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tions to be of the maximum utility must permit rapid and sensible procedure along a somewhat indistinct pathway. A rather extended experience in preparing laboratory directions has led me to the conclusion that sedulous care should be taken not only to eliminate ambiguity but to use simple sentences, short and adequate. Moreover these directions, to yield their greatest psychological profit, must not be interrupted by irrevelant questions. Such injections switch the brain upon a side track. Thus the directions for preparing oxygen from the usual mixture should not contain questions about the function of the manganese dioxide or the principle underlying the collection of gases over water. These queries may be introduced with propriety at some later place. Nor should directions involving a continuous operation be split asunder by questions about subordinate features of the manipulation. Thus a "why?" cannot with good judgment be inserted in the midst of a request to "introduce part of the water." Similar illustrations need not be cited.

It also seems well established that diagrams and models are indespensable in many cases. Descriptions fail to describe certain operations and many arrangements of apparatus. The eye is quicker than the brain. The use of such pictorial and material aids not only economizes time and facts but serves also to train the student in visualization-a factor in scientific education which yields a high rate of interest.

The mere performance of an experiment, as suggested above, is usually profitless. The student must observe certain phenomena and draw legitimate conclusions if his task is to be fruitful. Here again there are pitfalls. If he is asked simply "What" and "Why" or autocratically told to "Observe and explain," he may observe the essential scientific phenomena and draw a legitimate conclusion therefrom-but he may not. Certain experiments invariably reveal conspicuous facts and permit accurate deductions, but many do not. In this negative or indefinite class it is necessary to suggest the line of observation, such as change in color, evolution of gas, difference in temperature, formation of a precipitate, and so on. The facts need not be told outright. Such a departure from a rational procedure is rarely necessary though it is preferable usually to sacrifice a little infromation for the benefit of a basal mental process. Hints about the desired observations are entirely legitimate, indeed they determine to a considerable extent the rate at which

the student acquires an indispensable trait, viz., accurate observation of essential data.

I presume most students dislike to undertake voluntary thinking. Experiments are usually performed with pleasure, but when the time arrives for drawing conclusions from accumulated data, most students halt, evade, or utterly fail. It is necessary therefore to induce or compel such ultimate thinking by some device. Simple interrogative or imperative sentences are usually used. But these in themselves are not a panacea for the mental inertia exhibited by most students when confronted by an array of facts demanding classification. The student is not entirely to blame for this dilemma. Professor H. P. Talbot of the Massachusetts Institute of Technology recently raised the question as to how far we are justified in demanding conclusions from the experiments which now make up the traditional course in beginners' chemistry. The query is excellent. Do we not in many cases require students to draw conclusions which we as teachers could never draw from the meager data furnished by one or two experiments? I think we have failed to appreciate the situation from the learner's standpoint. We expect the immature beginner to judge as we judge now with our stock of information. We forget our own struggles and blunders and with the assurance characteristic of maturity calmly expect the child to be as wise as the parent.

Teaching, especially experimental science, has suffered too long from the Agassiz idea. In our veneration for a traditional method salutary for investigators we have forgotten that multitudes are not endowed with initiative and insight. It is imperative therefore to provide conditions favorable for this final mental leap which is to carry the student from the confused field of unrelated facts across the ditch of doubt to the firm ground of truth logically derived. Therefore in all cases where the conclusions like the observations are not quite obvious it is insufficient to say merely "Explain," "Why?" "Conclusion?" "What is your answer?"

To comply with these conditions which determine the mental gain or loss, the general nature of the conclusions must be indicated. Thus in the familiar experiment with sodium and water, it is not enough to ask, "What does the experiment prove?" but, "What does this experiment prove about the composition of water?" It is not always possible to select the most fruitful

question. Individuals differ widely in their capacity to reason, but fully 90 per cent of beginners need suggestions to enable them to derive valid and appropriate conclusions from the scanty data furnished by their experiments.

