go to college, and because the best preparation for life would be the best preparation for college also. It is only recently that the growth of state universities has brought them into relation with the high school, and it is thru these state universities in the intimacy of their relation to other parts of the great system of public education, and in their recognition of the genuine work of the high school, that much has been done to articulate the parts of the great system of public education which embraces all stages of development within the scope of its scheme. It has been the purpose of the high schools, of the north central section at least, to give their pupils a clear vision of the world and a vivid conception of its movements and forces, to show them the fields of human effort, and to prepare them to enter their chosen field with conscious possession of all their faculties; breadth of view, integrity of purpose, intensity of application, accuracy of knowledge have been the special features of their preparation for life. The object of the proposed federation of secondary associations is concert of action. If the teachers of secondary schools, recognizing the importance of their work, would in every state effect and maintain an active organization, holding state meetings for the consideration of living questions, and if these state organizations would choose delegates and alternates to attend a national convention to be held at a time immediately preceding the date of the meeting of the National Educational Association, with instructions to present for the discussion of this delegate body such questions as seemed of pressing importance, valuable practical results might follow. Then in turn the central delegate convention might deem it desirable to instruct the several delegates to report to their respective state associations for consideration such questions as seemed of special moment, that the sentiment of the country might be ascertained and formulated at a subsequent meeting of the federation of secondary organizations. The meeting of the Department of Superintendence is regarded by many as the most interesting and effective educational meeting of the year. Not less important might be the meeting of the federation of secondary associations. The influence of its deliberations and declarations of opinion would be of great weight, and would serve to call attention to questions of importance, if it did not determine their decision. For the purpose of securing definite action with regard to the formation of a federation of secondary associations, these suggestions are offered in the form of resolutions: RESOLUTIONS WITH REFERENCE TO THE FORMATION OF A FEDERATION OF SECONDARY SCHOOLS WHEREAS, It seems very desirable that there should be a consensus of opinion of secondary-school men in regard to matters of general importance which pertain to the conduct of secondary schools, and concert of action in matters with regard to which an agreement of sentiment and a concurrence of judgment can be reached, in order that the best interests may be conserved and the wisest action secured; now, therefore, Be it resolved, (1) That we, the undersigned, secondary-school men of the various states and territories affixed to our respective names, do hereby organize the Federation of Secondary Associations of the United States; (2) That hereafter this Federation shall consist of delegates chosen at a meeting of the secondary-school men held annually in each state, and at such time and place as may be determined by the associations of secondary-school men of the respective states and territories in meeting assembled for this purpose; (3) That each of the states and territories shall be entitled to two delegates, and as many more as will give it a representation proportionate to the high-school attendance as published in the latest annual report of the respective state superintendents; but to secure a full representation should choose alternates at the time of the election of delegates, to act as delegates in case of the absence of one or more delegates; (4) That the meetings of the Federation shall be held the Friday and Saturday of the week preceding the meetings of the National Educational Association, in the place chosen by that body, and in such locality as may be selected by the executive committee of the Federation, unless another time and place shall have been selected at a previous meeting of the Federation; (5) That the officers of the Federation of Secondary Associations shall be a president, a vice-president, a secretary, and a treasurer, and an executive committee of seven, consisting of the officers of the Federation and three other members chosen by the Federation at its regular annual meeting; (6) That the annual dues of state organizations to this Federation shall be five dollars, which must be paid to entitle the delegates to take part in the proceedings of any meeting of the Federation; (7) That enactment of further provisions for the conduct of the Federation shall be left to the Federation constituted as herein provided. The resolutions were seconded by Principal E. V. Robinson of the Central High School, St. Paul, Minn. DISCUSSION CHARLES F. WHEELOCK, of the University of the State of New York, said that he had corresponded with many associations of secondary schools, some of which were composed partly of college professors and partly of secondary-school teachers. State teachers' associations had been requested to organize high-school associations. Such organization of high-school teachers was one of the leading aims to be realized by the proposed federation. He moved an amendment to the resolutions that the time of meeting correspond with that of the meeting of the Department of Superintendence of the National Educational Association, which meets in February each year. E. W. LYTTLE, Albany, N. Y., opposed this amendment, because many state meetings would not be held before next year. It was also suggested that many high-school principals would not be allowed to go to a mid-year meeting without a loss of salary for the time lost. The question was asked: What is the need of such a federation? Is not the National Educational Association doing all that is needed? Another objection to the mid-year time of meeting for the federation was made to the effect that a large attendance was needed for the best success of the new organization. To this objection it was urged that nearly all the state meetings are held during the Christmas holidays, so as to make it feasible for plans affecting the federation to be carried out before the following February. Great numbers are not needed. Smaller meetings are better than large, crowded ones. PRINCIPAL JOHN T. BUCHANAN, De Witt Clinton High School, New York city. If meetings should be held in mid-winter, New York principals would not be allowed to attend. The new organization is not needed. If the National Educational Association cannot do the work required, the new body certainly could not. MR. LYTTLE.