Schools

The chief aim of the College Entrance ExCo-operation of the Secondary amination Board is to secure, by means of a co-operation between all those vitally interested, that uniformity of standards which is essential for the general systematic improvement of the conditions of secondary education. In this co-operation representatives both of colleges and of secondary schools must have part. The board recognizes that it would be quite as inappropriate for a body composed solely of college professors to decide by a vote questions affecting in an important way the curriculum of the secondary schools as it would be for a body of schoolteachers independently to determine questions affecting the college curriculum. In every important problem that affects the relations between the college and the secondary school, the judgment of those who have achieved for themselves eminence in the world of secondary education is at least of equal importance with the judgment of those who have attained similar distinction in the college world. In recognition of these facts secondary-school teachers have been associated with the work of the board at every stage. They are members of the board itself, they serve upon the committees of examiners and upon the committees of readers. Their criticisms and suggestions are invited in regard to every part of the work, and receive consideration equally with the suggestions and criticisms that come from the representatives of the colleges. There are indications that the secondaryschool teachers in no community thruout the country have failed to recognize the importance of the work that has been undertaken by the board, and it would not be surprising to the writer if it should turn out eventually that the general acceptance of the principles and of the standards for which the board stands will be due even more to the influence of secondary schools than to that of colleges.

Conclusion

The operations of the last twelve months, as described in the preceding report, make it evident that the work of the College Entrance Examination Board is progressing with long strides. The number of institutions that have assumed an immediate

responsibility for the work of the board has increased from 15 to 22. The very small number of institutions not accepting the board's examinations has diminished. The number of candidates attending the examinations has increased greatly; outside of New York. it has doubled. These and other phenomena, however, that may be shown by statistical tables, do not at all measure the growth of the board's influence and the increasing influence of the principles upon which its work is based. In every part of the country the work of the board has excited deep interest, and it is exerting an elevating influence upon the standards, not only of secondary, but also of collegiate instruction.

Respectfully submitted,

September 1, 1902

THOMAS S. FISKE, Secretary

V

DISCUSSIONS

CORRELATION OF ALGEBRA, GEOMETRY, AND PHYSICS

Two years ago, influenced by the report of the Chicago section of the American Mathematical Society, urging the simultaneous teaching of algebra and geometry, the high school at Lincoln, Neb., undertook the experiment of following the suggestion and introduced a course in mathematics, in which the two subjects were begun at the same time by pupils of the incoming classes. As many schools, likewise favorably impressed with the theory of the committee, are attempting to make a practical application, while other schools interested are waiting to see the outcome of the experiment before departing from a time-honored tradition, a report on results obtained in Lincoln will not be out of place at this time.

This school has gone farther than the correlation of algebra and geometry; it has introduced a large amount of sciencephysics and physical geography-for the sake of a broader concrete basis for the algebra and more interesting application of the geometry. In order that a clear understanding may be had of the feasibility of this plan, it will be necessary to describe another branch of the course of study. One of the required subjects for the first-year student is a course in what is termed "Elementary Science." It consists chiefly of recitation and laboratory experiments in the common elementary physical laws with which the child comes in daily contact. The study excites the keenest interest, and algebra based on this concrete notion of quantity, both positive and negative, has a life and meaning unattainable under the method of abstract -to the student meaningless-reasoning with symbols and rules. Indeed the clear comprehension of comparison of quantity which even the ninth-grade student acquires under the development of mathematics on a concrete basis is surprising. By means of material from the laboratory of actual measurement and weight, sustained by geometric intuitions.

of distances, areas, and angles, both positive and negative, algebraic principles are firmly fixed in the mind-the specific cases gradually giving way to symbols of general quantitative expression. For example, equation work is taught in connection with experiments on the balances. At first all problems leading to equations are taken from actual experiments made; then, as the pupil begins to feel the tediousness and uselessness of specific numbers of grams, decigrams, etc., in carrying out his thought, he is led to introduce general expressions in fact, many pupils will attempt this without suggestion on the part of the teacher and write w for weight of some substance, or c for number of centigrams, etc., or I for length of lines, a for size of angles; while under the direction of the teacher a more thoro comprehension of general quantitative expression is obtained than can be obtained under any other method of presentation. Furthermore, by means of geometric relations of magnitude and by laboratory study of such laws as that of the lever and Boyle's law, the student reaches an understanding of ratio, both direct and inverse, clearer to a degree than is ever possible under the isolated teaching of algebra. Positive and negative quantities become a reality thru geometric and physical examples. Solution by rule is unnatural to this method of teaching and is strictly guarded against. Mathematical operations must be performed in harmony with laboratory operations. It is not practical to add up all the positive quantities and then all the negative and take the difference of the sums in a test of temperature-addition is performed naturally as the work

proceeds.

Experiment leads the student to decide quickly the amount that must be added to one quantity in order to obtain another, so he does not change signs and add when he wishes to subtract. He has been led to the equation thru experiment with balances; he performs the operations of the reduction of the equation in the same manner as he performs the experiments with his balances; that is, having known and unknown quantities in each pan, he naturally takes an equal amount from each till he has only known in one pan and unknown in the other; so he sees the analogy and treats the equations likewise.

Thus thruout the entire first year the three studies, algebra, geometry, and physics, are kept together-the latter supplementing the former with concrete material, the former furnishing the solution of problems drawn from the experiments of the latter and leading to generalizations of results. The reasoning is similar if not the same in all, which fact is kept constantly before the student.

During the second year, when equation work is strongest, the geometry and physics furnish a body of material which can be utilized to create the greatest enthusiasm and interest in the subject. To add to this, the more elementary ideas of trigonometry are introduced in connection with ratio and proportion and similar triangles, thus opening up another line of practical applications.

The objection has been offered to this plan of teaching mathematics that it will require too much time. This is not true. The mathematics is completed in less time than is required by other schools in the State, or than was formerly required in this school under the single-study method, while a far greater degree of thoroness and insight into the subject is obtained.

The truth of this statement will easily impress itself upon anyone who stops to consider that, instead of being shot thru the algebra in a year and geometry in a year and a half, without any clear notion as to the use of either, the student spends in reality two and a half years on each. The principles are inculcated in such a way that they cannot be forgotten, while the application of mathematics to physics is clearly understood, and the knowledge of physical laws is utilized to stimulate the student in the pursuit of that branch of learning which alone embodies undisputable truth.

HIGH SCHOOL,

LINCOLN, NEB.

EDITH LONG

NEW YORK CITY SCHOOLS AND THE POOR

In the otherwise admirable paper contributed to the September EDUCATIONAL REVIEW by Miss Lucia Stickney of Cleveland, O., I was astonished to find the following: