My function in this discussion is the humble one of attempting to supply a rough scaffolding into which the durable parts of the edifice will be fitted by the other three speakers.

The teaching of algebra has never been dominated by a single work in the way in which Euclid for so long a time dominated the teaching of geometry For that reason, perhaps, the revolts in geometry have corresponded to quiet reforms in algebra, and the problems involved, though equally important, have never received the same amount of attention. On the teaching of the subject in schools, excellent books exist; there is Sir Percy Nunn’s classic, and more recently, a book by Durell, and much relevant matter in Godfrey and Siddons, Teaching of Elementary Mathematics.