-The gatherings of this proposed federation need not be large. Only delegates need attend. We should simplify the matter of arithmetic. Metric system could be secured if co-operation were brought about. Committees of correspondence are needed as in old days. We need to take hold and push together in the whole country. High-school principals and superintendents are losing places because the ethics of mutual relations are not known. We need to pass upon such questions. Lengthening the course of high schools to six years also needs much discussion. PRINCIPAL O. S. KRIEDEL, Perkiomen Seminary, Pennsburg, Pa.-We need to get together to compare methods, plans of work, etc. One meeting a year is needed. Great good would come out of it. Each of some ninety secondary schools in Pennsylvania knows very little of the others' work. Private and public high schools need to do some things in common. PRINCIPAL D. R. ELLABARGER, Richmond, Ind.-- Superintendents have organized. They seem to guide the educational work of the country. In Indiana high-school principals have no educational standing. We are asking that we be recognized in the educational work of the country. We need to do something that will give us recognition. W. A. WETZEL, Trenton, N. J.-We should go slowly in putting ourselves on record as attempting to secure recognition. We may at the outset arouse friction. The superintendent is naturally at the head of the educational system of any city. III. MATHEMATICAL CONFERENCE LEADER, DAVID EUGENE SMITH, TEACHERS COLLEGE, COLUMBIA The conference on mathematics was held Friday, July 10, at the close of a protracted session of the department. The leader, David Eugene Smith, in introducing the topic said that the object of associations such as proposed should be not so much mathematical research as improvement in the teaching of mathematics. Other subjects of the curriculum of secondary schools have their associations of teachers, and the results have been improvement in the teaching of those subjects. In England, France, and Germany there has been of late undoubted progress in methods of instruction in mathematics, due to the influence of such associations. The part of associations of teachers of mathematics is to give to this country its share in this progress. Several associations of the sort have recently been formed. The object of the conference is to talk over the methods of organization and the work of these associations, with a view to securing more support for them on the part of teachers of mathematics, and the organization of associations in other convenient centers thruout the country. CLARENCE E. COMSTOCK, Bradley Polytechnic Institute, Peoria, Ill., reporting upon the movement in the middle West, said that interest and consultation among teachers for a year or more past had culminated in the organization at Chicago, in April, 1903, of the Central Association of Science and Mathematics Teachers. The association is divided into various sections, including physics and mathematics, which hold special sessions in connection with the general annual meeting of the association. A system of local centers has been established in order to reach as many teachers as possible, and more frequent local meetings are held. Older clubs are being affiliated with this organization, and the Central Association will serve as a clearing house for expression and discussion for the. teachers of ten states. The constitution states three objects: (1) to promote better teaching of science and mathematics, especially in secondary schools; (2) to obtain a better correlation of these subjects to each other and to the other subjects of the curriculum; (3) to bring the college and the secondary school into closer relations. As to the teaching of mathematics, there appear to be three leading ideas at work in the mind of those most interested in the movement: (1) For the purposes of secondary education, pure mathematics does not in itself furnish the proper incentive for mathemati- . cal study; this implies a correlation of mathematics and natural science. (2) The meaning of mathematics is best appreciated, and its processes more easily and effectively mastered, by a disregard of the arbitrary divisions of mathematics; this implies a correlation of mathematical subjects-algebra, geometry, trigonometry, analytical geometry, and calculus. (3) The mind moves from the concrete to the abstract; this implies a recourse to experimental and inductive methods. At the April meeting of the association a committee reported upon the correlation of physics and mathematics. A monthly called School Science, with a quarterly mathematical supplement, has been made the organ of the Central Association and is furnished each member. J. S. FRENCH, Jacob Tome Institute, Port Deposit, Md., reported for the movement in the middle states and Maryland that a preliminary conference of teachers of mathematics in those states was held at Columbia University in May, 1903, and the organiza 1 This report, filling a sixty-page pamphlet, may be procured for fifteen cents from Mr. E. C. Woodruff, 5735 Monroe avenue, Chicago. tion would be effected, it was hoped, at the next Thanksgiving recess. Mr. French discussed the basis of the proposed organization and the work it might do. EDGAR H. NICHOLS, Cambridge, Mass., reported that the Association of Teachers of Mathematics in New England perfected its organization in April, 1903. An effort is being made to obtain a list of all teachers of mathematics in New England and interest them in the association with a view to the organization of local centers. There are already 175 members. The object of the association is the planning and execution of definite work for the promoting of interest in mathematical study. The special work that the association is undertaking thru a committee is the preparation of a syllabus of concrete geometry. Letters of inquiry have been sent to a large number of teachers to ascertain the extent to which they are teaching concrete geometry, together with the methods used and the results obtained; and much valuable information has been received in response. The movement