Concrete and Abstract Thinking

The maxim enjoined upon teachers, "to proceed from the concrete to the abstract," is perhaps familiar rather than comprehended. Few who read and hear it gain a clear conception of the starting-point, the concrete; of the nature of the goal, the abstract; and of the exact nature of the path to be traversed in going from one to the other. At times the injunction is positively misunderstood, being taken to mean that education should advance from things to thought—as if any dealing with things in which thinking is not involved could possibly be educative. So understood, the maxim encourages mechanical routine or sensuous excitation at one end of the educational scale—the lower—and academic and unapplied learning at the upper end.

The rule given to teachers, "to proceed from the concrete to the abstract," is perhaps familiar without being understood. Few who read or hear it clearly understand the starting point, the concrete. Few understand the nature of the goal, the abstract, or the exact path from one to the other. Sometimes the rule is completely misunderstood. It is taken to mean that education should move from things to thought. This is as if dealing with things without thinking could possibly be educational. Understood this way, the rule encourages mechanical routine or sensory stimulation at the lower end of education. At the upper end, it encourages academic learning that is not put to use.

Actually, all dealing with things, even the child's, is immersed in inferences; things are clothed by the suggestions they arouse, and are significant as challenges to interpretation or as evidences to substantiate a belief. Nothing could be more unnatural than instruction in things without thought; in sense-perceptions without judgments based upon them. And if the abstract to which we are to proceed denotes thought apart from things, the goal recommended is formal and empty, for effective thought always refers, more or less directly, to things.

In fact, all dealings with things, even a child's, are full of inferences. Things are surrounded by the ideas they suggest. They matter as challenges to interpretation or as evidence supporting a belief. Nothing could be more unnatural than teaching about things without thought, or about sense perceptions without judgments based on them. And if the abstract thought we are supposed to move toward means thought apart from things, the recommended goal is formal and empty. Effective thought always refers, more or less directly, to things.

Yet the maxim has a meaning which, understood and supplemented, states the line of development of logical capacity. What is this signification? Concrete denotes a meaning definitely marked off from other meanings so that it is readily apprehended by itself. When we hear the words, table, chair, stove, coat, we do not have to reflect in order to grasp what is meant. The terms convey meaning so directly that no effort at translating is needed. The meanings of some terms and things, however, are grasped only by first calling to mind more familiar things and then tracing out connections between them and what we do not understand. Roughly speaking, the former kind of meanings is concrete; the latter abstract.

Yet the maxim has a meaning that, when understood and supplemented, describes how logical capacity develops. What does it mean? A concrete meaning is clearly distinct from other meanings, so it is easy to grasp on its own. When we hear the words table, chair, stove, or coat, we do not have to think about what they mean. The words convey their meanings so directly that we need no effort to translate them. But we can grasp the meanings of some words and things only by first calling more familiar things to mind. We then trace the connections between those familiar things and what we do not understand. Roughly speaking, the first kind of meaning is concrete. The second kind is abstract.

To one who is thoroughly at home in physics and chemistry, the notions of atom and molecule are fairly concrete. They are constantly used without involving any labor of thought in apprehending what they mean. But the layman and the beginner in science have first to remind themselves of things with which they already are well acquainted, and go through a process of slow translation; the terms atom and molecule losing, moreover, their hard-won meaning only too easily if familiar things, and the line of transition from them to the strange, drop out of mind. The same difference is illustrated by any technical terms: coefficient and exponent in algebra, triangle and square in their geometric as distinct from their popular meanings; capital and value as used in political economy, and so on.

For someone thoroughly familiar with physics and chemistry, the ideas of atom and molecule are fairly concrete. Such a person uses these terms constantly without having to think hard about what they mean. But a layperson or beginning science student must first recall familiar things and slowly translate from them to these unfamiliar ideas. The terms atom and molecule also lose their hard-won meaning all too easily. This happens if the learner forgets the familiar things and the steps that lead from them to the unfamiliar ideas. The same difference appears with any technical terms: coefficient and exponent in algebra, triangle and square in their geometric rather than everyday meanings, capital and value in political economy, and so on.

