but conglomeration; but at a unification by means of underlying utility principles. For instance, if the pupil in studying geometry acquires the habit of selecting the best linear measurements on which to make the mensuration of the circle, cylinder, etc., depend, when he comes to physics he will be ready to apply the same idea to the measurement of physical magnitudes. If he learns to realize the advantage of using auxiliary lines in the vivid field of geometry, he should be ready to use auxiliary objects freely in physics, chemistry, engineering, in ethics, sociology, and in fact find in such use a principle having a hundred applications for him every day.

Before I close, allow me to say a word on one other aspect of the subject in hand. For the past generation, educational theory and practice have been mainly inspired and controlled by the doctrine of evolution. The evolutionary philosophy of education has taken up and dominated other ideas, as those of Herbart and Froebel. We owe to this philosophy of education much of theoretic value and practical worth. But as a whole its tendency is brutal and materialistic. In the nature of things it is but a preliminary step. For we no sooner announce the doctrine of the survival of the fittest, than the question arises, what is fitness? What is value? What is worth? Hence a new philosophy, termed pragmatism is springing up, which is trying to answer these questions and give a broader and higher view of things, which shall include the doctrine of evolution as a mere detail. Perhaps it may be possible to analyze fitness into the elements which compose it, and then devise economical and efficient ways of mastering these elements. Perhaps also after we have made this analysis we may be able to arrive at some more fundamental and inclusive category than fitness. Something worked out along this line must, in the end, profoundly influence educational theory and practice.

As a step in the new direction, let us make a distinction between concrete and abstract utilities. The use of similar triangles to determine the height of a steeple is an example of concrete utility, or of putting a geometric tool to a concrete use. The use of similar triangles to prove a set of lines proportional, or a pair of polygons similar, is an example of abstract utility. Now if the pupil's mind be fed on the concrete applications of mathematics alone or preferentially, a low grade and materialistic appetite is generated in him. His outlook and tastes are apt to be narrowed and he will be satisfied with nothing that does not have immediate material application. If, on the contrary, he gets an insight into abstract utilities, he finds that these are comprehensive and enlarging. They include practical applications as details, and suggest other particular concrete, as well as other more general abstract utilities.

Now the method of teaching originals presented above may be termed the method of abstract utilities, inasmuch as it puts abstract uses in the first place. Concrete utilities are brought in occasionally to sharpen and correct conceptions, and make interest more vivid, but abstract utilities are omnipresent and controlling, and fashion the development of the subject. When thus realized, the method which we here advocate is seen to have new and wider values than those mentioned hitherto. The ends which we aim at in the study of geometry are, first, practical results; second, general culture. The ancient Egyptians in their use of geometry in land surveying, temple building, and barn measuring, sought only the former. The Greeks aimed only at the latter; we desire both. In attaining the mastery of abstract utilities we, in a measure, attain both. The idea of abstract values mediates and harmonizes both kinds of value, and causes them to interact in multiplicative ways.

Hence it is suggested that it is a method which has a field of application wherever we find it desirable or necessary to combine technical and culture studies. In this age when new arts and sciences are raining down from the sky so fast that one is kept busy dodging them to save himself from destruction, if we can discover in each department a certain idealistic toolage, master this in one department and use it in others, it will be the source of much needed economy and uplifting power. It may be, therefore, that the method here suggested is a step toward meeting some pressing educational needs in their larger aspect.

II. TIME OF INTRODUCTION AND LIMITATIONS

J. MELVILLE MCPHERRON, HEAD OF DEPARTMENT OF MATHEMATICS,
HIGH SCHOOL, LOS ANGELES, CAL.

I am not expected to make any argument in favor of the value of original work in geometry. While some may dispute that the power of reasoning developed in the study of mathematics is available in other subjects, perhaps all will agree that the reasoningpower developed in the proper study of geometry is available in other branches of mathematics.

