We are apt to be so concerned over the infinitesimal features of pedagogy (a word so discredited as happily to be going out of fashion for the time being) that we forget the real problem that we have to meet in the teaching of arithmetic. To enter into "original research" as to whether a child shall first learn 0 + 2, or shall begin with 2 + 0, for example, is much like asking if we shall take a bite of meat before we take our bite of potato at luncheon, or shall take the potato first. Some things are big enough to make experimentation valuable, but a great mass of the experimental work in the schoolroom is of questionable importance, and in so far as it tends to keep us from doing the great thing that is to be done it is bad. So it is with the parrot-like analyses of children that a few years ago were deemed of much importance; they accomplished little, and they took the attention of teachers and pupils off the real subject at hand. In the same way, the narrative problem, while of some value, failed of its purpose because it, too, obscured the vision in looking for the essential points of arithmetic teaching.

It would be possible to carry this discussion much further and to select numerous features that have, from time to time, dulled the sight in its search for the real thing in arithmetic. Much of this material has already been banished from our elementary school, although much still remains in the upper grades, particularly in the treatment of compound numbers and of the inverse cases of percentage. In the primary grades we have a much cleaner slate, the course of study followed in New York City, for example, being quite free from unnecessary and unprofitable material.

But all this is negative. It does not get down to what is the essence of the work in arithmetic. And this essence is so simple and plain that it is a wonder that we do not see it with clearer vision. For, after all, the one great thing that we need in arithmetic is to know the forty-five combinations in addition and the fortyfive in multiplication. Not one man in a thousand in New York City will today use any of arithmetic that involves anything beyond these ninety facts. If they are perfectly known, as perfectly as the common words that we read, so perfectly that we can apply them without the slightest conscious hesitancy, arithmetic will not trouble any of us in actual business life. To be sure the child must know other things in arithmetic, but everything else is of minor importance as compared with these ninety number facts. The number of people who are multiplying or dividing by a threefigure number in New York today is very small, although we must prepare the pupils for this work. But the number who need to add a column of figures quickly and with certainty is very large, and the number who need to be able to multiply mentally by a onefigure multiplier is also large, and it is exactly here that our pupils fail.

No. 4.

It may be asked if subtraction is not of equal importance, as in the making of change. But when we consider that in subtraction we merely use the addition table, and in division we use the multiplication table, it will be seen that the work all comes down to these ninety number facts, and that our pupils do not know these facts.

When Mr. Courtis applied his tests recently in New York City, what did he find to be the greatest defect? Accuracy, and accuracy depending solely on the lack of complete knowledge of these ninety number facts. And it is so with all tests, in school or outthe weakness is invariably here. Reasoning on the actual problems of life will come with maturity, but the knowledge of these ninety facts must come in the primary grades or it will never come. The brain is plastic for memorizing at this stage, and it loses this plasticity in the upper grades. Here, then, is the great essential of primary arithmetic. The teacher who passes her children on to the fifth grade with these facts known with perfect certainty has accomplished the greatest thing in early arithmetic; she must accomplish other things, but they are not to stand in the way of this great need.

The strange thing is that we have eight school years in which to accomplish this result, and we fail. Eight years in which to teach ninety facts, and general inaccuracy as a result! What is the reason for our failure? It seems to me that it is because we have not recognized the root of the difficulty, and that we have tended to count all things in a curriculum as of equal importance. We teach the combinations, and then we leave them more or less in the background except as they appear in subsequent work. The value of drill, so abundantly proved by such scientific tests as those of my colleague, Mr. J. C. Brown, and of Dr. Stone and Mr. Courtis, has been forgotten in our attempts to make arithmetic soft. The fact is, as every teacher knows, children enjoy drill exercises if not carried to the fatigue point, and enjoy them quite as much as the applied problems that we manufacture for them. And it is only by drills that foster a memory that is oral, aural, visual, tactual-to use the phraseology of the educator-that we can fix these important facts so they will not escape us. The old oral arithmetic of Colburn was extreme, but the teacher who persistently devotes five minutes of every recitation to oral arithmetic will be well repaid for her drill upon these essential facts.

It may be felt that this is very commonplace. So it is, in a way, and so it is intended to be. It is an appeal for the spirit of Pestalozzi in our teaching-the spirit of a man who made arithmetic interesting, but who never lost sight of these essential features and who believed fully in the value of drill.

1. Who found a bag of flour? (Progressive.)

2. What can we make with flour?

3. Who ate the bread?

4. Close the door. Who can do it?

5. Read a small story, as "Black Cat and Gray Cat." Who can play this story? What does Black Cat say? What did they both do? Who met them? Why did they run away?

6. Find the girl with the red dress.

7. How many boys have blue coats?

8. Mary may go home. Commands and questions using sight words may be written on the blackboard for the pupils to answer or execute without any preliminary questions.

9. Find today's new words in this set of cards. Tell them to the class.

S

at

f

8. Ear Training-Distinguishing sounds by ear. Note.-Teacher pronounces, with great distinctness, a group of words having a common element.

What sound did you hear in each of the following words:

1. Oral Composition.-Note.-At the end of the first six months of school work the children should respond to the following test. Teacher states subject of composition, which may be any one of the following list of familiar subjects: