The object of the present article is to indicate the scope of graphical methods and the desirability of using them far more extensively in teaching elementary mathematics. Articles indicating some of the possibilities have appeared recently in the Mathematical Gazette, one by Dr. W G. Bickley, “Arithmetic, Algebra, and Calculus on the Drawing Board”, May 1941, Vol. XXV, No. 264, and another by C. Dudley Langford, “A graphical method of solving problems on ‘Rate of Work’ and similar problems”, Dec. 1941, Vol. XXV, No. 267. Graphical work is so universal in its application that it is impossible to deal with more than a very small section of work in the compass of a single article, and “Quadratic Equations” has been chosen for purposes of illustration. Through the medium of graphical methods and concrete numerical illustrations, the elementary student of mathematics gets a much clearer and more interesting view of the subject.

The recruitment of suitable teachers of ancillary subjects in technical schools and colleges was often difficult before the war, and even if the ideas of the Spens report did not imply a considerable increase in demand, it is time that this supply problem was faced. In the technical subjects themselves the problem is not so acute; the teacher of a branch of engineering is teaching the subject very much as he was taught it, to students whose outlook is very similar to his own. Teachers of physics or chemistry to the same students, although not in quite such a happy position, have certainly in their own studies met with frequent practical applications of their subject, and will usually be entirely sympathetic towards this aspect. With the majority of the teachers of mathematics, however, the position is very different.