promises well in the way of bringing together information as to best known methods and selection of subject-matter, and at any rate in saving teachers from working at cross-purposes. REPORT OF COMMITTEE ON ENTRANCE REQUIREMENTS IN MATHEMATICS H. W. TYLER, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, BOSTON, MASS., CHAIRMAN In July, 1899, a committee of the Departments of Secondary Education and Higher Education presented a report on college-entrance requirements, including a discussion of the scope, aim, and place of mathematical studies in the secondary schools and in preparation for college, with model courses in algebra, plane and solid geometry, and trigonometry, with methods to be used, time to be consumed, etc. To the details of this report it is not my purpose to refer. For several years a standing committee of the Society for the Promotion of Engineering Education has been occupied with the study of entrance requirements for engineering colleges, and has sought by various means to secure agreement of these colleges on standard formulations of requirements, particularly in mathematics, chemistry, physics, and mechanic arts. Committees for conference and co-operation have been appointed also by the National Educational Association, the American Mathematical Society, and the Eastern Association of Teachers of Manual Training. The committee of the American Mathematical Society prepared a provisional report, which, as chairman of the committee, I desire to present, informally, to this conference, with the understanding that at the present stage the report, while based on careful study, has no authoritative significance: PROVISIONAL REPORT OF THE COMMITTEE OF THE AMERICAN MATHEMATICAL SOCIETY First: To specify those mathematical subjects which are generally recognized as appropriate requirements for admission to college. Second: To specify details under these subjects in such a manner as to represent the standards of the best secondary curricula-the word "best" being interpreted in a qualitative rather than a quantitative sense. Third: The committee understands also that the consideration of pedagogic questions is not among its duties. It has therefore, made no attempt to deal with methods of secondary education in mathematics, or the order of taking up the subjects and their correlation with each other and with other sciences. The order in which the subjects and the topics under them are presented below does not necessarily imply preference of the committee as to order of teaching either the subjects or the topics. It is the opinion of the committee that these are the subjects and the topics which, according to the best present usage, should be offered for admission to colleges and scientific schools. The formulation is not to be interpreted as exhaustive. It represents rather the extent to which, in the opinion of the committee, definite specification should be undertaken by it; it is expected that further details will be determined in accordance with the judgment of the particular college, school, or teacher. The definitions proposed are based on present usage and standards. In case of divergence between standard text-books and what seemed a more scientific presentation of the subject in question, the committee has endeavored to make a choice which should not depart so far from current usage as to involve hardship to schools or teachers. The committee is of opinion that no formulation should be considered as having more than temporary validity. No advantages attendant upon uniformity of definition could counterbalance any tendency of the definitions to retard progress of scondary education in mathematics. It is, therefore, recommended that if the definitions are approved, they be revised at intervals, perhaps of ten years. The four fundamental operations for rational algebraic expressions. Factoring, determination of highest common factor and lowest common multiple by factoring. Fractions, including complex fractions, ratio, and proportion. Equations of the first degree, both numerical and literal, containing one or more unknown quantities; problems depending on such equations. Radicals, including the extraction of the square root of polynomials and of numbers. Exponents, including the fractional and negative. Quadratic equations, both numerical and literal, including simultaneous equations of which only one is quadratic. Problems depending upon quadratic equations. *Proof of the binomial theorem for positive integral exponents. (It is expected that the theorem will have been used at an earlier stage). *Arithmetic and geometric progressions. Thruout the course the pupil should be required to solve numerous problems which involve putting questions into equations. Some of these problems should be chosen from mensuration and from physics. The use of graphical methods in connection with the solution of equations is advised. The usual theorems and constructions of good text-books, including the general properties of plane rectilinear figures; the circle and the measurements of angles; similar polygons; areas; regular polygons, and the measurement of the circle. The solution of numerous original exercises, including loci problems. III. SOLID GEOMETRY The usual theorems and constructions of good text-books, including the relations of planes and lines in space; the properties and measurement of prisms, pyramids, cylinders, and cones; the sphere and the spherical triangle. The solution of numerous original exercises, including loci problems. IV. PLANE TRIGONOMETRY Definitions and relations of the six trigonometric functions as ratios; circular measurement of angles. Proofs of principal formulæ, in particular for the sine, cosine, and tangent of the sum and the difference of two angles, of the double angle and the half angle, the product expressions for the sum or the difference of two sines or of two cosines, etc. Inverse trigonometric functions. Solution of simple trigonometric equations. Theory and use of logarithms (without the introduction of work involving infinite series). The solution of right and oblique triangles, and practical applications. V. ADVANCED ALGEBRA Permutations and combinations, limited to simple cases. Complex numbers, with graphical representation limited to sums and differences. Determinants, chiefly of the second, third, and fourth orders, including the use of minors and the solution of linear equations, but not the multiplication of determinants. *A college finding it impracticable to meet this normal requirement is advised to require all topics not preceded by an asterisk, |