in connection with their shop-work. In the eleventh grade college algebra is taught and plane geometry reviewed. At the close of this year the boys come up for their college preliminaries with both algebra and geometry fresh in mind, the two having been studied continuously for almost four years. I have been repeatedly surprised by having boys in

my physics and chemistry classes ask for logarithm tables with which to work problems. I do not know of a better testimonial to the success of the arrangement. In the twelfth grade (senior year) solid geometry and trigonometry are studied by those who require them.

The success of the above-mentioned arrangement has led me to modify my views as to the desirability of correlating algebra, physics, and geometry, and has compelled me to believe that algebra and geometry, side by side with assistance from mechanical drawing, and possibly a few illustrative experiments from physics, give us the kind of a mathematics course we want. As such a course operates year after year, the subjects will be brought closer and closer together.

Now, as to the bearing of these remarks on individual or laboratory methods of instruction, we are all ready to grant that our present system of grades holds back the bright and discourages the slow boy. While objections to the individual method may be raised, none can carry much weight as long as satisfactory results can be obtained. The difficulties of applying it to geometry teaching are much greater than to algebra. The laboratory method as outlined for Bradley Polytechnic Institute does not from my experience justify the introduction of physics laboratory experiments into a course in geometry, not because the experiments themselves are not interesting and useful, but because the geometrical results can be arrived at more expeditiously in other ways. My experience does commend the introduction of graphic solutions of equations in algebra and the experimental verification of rules for areas, etc., by the use of cross-section paper, on the ground that they give meaning to the algebraic forms, and help to establish and to fix more firmly in mind the reasons for the rules in mensuration. Translation from ordinary and geometric language to algebraic symbols is a most important aspect of algebra, since algebraic translation is used continually in both geometry and physics. The experimental spirit of cut and try is a more important attainment than any special experimental knowledge. Observational geometry and mechanical drawing assist in cultivating this scientific spirit. The most important item, however, is such an arrangement of courses in arithmetic, algebra, and geometry as to form a consecutive mathematical whole, so that algebra and geometry are kept continuously before the pupil for a period of years, compelling, as in strictly laboratory courses, the mind to dwell for a considerable time on a particular topic, and thus giving the ideas involved a chance to "soak in."

DISCUSSION

JOSEPH V. COLLINS, State Normal School, Stevens Point, Wis. --In this country we have what Professor James calls the "American recitation method" used in all studies According to the law of evolution, most teachers will do better to improve this method, rather than make a radical change. The question presents itself: Are there plans which possess the merits of both class and individual instruction? To save time, several such expedients are stated formally, viz.:

1. The setting apart of regular consultation periods to be used to assign extra outside work to strong members of the class and to aid weaker ones over difficulties.

2. Brief conferences at the end of recitations for the same purpose.

3. Individual instruction during the first part of the hour, followed by class work covering the same ground.

4. The discontinuance of the class form of instruction before the end of the hour, followed by individual study of the work on the blackboard.

5. The "chalk and talk" method in which all members work with pencils on the same problem, one student talking, teacher supervising.

6. The "chalk and talk" method in which one student works and talks at the blackboard, and the others give attention, the teacher supervising.

The first three of these plans are doubtless already in wide use. I fancy the fourth is more or less novel. I have found it to work well. The fifth, a compromise between class and individual instruction, is much used in German schools. Personally I have got the best results from the sixth. Usually in class instruction, as Professor Jones points out, the difference in ability and attainment between members causes waste, the weaker mernbers being too slow to understand the recitations of the brighter ones, and the brighter ones being bored by the dullness of the others. This, I should say, is the bane of the class form of instruction. The sixth plan rightly used obviates to a certain extent these difficulties.

In conclusion I may say that this question of the form of the recitation has interested me much during the past four or five years. Thru such correspondence as I have had I am led to believe that our progressive teachers are rapidly breaking away from old customs, and are introducing all sorts of methods and expedients adapted to their own conditions. Evidently this is a most hopeful sign.

C. E. COMSTOCK, Bradley Polytechnic Institute, Peoria, Ill.-A word in regard to the trial of the Bradley Polytechnic Institute outlines made by Mr Jones. He used the secondyear work only. The work he substituted is done by us in the first year, and is presupposed in the work of the second year. The justification for the use of physical experiments in classes in geometry and the results we have obtained I have discussed in a paper before the Science Department on Tuesday. The individual method tends to produce mechanical rather than thoughtful algebraists. There is a waste of time in repeated explanations. The student who is not serious does not receive the proper incentive to work when he works alone. The class system incites to work. It enables a student to learn other ways than the one he has hit upon. In open class discussion he gains inspiration and breadth of view. He learns from his fellows as well as from his teacher. There should always be the greatest possible degree of personal contact between teacher and pupil. A judicial combination of individual instruction and class instruction will, in my mind, yield the best results.

H. CLAY HARVEY, State Normal School, Kirksville, Mo.-We are hearing a great deal just now concerning individual instruction in secondary mathematics, some teachers reporting results of their experiments with such enthusiasm as to compel investigation and comparison by those of us who still believe there are many more advantages with fewer defects in collective teaching.

