and the placing together of these common characteristics to form the general idea. Moreover, not the teacher but the pupils must do it. The question arises, "How?" Certainly not by an elaborate formal process. This is just the error found in many lessons; the pupils are made to lay bare the mental process by which they arrive at the general idea, and that is exactly the thing they cannot do. It leads to the often-heard remark, "I can do it for you but I cannot tell you how." There are two ways for them to show that they have made the generalization: One is to express the general truth in words; the other is to use it. Unfortunately, the common practice of teachers of mathematics is to insist too soon and too much upon the first way. They present particular cases of some general idea thoroughly and then ask for "the rule", as evidence that the pupils have grasped the idea. The expression of the idea in words is, as a matter of fact, difficult for children. As opposed to this plan, there is the preferable alternative of permitting the pupils to show their grasp of the idea by using it. McLellan and Dewey have expressed this thought well in their "Psychology of Number" in the words, "The natural psychological law in all cases is first the use of a process in a rational way, and then, after it has become familiar, abstract recognition of it." This quotation should be placed by every teacher of elementary and secondary mathematics, where it will be a constant reminder and guide in his or her work.

Formulation. In order to emphasize still further the thought contained in the latter part of the preceding paragraph, it seems wise to consider the expression of the general truth in words or symbols a separate stage of the lesson. After the idea is familiar, it should by all means be given some brief expression as an additional means of fixing it upon the minds of the pupils. The pupils should be encouraged to express this rule or relation themselves; when some definite form of expression is desired, the pupils should be led to the point where, if possible, they can give it. Aside from the educational value of such training, the opportunity of arousing interest in this way is great.

Application. There remains now for the teacher only the task of fixing the idea in the minds of her pupils. This is the drill stage of

the lesson, where, by repeated use, the idea is made increasingly clear. Here it is important to remember that an abundance of carefully graded, simple exercises are more effective for drill purposes than a few relatively more complex exercises. There is no implication that no new thoughts will be introduced in the application stage. Quite the contrary. Since it is wise to limit the first instruction on any new idea to the first essentials of it, the fine points should be given during the application stage, if at all.

Summary. The five stages of the lesson will now be repeated.

1. Preparation of the minds of the pupils for the new idea. Make it brief.

It is one of the special advantages of mathematics that it lends itself to this mode of instruction. The truths of mathematics are separable into simple portions, each of which can be presented through easy steps which are within the comprehension of the pupils and from which they can generalize. The pupils delight in such work, and rarely complain then that they do not see what the teacher means. It is worth mentioning that some of the criticisms of mathematics made in the past have proceeded on the assumption that it is taught deductively rather than as outlined here; hence the statement that mathematics has small educational value as it does not give training in weighing and balancing situations and in generalizing. The fault is not in the mathematics but rather in the manner in which it is taught. Elementary mathematics should be taught inductively for every sound pedagogical reason that can be advanced, and being so taught, is not subject to some of the criticisms made of it in the past, to which great weight has been attached. More

2. If you haven't attained that degree of success to which you seem to be entitled, go to meet those who may be able to enlighten you as to wherein lies your deficiency.

3. If you are successful in dealing with a certain problem, go, take part in the discussions and give others the benefit of your experience. Go to get inspiration that will make you want to keep on trying to make a success of your work.

6. Go, keep up with the progress of the profession or you will eventually lose out.

7. One ought to be an enthusiast over the profession of education first and then over her particular phase of it, be she a primary teacher or a university president.

Why Children Liked Their Teacher
She could stand some fun.
She had no "pets."

The children feel as if she was one of them.

The principal reason I liked her was because she liked me and showed it once in a while.

If you did not get your lessons, she Was SO sorry that it made you ashamed.

She took a great deal of interest in us.
Put us on our honor.

She never punished the pupils because she didn't feel good.

Never flew off the handle.

Does not scold us one time, and then be awful good for a while.

Always meant what she said.

She made things pleasant, so I felt like working.-Selected.

Suggestions

I. If you haven't already done so read in the June number of this Journal "Art in the Public Schools of Madison" by Harriet F. Estabrook O'Shea and "The Ideal Kindergartner in her Relation to Children" by Ruth Waterman Norton. The former contains some practical suggestions that may be made use of in any community. The latter is well worth reading. If you favor kindergarten work, read it. If you do not favor it, read it. If you are a kindergartner, read it.

II. Familiarize yourself with the "World's Chronicle." (358 Dearborn St., Chicago.) It is just the paper for the busy teacher. It is an inexpensive record of what our nation is doing and what is going on abroad. It contains material for all grades. It will help you with your work in civics and ethics.

III. Have you arranged your permanent program and placed it where your pupils can see it? This is the second month of school, you know.

IV. Have you found out some good things about the boys and girls in your school? This is a good time to report it to fond fathers and mothers. They will approve of it and incidentally perhaps "approve" of you.

V. Spare a little time from reading, writing and arithmetic to be an inspiration to your pupils in good morals, and habits of health.

VI. We hear much about dramatization in the first three grades. Why not more of it in the upper grades? What possibilities in history, geography, and literature! The Journal would like to hear from anyone who has experimented with this work.

VII. Are you teaching "ugh" and "thugh” and "tugh" for "a" and "the" and "to"? Stop it. (Read P. 349, American Journal of Education for May, 1911.)

1. Do you think I ought to keep written "plans"? Yes. You will be sure to plan your work more carefully if you get into the habit of making written notes. Your notebook will be helpful also as a record of work done,

2. To what extent should spelling and penmanship control the marks given a pupil, in g ography, for instance?

A geography examination should be a measure of geographical knowledge only.

3. Why is less emphasis being placed upon teaching the effects of narcotics than formerly?

The "effects" appear too far in the future to have much effect upon the average pupil. The primary purpose in all phases of work in physiology should be to lead pupils to a practical knowledge of the laws of health including hygiene, foods, and first aid to the injured, 4. How may I best teach "distance"?

Give considerable practical experience with ruler and tape. Estimate distances and correct by actual measurement.

5. If I begin the teaching of reading by the sentence method, how long is it advisable to use it exclusively?

As a rule teachers cannot carry the sentence method to advantage longer than six weeks, then supplement it by the word method, In another six weeks rely to quite an extent for the recognition of new words upon some simple plan in phonics. While doing analytic work, however, keep the interest mainly on the thought.

6. What bulbs are best for me to put out this fall? Try daffodill, crocus, hyacinth, and snowdrop. Set out this month and you will have the blossoms before school is out in the spring.