MATHEMATICAL NEWS ITEM FROM COLORADO. The mathematical organization of this state is known as the Colorado Mathematical Society. The meetings are held at Denver. This city will probably be the permanent meeting place, as it is more centrally located than are the other educational centers of the state. The Colorado Scientific Society has given them the use of their rooms in the Chamber of Commerce Building. The membership is constantly growing and all members are workers. The officers are Professor Ira M. DeLong, State University, Boulder, President; and Alwyn C. Smith, State School of Mines, Golden, Secretary-Treasurer. IOWA STATE TEACHERS ASSOCIATION, DES MOINES, IA. DECEMBER 27, 1906. MATHEMATICS ROUND TABLE. Leader, W. J. Rusk, Grinnell; Secretary, Martha A. Beeson, Des Moines. "Methods in Teaching Algebra," Mabel M. Foster, Iowa City High School; "How Long Should the High School Course in Algebra Take?" J. L. Thatcher, Davenport High School; "Mathematics as a Factor in Character Building," Ira S. Condit, Iowa State Normal School; report of the committee appointed at last year's meeting upon "A Practical Course of Study in Mathematics for High Schools," W. A. Crusinberry, West Des Moines High School, Chairman. The above program was carried out. For lack of time, no discussion of papers was held; for the same reason no action was taken on the report of the committee as noted above. The following motion was made and carried: That it is the sense of this mathematics round table that it would be better to leave the entire afternoon of the first day of the state meeting open for round table discussions; also that the secretary report this action to the chairman of the next executive committee. Officers were chosen for next year as follows: Chairman, J. L. Thatcher, Davenport, Ia.; Secretary, Miss Mabel M. Foster, Iowa City, Ia. MARTHA A. BEESON, Secretary. CHEMISTRY TEACHERS CLUB OF NEW YORK CITY—SIX TEENTH MEETING, OCTOBER 27, 1906. As has been customary for several years, the club opened the season of 1906-07 with an excursion. The plant visited was the Atlantic White Lead works at the corner of Marshall and Gold Streets, Brooklyn, N. Y., directly on the East River. Twenty-one members and friends of the club met at 8:45 A. M. on the plaza at the Brooklyn Bridge, and at 9:05 proceeded on foot to the works. Here we were received most hospitably, the entire plant being thrown open for inspection, and both the superintendent, Mr. H. P. Cavarly, and the assistant superintendent, Mr. F. H. Doughty, volunteering to act as guides to the party. The output of the Atlantic works consists almost exclusively of three products, viz., white lead, linseed oil and lead (and solder) wire, sheet and tubing. As a detailed description of the processes used in making these would be too long for this report, only the briefest statement concerning them can be made. The white lead is made by the old Dutch process, since this, on the whole, gives the most satisfactory product. From 35 to 40 tons of lead are daily used at these works, the output of white lead being approximately 45 tons. Ten thousand gallons of linseed oil are daily expressed here, the seed being first heated, since the yield under these conditions is 25 to 30 per cent greater than when cold pressed. The manufacture of lead sheet, pipe and wire and of solder wire was also seen. The entire visit was most instructive and enjoyable. Much of the pleasure was due to the attitude of Messrs. Cavarly and Doughty, each of whom gave practically a half day of time to the club. Too much cannot well be said of their unfailing courtesy and kindness, their readiness to answer all questions and the generous way in which they threw the entire plant open for inspection. Jos. S. MILLS, Secretary. NEW ENGLAND ASSOCIATION OF CHEMISTRY TEACHERS. The twenty-seventh meeting was held in Boston, November 10, 1906. The following were elected as officers for the year 1906-07: President, James F. Norris, Simmons College, Boston, Mass.; Vice-president, Edward F. Holden, High School, Charlestown, aMss.; Secretary, Augustus Klock, High School, Beverly, Mass.; Treasurer, Miss Lillie C. Smith, High School, Brookline, Mass.; additional members of the Executive Committee: H. P. Talbot, Institute of Technology, Boston, Mass.; Sidney Peterson, High School, Brighton, Mass.; Harold Bisbee, High School, Dorchester, Mass. The following were also elected to membership: Arthur J. Hopkins, Amherst College, Amherst, Mass.; S. Walter Hoyt, High