, on the other hand, is a procedure for solving a problem which, if followed accurately, guarantees that in a finite number of steps you will find a solution to the problem if the problem has a solution. Heuristic procedures are often available when no algorithmic procedures are known; this is one of their advantages. Moreover, even when an algorithm is available, heuristic procedures are often much faster. Will the teaching of certain heuristic procedures facilitate intuitive thinking? For example, should students be taught explicitly, "When you cannot see how to proceed with the problem, try to think of a simpler problem that is similar to it; then use the method for solving the simpler problem as a plan for solving the more complicated problem?" Or should the student be led to learn such a technique without actually verbalizing it to himself in that way? It is possible, of course, that the ancient proverb about the caterpillar who could not walk when he tried to say how he did it may apply here. The student who becomes obsessively aware of the heuristic rules he uses to make his intuitive leaps may reduce the process to an analytic one. On the other hand, it is difficult to believe that general heuristic rules -the use of analogy, the appeal to symmetry, the examination of limiting conditions, the visualization of the solution-when they have been used frequently will be anything but a support to intuitive thinking.

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 thinl{ing 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 lil{e to educate students to do nothing but guess, for guessing should always be followed up by 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 guesses. 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 data must take account of both probability and costs. What we should teach students to recognize, probably, is when the cost of not guessing is too high, as well as when guessing itself is too costly. We tend to do the latter much better than the former. Should we give our students practice not only in making educated guesses but also in recognizing the characteristics of plausible guesses provided by others-knowing that an answer at least is of the right order of magnitude, or that it is possible rather than impossible? It is our feeling that perhaps a student would be given considerable advantage in his thinking, generally, if he learned that there were alternatives that could be chosen that lay somewhere between truth and complete silence. But let us not confuse ourselves by failing to recognize that there are two kinds of self-confidenceone a trait of personality, and another that comes from knowledge of a subject. It is no particular credit to the educator to help build the first without building the second. The objective of education is not the production of self-confident fools.

Yet it seems likely that effective intuitive thinking is fostered by the development of self-confidence and courage in the student. A person who thinks intuitively may often achieve correct solutions, but he may also be proved wrong when he checks or when others check on him. Such thinking, therefore, requires a willingness to make honest mistakes in the effort to solve problems. One who is insecure, who lacks confidence in himself, may be unwilling to run such risks.

Observations suggest that in business, as the novelty or importance of situations requiring decision increases, the tendency to think analytically also increases. Perhaps when the student sees the consequences of error as too grave and the consequences of success as too chancy, he will freeze into analytic procedures even though they may not be appropriate. On these grounds, one may wonder whether the present system of rewards and punishments as seen by pupils in school actually tends to inhibit the use of intuitive thinking. The assignment of grades in school typically emphasizes the acquisition of factual knowledge, primarily because that is what is most easily evaluated; moreover, it tends to emphasize the correct answer, since it is the correct answer on the straightforward examination that can be graded as "correct." It appears to us important that some research be undertaken to learn what would happen to the development of intuitive thinking if different bases for grading were employed.

Finally, what can be said about the conditions in which intuitive thinking is likely to be particularly effective? In which subjects will mastery be most aided by intuitive procedures followed by checking? Many kinds of problems will be best approached by some combination of intuitive and other procedures, so it is also important to know whether or not both can be developed within the same course by the same teaching methods. This suggests that we examine the mode of effective operation of intuition in different kinds of fields. One hears the most explicit talk about intuition in those fields where the formal apparatus of deduction and induction is most highly developed-in mathematics and physics. The use of the word "intuition" by mathematicians and physicists may reflect their sense of confidence in the power and rigor of their disciplines. Others, however, may use intuition as much or more. Surely the historian, to take but one example, leans heavily upon intuitive procedures in pursuing his subject, for he must select what is relevant. He does not attempt to learn or record everything about a period; he limits himself to finding or learning predictively fruitful facts which, when combined, permit him to make intelligent guesses about what else went on. A comparison of intuitive thinking in different fields of knowledge would, we feel, be highly useful.
最后,关于能使直觉思维特别有效的条件,我们能够说些什么呢?在哪些学科的掌握中,用直觉程序,并继之以检验,会最有助益?解决各种各样问题的途径,最好借助直觉程序和别的程序的结合来进行,所以,知道是不是两种程序在用同样教学法的同样课程内都能得到发展,也是重要的。这就提出要我们去考查在不同领域内直觉的有效运转方式。我们听到人们最明确地谈论象数学和物理学这些演绎和归纳的形式装置(formal apparatus) 高度发展的领域里的直觉。数学家和物理学家使用“直觉”一词,可能反映他们对自己专业训练的力量和严肃性的确信之感。然而,其他的人几乎也同样使用直觉,或者用得更多。单以历史学家为例。历史学家在探索他的学科时,大量地依靠直觉程序,因为他必须选择有关联的事物。他并不试图查明或记录某一时期的全部事情;他自己只限于去发现或预知有成果的各种论据,这些论据结合起来,就能使他明智地猜想还发生过什么别的事情。我们觉得,各种不同知识领域里直觉思维的比较研究,肯定非常有用。

We have already noted in passing the intuitive confidence required of the poet and the literary critic in practicing their crafts: the need to proceed in the absence of specific and agreed-upon criteria for the choice of an image of the formulation of a critique. It is difficult for a teacher, a textbook, a demonstration film, to make explicit provision for the cultivation of courage in taste. As likely as not, courageous taste rests upon confidence in one's intuitions about what is moving, what is beautiful, what is tawdry. In a culture such as ours, where there is so much pressure toward uniformity of taste in our mass media of communication, so much fear of idiosyncratic style, indeed a certain suspicion of the idea of style altogether, it becomes the more important to nurture confident intuition in the realm of literature and the arts. Yet one finds a virtual vacuum of research on this topic in educational literature.

The warm praise that scientists lavish on those of their colleagues who earn the label "intuitive" is major evidence that intuition is a valuable commodity in science and one we should endeavor to foster in our students. The case for intuition in the arts and social studies is just as strong. But the pedagogic problems in fostering such a gift are severe and should not be overlooked in our eagerness to take the problem into the laboratory. For one thing, the intuitive method, as we have noted, often produces the wrong answer. It requires a sensitive teacher to distinguish an intuitive mistake-an interestingly wrong leap-from a stupid or ignorant mistake, and it requires a teacher who can give approval and correction simultaneously to the intuitive student. To know a subject so thoroughly that he can go easily beyond the textbook is a great deal to ask of a high school teacher. Indeed, it must happen occasionally that a student is not only more intelligent than his teacher but better informed, and develops intuitive ways of approaching problems that he cannot explain and that the teacher is simply unable to follow or re-create for himself. It is impossible for the teacher properly to reward or correct such students, and it may very well be that it is precisely our more gifted students who suffer such unrewarded effort. So along with any program for developing methods of cultivating and measuring the occurrence of intuitive thinking, there must go some practical consideration of the classroom problems and the limitations on our capacity for encouraging such skills in our students. This, too, is research that should be given all possible support.

These practical difficulties should not discourage psychologists and teachers from making an attack on the problem. Once we have obtained answers to various of the questions raised in this chapter, we shall be in a much better position to recommend procedures for overcoming some of the difficulties.

TAG: 布鲁纳 分析思维 直觉思维
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