A History of the Teaching of Modern Mathematics in England

Abstract

The Editor is under the impression that I am conversant with all the experimental work in this country that is directed towards modernising the syllabus in schools. This is a fallacy. A great deal is going on, but only a small part of the iceberg shows above the surface (an unsuitable analogy, however, for a topic so often associated with hot air!). But the genuine innovator is usually modest and self-critical; when discovered, and the question put: “Why don’t you send an account of this to The Gazette, it is just what is wanted” the invariable reply is : “Oh, this is a very amateurish effort, surely there are lots of others making a much better job of it”. There have always been experimenters, because of the nature of the English temperament and the absence of a central syllabus (though that would probably make little difference) ; and until the last War there was no lack of able mathematicians in the schools, as is shown by the large number of original (and consequently unsuccessful) textbooks published during the past hundred years. Forty years ago Mr. Hope-Jones was teaching probability and pleading for its adoption by all ; it has been available in several examination syllabuses since the War. Others advocated the earlier introduction of trigonometry or vectors, but use of these in a geometry paper could be dangerous ; nowadays an examiner would hesitate to mark-down a candidate who used vectors instead of congruent triangles in solving a problem. It is not uncommon, of course, for the unenterprising teacher to say that if such-and-such a modern topic were in the examination syllabus he would be glad to deal with it, but at present he dare not risk his pupils’ future careers, etc. But a new examination syllabus, though desirable, is neither a necessary nor a sufficient condition for the success of an experiment. There appears to be some acceptance of what might be called the First Law of Motivation, namely, that every boy (and master?) continues in his state of rest, or of uniform motion along the tramline, except insofaras he may be compelled by externally applied force or an external examination to change that state.