How to Study and Teaching How to Study · Chapter 5Chapter V
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A. The different values of facts, and their grouping into "points"
Extent to which teachers treat facts as equal in value
In several branches of knowledge in the primary school it is customary for teachers to attach practically the same importance to different facts. This is the case, for instance, in spelling, where a mistake counts the same, no matter what word be misspelled. It is largely the case in writing. In beginning reading one word is treated as equal in value to any other, since in any review list every one is required. In beginning arithmetic this equality of values is emphasized by insistence upon the complete mastery of every one of the combinations in the four fundamental operations. Throughout arithmetic, moreover, failure to solve any problem is the same as the failure to solve any other, judged in the light of the marking systems in use.
The same tendency is less marked, but still evident, in many other subjects, some of them more advanced. In geography, teachers seldom recognize any inequality of value in the map questions, even though a question on the general directions of the principal mountain systems in North America be followed by a request to locate Iceland. The facts, too, are very often strung along in the text in such a manner that it is next to impossible to distinguish values. Here is an example from a well-known text: "Worcester is a great railroad center, and is noted for the manufacture of engines and machinery. At Cambridge is located Harvard University, the oldest and one of the largest in the country. Pall River, Lowell, and New Bedford are the great centers of cotton manufacture; Lawrence, of both cotton and wool; Lynn, Brockton, and Haverhill make millions of boots and shoes; and at Springfield is a United States arsenal, where firearms are made. Holyoke has large paper mills. Gloucester is a great fishing port. Salem has large tanneries." How does this differ from a spelling list, so far as equality of values is concerned?
In nature study all have witnessed the typical lesson where some object, such as a flowering twig, for example, is placed in the hands of every pupil and each one is requested to tell something that he sees. Anything that is offered is gratefully accepted. While this particular kind of study is fortunately disappearing, the common tendency to regard all facts alike is still clearly shown in the case of the topic, cat, discussed on page 40.
In literature, failures are very often condemned alike, whether they pertain to the meanings of words, of sentences, of references, or of whole chapters.
Until very recently at least, even in universities, it has been common to assign lessons in history textbooks by pages, and to require that they be recited in the order of the text. The teacher, or professor even, in such cases has shown admirable ability to place the burden of the work upon the students by assigning to himself the single onerous task of announcing who shall "begin" and who shall "go on." What recognition is there of varying values of facts in such teaching?
The effect of such teaching on method of study
Not all of such instruction is avoidable or even undesirable; but it is so common that it has a very important effect on method of study.
So long as facts are treated as approximately equal in worth, the learner is bound to picture the field of knowledge as a comparatively level plain composed of a vast aggregation of independent bits. In spelling, writing, and beginning reading it is so many hundreds or thousands of words; in beginning arithmetic it is the various combinations in the four fundamental operations; in geography it is a long list of statements; in history it is an endless lot of facts as they happen to come on the page; in literature it is sentence after sentence.
One can get possession of this field, not by taking the strategic positions,—for under the assumption of equality there are none,—but rather by advancing over it slowly, mastering one bit at a time. Thus the words in beginning reading, writing, and spelling are learned and reproduced in all orders, proving them to be independent little entities. In geography and history, when the facts are not wormed out of the pupil by questions, he sees the page before him by his mind's eye,—a fact frequently revealed by the movement of his eyes while reciting,—and attempts to recall each paragraph or statement in its order. In literature he masters his difficulties sentence by sentence, a method most clearly shown in the case of our greatest classic, the Bible, which is almost universally studied and quoted by verses.
Thus the unit of progress in study is made the single fact; the whole of any subject becomes the sum of its details; and a subject has been supposedly mastered when all these bits have been learned. This might well be called the method of study by driblets. It is probably safe to say that a majority of the young people in the United States, including college students, study largely in this way.
While this method of study is bad in numerous ways, there are three of its faults in particular which need to be considered here.
