No one can possibly welcome more cordially than I do the widening of the school curriculum in mathematics that has taken place during the last twenty years. Even I can remember the days when “Conics” and “Mechanics” were the privilege of a select few, and only a prodigy was initiated into the mysteries of the Differential (much less the Integral) Calculus. All this is changed now, and it is fairly safe (at least that is my experience) to assume that a boy who has won a scholarship has learnt something about the Integral Calculus at school.

A series of investigations is being planned by a section of the Board of Studies for Mathematics in the Institute of Education of the University of Birmingham, with the object of gaining information about the types of difficulty experienced by children in various branches of grammar school mathematics, and the types of error made. An analysis of these errors, both from the mathematical and psychological points of view, is highly informative and relevant to a discussion of teaching methods in the subject. It is hoped that later it will be possible to prepare standardised tests which would be of diagnostic value to teachers. The co-operation of other teachers would be welcomed in furthering this investigation, either in the form of comments or criticisms in the light of their own experience, or in helping to widen the sample of children tested in future work.