Frank A. Hill, of Boston, in the Educational Review, some years ago said:

One peculiar advantage of right mathematical work lies in the completeness and accuracy of the results attainable. I am not underrating the value of study in English, in history, or in any of the vast, indefinite and never-to-be-compassed fields. I am simply saying that the demonstration of a theorem in geometry, for instance, may be brought to a kind of finish and completeness impossible in the study of a paragraph about the character of Henry VIII. or the causes of the Civil War, and that the student enjoys a unique consciousness of power in mathematics when he brings a piece of work to a triumphant end. I have noticed that when boys and girls in geometry, for instance, become once imbued with a thinking, investigating, inventive spirit, and with that conception of a proof which gives the child who has it confidence to stand against the world, the subject has a peculiar fascination for them. They work with enthusiasm; the real student glow is there; the inspiration continues operative away from the special influence of the classroom; and the emotional excitement of the "eureka" when the way has been discovered is hardly equaled in any other student experience.

My own experience and observation compel me to agree heartily with the author just quoted.

When should this original work begin? After many years of experience and, I confess, some experimenting, I am fully convinced that the time for this work to begin is when the study of demonstrative geometry is entered upon. Surely the student is entitled to all the help and inspiration he can get from the beginning.

I talked with one noted teacher and book-maker who advocated the plan of going thru the book, omitting the exercises entirely and then returning to the beginning and making a specialty of the originals. I am satisfied he was wrong on this point. I find it very hard to interest pupils in original work, who have been over the propositions of which the proofs are given in the book. It seems hard for them to appreciate the necessity, or the advantage at that stage of the work of their doing anything themselves.

At first only easy theorems and problems should be offered, and some of these of a practical nature so as to enlist the interest of those pupils who do not take naturally to pure geometry or to reasoning at all—and their name is legion. Put a little romance into some of the problems. Great patience and sympathy are required in the beginning with the average pupil. The teacher should put himself in the attitude of the investigator along with the pupil. Let it be understood that we are seeking the solution.

If you have never tried it I think you will find it much easier to stimulate interest in this way than to assume the attitude of being perfectly familiar with these things.

At a very early stage in the work pupils should be asked to give complete proofs without the use of paper or blackboard. It is interesting as well as surprising to notice how some will draw the figure, letter it, and give the demonstration as a purely mental exercise. I have found this exercise helpful in securing the attention of the class. Frequently the one reciting will be corrected for misplacing a letter, or something of that kind.

I think it is a great mistake to suppose that all valuable work done in geometry must be original with the pupil.

A glance at the textbooks in use 50 or 60 years ago will show that original work had no place in the course of study and apparently it had none in the mind of the teacher.

When the new plan was introduced, some went to the extreme that all work should be original, and they discarded the textbook altogether. Perhaps this was to be expected but was none the less a mistake. The pupil has not the time to find the proofs for all the material he will need in his future work. Besides it is very important to be able to take in readily a proof given. Even when originals are required it is of great value to direct somewhat as to methods and plans. In problems of construction, I would emphasize the idea of assuming the problem done and then finding such relations as will lead to the correct solution. I would also emphasize certain plans, as, for instance, when the hypotenuse of a right triangle is given as one of the hypotheses, it is always safe, as the first step, to describe a circumference on the hypotenuse as diameter.

Or a little more generally, when the base of a triangle and the angle opposite the base are given, construct the segment of a circle in which the given angle may be inscribed. The fact that the proofs that the circumference and the arc are the loci of the vertices of the triangles are so important and easy, adds to the value of this suggestion. These are of course only examples of many such plans.

These limitations for the mass of pupils leave abundant opportunity, for the full and free exercise of the genius of the best pupils. In my own experience, even with all the helps, suggestions, and devices at my command, while I have seen some good results and had much encouragement, I still have all too frequent occasion to repeat the beatitude: "Blessed is he that expecteth nothing for he shall not be disappointed."

C. HISTORY ROUND TABLE

THE NOTEBOOK: ITS VALUE AND ITS LIMITATIONS

MRS. ADA I. ATKINSON, HEAD OF DEPARTMENT OF HISTORY, HIGH SCHOOL, OMAHA, NEB. Great difference of opinion prevails among teachers in the secondary schools as to the value of notebooks.

