The Report on “The Teaching of English in England” lays great stress on the important truth that the use of English concerns all teachers, but when it deals with the matter more closely it enumerates teachers of history, languages, geography and science, and says nothing about mathematics (e.g. § 110).

Many of us who learned Euclid in our schooldays, feel that something substantial has been lost in the training in precise expression and logical statement that it gave. Even those mathematical teachers who would admit no such thing, must admit, if their experience is anything like my own, that many of their colleagues, particularly science teachers, have deplored the loss of what was at least a standard of reference for logical form.

Construction. As we depart widely from Euclid’s ideas in the proofs of Stage B, it seems to be thought by many people that go-as-you-please methods are good enough for constructions as well. Now, “trial” methods of construction are sometimes useful in more advanced work ; but they are tolerated only when a geometrical method is impossible ; they are means to get a solution, but there is no instruction to be had from such a method. We would therefore urge that a certain severity be still maintained in problems of construction.

Most mathematical students are familiar with Pascal’s statement, made in a communication to a learned society in Paris in 1653, that he had a number of mathematical treatises, chiefly geometrical, ready for publication, amongst them being the following : Conicorum opus completum, et conica Apollonii et alia innumera unica fere propositione amplectens ; quod quidem nondum sex decimum aetatis annum assecutus excogitavi ; et deinde in ordinem congessi.

The following remarks are based on the assumption, which I believe to be a true one, that there is a desire for more advanced mathematical knowledge among many people in this country, such as those engaged in teaching mathematics in secondary schools, technological institutions, and colleges, as well as others not professionally associated with mathematics. At present the means of satisfying this desire, at least as regards organised courses of post-graduate study available for persons employed in teaching or otherwise, are almost entirely lacking in England. The most that is available, and that only in a few university centres, consists of occasional lectures given under the auspices of universities and such bodies as mathematical societies and branches of the Mathematical Association. Able and interesting as these lectures may be, the knowledge to be acquired from them must, in the nature of things, be somewhat disconnected and superficial. Their value lies in the introductory glimpse which they give of unfamiliar branches of study, or in their rapid survey of a wide field of knowledge. They are useful complements to more systematic study, but are not a substitute for it.

The Mathematical Association has done in the past, and continues to do, work of the’highest importance in connexion with the teaching of Mathematics in Secondary Schools. Its activities have reacted with advantage on courses of instruction, methods Of teaching, and inevitably also on examination syllabuses. The Report on the Teaching of Geometry, which is one of its most recent publications, is a valuable document, the influence of which may be far-reaching.