Thinking and learning to think - Nathan C. Schaeffer (romantic story to read .txt) 📗
- Author: Nathan C. Schaeffer
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At one time it was a mooted question whether the mind can think of more than one thing at a time. As a matter of doubt this question is no longer discussed. For, since all thinking involves comparison, if two objects are to be compared, they must be held before the mind at one and the same time. A good memory is, therefore, a very important aid to reflection.
And yet Thucydides and Lord Bolingbroke are said to have complained of a memory so retentive of details that it seriously interfered with their processes of thought. It is commonly believed that much memory work interferes with the growth and development of a pupil’s ability to think. “Much memorizing deadens the power of thought,” says W. T. Harris, who is recognized at home and abroad as one of the profoundest thinkers that America has produced. Innumerable anecdotes are told of great thinkers to show their forgetfulness in the commonest details of every-day life. These anecdotes are handed down from one generation of students to the next; their mirth-provoking character gives them vitality; they grow more ludicrous the oftener they are told; they do harm because they lead pupils to undervalue the importance of a good memory to those who are ambitious to shine as thinkers. Often, after it is too late, the student finds how he has crippled his whole intellectual life by neglect and abuse of the memory. A correct conception of the nature of memory and its function in every department of thought and research is of immense importance to those who teach, as well as to those who have gone far enough in their studies to give conscious direction to their own intellectual life. Most writers on education have treated, directly or indirectly, of the use and abuse of the memory; every examiner appeals to it more or less in the questions he puts; and every teacher shows the nature and extent of his skill in the kind of demands he makes upon the retentive power of his pupils. Take, for instance, the lesson in geometry. There are two ways of learning and giving the proof of a theorem: the language of the text-book may be committed to memory, and accepted in the class-room; or the pupil may fix in his mind the line of argument and give in his own language the successive steps of the demonstration. The former method is a sure sign of bad teaching and of defective habits of study. Whenever a skilful teacher finds his pupils giving the exact words of the text-book on geometry, he changes the lettering of the figure, and sometimes even the figure itself. He is not satisfied until he feels sure that the pupil is thinking the thoughts of the geometry and recalling the ideas by the inner nexus which binds them into a line of argument. He insists on it that the learner shall cultivate a memory for ideas rather than words.
Does it follow that the verbal memory is to be neglected and despised? This is the feeling of the learner who has tasted the joys of thinking; he hates the drudgery of learning by heart, because he has reached the age when logical memory begins to assert itself at the expense of the verbal memory. No less a psychologist than Professor James of Harvard has recently put in a plea for the verbal memory which, by reason of the abuses to which it was formerly subjected, has fallen into such disuse that pupils on reaching the high school are often unable to quote a single stanza of poetry. In his “Talks on Psychology to Teachers” he says,—
“The older pedagogic method of learning things by rote, and reciting them parrot-like in the school-room, rested on the truth that a thing merely read or heard, and never verbally reproduced, contracts the weakest possible adhesion to the mind. Verbal recitation or reproduction is thus a highly important kind of reactive behavior on our impressions; and it is to be feared, in the reaction against the old parrot recitations as the beginning and end of instruction, the extreme value of verbal recitation as an element of complete training may nowadays be too much forgotten.”[22]
Psychologists have shown that, in remembering and recollecting, the mind works according to certain laws of association. Of two words or ideas which have been before the mind at the same time, or in immediate sequence, the one naturally tends to suggest the other. If the attention is directed to the words as they follow each other in a line of poetry, the memory will recall these in the order in which they occur. If the mind’s eye is fixed on the ideas which the words express, the memory may carry these by reason of the logical connection which exists between them. Often the connection between the two things which are to be remembered is purely arbitrary. Then the link which binds them together must be forged by some mechanical process like frequent oral repetition, or by constant gazing at them upon the printed page, or by writing them out so that the impression made upon the mind through the eye and the ear is further strengthened through the muscular sense. The latter species of memory is usually called the mechanical memory, in distinction from the memory for ideas, which has been aptly styled the logical memory.
