§ 1. Definition of aim. A distinguished psychologist recently addressed a body of our American colleagues on the teaching of physics. “Your aim in the teaching of physics,” he told them, “should be—to teach physics” The advice was excellent—especially from one who is apt to be regarded as an intellectual Strong Man, full of esoteric knowledge about the development of mental muscle. Substituting “mathematics” for “physics” we may well adopt the maxim with all its implications, negative and positive.

§ 2. Negative implications. Beginning with the negative implications our amendment of Prof. Baldwin's dictum may be expanded as follows. In the first place, the central purpose in teaching mathematics is not to “train the power” of reasoning, of generalising, of “mental accuracy,” etc. The fallacies embodied in the persistent heresy of “formal training” have been repeatedly exposed, and need not detain us here. The time should soon come when an educational writer may ignore them. The chemist does not feel bound to begin his text-book by rebutting the phlogiston-theory, nor the geographer to demolish the sophistries of the flat-earthers.