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.

The writer has had an interesting experience illustrating the point involved here. A pupil in the A concrete instance seventh grade of a city school illustrating the had for his lesson one day to vital teaching determine the yield per acre of of arithmetic 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

When he got

was twice as long as he usually applied himself, and he solved all the problems. 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

accumulate data regarding all these matters in his own city, and have them for his pupils year after year. The gathering of the problems at the outset would involve some labor, but once collected they would be of service without modification for a considerable period. The point is that what is needed in arithmetic is to apply it to the practical situations presented in the pupil's daily life. Most of the necessary drill can be secured through the solution of such problems.

It is not intended to say that problems should all be of this character; but most of them should be. It is cause for rejoicing that the new text-books in arithmetic are eliminating the formal, remote problems, and bringing the study right to the door of the pupil, and making it interpret and illumine his environment. This kind of arithmetic will make a pupil more appreciative of what is going on around him than he would be without it. He can be led to think of the amount of rainfall in his region in precise terms, the amount of energy generated by a ton of coal, the average growth of plants per day, the relative amount of heat energy expended by the sun at different seasons, and so on at any length. If arithmetic could be generally treated in this way, it would become of far greater interest and greater dignity than it has been in the past, and than it now

is in many communities where the traditional attitude toward it is maintained.

accurate think

We may look now for a moment at inaccurate thinking in this field. Many of the errors in arithThe cure for in- metic made by pupils after the fourth grade are due to their ining in this field ability correctly to interpret the relations expressed in problems. When a teacher finds pupils inaccurate in this way it will do no good for her to say, "Now, be more careful next time," or, "If you do not pay closer attention, I will keep you after school", or, "I will put you back in a lower grade", and the like. Pupils who have not formed habits of accuracy can not correct their inaccuracy by simply saying to themselves, "Now, I must not make any errors." It is an easy thing for us to assume that a pupil can on his own initiative eliminate errors from his work, if he only wills so to do; but experience should teach us that no good comes from threatening or exhorting pupils who have developed inaccurate methods of work. The efficient teacher will analyze the situation before her, seeking to discover the cause of a pupil's errors; and then she will set about developing new habits. For after all, inaccuracy is a habit of mind which is the result of a relatively long process of doing a thing in a certain way. This habit can not be broken up in an instant;