education in the hands of intelligent and skillful teachers, may go into life with serious mental defects uncorrected, and even unsuspected; defects which will grow more serious and more hopeless with the progress of time and with experience of life.

ADDRESS BEFORE THE SCHOOL COMMITTEE OF THE CITY OF BOSTON, APRIL 12, 1887. PUBLISHED AS School Document No. 9, 1887.

Largely because of President Walker's vigorous efforts, more rational methods of teaching arithmetic have been followed in Boston during and since his service upon the School Committee.

ARITHMETIC IN THE PRIMARY AND GRAMMAR

SCHOOLS.

WHEN I moved, last winter, the resolution which has become the subject of the report of the Committee on Examinations this evening, it was without any purpose of taking part in the inquiry proposed. But the course of public discussion since that time, and my own appointment to the Committee on Examinations, have seemed to require something to be said by me regarding those features of the study of arithmetic in our common schools to which exception has been taken, and which the Committee, through their chairman, have unanimously recommended should be reformed in part or reformed altogether. And, first, it may be said that, if there be any reason whatsoever for believing that the course in arithmetic can be simplified and shortened, the matter is not one of slight importance. The cry of overwork frequently comes from pupils, parents, and physicians who are undoubtedly sincere, even if mistaken in this view; while if we reject the plea of overwork and conclude that the amount of study required of our children is, as an aggregate, not too large, we still have to encounter the almost unanimous complaint of teachers that studies are set down in the official courses which

These recommendations appear, in substance, at the beginning of the following address. See p. 235 infra.-ED.

they have not time to teach as they ought to be taught, many going so far as to say that it would be better that some of these subjects should not be broached at all if they are not to be dealt with more thoroughly and systematically than is possible at present with the time allowed. If, then, the course in arithmetic can be abridged, without injury on that side of our public schools, we know very well what to do with the time so released. It may be applied, in the discretion of the School Board, either to relieve the pupils from the general strain of their work, or to allow the further cultivation of natural science, or to afford additional practice in the art of observation, or to make way for the new mechanical and industrial exercises demanded by so many of our citizens.

Let me not be understood as disparaging the importance of the proper study of arithmetic in our public schools.

No one has a higher appreciation of the vital, practical importance of having our children taught to perform ordinary arithmetical operations with absolute accuracy and with a good degree of facility. Indeed, it is one of the gravest accusations brought against our public schools, as at present administered, that the old-fashioned readiness and correctness of "ciphering" have been, to a large degree, sacrificed by the methods which it is now proposed to reform. A false arithmetic has grown up and has largely crowded out of place that true arithmetic which is nothing but the art of numbers. But to this