School Certificate Mathematics

    Abstract

    A conference of representatives of examining bodies and teachers' associations was held in April 1944 and drew up a new syllabus designed to sweep away the traditional divisions of the various mathematical subjects studied at the School Certificate stage. The suggested new syllabus, which has now been printed with specimen papers (Mathematical Association), is arranged under seven headings: numbers; mensuration; formulae and equations; graphs, variation and functionality; two-dimensional figures; three-dimensional figures; practical applications. The main points of it may be summarized as follows. (1) The whole syllabus is designed to bring mathematics more closely into relation with the life and experience of the pupils. (2) It is infended to be alternative to the existing syllabuses and of equal weight. It is not suggested that it has been framed for weaker candidates by any lowering of the standard. (3) The fusion of the relevant mathematical subjects, particularly geometry and trigonometry, should be developed by the setting of mixed papers, three in number each of 2¼ hours duration, so that complete freedom of method should be permitted. This freedom should extend to the use of mathematical tables and instruments. (4) To remove much of the emphasis from formal work, only proofs of key theorems should be demanded. From these key theorems many others can be deduced and proofs of these are unnecessary. The Conference admits that the list of key theorems given is not ideal; but it is about the desired length of the essential formal work. (5) Perhaps the most striking feature of the syllabus is the inclusion of the beginning of the calculus, which should grow naturally and easily out of the consideration of graphs. (6) Heavy arithmetical calculations and algebraic manipulation must be excluded. The omission of these will allow the due emphasis needed on the all-important ideas connected with functionality, which begins with graphs and leads naturally to gradients. The whole report is inspiring, and if the basic ideas of it can be successfully carried out, mathematics should indeed become a really vital subject. Too long have we encouraged the blind manipulation of the symbol, with little or no relation to reality, while the deadening influence of the traditional formality in geometry has almost completely obscured the many ramifications of the subject in everyday life. It is to be hoped that this encouraging beginning will lead to the removal of many more artificial divisions in the mathematical honeycomb.

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    School Certificate Mathematics. Nature 154, 234–235 (1944) doi:10.1038/154234d0

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