Respects in which this method of study is wrong 1. Facts, as a rule, vary greatly in value
In the first place, facts vary indefinitely in value. In parts of a few subjects they do have practically the same worth, which is, no doubt, a source of much misconception about proper methods of study. In spelling, for instance, which is probably as important a word as when, and sea as important as flood. In a list of three hundred carefully selected words for spelling for third-year pupils, any one word might properly be regarded as equal to any other in worth. This may be said also in regard to a list for writing. Much the same is true in regard to a possible list of four hundred words for reading in the first year of school. In arithmetic one would scarcely assert that 4X7 was more or less important than 9X8, or 8/2, or 6-3, or 4+2. In other words, the various combinations in the four fundamental operations are, again, all of them essential to every person's knowledge, and therefore stand on the same plane of worth.
To some extent, therefore, the three R's and spelling are exceptions to an important general rule. Yet even in spelling and beginning reading not all words by any means have the same value. Children in the third year of school who are reading Whittier's Barefoot Boy ought to be able to recognize and spell the word robin; perhaps, also, woodchuck and tortoise; but eschewing is not a part of their vocabulary and will not soon be, and probably the less said about that word by the teacher the better.
The moment we turn to other subjects, facts are found to vary almost infinitely in value, just as metals do. Judged by the space they occupy, they may appear to be equally important; but they are not to be judged in this way, any more than men are. According to their nature, thoughts or statements are large and small, or broad and narrow, or far-reaching and insignificant. A general of an army may be of more consequence to the welfare of a nation than a thousand common soldiers; so one idea like that of evolution may be worth a full ten thousand like the fact that "our neighbor's cat kittened yesterday."
2. They are dependent upon one another for their worth
In the second place, facts can by no means be regarded as independent. As before, to be sure, the three R's and spelling afford some exception to this rule. In spelling, writing, and beginning reading it is important that any one of a large number of words be recognized or reproduced at any time, without reference to any others. All of these, together with the combinations in the fundamental operations in arithmetic, are often called for singly, and they must, therefore, be isolated from any possible series into which they might fall, and mastered separately.
Aside from these subjects, facts are generally dependent upon their relations to one another for their value. Taken alone, they are ineffective fragments of knowledge, just as a common soldier or an officer in an army is ineffective in battle without definite relations to a multitude of other men.
If the first sentences on twenty successive pages in a book were brought together, they would tell no story. They would be mere scattered fractions of thoughts, lacking that relation to one another that would give them significance and make them a unit. Twenty closely related sentences might, however, express a very valuable thought.
James Anthony Froude, impressed with this truth and at the same time recalling the prevalent tendency to ignore it, declares: "Detached facts on miscellaneous subjects, as they are taught at a modern school, are like separate letters of endless alphabets. You may load the mechanical memory with them, till it becomes a marvel of retentiveness. Your young prodigy may amaze examiners and delight inspectors. His achievements may be emblazoned in blue books, and furnish matter for flattering reports on the excellence of our educational system. And all this while you have been feeding him with chips of granite. But arrange your letters into words, and each word becomes a thought, a symbol waking in the mind an image of a real thing. Group your words into sentences, and thought is married to thought, and the chips of granite become soft bread, wholesome, nutritious, and invigorating." [Footnote: James Anthony Froude, Handwork before Headwork.]
A very simple illustration is found in the study of the dates for the entrance of our states into the Union. Taken one at a time, the list is dead. But interest is awakened the moment one discovers that for a long period each Northern state was matched by one in the South, so that they entered in pairs.
3. The sum of the details does not equal the whole.
Finally, the whole of a subject is not merely the sum of its little facts. You may study each day's history lesson faithfully, and may retain everything in memory till the book is "finished," and still not know the main things in the book. You may understand and memorize each verse of a chapter in the Bible until you can almost reproduce the chapter in your sleep, and still fail to know what the chapter is about. Probably some readers of this text who have repeated the Lord's Prayer from infancy, would still need to do some studying before they could tell the two or three leading thoughts in that prayer.
An especially good illustration of this fact in my own experience as a teacher has been furnished in connection with the following paragraph, taken from Dr. John Dewey's Ethical Principles underlying Education. "Information is genuine or educative only in so far as it effects definite images and conceptions of material placed in social life. Discipline is genuine and educative only as it represents a reaction of the information into the individual's own powers, so that he can bring them under control for social ends. Culture, if it is to be genuine and educative, and not an external polish or factitious varnish, represents the vital union of information and discipline. It designates the socialization of the individual in his whole outlook upon life and mode of dealing with it." I have had a large number of graduate students who found it very difficult to state the point of this paragraph, although every sentence is reasonably clear and they are in close sequence.
