By science is meant, as already stated, that knowledge which is the outcome of methods of observation, reflection, and testing which are deliberately adopted to secure a settled, assured subject matter. It involves an intelligent and persistent endeavor to revise current beliefs so as to weed out what is erroneous, to add to their accuracy, and, above all, to give them such shape that the dependencies of the various facts upon one another may be as obvious as possible. It is, like all knowledge, an outcome of activity bringing about certain changes in the environment. But in its case, the quality of the resulting knowledge is the controlling factor and not an incident of the activity. Both logically and educationally, science is the perfecting of knowing, its last stage.

Science, in short, signifies a realization of the logical implications of any knowledge. Logical order is not a form imposed upon what is known; it is the proper form of knowledge as perfected. For it means that the statement of subject matter is of a nature to exhibit to one who understands it the premises from which it follows and the conclusions to which it points (See ante, ch. XIV p. 3). As from a few bones the competent zoölogist reconstructs an animal; so from the form of a statement in mathematics or physics the specialist in the subject can form an idea of the system of truths in which it has its place. To the non-expert, however, this perfected form is a stumbling block. Just because the material is stated with reference to the furtherance of knowledge as an end in itself, its connections with the material of everyday life are hidden. To the layman the bones are a mere curiosity. Until he had mastered the principles of zoölogy, his efforts to make anything out of them would be random and blind. From the standpoint of the learner scientific form is an ideal to be achieved, not a starting point from which to set out. It is, nevertheless, a frequent practice to start in instruction with the rudiments of science somewhat simplified. The necessary consequence is an isolation of science from significant experience. The pupil learns symbols without the key to their meaning. He acquires a technical body of information without ability to trace its connections with the objects and operations with which he is familiar—often he acquires simply a peculiar vocabulary.

There is a strong temptation to assume that presenting subject matter in its perfected form provides a royal road to learning. What more natural than to suppose that the immature can be saved time and energy, and be protected from needless error by commencing where competent inquirers have left off? The outcome is written large in the history of education. Pupils begin their study of science with texts in which the subject is organized into topics according to the order of the specialist. Technical concepts, with their definitions, are introduced at the outset. Laws are introduced at a very early stage, with at best a few indications of the way in which they were arrived at. The pupils learn a "science" instead of learning the scientific way of treating the familiar material of ordinary experience. The method of the advanced student dominates college teaching; the approach of the college is transferred into the high school, and so down the line, with such omissions as may make the subject easier.

The chronological method which begins with the experience of the learner and develops from that the proper modes of scientific treatment is often called the "psychological" method in distinction from the logical method of the expert or specialist. The apparent loss of time involved is more than made up for by the superior understanding and vital interest secured. What the pupil learns he at least understands. Moreover by following, in connection with problems selected from the material of ordinary acquaintance, the methods by which scientific men have reached their perfected knowledge, he gains independent power to deal with material within his range, and avoids the mental confusion and intellectual distaste attendant upon studying matter whose meaning is only symbolic. Since the mass of pupils are never going to become scientific specialists, it is much more important that they should get some insight into what scientific method means than that they should copy at long range and second hand the results which scientific men have reached. Students will not go so far, perhaps, in the "ground covered," but they will be sure and intelligent as far as they do go. And it is safe to say that the few who go on to be scientific experts will have a better preparation than if they had been swamped with a large mass of purely technical and symbolically stated information. In fact, those who do become successful men of science are those who by their own power manage to avoid the pitfalls of a traditional scholastic introduction into it.

The contrast between the expectations of the men who a generation or two ago strove, against great odds, to secure a place for science in education, and the result generally achieved is painful. Herbert Spencer, inquiring what knowledge is of most worth, concluded that from all points of view scientific knowledge is most valuable. But his argument unconsciously assumed that scientific knowledge could be communicated in a ready-made form. Passing over the methods by which the subject matter of our ordinary activities is transmuted into scientific form, it ignored the method by which alone science is science. Instruction has too often proceeded upon an analogous plan. But there is no magic attached to material stated in technically correct scientific form. When learned in this condition it remains a body of inert information. Moreover its form of statement removes it further from fruitful contact with everyday experiences than does the mode of statement proper to literature. Nevertheless that the claims made for instruction in science were unjustifiable does not follow. For material so taught is not science to the pupil.

Contact with things and laboratory exercises, while a great improvement upon textbooks arranged upon the deductive plan, do not of themselves suffice to meet the need. While they are an indispensable portion of scientific method, they do not as a matter of course constitute scientific method. Physical materials may be manipulated with scientific apparatus, but the materials may be disassociated in themselves and in the ways in which they are handled, from the materials and processes used out of school. The problems dealt with may be only problems of science: problems, that is, which would occur to one already initiated in the science of the subject. Our attention may be devoted to getting skill in technical manipulation without reference to the connection of laboratory exercises with a problem belonging to subject matter. There is sometimes a ritual of laboratory instruction as well as of heathen religion.

It has been mentioned, incidentally, that scientific statements, or logical form, implies the use of signs or symbols. The statement applies, of course, to all use of language. But in the vernacular, the mind proceeds directly from tie symbol to the thing signified. Association with familiar material is so close that the mind does not pause upon the sign. The signs are intended only to stand for things and acts. But scientific terminology has an additional use. It is designed, as we have seen, not to stand for the things directly in their practical use in experience, but for the things placed in a cognitive system. Ultimately, of course, they denote the things of our common sense acquaintance. But immediately they do not designate them in their common context, but translated into terms of scientific inquiry. Atoms, molecules, chemical formulæ, the mathematical propositions in the study of physics—all these have primarily an intellectual value and only indirectly an empirical value. They represent instruments for the carrying on of science. As in the case of other tools, their significance can be learned only by use. We cannot procure understanding of their meaning by pointing to things, but only by pointing to their work when they are employed as part of the technique of knowledge.

Even the circle, square, etc., of geometry exhibit a difference from the squares and circles of familiar acquaintance, and the further one proceeds in mathematical science the greater the remoteness from the everyday empirical thing. Qualities which do not count for the pursuit of knowledge about spatial relations are left out; those which are important for this purpose are accentuated. If one carries his study far enough, he will find even the properties which are significant for spatial knowledge giving way to those which facilitate knowledge of other things—perhaps a knowledge of the general relations of number. There will be nothing in the conceptual definitions even to suggest spatial form, size, or direction. This does not mean that they are unreal mental inventions, but it indicates that direct physical qualities have been transmuted into tools for a special end—the end of intellectual organization. In every machine the primary state of material has been modified by subordinating it to use for a purpose. Not the stuff in its original form but in its adaptation to an end is important. No one would have a knowledge of a machine who could enumerate all the materials entering into its structure, but only he who knew their uses and could tell why they are employed as they are. In like fashion one has a knowledge of mathematical conceptions only when he sees the problems in which they function and their specific utility in dealing with these problems. "Knowing" the definitions, rules, formulæ, etc., is like knowing the names of parts of a machine without knowing what they do. In one case, as in the other, the meaning, or intellectual content, is what the element accomplishes in the system of which it is a member.