Some of you will maintain that a notebook is a positive hindrance; that a pupil is usually content to put into it what he ought and otherwise would put into his head; that it is not a crutch to support the cripple, but that it actually causes the infirmity it is intended to cure. And others will say that the time spent in making a notebook would be more profitably expended in acquiring a better grasp of the subject-matter; that it is, therefore, a waste of time. Worse than all this, it is said to create in the pupil a dislike of history; that he rages, longing for the day of his deliverance; that the notebook is, to borrow a scientific term, a species of auto-intoxication, a natural and final putting to sleep of all interest in history. And, finally, it is solemnly averred by these advocates of "soft pedagogy" that the notebook is physically injurious; that it has even been known to cause nervous prostration.

These, then, are the main objections: dependence, waste of time, dislike of the subject, physical injury. A formidable list, if valid.

What, now, are the items on the other side of the balance sheet? Of what use are notebooks?

Can it be shown that the notebook fits into the general scheme of public education? Does it help attain the great object of education? What is that object? Many answers rise in your minds. Summarized, they perhaps come to something like this: "The acquisition of knowledge and the development of power." If inquiry should show that the notebook adds to knowledge and increases power, it may claim a permanent place in the schedule.

In the course of this inquiry its value and its limitations will be incidentally defined. Waiving the discussion of the comparative desirability of knowledge and power, let us look at a properly made notebook.

The table of contents is well ordered in chapters with subdivisions appropriate to the titles; neatly lettered and accurately paged, this table, made from time to time, is, by the end of the year, a complete syllabus of the entire year's work.

Let us see what one of the chapters contains.

It opens with a short, suggestive outline, furnished by the teacher, who wishes the pupil to forsee what his study will make plain to him, and, to guard against one-author narrowness, here is a list of accurate references to both source and secondary authorities. Still further to point the way and give definiteness of assignment and preparation, here are questions set as problems for solution, variously framed to effect their various purposes; some of them grammatical, compelling the pupil to wrest the author's meaning from the text; others cultivate the historical imagination; some develop the setting of the period, leading the pupil to see it as a reaction from previous conditions and circumstances; still others lead to the grouping of facts; and some may even be beyond the ability of the pupil to solve with his present knowledge. The student's first exercise is the making of a text analysis as the basis for his further study. While the paragraph captions of the modern text interfere in a measure with the benefit to be got from this exercise, it may be made helpful by insisting that the pupil supply original expressions for the main heads of the analysis, and by requiring him to express under each of these heads the substance of the author's statements in the pupil's own words. The answers to the questions are next to be worked out; and in the recitation upon them we see that the pupil has gained by comparing his conclusions with those of his classmates; for here are class notes, set down, not in hiccoughing fashion, with dots and dashes to represent what he did not get, but in outline form, intelligently grouped in main and subordinate heads. Could he do this without understanding the matter under discussion, without attention riveted on it? Beside he is thus being taught to discriminate between main and minor points; he learns the beauty of tolerance; he tastes the joy of authoritative assertion. Moreover, by this exercise, that much-tobe-desired condition is secured of recitation by all of the pupils all of the time.

Now come reading-notes from source and narrative history. The author, title, and portion of the work read are accurately noted, and a few clear, concise statements show a summary of the pages covered. These notes are evidence that he has grasped the author's meaning; they have arrested his straying attention; they have compelled him to abandon the pernicious practice, too often indulged in, of penitential repetition of mere words which convey no clear idea to his mind.

From the reading of a simple source he has taken a refreshing draught from the fountain of history and has had a glimpse of how history is written from sources. By comparing the statements of different authorities and measuring them by a source he learns to be critical; he no longer accepts unquestioningly what is asserted; he ceases to be the puppet of the demagogue; the editor can no longer satisfy him with blatant declaration; his mind is broadened, his knowledge enriched; he learns to be accurate; he acquires the habit of authoritative statement; he scorns mere assertion of unsupported opinion.

