[Letters to Editor]

Abstract

IN spite of Prof. Carslaw's assurance that pupils on entering secondary schools have reached the age of thirteen or thirteen and a half and have had a full year's work at geometry, the writer of your article feels most strongly that it is extremely unwise to impose on them in their first year at the secondary school a logical treatment of the fundamental theorems of congruence and parallels. Anyone who has had much experience of teaching pupils of that age knows how difficult it is to teach this work and how little impression it makes except on a very small minority; on the other hand, if these theorems are frankly assumed (after the pupils thoroughly understand their meaning) the rest of the geometry usually done in secondary schools can be treated logically, and the vast majority of pupils will get a proper grasp of the ideas of logical geometry. In the latter case the foundations are broad and the structure is firm at every stage; if the fundamental theorems are treated logically, an attempt is made to build on a narrower base, but in the majority of cases the lower stories of the structure are insecure.