Primarily for teachers and teaching courses, this however may be of some help to parents struggling through the progressive teaching of numbers, for it explains not only the methods but also the aims of the new systems of education in numerical work. From the earliest conditioning, at nursery school age, this shows how knowledge is absorbed rather than taught, how through experience, with blocks, tracks, and actual work in counting, adding, subtracting, such systems carry through to more advanced work. It is the work of the Director of the Castle School in New York and sympathetically introduced by Professor Marguerite Lehr, of Bryn Mawr, and provides a detailed explanation and outline of this new structural arithmetic.