V. The profit and loss in experimental chemistry is doubtless largely determined by the establishment of points of contact between the old world and the new world of the student, by the use of a judiciously balanced course of experiments and by the incorporation of the psychological principles of mental fatigue, concepts, and suggestion. But these factors, however valuable, are insufficient without a fourth, viz., the attitude of the teacher. He must be a personal supervisor. In his hands rests the key which locks or unlocks the door of the student's mind. Imbued with the spirit of science and filled with a sympathy for youth he can inspire his students with a love for truth. But if he is impelled to labor by mercenary motives or filled with contempt for those who are toiling up the heights of knowledge, he may turn an experience essential to mental growth into a profitless task. No laboratory can run itself, and no teacher is influential enough to conduct courses in absentia. A small amount of teacher cannot transform à large amount of student. There is no such thing as pedagogical catalysis. The greatest teachers the world has ever seen lived with their students. In his "Life and Experiences" Roscoe writes this of Bunsen, his teacher: "This constant presence of the master, this participation of him in the work of the persons both young and old, bore in on the minds of all the lesson that it is the personal and daily contact with the leader which creates a successful school; and that whilst fine buildings and well equipped laboratories are good things in their way, they are as tinsel and dross, unless accompanied by the devotion and collaboration of the teacher." And Roscoe himself believed and practiced the principles of his teacher, for he says elsewhere: "The personal and individual attention of the professor is the true secret of success; it is absolutely essential that he should know and take an interest in the work of every man in his laboratory, whether at the beginning or at the finish of his course." The rise and development of the French chemistry was partly due to the personal attention bestowed upon students by Morveau, Fourcroy, Vauquelin and their immediate successors. And the commanding power of German chemists today began in Liebig's laboratory many years

ago. Some one may say this personal supervision is well enough in colleges where research is in progress, but it is hardly necessary with high school pupils. Indeed there is a strong tendency to let youth develop without restraint and supervision, it being argued that he gains experience thereby, that he needs. to know failure as well as success. Granting the general truth in this argument, I deny its validity when applied to experimental science. It is quite correct to eliminate coddling and emotionalism from professional intercourse with students. But a course in experimental science demands that a teacher shall have a psychological and ethical viewpoint quite different from anything that partakes of paternalism. Personal supervision implies a judicious and well balanced combination of all factors essential to good teaching-accurate and available knowledge of the subject from all standpoints, unlimited patience with clumsiness of hand and dullness of brain, continuous poise of body, sympathy tempered with firmness and high intellectual standards, the ability to impart facts unpretentiously but with conviction, a spirit of co-operation at all times but especially when the student is bewildered or in a mental crisis, toleration of the proverbial and traditional habits of students, a perennial sense of humor, unlimited faith in the educative power of experimental science, and an ethical standard as high and broad as Christianity itself. In every laboratory there is constant need of someone great in mind and good in heart to allay fears, encourage those who are being outstripped by their companions, assist in manipulation, answer reasonable questions, give hints at critical times, compel observance of printed directions, aid in the search for sources of error, require repetition if it will correct blunders, and prevent deliberate theft of another's thought.

As the days go by filled with tasks it sometimes seems as if we accomplished little or nothing. We are sure of the loss, for it is persistently evident, but we are not positive about the profit. Let us, however, remember that the bookkeeping of pedagogy is a difficult system and that intellectual growth is not readily transformed into figures. So if we as teachers are careful to keep our souls open for the reception of truth and are sensible, faithful, and honest in the preparation and performance of our share of the laboratory work, then the accounts will show a balance on the profit side.

SOME MODERN NOTIONS IN THE RATIONAL TEACHING OF ELEMENTARY ALGEBRA.

BY JAS. F. MILLIS,

Shortridge High School, Indianapolis, Ind.

It is my intention, in this paper, to suggest a few of those things in a course in elementary algebra which should receive and, in some schools are now receiving, more attention than they have received in the past.

What things should receive emphasis in the teaching of elementary algebra will be determined mainly by the purpose of putting the subject into the school course. Why do we teach algebra to all high school pupils? Why should girls in the high school be made to take algebra for a year and a half? What good are they to get from it? Is the time spent in the study of algebra as it is now studied well spent by the great body of students who do not go to college?

I believe that we will agree that the following three things constitute the main purposes of putting algebra into the high school course:

1. To gain accuracy and speed in the fundamental algebraic processes and a knowledge of algebraic principles;

2. To develop the habit of right thinking;

3. Through the extension of the child's notions of number and number processes to gain a mastery of the world on the quantitative side.

Accuracy and speed in the fundamental processes are fundamental of course. They are essential. But they are the means and not the end. They have long been thought, apparently, to be the end itself. That seems to be a widespread notion even today. Now I claim that the teaching of algebraic processes and algebraic principles for the sake of those processes and principles alone is indefensible. The teacher whose sole ambition is to make the pupil ready to take an examination in algebraic processes is not teaching at all. Rather, he is teaching the subject instead of the child. Then, I repeat, accuracy in using the rules which are arbitrarily laid down for the child in the performance of algebraic processes is not all that is to be gotten from the subject; though this is necessary.

Accuracy is to be gained in several ways. (1) By familiarity with the symbolism of algebra. The pupil must know the exact