In all this there is one confusion which we must keep clear of. When we say that all training is specific we do not mean that education should be narrow. It can not be that and be the kind of education that we want or that most people want. It was sufficient for the hunter to teach his son to shoot with the bow and arrow, but we have many kinds of bows and arrows now, rifles and 42-centimeter guns and systems of national and international law and morals and sciences and histories and literatures and philosophies. They are all instruments which we must learn to work and each one must be taught to shoot with a representative number of them. But general education in this sense is a combination of special or particular forms of education. DOES THE STUDY OF MATHEMATICS TRAIN THE MIND SPECIFICALLY OR EDUCATION is, or at least aims to be, a conscious process and a purposive undertaking. To teach anything we must first know what purpose is to be served by it and how it must be taught so that that purpose will be served. As there are many subjects which might be studied and many ways in which each one of them might be presented, our first and continuing duty is to select from the whole number of possible subjects those few which are indispensable for the purposes of life, and when we have done that, we must next select from the many possible ways of studying these subjects those few ways of approaching them which are likely to lead to valuable results. Now, why should one study anything? As nearly as I can discover there are three answers which are given to this question. First, we must study subjects because we owe it to them to do so. It is a debt of honor, of reverence, of obeisance, or worship which we should pay them. We do not study them for what they do for us or us to do. They are the ends. We are the means. This is subject worship, a kind of liturgical devotion what they will enable 1 An address before the Association of Teachers of Mathematics in New England, April 28, 1917. which we are told we must pay to science, literature, mathematics, philosophy when they are hypostatized into self-existing realities. Its favorite call to prayer is science for the sake of science, literature for the sake of literature, knowledge for the sake of knowledge, and art for art's sake. This is a peculiarly inhuman belief which annually requires the sacrifice of hecatombs of young lives. It seems to us to be just as idolatrous to worship the creations of men's minds as to worship the creations of men's hands. We are recommended to beware of idols. The creator is more to be revered than his creation. When the creation is ascribed virtue in itself, the proper relations are reversed. Knowledge, art, science, literature, philosophy and mathematics exist for man's sake, not he for them. The question always is, what are they to him, what can he make out of them? what can he do with them? Knowledge can not be its own end. It must be for something. It must perform some work, must offer some assistance, must serve some human purpose. We may take it on credit, but the time must come when it will pay some sort of dividends. If it does not, it is simply useless and unmeaning. It makes no difference in a world in which only such things are regarded as real as make a difference. The second reason for studying anything is that we can not get along without it. It is an indispensable aid to us in doing our work. It may serve us in many ways, but we want it because in days to come we shall use it. It is because we are going to read that we study reading, are going to write that we study writing, are going to use geography and history, literature and science as long as we live that we study geography, history, literature and science; and the parts of these studies which are outworn or have no definite utility we omit, giving our attention exclusively to those aspects of them which have abiding value. According to this view studies are for use and education is preparatory. There are so many difficult things that each one of us must know how to do in order to get on with nature and with our fellowmen, that the whole of life is not sufficient for us to learn them. All that we can do in youth is to master the beginnings of a few of the great human operations. Advanced life must help us to perfect our knowledge of them. From this point of view it is immeasurably important that we do not waste our time upon studies or parts of studies which we can not use in after years and immeasurably important that we study the subjects that have definite utility in such ways that we will go on using them and increasing our mastery of them through the years that are to come. The school, then, exists to provide special opportunities for us to become acquainted with the first stages of our life business and must introduce us to it in such a way that we shall, from the first, appreciate its meaning and perform it with a growing interest and an expanding sense of its worth, so that when our school days are over we shall know that our education has but begun and will go on applying and using and perfecting our skill in the great arts of which it has taught us the fundamentals as long as we may live. Educa H tion, according to this view, is specific throughout. Its purpose is to enable the student to acquire the beginnings of certain indispensable forms of human skill without which he can not be a society-supporting unit in a world in which men must live and let live and help themselves and each other in doing so. Every form of skill that we attempt to teach him gets its place in the school program solely because he can not live a civilized life without practicing it. Traditional reasons are not a sufficient warrant for teaching anything. The course of study is to be made with reference to the future, not because of veneration for the past or because of blind adherence to the prevailing practice of to-day. The training of the young is so serious a responsibility that it must be made throughout a conscious undertaking. Their time must not be wasted and their futures must not be trifled away. Nothing must be attempted in their education without demonstrable reasons for attempting it. Few men who have not followed closely the advances which have been made in the science of education in recent years know how completely present-day educational theory differs from the crude traditionalism of an earlier time. The new efficiency program which schools are trying to put into practice now is first to analyze the habits we want the young to form, to set up specific aims by whittling our purposes to the finest point in helping them to form them, and to measure carefully the results which are brought about by instruction. The effort of to-day is to do away with aimless routinary education, by substituting for it an intelligent pro |