Thus the larger thoughts, instead of being the sum of the details, are an outgrowth from them, an interpretation of them; they are separate and new ideas conceived through insight into the relations that the individual statements bear to one another.
The proper unit of progress in study
From the foregoing we see that some facts are very large, while others are of little importance, and that any one statement, taken separately, lacks significance.
The field of thought, therefore, instead of being pictured as a plain, is to be conceived as a very irregular surface, with elevations of various heights scattered over it. And just as hills and mountains rest upon and are approached by the lower land about them, so the larger thoughts are supported and approached by the details that relate to them.
A general of an army, desiring to get possession of a disputed region, does not plan to take and hold the lower land without the higher points, nor the higher points without the lower land. On the contrary, each vantage point with its approaches constitutes, in his mind, one division of the field, one strategic section, which is to be seized and held. And these divisions or units all taken together constitute the region.
So any portion of knowledge that is to be acquired should be divided into suitable units of attack; one large thought together with its supporting details should constitute one section, another large thought together with its associated details a second, etc.; all of these together composing the whole field. In other words, the student, instead of making progress in knowledge fact by fact, should advance by groups of facts. His smallest unit of progress should be a considerable number of ideas so related to one another that they make a whole; those that are alike in their support of some valuable thought making up a bundle, and the farther-reaching, controlling idea itself constituting the band that ties these bits together and preserves their unity. Such a unit or, "point," as it is most often called, is the basal element in thinking, just as the family is the basal element in society.
The size of such units of advance.
Such units of advance may vary indefinitely in size; but the danger is that they will be too small. A minister who reaches his thirteenthly is not likely to be a means of converting many sinners. A debater who makes fifteen points will hardly find his judges enthusiastic in his favor, no matter how weak his opponents may be. A chapter that contains twenty or thirty paragraphs should not be remembered as having an equal number of points. What is wanted is that the student shall feel the force of the ideas presented, and a great lot of little points strung together cannot produce a forceful impression.
Any thought that is worth much must be supported by numerous facts and will require considerable time or space for presentation. A minister can hardly establish a half dozen valuable ideas in one sermon; he does well if he presents two or three with force; and he is most likely to make a lasting impression if he confines himself to one. Drummond's The Greatest Thing in the World is an example of the possibilities in this direction.
Accordingly the student, in reading a chapter or listening to a lecture, should find the relationships among the smaller portions of the thought that will unify the subject-matter under a very few heads. If several pages or a whole lecture can be reduced to a single point, it should be done. He should always remember that to the extent that the supporting details are numerous they will have a cumulative effect, thereby rendering the central thought strong enough to have a permanent influence.
The meaning of organization of knowledge, and its value.
Such grouping of ideas as has thus far been considered, although of the greatest importance, is only the beginning of the organization of knowledge. For thus far only the minimum unit of advance has been under discussion. Asone proceeds in the study of a subject these smaller units collect in large numbers, and they must themselves be subordinated to still broader central thoughts, according to their nature. This grouping of details, according to their relationships, into points, and of such points under still higher heads, and so on until a whole subject and even the whole field of knowledge is carefully ordered according to the relationships of its parts, is what is meant by organization of knowledge.
Sometimes an entire book is thus organized under a single idea, Fiske's Critical Period of American History being an excellent example. In this volume the conditions at the close of the Revolutionary War are vividly described. It is shown that great debts remained unpaid, that different systems of money caused confusion, and that civil war was seriously threatened in various quarters. These and other dangers convinced sober men that a firm central government was indispensable. But then, it was no easy matter to bring such a government into existence; and it is shown how numerous heroic attempts in this direction barely escaped failure before the constitution was finally adopted. On the whole, it is safe to say that each paragraph or small number of paragraphs, while constituting a unit, is at the same time a necessary part of the chapter to which it belongs; likewise, each chapter, while constituting a unit, is an integral part of the book as a whole; and all these parts are so interrelated and complete that the whole book constitutes a unit.
