have been and are now asked to solve. In the oldentime text-book, problems were all of a certain general type form. Pick up a text-book which was in use twenty-five years ago, and you will not find many problems concerning the actual situations in which a pupil would be placed outside of school. The exercises were much the same in all the text-books of that time-formal, remote problems in buying and selling, for instance. The articles bought and sold, the price of the same, and the conditions under which the transactions were made were more or less exceptional or unreal. They were not such as pupils would actually have to deal with if they should engage in buying and selling most of the articles used in daily life. Again, there were problems involving the application of various tables of measurement, of weight, of money, and the special tables relating to masonry, etc.; but these problems too, as one reads them to-day, seem remote from real life. A pupil might be able to solve the masonry problems given in his book, but be quite helpless when he was presented with an actual masonry problem in the building of his father's house.

The writer has been able to see this principle illustrated in some work done by pupils to-day in schools where the old style text-books are in use, or where teachers set problems of a formal pattern. In one

such school, typical of many others in a state in the Middle West, the teacher sets most of the problems to be solved, and not ten per cent. of all those she gives her pupils have any connection with their needs outside of school. She is teaching in a prosperous farming community, and she could utilize a great many problems relating to agriculture, to the mechanics of the farm, to the cost of the production of crops, their harvesting, storage, transportation, etc.; but it has not occurred to her that such problems could be or ought to be used in the arithmetic class. In this community the pupils study percentage, taxes, and the like; but the school trustee has to employ an accountant to make out the tax roll for this district. Farmers whose sons solve type problems in cubic measure build their granaries and their cisterns by guesswork. The arithmetic instruction in the school does not reach out vitally into the practical work of the farm.

In a teachers' meeting held recently in the county in which the woman referred to teaches, the folMaking problems lowing question was proposed: "Should the problems in arithmetic be drawn from the pupil's daily life, or should they be numerical problems given them for the purpose of drilling on the fundamental operations in the ap

relate to the pupil's actual needs and experience

plication of tables?" It was significant that most of the teachers who attended that meeting had not thought of the possibility or the desirability of drawing problems from the pupils' actual experiences outside of the school. While theoretically they believed that arithmetic should be taught for the purpose of helping the child in his daily needs, still practically they taught it as though it were for the purpose of drilling him in formal processes, without employing these in useful ways in actual life. Of course, pupils who were so trained could not fail to gain something which would be of benefit to them in their practical affairs; but it is equally certain that they could get the benefit of drill, and at the same time learn to solve problems which would greatly illumine the situations in which they were placed outside of school.

The writer knows of some authors who are at work upon arithmetic text-books especially designed for country schools. These authors are drawing all their problems from the operations on the farm, and from interests that are related thereto. For instance, some of the problems relate to the average yield per acre of wheat and other grains throughout the country. This affords an opportunity for excellent drill in long division. At the same time it gives the pupil information which is

of interest to him, and which he can not get effectively in any other way. If he should sit down and learn by heart a table giving the yield per acre of wheat in the different states of the country, it would be a distasteful task for him; but when he works it out arithmetically the results become fixed in his mind, and the information he gets helps to make the process tolerable.

A concrete instance
illustrating the
vital teaching
of arithmetic

The writer has had an interesting experience illustrating the point involved here. A pupil in the seventh grade of a city school had for his lesson one day to determine the yield per acre of wheat in the different states of the country. The total acreage and the total yield in each state were given. At the outset he was angry at such a task. He thought it was simply a problem in long division, which he had already learned to dislike, because up to this particular day his problems had all been of the numerical kind. But on this occasion the boy's father went through the process with him; and as they worked they talked about the results, and commented upon the variation in productivity in the different states. This led to a consideration of why one state produces so much more than another state. The boy worked at this task for about forty minutes, which

was twice as long as he usually applied himself, and he solved all the problems. When he got through he was genuinely interested in his results, and the father asked that other problems of like character be worked out on succeedings evenings, which was done, and with uniform pleasure to the boy.

Now, note that he was profiting in at least two ways. He was receiving valuable drill in one of the fundamental processes in arithmetic, and he was acquiring information which was of interest and of distinct profit to him. The writer thinks this kind of knowledge can be better given in arithmetic than in geography, though, of course, it is in one sense geographical information. This is perhaps a fit place to remark that many of the most useful problems in arithmetic can be drawn from geography, particularly commercial geography.

For pupils who live in the city, there are all sorts of situations which permit of arithmetical Useful problems treatment, and in which the pupil for the city pupil will be genuinely interested. Take the matter of laying out streets, the selling of lots, the cost of paving, the total length of water-mains in a city, having given the average length of streets and the amount on any one street, the cost of city government, the rate of taxation for various purposes, and so on ad libitum. A teacher could easily