And next, out of these various materials text analysis, reading-notes, and class notes, he makes his logical, final outline of the period. Having constructed the skeleton, he is ready to clothe it in a short narrative on some well-selected theme which calls into play his newly acquired knowledge, but along fresh lines.

Here is no dull repetition or plagiarism, clumsy and naïve, but clear setting forth in his own words of his own interpretations, sealed with the seal of original language.

The benefit from the narrative is great; it rests on the principle that only when knowledge has been expressed, orally, or in written form, or in thought may it be properly termed knowledge. In this day of large classes, individual oral expression is necessarily limited; the narrative furnishes the next best substitute. By it the pupil is brought face to face with what he knows, and, what is of quite as much importance, with what he does not know. How often we hear children say, "I know it, but I can't say it." Let them see their knowledge and their ignorance in the relentless mirror of expression.

Each page is, we see, headed to show the nature of its contents, and in the margin of the narrative are crisp, concise phrases summarizing each paragraph.

And here at the end is an alphabetical index of the chief events and personages mentioned in the book.

Now do you doubt that the pupil has gained both knowledge and power by the making of his book?

Understand me, no claim is made for the notebook as a panacea. Tact, indeed, and the judgment and skill of the trained teacher should guide the making; and, no doubt, in the hands of the tyro more harm than good would result; but, properly used, the notebook becomes of manifest benefit to the pupil who sees in it a means of apprehending and assimilating knowledge not the mere exploitation of a fad.

It is a great mistake to suppose that young people do not enjoy doing a hard thing; they like it, and are proud of their ability to do it. Moreover, as with the body, so with the mind, exercise whets appetite. And it is this tough fiber which the citizen of these United States must develop in order that he may combat and conquer the difficulties which confront him at the present time. Even to the superficial observer the times look threatening; to a student of history they are big with danger. It is the solemn duty of those who have intrusted to them the shaping of the character, the training of the intellect of the youth of this great nation of ours, to prepare and fit them for their civic duties.

I dare to cherish the hope that by this earnest conscientious, painstaking, loving work of making notebooks, these children are learning the fundamentals of citizenship; thoroness, accurracy, breadth of view; the power of neatness; the power to analyze; the power to construct; the power of sustained expression; the power of system; the power to carry out a plan; the power to look beneath the surface of an event for its cause; the power of suspending judgment; the power of patience; the power of efficiency; the power of truth.

The notebook is of positive use in the acquisition of knowledge and the development of power. Its limitations are the metes and bounds of trained judgment and common

sense.

THE PLACE OF MODERN HISTORY IN THE HIGH-SCHOOL

CURRICULUM

E. I. MILLER, PROFESSOR OF HISTORY AND POLITICAL SCIENCE, STATE NORMAL
SCHOOL, CHICO, CAL.

The why of history teaching is a prerequisite to the what, the how, and the how much of history teaching. That is, it is essential first to know why history should be taught at all, what educational results are to be secured from teaching it, before we can know what part or how much of the limitless field to select and how it shall be presented to the students. Therefore the first thing is to determine what are the educational reasons for teaching history in the high school. The first part of this paper will be devoted to a brief consideration of this question.

It must be said that in some respects the reasons for teaching history are the same for the high schools as for the elementary school, and for the university. Of course there is some difference in the degree that these aims apply to the different grades, but the same ideas are or ought to be considered.

All subjects of the public-school course are in that course because they afford information or give a facility which will be useful in life, or a subject may give both information and facility. In some subjects the emphasis is on the information, in others on the facility. But the information or the facility gained in the one subject cannot be carried over into another, unless that other is similar in some way. That is, a power of reasoning in one set of ideas does not imply a power of reasoning in another set, unless that other set is in some way like the first. Reasoning-power in mathematics does not imply reasoning-power in biology or in history; nor does the reverse hold good. However, reasoning-power

in