The difference as noted is purely relative to the intellectual progress of an individual; what is abstract at one period of growth is concrete at another; or even the contrary, as one finds that things supposed to be thoroughly familiar involve strange factors and unsolved problems. There is, nevertheless, a general line of cleavage which, deciding upon the whole what things fall within the limits of familiar acquaintance and what without, marks off the concrete and the abstract in a more permanent way. These limits are fixed mainly by the demands of practical life. Things such as sticks and stones, meat and potatoes, houses and trees, are such constant features of the environment of which we have to take account in order to live, that their important meanings are soon learnt, and indissolubly associated with objects. We are acquainted with a thing (or it is familiar to us) when we have so much to do with it that its strange and unexpected corners are rubbed off. The necessities of social intercourse convey to adults a like concreteness upon such terms as taxes, elections, wages, the law, and so on. Things the meaning of which I personally do not take in directly, appliances of cook, carpenter, or weaver, for example, are nevertheless unhesitatingly classed as concrete, since they are so directly connected with our common social life.

As noted, the difference depends entirely on an individual’s intellectual development. What is abstract at one stage of growth may be concrete at another. The reverse can also happen, when we find that supposedly familiar things contain strange elements and unsolved problems. Nevertheless, there is a general dividing line between the concrete and the abstract that is more lasting. On the whole, it determines which things are familiar and which are not. These limits are set mainly by the demands of practical life. Sticks and stones, meat and potatoes, houses and trees are constant features of our surroundings. We must take them into account to live, so we soon learn their important meanings. We then associate those meanings inseparably with the objects. We know a thing, or find it familiar, when we deal with it so often that its strange and unexpected aspects are worn away. The demands of social interaction make terms such as taxes, elections, wages, and the law similarly concrete for adults. I may not personally understand the meaning of certain things directly, such as the tools of a cook, carpenter, or weaver. Nevertheless, we classify them as concrete without hesitation because they are so directly connected with our shared social life.

By contrast, the abstract is the theoretical, or that not intimately associated with practical concerns. The abstract thinker (the man of pure science as he is sometimes called) deliberately abstracts from application in life; that is, he leaves practical uses out of account. This, however, is a merely negative statement. What remains when connections with use and application are excluded? Evidently only what has to do with knowing considered as an end in itself. Many notions of science are abstract, not only because they cannot be understood without a long apprenticeship in the science (which is equally true of technical matters in the arts), but also because the whole content of their meaning has been framed for the sole purpose of facilitating further knowledge, inquiry, and speculation. When thinking is used as a means to some end, good, or value beyond itself, it is concrete; when it is employed simply as a means to more thinking, it is abstract. To a theorist an idea is adequate and self-contained just because it engages and rewards thought; to a medical practitioner, an engineer, an artist, a merchant, a politician, it is complete only when employed in the furthering of some interest in life—health, wealth, beauty, goodness, success, or what you will.

By contrast, the abstract is the theoretical, or what is not closely connected with practical concerns. The abstract thinker, sometimes called the person of pure science, deliberately sets aside practical applications. In other words, the abstract thinker leaves practical uses out of account. This, however, tells us only what is excluded. What remains when connections with use and application are excluded? Clearly, only what concerns knowledge as an end in itself. Many scientific ideas are abstract, not only because understanding them requires long training in the science. The same is true of technical matters in the arts. Scientific ideas are also abstract because their entire meaning has been shaped solely to make further knowledge, inquiry, and speculation easier. When thinking serves an end, good, or value beyond itself, it is concrete. When thinking serves only to produce more thinking, it is abstract. For a theorist, an idea is adequate and complete in itself because it engages and rewards thought. For a medical practitioner, engineer, artist, merchant, or politician, an idea is complete only when used to advance some interest in life, such as health, wealth, beauty, goodness, success, or whatever else one values.

For the great majority of men under ordinary circumstances, the practical exigencies of life are almost, if not quite, coercive. Their main business is the proper conduct of their affairs. Whatever is of significance only as affording scope for thinking is pallid and remote—almost artificial. Hence the contempt felt by the practical and successful executive for the "mere theorist"; hence his conviction that certain things may be all very well in theory, but that they will not do in practice; in general, the depreciatory way in which he uses the terms abstract, theoretical, and intellectual—as distinct from intelligent.

For the great majority of people in ordinary circumstances, the practical demands of life are almost, if not entirely, compelling. Their main business is to manage their affairs properly. Anything valuable only because it gives them a chance to think seems dull and remote, almost artificial. This is why the practical, successful executive looks down on the "mere theorist." It is why he believes that certain things may be fine in theory but will not work in practice. More generally, it explains his dismissive use of abstract, theoretical, and intellectual, as distinct from intelligent.

