it can be corrected only by slowly building up a different sort of habit, which will in time replace the undesirable one.

This last point will bear elaboration. Most teachers find that their chief difficulty in the teaching of The evil of in- arithmetic to young children is to get accuracy in them to be accurate in their work on school work their own initiative. Indeed, in some schools the only trouble teachers encounter is in respect to the errors which even the brightest children make. Any observing teacher knows that young pupils do not readily detect their own errors; and this is, of course, true of them in other work than in arithmetic. When the novice executes anything, whether it be a process in arithmetic, or spelling a word, or writing a sentence, he is practically unable to go back over the detailed steps, and detect the one that is wrong. It is a trait of the child mind to view things as wholes; and once executed they must be right. This is one reason why many teachers accomplish so little when they give the following direction to their pupils: "Now look over your work, and see that it is correct." It is difficult enough for even an adult to detect errors in what he has done. The very fact that he has solved a problem in a certain way, or constructed a paragraph after a given pattern, is evidence that he thinks it is correct; and

when he goes over it he tends always to see it as correct and not as erroneous. If it is difficult for the adult to restrain the tendency to see as correct what has once been executed, how much more likely is this to be characteristic of young pupils. And how futile it must be to keep urging them to "look over your work to see that it is right."

And yet we must, to the fullest extent possible, develop in our pupils the ability to review their work Self-correction of and detect errors. They can be inaccurate work made self-helpful in eliminating mistakes from all their work, but especially from their arithmetic, by requiring them always to check every process and "prove" every problem. No solution of a problem should be accepted from a pupil until it has been checked. When a pupil goes back over his own work and discovers his error, this furnishes the greatest precaution against his making the error again. In this way he learns what his tendencies are, and he will be on his guard against them.

Then in this work of checking, pupils receive valuable drill in performing the fundamental operations, and in seeing the relations in a problem in every way they can be viewed. To know how to check a problem is just as valuable as to know how to solve it. Of course, as pupils go on into the fifth or sixth grade, there may be no need for checking when they

are working upon familiar problems; but whenever they attack new processes, it is always well to require them to "prove" their results, and never to submit a problem unless they have assured themselves by a checking test that their work is accurate.

CHAPTER V

TEACHING PUPILS TO THINK-CONCLUDED

WE may here glance at the relation which exists between clear thinking and a good memory. An Clear thinking and earnest teacher was recently oba good memory served instructing what she said was a dull class. The pupils were taking their first lessons in fractions, and they were progressing very, very slowly. Indeed, after twenty-five minutes of struggle and tension, it was not easy to discover that they had learned much, if anything, concerning the topic being taught. The teacher felt discouraged, and her state of mind was expressed in her tone of voice, her features, and even in her bodily attitudes. She was irritated over what she thought was wilful stupidity. She felt her pupils could grasp the simple relations she was trying to teach them, if only they would make an effort so to do. During the entire period she was chiding them, upbraiding them for their lack of application, and charging them with carelessness and indifference. It

was a disagreeable hour, alike for the pupils, for the teacher, and for the visitor.

One of the phrases which the teacher used most freely in the attempt to quicken the mental processes of her pupils was, "I told you that yesterday; why can't you remember it to-day?" This phrase is heard very frequently in the class-room, and it always comes readily from the tongue of almost any teacher. When one has told a pupil a fact, it would seem that he ought to retain it for a day at least. The teacher can easily retain it himself, and the pupil could do so, "if he was only in earnest about the matter". But is this sound psychology? Can a novice remember any fact as readily as one who is already familiar with it? The very question sounds absurd; and yet it is an entirely reasonable one, considering the attitude of most teachers toward a learner who forgets what has been told him. It is likely to seem so simple to the instructor that he can not easily forgive any pupil who fails to retain it when it is presented to him.

Let us take a concrete instance. A teacher is endeavoring to lead her pupils to discover what is the A concrete instance result of multiplying one-fourth of obscure teaching by one-fifth. They sit on the recitation bench while she talks about multiplying the numerators together for a new numerator, and