Observe the advantage of such organization. The period of our history immediately following the Revolution used to be one of the least interesting of topics. Under the title "The Period following the Treaty of Paris," or "The Period from the Close of the Revolutionary War to the Adoption of the Constitution," the textbooks attempted nothing more than an enumeration or history of the chief difficulties and struggles of our youthful nation. In some cases, if I remember correctly, this was designated "The Period of Confusion," and its description left the reader in a thoroughly confused state of mind.
Fiske's book was a revelation. What had seemed very complex and confused became here extremely simple; what had been especially dull became here perhaps the most exciting topic in all our history. And the secret of the advance is found to a large extent in the organization. Thus organization is a means of effectiveness in the presentation of knowledge, as in the use of a library or the conduct of a business.
The basis for the organization of knowledge in general.
All the facts in Mr. Fiske's book are organized about the stirring question expressed in his title, i. e., how our ship of state barely escaped being wrecked. Because this idea is of intense interest to us, and the entire book bears upon it continually, the story is read with bated breath. Drummond's Greatest Thing in the World is another excellent example on a smaller scale of ideas centered about a vital human question. Thus specific problems of various degrees of breadth, that are intimately related to man, can well be taken as the basis for the organization of knowledge in general. Classical literature is organized on this basis, which is called the pedagogical or psychological basis, and it seems desirable that other fields should also be.
Yet there are other kinds of organization in which the relation to man is not so plainly, or not at all, taken as the controlling idea. For example, biology is often organized on the basis of the growing complexity of the organism, the student beginning with the simple, microscopic cell, and advancing to the more and more complex forms. Formerly, after the Linnaean system, plants were classified according to their similarity of structure. Now both plants and animals are often classified on the basis of their manner of adaptation to their environment. Thus within the field of science there is what is called the scientific basis of organization.
There is also the logical basis of organization of thought, according to which some most fundamental idea is taken as the beginning of a system, or the premise, and other ideas are evolved from this first principle. Rousseau attempted to develop his educational doctrine in this way, starting with the assertion that everything was good as it came from the Creator, but that everything degenerated in the hands of man. John Calvin did the same in his system of theology; and he reasoned so succinctly from his few premises that any one granting these was almost compelled to accept his entire doctrine.
Attention is called to these facts here in order to suggest that, while the scientific and the logical bases of organization are in common use, neither of them is adequate as the main basis of organization for a young student who is studying a subject for the first time. The reason is that each of them secures a careful ordering of facts only with reference to the relations that those facts bear to one another, and not with reference to the relation that they bear to man; and in thus ignoring man they show grave faults. They are indifferent to interest on the part of the learner; they offer no standard for judging the relative worths of facts to man; and instead of exerting an influence in the direction of applying knowledge, they exert some influence in the opposite direction by their indifference to man's view-point. It must be admitted that they are of great assistance in securing thoroughness of comprehension by their revelation of the relations existing among facts, and also that they classify facts in a convenient way for finding them later; but they are of greatest use to the advanced student, who is already supplied with motive and with standards for judging worth, and who has proper habits of study already formed; they can well follow but they should not supplant the psychological basis.
The student's double task in the organization of ideas.
An author's organization of subject-matter is frequently poor. But whether it be poor or good, some hard work on the part of the student is necessary before the proper grouping of ideas can take place in his own mind. The danger is that there will be practically no arrangement of his thoughts, as is well illustrated in the following letter from an eight-year-old boy.
Will you please buy some of my 24 package of my Bluine, if you will please buy one package it will help me a lot. One Saturday we played ball against the east side and beat twelve to 1. I will get a baseball suit if I can sell 24 packages of Bluine. We had quite a blizzard here to-day. For one package it costs ten cents. When we played ball against the east side we only had 6 boys and they had twelve. We have a base ball team, and I am Captain, so you see I need a suit. Gretchen and Mother are playing backgammon with one dice. I catch sometimes when our real catcher is not there. When he is there I play first Base. Your loving nephew, JAMES.
There is one prominent idea in this letter, touching the sale of Bluine, with reasons; and parts of two others, concerning the weather and the occupation of mother and sister. The first is the most fully treated; but, as might be expected from an eight-year-old child, no one idea is supported by sufficient detail to round it out and make it strong.