School, Fitchburg, Mass.; Grace E. Purinton, High School, Middletown, Conn.; Leroy F. Swift, High School, Lowell, Mass.; Frank T. Dillingham, Bussey Institute, Jamaica Plain, Mass. The annual reports of the secretary and the treasurer reviewed the work of the past year and showed the association to be in a flourishing condition. The total membership is now 121. The chief paper was read by Augustus Klock on "High Explosives." Through the courtesy of Mr. Klock, SCHOOL SCIENCE AND MATHEMATICS will soon publish an article by him embodying the essential parts of this paper. Following the paper on explosives there was a symposium on "The Teaching of Chemical Arithmetic." The subject was presented by Professor James F. Norris and Mr. R. P. Williams, and a brief discussion followed. So much interest was aroused by this subject that it was voted to continue the discussion at the next meeting. Professor Norris emphasized the necessity of teachers having definite knowledge of the ability of each student, the importance of having students grasp the full meaning of a chemical symbol, the advisability of requiring students to visualize the problem, the desirability of testing answers, the value of regular and constant solution of problems, graded problems, correlation of problems and quantitative laboratory work, and individual instruction. Mr. Williams outlined by diagrams and blocks his method which has given good results for many years. ASSOCIATION OF MATHEMATICS TEACHERS OF NEW ENGLAND. The fourth annual meeting of the Association of Mathematics Teachers in New England was held at Simmons College, Boston, Saturday, December 8. In the morning session reports of the committees on Arithmetic and on pattern examination papers in Algebra and Geometry were given. Professor Levi L. Conant of the Worcester Polytechnic Institute read a very interesting paper on "The Beginnings of Number." Professor Conant stated that the life of the individual is an epitome of the life of the race. The child first perceives number when he distinguishes between one and two. Number as an abstract idea comes late in human development. Probably cardinal numbers were used before ordinals. Illustrations of number concepts of animals and insects were given. Number sense in primitive man was not much higher than in some animals. The speaker discussed the ability of the mind to grasp the meaning of large numbers. He stated the advantages of twelve as a base instead of ten. He showed primitive number systems with bases five, ten, and twenty, proving conclusively that the fingers and toes were used as counters in the beginnings of number. Discussion of Professor Conant's paper led the association to the metric system and the desirability of using it instead of our present measures. It was agreed that teachers of mathematics should unite in urging the national government to make the change as soon as possible. Lunch was served to seventy-five members in the dining hall of the college. After lunch an opportunity was given to examine the buildings and equipment of the college. Officers for 1907 were elected at the beginning of the afternoon session. Mr. George W. Evans, principal of the Charlestown High School, reported for the committee on geometry. He gave the vote taken by mail on the desirability of adopting the syllabus of Geometry prepared by the committee. The vote was strongly in favor of the syllabus. The chief objection was due to fear that liberty in teaching might be lessened by a syllabus. This fear was caused by misunderstanding the use which the committee intended should be made of the syllabus. Further action on the syllabus was left in the hands of the council of the association and the council was empowered to print and distribute the syllabus. Professor Edward V. Huntington of Harvard reported on the June examinations for Harvard in Algebra, advanced Algebra and Trigonometry. He showed solutions of the problems and illustrated the methods used by students. He gave the percentage of success and failure for each question. A great many questions were asked the speaker and he answered them very carefully and completely. Professor Charles L. Bouton of Harvard explained the paper in Plane Geometry. A lively discussion followed. It was felt by the association that the work of the afternoon was very helpful, since teachers were shown where students failed and why they failed. Votes of thanks were given Professors Huntington and Bouton. A vote of thanks was given to the president