The question about the teaching of Mathematics considered most frequently and with most detail is How? This is the main preoccupation of the Mathematical Association Reports on separate subjects : it is of special interest to note that in the Report on the Teaching of Calculus oft repetition of the phrase “ the teacher will know ” implies that the topic is as rich as human nature. Yet for writers in the Mathematical Gazette, and for most scholarship winners, the question is superfluous, though all appreciate a good teacher. (For these too the answer to Why? is simple—the urge of joy or duty.) On the other hand, it would scarcely be denied that for more than two-thirds of the pupils in our schools the question How? is unanswerable under present conditions : for them we are attempting the impossible.