Mathematics in the Cambridge Locals

Abstract

ON May 29 (vol.lxvi. p. 17), we announced an important change in the geometry of the Oxford local examinations for 1903. Quoting from the notice which had just been issued, attention was directed to the important statement that “Questions will be set so as to bring out as far as possible a knowledge of the principles of geometry, a smaller proportion than heretofore consisting of propositions as enunciated in Euclid. Any solution which shows an accurate method of geometrical reasoning will be accepted. No question will be set involving necessarily the use of angles greater than two right angles. Geometrical proofs of the theorems in Book ii. will not be insisted upon.” We have now received the schedules in geometry that have been adopted for the Cambridge preliminary and junior local examinations in 1903. In these, we are glad to see that the Cambridge Syndicate has adopted to an even greater extent the reforms suggested by the recent British Association Committee. For the preliminary, junior and senior examinations:—“Any proof of a proposition will be accepted which appears to the examiners to form part of a logical order of treatment of the subject. In the proof of theorems and deductions from them, the use of hypothetical constructions is permitted.” No schedule will be published for the senior examination. The importance of the schedules now published for the preliminary and junior examinations will be apparent when it is considered that they may be said to cover the work done by the boys and girls in all secondary schools up to the age of sixteen years, and the work of such older boys and girls as are not trying for marks of distinction. Their influence is great, and we heartily welcome the important change that they place much greater stress upon observation, measurement and experiment than on abstract reasoning. It is to be observed also that there is no mere pretence of accuracy:—“Every candidate must be provided with a ruler graduated in inches and tenths of an inch, and in centimetres and millimetres, a small set square, a protractor, compasses furnished with a hard pencil point, and a hard pencil.” This mention of the hard pencil is business-like; as soon as boys understand that in their measurements of lines they must not make errors of even one-hundredth of an inch, their true scientific education begins. As for demonstrative geometry, a great number of Euclid's propositions are left out altogether. Books ii. and iv. have completely disappeared. Twenty-eight out of the forty-nine propositions of Book i. have to be studied for the preliminary and junior. Of the thirty-seven propositions of Book iii., only ten have to be studied for the preliminary and four more for the junior. Of the thirty-five propositions of Book vi., only thirteen are required for the junior. The most important part of the geometry examination is called practical geometry, and there is every inducement to all teachers now to dwell largely on experimental geometry, as all good teachers have done for many years.