his analysis because he stumbles and halts, and can not choose the right terms when he attempts to go through with the form given him by the teacher. He can explain in his own way so that it will be clear to any one; but his mind seems to resist the particular formula which the teacher wants him to use. He can work very rapidly through any problem presented to him, and he is quite accurate; but his teacher thinks the matter of supreme importance is that he should follow her form in explaining what he does. She attaches more importance to his analysis according to the formal pattern in use, than to his being able to reach the right results rapidly and without error.

Analysis has its place when the pupil is beginning to solve anything which brings in new relations or new processes, but it is of value only because it requires him to grasp these relations in the right way. The moment he can do this he ought to abandon his analysis, and cultivate speed and facility. He ought not to be at all conscious of any formula; and if he be kept upon analysis it will simply hinder him in his development. That pupil who can eliminate the greatest amount in his arithmetical work, provided he reaches the right results, is the one who has gained most from his training. What we must strive after in our arithmetical work are accuracy

and speed, with all unnecessary processes eliminated. If a child can regularly solve a problem involving any sort of arithmetical relations he should not be asked to analyze it; the fact that he can solve it is sufficient evidence that he has grasped those relations. Much less should he be required to analyze according to a special form of which the teacher approves. We are coming to appreciate in education that there is no value in doing things in a formal, elaborate way just for the sake of being complete and explicit. We must eliminate every place we can; and in no work is this more essential than in arithmetic.

CHAPTER VIII

TEACHING THE ARTS OF COMMUNICATION

OBSERVE a child six months old when he is just beginning to make connections between words and

How the child gets at the meaning of words

the things or experiences they symbolize. If you notice carefully you will see that in the beginning he gets his cue as to meaning from the facial and bodily expression of the one who is speaking, and also from the tone and timbre of the voice. Words at first denote emotional states to the child; and emotions can be deciphered by means of the vocal and bodily expressions of the speaker more easily and accurately than by means of pure symbols. This is probably true in the case of adults, as it certainly is true in respect to the child, and to some animals, as the dog and the horse. But, unlike the dog and the horse, the child, if he develops normally, can associate words as formal, conventional symbols with definite objects and phenomena and abstractions.

The first thing that strikes one as he studies the babe getting at our meanings for verbal symbols is the latter's lack of precise discrimination as to what is denoted by the words we employ. Let us suppose he is looking out of the window, apparently at the sky, and I say, “sky, sky", and I point at the object, look up at it, and try to get him to look where I do. This is the way people usually proceed with the babe; and they do this because they think he will connect the things he sees with what he hears, and will thus bind together the word and the object designated. This seems to be good logic; but the trouble is with the premises. It is assumed that the child sees what the speaker does; and this assumption amounts ordinarily to a stupendous error. The child does not differentiate the sky proper, as I regard it, from everything else within the range of his vision. If there are clouds in view, these are included; if there be smoke floating in the air, this may occupy a more important place in his attention than the ethereal blue I wish him to direct his vision upon. If there be a tree or a house in the picture, the chances are that these will stand out much more distinctly than the sky.

When I ask him next day, "Where is the sky?" and he points to the chimney of the house opposite, I

The chief distinction between the child and the adult in attending

to objects or situations

am amazed, since I took so great pains to teach him the sky as distinct from other things. He must be stupid. From the standpoint of the adult's ability to differentiate in attention specific objects or qualities from a general whole, the babe is stupid, for he can not do it. If he could do this he would be mature; for really that is the chief characteristic of maturity as distinguished from immaturity. The principle applies to some extent, of course, to the five- and tenand fifteen-year-old, as compared with the fully matured adult.

How often one sees a teacher directing a child's attention to a new situation, pointing out some special phase of it which she appreciates, the while expecting the novice to see it as she does. Then the next day, when the learner shows that he is confused, that he did not make the discrimination expected of him, the teacher may be impatient, and she may hold up the unfortunate pupil before the school as a dunce or a goose. The chief error in most of our teaching is that we do not skilfully isolate just the thing we want attended to, and then employ such effective methods that the learner's attention can not go astray. It is a simple psychological law that attention always tends to follow the lines of least