In the time at my disposal, I can only speak briefly of what appear to me to be the most prominent objections to the individual treatment of a boy or girl studying mathematics.

We believe that the teacher's aim should be so to direct the child as to arouse interest and enthusiasm for the subject under consideration, so as to lead him to investigate, and thus to broaden his intellectual horizon; to lead him to discover his own misconceptions, and overcome his own difficulties-to teach him how to study, to acquire mental power and habits of quick, accurate, and logical thinking. Can this be accomplished by the individual method? We think not. The inspiration of numbers is second only in importance to a skillful teacher in accomplishing this work. The clash of thought between student and teacher, and between student and student, so necessary in securing the desired end, is impossible without numbers. In a class many questions asked publicly by the students will be of great value to the entire class, and would likely be overlooked by both teacher and student in the individual method.

In problem-solving six questions should be kept constantly before the student: (1) "What have you given ?" (2) "What do you wish to obtain ?" (3) "How can this

be obtained ?" When these three questions are satisfactorily answered, the problem is solved. Then three other questions arise: (1) "How did you obtain the result ?" (2) "Why did you take each step that was taken in the solution?" (3) "What authority is there for each step that was taken ?"

Can you accomplish all of these things by the method of individual instruction, where there are twenty-five or thirty students in your class? Most certainly not. The best that you can hope to do, in the time at your disposal, is to make clear the how. Can all of these things be accomplished by the method of class recitation directed by a skillful teacher ? I answer most emphatically “yes.” I have seen it done over and over again. These intellectual bouts indulged in by the different members of the class are of great value to the entire class, and often to the teacher as well. The weak student grows strong because of his association with, and because of what he learns from, the strong one; and the strong grows stronger because of what he learns from the teacher, and often from the weak student as well. The best teacher works his students under some pressure in the recitation. You can never develop that speed and accuracy necessary to the great scholar without working him with a running mate and under pressure. By this method you are arousing an interest which could never be aroused by individual instruction. You are solving problems and developing power as well, while in individual instruction you are solving problems and developing but little power.

To sum up what has been said, the advantages of class instruction over the individual instruction are these: The student has a chance to learn from others; it teaches how to study; questions by the class are valuable; it offers a better opportunity to develop mind; the teacher has a better opportunity to discover the student's difficulties.

There should be a specific aim in class instruction. There can be none in individual instruction. Individual instruction is poor economy of both time and energy. A thoro test in Kansas City Manual Training High School proved individual instruction a failure. Let us, then, use a method that is up to date-a method which will enable us to concentrate our time and energy so as to accomplish the greatest good to the greatest number.

E. CLASSICS CONFERENCE

THE COLLEGE REQUIREMENTS AND THE SECONDARY-SCHOOL

WORK

JOHN C. KIRTLAND, JR., professor OF LATIN, PHILLIPS EXETER ACADEMY, EXETER, N. H.

[ABRIDGED BY THE AUTHOR]

The vexatious question of the college-entrance requirements in Latin and Greek cannot be accepted as settled, and it is of the greatest importance that the present movement toward uniformity should not be allowed to fix finally upon the schools a fundamentally wrong and unfair standard, one that must inevitably contract their ideals to the narrowest utilitarianism and wholly vitiate their work. At the present time the attitude of many colleges is one of arrogance, tempered by the desire for students; the attitude of most schools, servile. I do not mean that either attitude is conscious, and I realize that both are natural. But arrogance is no less arrogance when it seems to the arrogant a mere assertion of superior wisdom for the guidance of the erring or the maintenance of rights; and servility is no less servility when it seems to the servile the counsel of expediency for the attainment of a desirable end. The college feels that it is the sole arbiter of the preparation of the candidate for admission, and that it is its duty to impose upon the school a correct standard of work. The school knows that it is judged largely by its success or

failure in getting boys and girls into college. Both need a clearer understanding of the situation, a higher sense of their duty to each other, a better criterion of judgment.

What, then, do the colleges wish? I take it that they desire evidence that the applicant for admission has the power and has had the training that will enable him to do their work effectively. The entrance examination has both a general and a particular aspect. It determines whether the applicant is prepared to do the freshman work in the given subject; it may also be used, together with the examinations in other subjects, to determine whether the applicant has sufficient ability, and has had adequate training for such work as is required of freshmen in the various courses open to them. The latter is the more important in the case of colleges allowing to the student from the outset a wide choice of studies; the former, where the course of study requires the continuance during the freshman year of the subjects in which the applicant is examined. In neither case is it feasible to demand accurate knowledge of large fields. Power, not organized knowledge, is the end of school training. Even if this were not so, the demands upon the secondary schools are so great and so various that it would be impossible for them, in the present state of American education, to equip their students to meet severe tests of their knowledge of the many subjects which it is necessary that they should study.