This attitude is justified, of course, under certain conditions. But depreciation of theory does not contain the whole truth, as common or practical sense recognizes. There is such a thing, even from the common-sense standpoint, as being "too practical," as being so intent upon the immediately practical as not to see beyond the end of one's nose or as to cut off the limb upon which one is sitting. The question is one of limits, of degrees and adjustments, rather than one of absolute separation. Truly practical men give their minds free play about a subject without asking too closely at every point for the advantage to be gained; exclusive preoccupation with matters of use and application so narrows the horizon as in the long run to defeat itself. It does not pay to tether one's thoughts to the post of use with too short a rope. Power in action requires some largeness and imaginativeness of vision. Men must at least have enough interest in thinking for the sake of thinking to escape the limits of routine and custom. Interest in knowledge for the sake of knowledge, in thinking for the sake of the free play of thought, is necessary then to the emancipation of practical life—to make it rich and progressive.

Of course, this attitude is justified under certain conditions. But common sense recognizes that dismissing theory is not the whole truth. Even from a common-sense standpoint, it is possible to be "too practical." A person can focus so closely on immediate practical concerns that they cannot see beyond the end of their nose. Or they may cut off the limb they are sitting on. The question is about limits, degrees, and adjustments, not an absolute separation. Truly practical people let their minds explore a subject freely. They do not constantly ask what benefit they will gain at every point. Focusing only on use and application narrows their vision so much that it defeats its own purpose in the long run. It does not pay to tie one's thoughts to the post of use with too short a rope. Effective action requires a broad and imaginative vision. People must have at least enough interest in thinking for its own sake to escape the limits of routine and custom. An interest in knowledge for its own sake, and in thinking for the sake of free thought, is therefore necessary for the emancipation of practical life. Such interest makes practical life rich and progressive.

We may now recur to the pedagogic maxim of going from the concrete to the abstract.

We may now return to the teaching principle of moving from the concrete to the abstract.

1. Since the concrete denotes thinking applied to activities for the sake of dealing effectively with the difficulties that present themselves practically, "beginning with the concrete" signifies that we should at the outset make much of doing; especially, make much in occupations that are not of a routine and mechanical kind and hence require intelligent selection and adaptation of means and materials. We do not "follow the order of nature" when we multiply mere sensations or accumulate physical objects. Instruction in number is not concrete merely because splints or beans or dots are employed, while whenever the use and bearing of number relations are clearly perceived, the number idea is concrete even if figures alone are used. Just what sort of symbol it is best to use at a given time—whether blocks, or lines, or figures—is entirely a matter of adjustment to the given case. If physical things used in teaching number or geography or anything else do not leave the mind illuminated with recognition of a meaning beyond themselves, the instruction that uses them is as abstract as that which doles out ready-made definitions and rules; for it distracts attention from ideas to mere physical excitations.

1. The concrete means thinking applied to activities to deal effectively with practical difficulties as they arise. So "beginning with the concrete" means placing great emphasis on doing from the start. In particular, we should emphasize activities that are not routine or mechanical. Such activities require thoughtful selection and adaptation of methods and materials. We do not "follow the order of nature" by simply increasing sensations or collecting physical objects. Number instruction is not concrete merely because it uses sticks, beans, or dots. Whenever learners clearly understand the use and significance of number relationships, the idea of number is concrete, even if only figures are used. The best kind of symbol to use at any moment, whether blocks, lines, or figures, depends entirely on the situation. If physical objects used to teach number, geography, or anything else do not help learners recognize a meaning beyond the objects themselves, the instruction is just as abstract as instruction that hands out ready-made definitions and rules. Such instruction distracts attention from ideas and directs it toward mere physical sensations.

The conception that we have only to put before the senses particular physical objects in order to impress certain ideas upon the mind amounts almost to a superstition. The introduction of object lessons and sense-training scored a distinct advance over the prior method of linguistic symbols, and this advance tended to blind educators to the fact that only a halfway step had been taken. Things and sensations develop the child, indeed, but only because he uses them in mastering his body and in the scheme of his activities. Appropriate continuous occupations or activities involve the use of natural materials, tools, modes of energy, and do it in a way that compels thinking as to what they mean, how they are related to one another and to the realization of ends; while the mere isolated presentation of things remains barren and dead. A few generations ago the great obstacle in the way of reform of primary education was belief in the almost magical efficacy of the symbols of language (including number) to produce mental training; at present, belief in the efficacy of objects just as objects, blocks the way. As frequently happens, the better is an enemy of the best.

