How to study

by George Fillmore Swain

What the student gets out of his education depends largely upon what he puts into it. The student is not an empty vessel to be pumped full of learning; he is a complex machine which education should help to run properly.

aim of education is purely utilitarian,

more clearly by the w...

Its object is to give the man power to meet the problems of life, and to develop all his facul...

Whatever makes a man more capable of legitimate enjoyment, or helps to make him contented and happy, or to enlarge his breadth of view, is really useful and helps to give him power.

only way that power and strength can be developed is by effort on the part of the student.

The only real education is self-education.

"If little labor, little are our gains; Man's fortunes are according to his pains."

"How to Investigate a Problem." In doing this the first step is to get together all available information regarding the problem, including books, experimental data and results of experience, and to consider and digest this material. Personal investigations and inquiry, further experimental research, correspondence, travel, etc., may then be necessary.

If for any reason we are unable to do this, we should close the book, take some exercise or recreation, or at any rate do something else, for we are not at the moment fitted for study.

Very different are conclusions or opinions deduced from facts; and logical conclusions are very different from mere opinions. The facts may be sufficient to prove logically a certain conclusion. On the other hand, the facts may simply give reasonable ground, or appear to give reasonable ground, for a certain opinion, though they may fall far short of demonstration.

therefore, discriminate constantly between mere statements of facts, necessary conclusions which follow therefrom, and mere opinions which they seem to render reasonable.

he should perceive that he cannot at that stage try to get back of these facts, but he may well make a note of them as questions to be later examined, if not as to the cause, at least as to how the fact is ascertained.

he should constantly endeavor to explain or seek the reason for new statements by relating them to the body of knowledge which he has previously gained.

It is always possible to ascertain, at least in a general way, how a fact is ascertained, though it may not be possible to determine the reason for the fact.

also inquire how it was ascertained, and we may further perceive that this is a fact for which there must be a reason,

Indeed by selecting certain statistics and excluding others, almost anything depending upon statistics may be proved.

It is also important to make it a rule to ask whether any result when reached appears to be reliable in the light of common sense.

and to confute, nor to believe and take for granted, nor to find talk and discourse, but to weigh and consider."[

Cultivate the scientific attitude of mind, which means, first to formulate clearly a problem, then to get together all the pertinent facts, and then to draw the logical conclusions.

even in subjects like mathematics or mechanics; and terms like "energy," "momentum," "rate of change," "period of vibration," "value," "social justice," etc., are often used without a clear understanding, and sometimes without any understanding at all, of what they mean.

facts or things cannot be reasoned about intelligently unless a definite idea is formed of the facts or things themselves.

A half knowledge of a thing may not be useless, but it is generally found that it is the other half that is needed.

The study of language, and particularly of the classics, if properly pursued, may be of great benefit, because it involves translating from one language into another, and

should include much practice in discovering the precise word or phrase to express an idea.

in the study of the classics these objects are entirely absent, and the attention is more apt to be concentrated on studying delicate shades of meaning.

The habit of forming definite ideas may also be cultivated by each day attempting to define a certain number of common words, and after making as good a definition as possible comparing the result with that in the dictionary.

According to Liebnitz, perfect knowledge is clear, distinct, adequate, and intuitive.

Without it one cannot acquire more than a partial knowledge, and one is always liable to those errors of reasoning which arise from the use of equivocal language, which may lead us unconsciously from one meaning of a word to another—a logical error which is perhaps the most fruitful cause of fallacious reasoning.

Logic is the science of correct reasoning.

It teaches us how to discover truth, how to recognize it when discovered, how to arrive at general laws from facts collected by observation or experiment, and how to deduce...

But there are many chances for error in this process; for instance, I might say: "To call you an animal would be to state the truth"—to which you would agree; and, "To call you an ass would be to call you an animal"—to which you would also agree; from which I might conclude that, "To call you an ass would be to state the truth"—which you might have a vague idea was not true. If you wish to be sure that this conclusion is incorrect, you must be able to show just why it is incorrect. The study of logic would enable you to see just where the error lies. You must not be governed by vague ideas, or you will be intellectually at anybody's mercy.

Pascal laid down the essentials of logical method in the statement "Define everything and prove everything." In other words, do not attempt to think about a term until you have defined the term and have a clear idea what it means; and insist upon proving every statement at which you arrive, before accepting it finally and definitely; although for want of time, you may be obliged sometimes to accept or form a conclusion tentatively or provisionally.

Selenium is a dyad element" and "A dyad element is one capable of replacing two equivalents of hydrogen," I can correctly draw the conclusion that, "Selenium is capable of replacing two equivalents of hydrogen," but I cannot know that the conclusion is correct unless I understand the meaning of the terms in the premises and so can be sure of the correctness of those premises.

Every student should, therefore, in the writer's opinion, take a systematic course in logic, or carefully study by himself

A student should practise doing this, first stating a principle perhaps from the mathematical point of view, and then in simple untechnical language that can be understood by one who is not a mathematician.

habit of stating even technical matters in simple untechnical language should be practised continually.

When a result or a principle is arrived at, it is essential not only to see that it is true, but how far the reverse is untrue. The student does not really understand a thing unless he recognizes it from any point of view, can describe it from any point of view, can state it in language to suit the particular emergency, and can see why the other thing is untrue.

we must analyze every statement which is the result of reasoning, or a statement of opinion, and see what objections, if any, can be brought against it, and then convince ourselves where the truth lies and why.

Professor Palmer, in his interesting book, "The Problem of Freedom," says: "Until we understand the objection to any line of thought, we do not understand that thought; nor can we feel the full force of such objections until we have them urged upon us by one who believes them."

IN STUDYING A STATEMENT, OBSERVE WHICH ARE THE NECESSARY WORDS AND WHETHER THERE ARE ANY UNNECESSARY ONES WHICH MIGHT BE OMITTED.—For

Note whether another word could be substituted for one used, without rendering a statement incorrect, or whether such change would improve it and make it more accurate.

Note what word or words should be emphasized in order to convey the intended meaning.

Students frequently seem to lack all sense of proportion and fail to acquire definite ideas

REFLECT UPON WHAT IS READ: ILLUSTRATE AND APPLY A RESULT AFTER REACHING IT, BEFORE PASSING ON TO SOMETHING ELSE.[

In illustrating, so far as time permits, the student should use pencil and paper, if the case demands, draw sketches where applicable, write out the statement arrived at in language different from that used by the author, study each word and the best method of expression, and practise to be concise and to omit everything unnecessary to the exact meaning.

An equation tells us something. Let the student state what it tells in ordinary non-mathematical language. Then again, a certain combination of equations, taken together, may express some single fact or conclusion which may be stated entirely independent of the terms of the equations.

Following this farther, the student should perceive, in non-mathematical language, that an equation is independent of other equations if the fact that it expresses is not expressed by any of the others, and cannot be deduced from the facts expressed in the others.

Every student of Algebra learns the binomial theorem, or expression for the square of the sum of two quantities; but he does not reflect upon it, illustrate it, or perceive its every-day applications, and if asked to give the square of 21, will fail to see that he should be able to give the answer instantly without pencil or paper, by mental arithmetic alone. Any student who fully grasps the binomial theorem can give (without hesitation) the square of 21, or of 21.5, or any similar quantity.

exert the mind.