In avoiding such defects two things are necessary: First, the student must decide what points he desires to make. They should be so definitely conceived that they can be easily distinguished from one another and can even be counted. Then, in the second place, all the details that bear upon a central idea should be collected and presented together in sequence under the point concerned. By this massing of all supporting statements under their proper heads, overlapping or duplicating is avoided, and clearness is gained. Also, force is secured by the cumulative effect of intimately related facts, just as it is secured by the concerted attack by the divisions of an army.
Even the better students often stop with finding the main thoughts alone. And the temptation to do no more is strong, since teachers seldom require a forceful presentation of ideas in recitation; they are thankful to get a halting statement of the principal facts. But the student should remember that he is studying for his own good, not merely to keep teachers contented; and he should not deceive himself by his own fluency of speech. He should form the habit of often asking himself, "What is my point?" also, "What facts have I offered for its support, and have I massed them all as I should?" He must thus form the habit of arranging his ideas into points if he wishes to be pointed.
Precautions against inaccuracy in the grouping of facts into points.
The dangers of inaccuracy in this kind of study are numerous. First the individual statements must be carefully interpreted. A certain very intelligent ten-year-old girl studying arithmetic read the problem, "What is the interest on $500 at six per cent for one year?" Then, probably under the influence of some preceding problem, she found four per cent of the principal, and added the amount to the principal for her answer, thus showing two mistakes in reading. Perhaps half of the mistakes that children make in the solution of problems is due to such careless reading. A certain fifth-year class in history read a very short paragraph about the three ships that were secured for Columbus's first voyage, the paragraph ending with the statement, "On board the three [ships] were exactly ninety men." When they were asked later how many men accompanied Columbus the common answer was, "Two hundred and seventy, since there were ninety men on each ship."
These mistakes are typical of those that are common, even among adults, as in the reading of examination questions, for instance. I have more than once asked graduate students in a university to state the one principal thought obtained from the extended study of an article on education, and have received a paper with a threefold answer, (a), (b), (c). Such responses are due to extreme carelessness in reading the questions asked, as well as to a desire to be obliging and allow an instructor some freedom of choice. Thus the meaning of the individual statements that constitute the material out of which larger truths are derived, must be carefully watched if the final interpretation of an author's thought is to be accurate.
The tendency toward error is greater still when it comes to finding the central thought for a portion of text. This was once amusingly illustrated by a class composed only of the principals and high-school teachers in a county institute, some seventy-five persons in all. The text under discussion was the first chapter of Professor James's well- known book, Talks to Teachers. The title of the chapter is "Psychology and the Teaching Art"; and Professor James, fearing that teachers might be expecting too much from his field, sets to work to discourage the idea that psychology can be a panacea for all of a teacher's ills. The larger portion of the twelve pages is devoted to this object, although the explicit statement is made, on the third page, that "psychology ought certainly to give the teacher radical help." But so little space is given to this declaration that, in spite of its definiteness and positive character, the class as a whole reached the conclusion that he was advising teachers not to study psychology at all. In other words, they had failed to balance up one part of the chapter against the other; and their failure left them in the ridiculous position of assuming that an author of a book for teachers was dissuading teachers from reading his book.
A third and perhaps the most common source of error is found in the particular wording given to the central thought. In order to be perfectly definite and accurate any thought should be expressed in the form of a full statement. It ordinarily takes at least a whole sentence to express a whole thought. But it is very common for students even, who have formed the habit of thinking by points, to allow brief headings, consisting of single words or short phrases, to represent entire thoughts. Although such headings, on account of their brevity, may be useful, they are merely names for the thought, not statements of the thought itself; and it means the loosest kind of thinking to stop with them. A mere title, as a lecture "About Russia," for instance, designates only the outside limits to which a person confines himself—provided he sticks to his theme. It often tells no more about the substance of the thought within those limits than a man's name tells about his character. It is usually easy to tell "what a page is about"; but it usually requires keen thinking to word its principal idea sharply in a full sentence. Many students are inaccurate in the interpretation of authors and in their own thinking, not so much because they lack mental ability as because they lack the energy to continue their thinking to this point of wording the central idea accurately in a full sentence.