The idea that we need only put physical objects before the senses to impress certain ideas on the mind is almost a superstition. Object lessons and sense training were a clear advance over the earlier method of using language symbols. But this advance tended to blind educators to the fact that they had only gone halfway. Things and sensations do help children develop, but only because children use them to master their bodies and carry out activities. Suitable ongoing tasks or activities involve using natural materials, tools, and forms of energy. They also compel children to think about what these things mean, how they relate to one another, and how they help achieve goals. By contrast, simply presenting objects in isolation is barren and lifeless. A few generations ago, the main obstacle to reforming primary education was belief in the almost magical power of language symbols, including numbers, to train the mind. Today, belief in the power of objects as objects blocks the way. As often happens, the better is an enemy of the best.

2. The interest in results, in the successful carrying on of an activity, should be gradually transferred to study of objects—their properties, consequences, structures, causes, and effects. The adult when at work in his life calling is rarely free to devote time or energy—beyond the necessities of his immediate action—to the study of what he deals with. (Ante, p. 43.) The educative activities of childhood should be so arranged that direct interest in the activity and its outcome create a demand for attention to matters that have a more and more indirect and remote connection with the original activity. The direct interest in carpentering or shop work should yield organically and gradually an interest in geometric and mechanical problems. The interest in cooking should grow into an interest in chemical experimentation and in the physiology and hygiene of bodily growth. The making of pictures should pass to an interest in the technique of representation and the æsthetics of appreciation, and so on. This development is what the term go signifies in the maxim "go from the concrete to the abstract"; it represents the dynamic and truly educative factor of the process.

2. Interest in results, and in carrying out an activity successfully, should gradually shift toward studying objects. This means studying their properties, consequences, structures, causes, and effects. Adults at work in their chosen occupations are rarely free to spend extra time or energy studying what they work with. Their immediate tasks take up their time and energy. (Ante, p. 43.) Children’s educational activities should be arranged differently. Their direct interest in an activity and its outcome should create a need to attend to other matters. These matters should have an increasingly indirect and remote connection to the original activity. A direct interest in carpentry or shop work should naturally and gradually lead to an interest in geometry and mechanics. An interest in cooking should grow into an interest in chemical experiments. It should also lead to an interest in the physiology and hygiene of bodily growth. Making pictures should lead to an interest in techniques of representation and the aesthetics of appreciation, and so on. This development is what go means in the maxim "go from the concrete to the abstract." It is the dynamic and truly educational part of the process.

3. The outcome, the abstract to which education is to proceed, is an interest in intellectual matters for their own sake, a delight in thinking for the sake of thinking. It is an old story that acts and processes which at the outset are incidental to something else develop and maintain an absorbing value of their own. So it is with thinking and with knowledge; at first incidental to results and adjustments beyond themselves, they attract more and more attention to themselves till they become ends, not means. Children engage, unconstrainedly and continually, in reflective inspection and testing for the sake of what they are interested in doing successfully. Habits of thinking thus generated may increase in volume and extent till they become of importance on their own account.

3. The outcome, the abstract goal of education, is an interest in intellectual matters for their own sake. It is a delight in thinking for the sake of thinking. It is an old story: actions and processes that begin as a means to something else develop a compelling value of their own. The same is true of thinking and knowledge. At first, they are means to results and adjustments beyond themselves. Gradually, thinking and knowledge draw more attention in their own right, until they become ends rather than means. Children freely and continually examine and test things thoughtfully to succeed at what interests them. The habits of thinking they develop in this way may grow in scope and strength until they become important in themselves.

The three instances cited in Chapter Six represented an ascending cycle from the practical to the theoretical. Taking thought to keep a personal engagement is obviously of the concrete kind. Endeavoring to work out the meaning of a certain part of a boat is an instance of an intermediate kind. The reason for the existence and position of the pole is a practical reason, so that to the architect the problem was purely concrete—the maintenance of a certain system of action. But for the passenger on the boat, the problem was theoretical, more or less speculative. It made no difference to his reaching his destination whether he worked out the meaning of the pole. The third case, that of the appearance and movement of the bubbles, illustrates a strictly theoretical or abstract case. No overcoming of physical obstacles, no adjustment of external means to ends, is at stake. Curiosity, intellectual curiosity, is challenged by a seemingly anomalous occurrence; and thinking tries simply to account for an apparent exception in terms of recognized principles.

The three examples cited in Chapter Six moved progressively from the practical to the theoretical. Thinking about how to keep an appointment is clearly a concrete example. Trying to figure out the purpose of a particular part of a boat is an intermediate example. The pole exists and is positioned where it is for a practical reason. So, for the architect, the problem was purely concrete: maintaining a particular system of action. But for the passenger on the boat, the problem was theoretical and somewhat speculative. Whether he figured out the purpose of the pole made no difference to his reaching his destination. The third example, the appearance and movement of the bubbles, is strictly theoretical or abstract. There are no physical obstacles to overcome, and no external means to adjust to achieve an end. A seemingly unusual event challenges intellectual curiosity. Thinking simply tries to explain this apparent exception in terms of recognized principles.