of Simmons College for the hospitality of the college. The officers of the association for 1907 are: President, Charles D. Meserve, Newtonville High School; Vice-president, Harry W. Tyler, Massachusetts Institute of Technology; Secretary, George W. Evans, principal of the Charlestown High School; Treasurer, William B. Carpenter, Boston Mechanic Arts High School; Council, Professor Charles L. Bouton, Harvard University; Professor Thomas W. D. Worthen, Dartmouth College; Henry M. Wright, Boston English High School; Professor Ellen L. Burrell, Wellesley College; Miss Parnell S. Murray, Boston Girls' High School; William T. Campbell, Boston Latin School. WILLIAM A. FRANCIS. REPORT OF THE MEETING OF THE ASSOCIATION OF TEACH- The seventh meeting of the Association of Teachers of Mathematics in the Middle States and Maryland was held at the Central High School, Philadelphia, Saturday, December 1. Both morning and afternoon sessions were well attended. Dr. Robert Ellis Thompson, president of the Central High School, in his address of welcome among other pertinent suggestions called attention to the overuse or abuse of the blackboard, especially in mathematical teaching. From his own early experience and in later years in watching the experience of others, he has reached the conclusion that a close adherence to written work tends to weaken the student's mental power. Dr. John Anthony Miller, professor of mathematics and astronomy at Swarthmore College, read a paper on "The Fundamental Theorems of Elementary Mathematics." Professor Miller stated that a large number of the recently published algebra text-books do not give rigorous proofs of fundamental theorems. A faulty proof is worse than no proof. In most cases, until the student is sufficiently mature to appreciate a rigorous proof, it is better to give him a plain statement of the theorem postponing the proof, rather than attempt to force upon him a line of reasoning which subsequent study will reveal is either fallacious or incomplete. The ordinary beginner's algebra gives too much space to defining number, to distinguishing between signs of quality and operation. While theorems that introduce such difficulties as to be beyond the comprehension of the beginner should be postponed, on the other hand those that admit of clear and rigorous proof should be thoroughly mastered. Harry English, director of mathematics of the Washington high schools, spoke next on the topic, "The Teacher-His Preparation, Place, and Power." The address was a forceful presentation of the necessity of recognizing and dignifying the profession of the teacher. His problems are as complex and exacting as those which face the lawyer, the physician, or the clergyman. His relation to the home and to the state are as important. His general culture and his special training should be as broad and as thorough as those which are demanded in the other learned professions. Superintendent Rau, of the Moravian Parochial School, Bethlehem, Pa., treated the topic, "Co-ordination in Mathematics." The speaker contended that in certain sections the laboratory method had been unduly magnified; that teachers of mathematics had more to gain by a closer co-ordination of the recognized divisions of mathematics than by an excess of applications from the natural sciences. Mr. Rau especially advocated a closer union of geometry and trigonometry. He feels that the course in geometry should be much abridged by treating those elementary theorems of which all students have correct ideas as axiomatic, and proceeding to demonstrate propositions not so familiar. Thus he would classify most of the propositions concerning parallels and perpendiculars as fundamental propositions requiring no proof. He would use the time thus gained in more advanced work in geometry and trigonometry. Dr. Alice M. McKelden of the Girls' High School, Philadelphia, led a general discussion with her paper, "The Problems that Arise in the Teaching of Elementary Algebra." Miss McKelden believes that teachers should carefully instill accurate definitions with plenty of drill. In addition to exercises worked on paper or blackboard, part of the daily lesson should be some mental algebra. Such easy questions as the following are most fruitful of good results: 1. What number must be added to r to make y? 2. By what number must 3 be multiplied to make a? 3. If a is one factor of b, what is the other? 4. What is the price in cents of 100 oranges, when a oranges cost 6 cents? Etc., etc. |