We must train the mind to be a good instrument for the work of the college. That is the demand that we are facing in this view of the college-entrance requirements. I purpose to turn to the classics, and to endeavor to make it clear that the college and the school may unite to their mutual advantage upon a true test of the preparatory work which shall not impose upon the school an alien and tyrannical authority. I shall confine myself in the treatment of details to Latin, for the sake of the gain in definiteness. At what should the teacher of Latin aim? It seems to me that the Latin course of the secondary school may be divided into two periods. In the first of these the language should be taught with reference to the training of the mind in logical and methodical habits, to the mastery of the elements of grammar and rhetoric of universal application, and to the cultivation of the power of attention and concentration. I believe that so much Latin as will accomplish these things may profitably be required of all students in our secondary schools. Two years' study of the language should suffice for this. I would have the work of these two years planned and carried out without the slightest reference to collegeentrance requirements or examinations. Only those should go on who are likely to get an adequate return for the time spent, either in the way of literary training or in helpful knowledge of ancient life and thought. The work will center in the study of formal grammar, the memorizing of forms, and the application of rules of syntax to discover the exact meaning of the text read.

During the later years of the course the chief object should be the cultivation of literary taste, and the second place should be given to the Romans themselves, their institutions, and the influence they exerted upon European civilization. There should be large and varied reading of the best authors, the study of the science of translation, and the closest possible approximation to the art of translation; and so much consideration of men and events and institutions mentioned as is necessary to make the writer's meaning plain. The choice of authors and the choice between different parts of the works of each, together with the order in which they are to be read, should be left largely or wholly to the schools. I know by experience that the course of reading which proves good for one school may not meet the needs or the tastes or the abilities of another. Much, indeed, depends upon the teacher. His class will surely enjoy most the authors which he enjoys most and reads with greatest enthusiasm. Moreover, the teacher is more likely to grow, less likely to petrify into an automaton, if his teaching ranges over a large field of literature. The same vivifying influence is felt directly in the school, as well as indirectly by reflection from the interest of the teacher. Every year, after the first, some poetry should be read, and the study of an author should not continue so long at a time that teacher and student alike are utterly tired of him.

The certificate system of admission to college has this advantage, in the case of Latin and Greek, that the colleges admitting on certificate are generally willing to accept any reading of the required amount and the right sort, and without regard to the time when the particular author was read; whereas the examination system requires that the authors set for examination be read in the year of the examination. This, at any rate, most teachers feel to be necessary, if their students are to make a creditable showing on the examination. Could not the colleges which are unwilling to rely entirely upon certificates of the candidate's preparation safely and properly accept the statement of the schools. as to the amount of Latin and Greek read? I hope to show that they might still reserve to themselves an adequate test of the candidate's fitness to continue the study of the language in college, and of his training. Indeed, I believe that the weakness of the certificate system might be remedied by such a test.

I think it will be agreed that, granting our premises, the test that will most surely discover the candidate's preparedness or unpreparedness for college, and at the same time do least violence to the ideals of the schools, the one that will bring school and college into the closest harmony, is the sight-examination. The ability to translate into idiomatic English a new piece of Latin gives evidence of an adequate preparation for the freshman Latin courses of the colleges, and of mental power and mental discipline. Such an examination can be made, moreover, to serve practically all the purposes of any examination in Latin. It will show the state of the candidate's knowledge of forms and of syntax, the extent of his vocabulary, his command of his own tongue, and even, if the passages are carefully chosen, his acquaintance with classical antiquity.

It is my belief that it is entirely possible to set passages in infinite number and variety, previously unknown to the candidate, and so simple that the examiner may confidently say that those who cannot read them either are not of the caliber desired by the college or have not had the necessary training in the subject. The passage should be clear and complete in its meaning, and that meaning should be simple (for this reason description and narrative are the best material), and the words should be those of commonest occurrence, or, in case they are likely to be strange, their meaning should be given. But I should not make the sight-examination the sole test, lest the blindness that sometimes falls upon the boy and girl on examination cause injustice to be done in occasional cases, and lest the school and the student lose sight of the fact that the ability to translate at sight comes only by mastering the language and thoughtful reading. The preliminary examination should include a test in grammar, and both the preliminary and the final examination might well include a searching test of the candidate's study of a small portion of the literature. The portion should be very small, so small that the study of it will not form a large part of the year's work or hamper the teacher in the choice of reading. I am of the opinion that a single oration of Cicero or a single book of Vergil is enough. If there is not to be both prose and poetry at sight, as I think there should be on both examinations, the preliminary as well as the final examination should have these set portions of both styles. This I urge from the conviction, already expressed, that no one of the later years of the course should be given exclusively to either prose or poetry. The prose, especially

if only one author is read, palls, and the long-continued reading of poetry by young students leads to neglect of the grammar. The requirements now generally in force bring about the division of the last two years of the course into one of undiluted Vergil and one of undiluted Cicero.

To sum up, the best and fairest college-entrance examination is sight-translation; the results of the sight-examination might be corrected by the addition of tests of the work done on a very small amount of prescribed reading, and by grammatical questions; if a larger amount of prescribed reading must be made sure of, the certificate of the school should be accepted for this; the questions on the subject-matter should be limited to such as may be answered by one who understands the meaning of the passage. The preliminary examination would consist, then, of sight-translation of easy narrative or descrip