(i) Abstract thinking, it should be noted, represents an end, not the end. The power of sustained thinking on matters remote from direct use is an outgrowth of practical and immediate modes of thought, but not a substitute for them. The educational end is not the destruction of power to think so as to surmount obstacles and adjust means and ends; it is not its replacement by abstract reflection. Nor is theoretical thinking a higher type of thinking than practical. A person who has at command both types of thinking is of a higher order than he who possesses only one. Methods that in developing abstract intellectual abilities weaken habits of practical or concrete thinking, fall as much short of the educational ideal as do the methods that in cultivating ability to plan, to invent, to arrange, to forecast, fail to secure some delight in thinking irrespective of practical consequences.

(i) Abstract thinking, it should be noted, is an aim, not the aim. The ability to think at length about matters far removed from immediate use grows out of practical, immediate ways of thinking. But abstract thinking is not a substitute for them. Education should not destroy the ability to think through obstacles and match means to ends. Nor should it replace that ability with abstract reflection. Theoretical thinking is not a higher form of thinking than practical thinking, either. A person who can use both kinds of thinking is better equipped than someone who has only one. Some teaching methods develop abstract intellectual abilities but weaken habits of practical or concrete thinking. Other methods develop the ability to plan, invent, organize, and anticipate, but fail to foster some enjoyment of thinking for its own sake, regardless of practical results. Both kinds of methods fall equally short of the educational ideal.

(ii) Educators should also note the very great individual differences that exist; they should not try to force one pattern and model upon all. In many (probably the majority) the executive tendency, the habit of mind that thinks for purposes of conduct and achievement, not for the sake of knowing, remains dominant to the end. Engineers, lawyers, doctors, merchants, are much more numerous in adult life than scholars, scientists, and philosophers. While education should strive to make men who, however prominent their professional interests and aims, partake of the spirit of the scholar, philosopher, and scientist, no good reason appears why education should esteem the one mental habit inherently superior to the other, and deliberately try to transform the type from practical to theoretical. Have not our schools (as already suggested, p. 49) been one-sidedly devoted to the more abstract type of thinking, thus doing injustice to the majority of pupils? Has not the idea of a "liberal" and "humane" education tended too often in practice to the production of technical, because overspecialized, thinkers?

(ii) Educators should also recognize the great differences among individuals. They should not try to force everyone into the same pattern or model. For many people, probably the majority, the practical tendency remains dominant throughout life. They think for the sake of action and achievement, not for the sake of knowledge. Engineers, lawyers, doctors, and merchants are far more numerous among adults than scholars, scientists, and philosophers. Education should strive to develop people who share the spirit of the scholar, philosopher, and scientist, however prominent their professional interests and goals. But there seems to be no good reason for education to regard either mental habit as inherently superior. Nor is there reason to deliberately try to turn practical thinkers into theoretical ones. Have our schools been too one-sidedly devoted to abstract thinking, thus treating the majority of pupils unfairly? This possibility was suggested earlier (p. 49). In practice, has the idea of a "liberal" and "humane" education too often produced technical thinkers because they are overspecialized?

The aim of education should be to secure a balanced interaction of the two types of mental attitude, having sufficient regard to the disposition of the individual not to hamper and cripple whatever powers are naturally strong in him. The narrowness of individuals of strong concrete bent needs to be liberalized. Every opportunity that occurs within their practical activities for developing curiosity and susceptibility to intellectual problems should be seized. Violence is not done to natural disposition, but the latter is broadened. As regards the smaller number of those who have a taste for abstract, purely intellectual topics, pains should be taken to multiply opportunities and demands for the application of ideas; for translating symbolic truths into terms of social life and its ends. Every human being has both capabilities, and every individual will be more effective and happier if both powers are developed in easy and close interaction with each other.

Education should aim to bring the two types of mental attitude into balanced interaction. It should also respect each individual’s natural tendencies, so that their natural strengths are not held back or weakened. People with a strong preference for concrete thinking need to broaden their outlook. Every opportunity in their practical activities should be used to develop their curiosity and openness to intellectual problems. This does not go against their natural tendencies. Instead, it broadens them. For the smaller number who enjoy abstract, purely intellectual subjects, care should be taken to create more opportunities and demands for applying ideas. They should have more chances to translate symbolic truths into terms of social life and its purposes. Every human being has both abilities. Each person will be more effective and happier if both are developed and work together easily and closely.