The verbal memory is but one form of the mechanical memory. There is no necessary connection between persons and their names, between events and dates, between things and their symbols; these must be learned by bringing them together before the mind until by the law of association, called contiguity in time and place, the link that binds them is forged; or, to change the figure, until they occupy places side by side on the tablets of the mechanical memory. It is sometimes supposed that there is a necessary connection between the two factors and their result in the multiplication table. But the moment we construct an arithmetical scale based on the dozen instead of ten, 7 × 8 = 48 instead of 56 (the former combination of figures signifying four twelves and eight ones), and the arbitrary character of the combinations in the Arabic notation becomes apparent at a glance. Sometimes a peculiarity in a rule like that for the middle and the opposite parts in the right-angled spherical triangle may assist the memory; but in most cases the formulas which are in constant use in the higher mathematics must be fixed by the methods of drill appropriate for the mechanical memory.
It is a mistake in teaching as well as in practical life to neglect the mechanical memory. In many directions it takes care of itself through the conditions and requirements of a person’s daily occupation. The salesman in a large store, the conductor on a railway, the politician on the hustings remembers many things in this way, and not because they are bound together by a logical nexus like that which binds together the thoughts of a geometrical proof. Many things which the pupil must carry from the school into practical life must be retained through drill and repetition. Pestalozzi imagined that if he taught pupils how to construct the multiplication table it would not be necessary for them to commit it to memory. The Swiss teachers long ago found out the insufficiency of his method; found out that, whilst it pays to let a pupil construct the table for himself, because it increases his interest in the combinations, and thus lightens the burden of the mechanical memory, the drill must be kept up until the sight of two factors suggests their product with infallible accuracy. Valuable time can be saved if the teacher will make a list of things that must be fixed in the mechanical memory for the purpose of facilitating the thought-processes in more advanced stages of instruction and in the discharge of the duties of practical life. The following are typical examples of what should be lodged in the mechanical memory:
1. A reasonable vocabulary of words in the mother tongue.
2. A working vocabulary of words in the foreign languages which the circumstances or occupation of a student will compel him to use.
3. The combinations of addition up to one hundred, the multiplication table, and the tables of weights and measures.
4. Algebraic and other formulas which constantly recur in the higher mathematics.
5. The fundamental formulas in chemistry, physics, and other sciences.
6. Declensions, conjugations, comparison, and genders of words in such foreign languages as the pupil expects to read, write, and speak.
7. The most necessary fact-lore of history and geography.
8. Choice selections from the best literature and such definitions as mark a triumph of intellect in the history of human thought.
This enumeration may indicate the range and kind of knowledge which should be fixed in the mechanical memory so that the mind may be in possession of the best instruments of thought evolved by ages of civilization. Many of the things above named must be learned by an effort of retention, pure and simple, like that of the boy who is sent to a store to buy half a dozen sheets of paper, two yards of ribbon, five dozen eggs, and specified quantities of salt, flour, and other provisions. He may write these on paper and thus ease the memory burden, but in solving mathematical problems and in reading, writing, or speaking a foreign language it is impossible always to carry for use written or printed tables, vocabularies, and lexicons. To use these in thinking, one must have them on his tongue and at his fingers’ end. Of course it makes a difference whether one wishes simply to read a language, like Latin or Greek, or to use it, like French and German, in conversation and correspondence. In the former instance it is sufficient to learn the language symbols through the eye; in the latter they must be acquired through the ear, the tongue, and the pen.
It is a wise provision of nature that the perceptive powers and the mechanical memory are most active in childhood and youth. The normal child is hungry for words and facts, and gathers information from every conceivable quarter. The judgment and the reason develop after the mind has been stored with the materials upon which these may act. Parents and teachers who are ignorant of this order of development often force the reasons for arithmetical processes upon the pupil when these are difficult and when he could learn the eleven hundred variations of the Greek verb without difficulty, whilst the study of the classical and foreign languages is postponed to an age when the acquisition of a new language becomes a difficult task because the logical memory has driven the mechanical into the background, and the growth of judgment and reason makes the pupil crave the intellectual food furnished by the thought-studies. It is a species of cruelty to force upon children the consideration of the why’s and the wherefore’s of mathematical operations, when learning how to go through the motions would be quite enough of a tax upon their mental strength. Some of the demonstrations in arithmetic are logically more difficult than many of the proofs in geometry; hence no pupil should be asked to pass his final examination in arithmetic before he has mastered the elements of geometry. The proper sequence of subjects is of immense importance in leading the child from the lower to the higher forms of intellectual activity. With the proper study of geometry the logical memory steps to the front, and the thought-studies should then supplant those which largely appeal to the mechanical memory.
Nevertheless,
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