NUMBER AS OBJECT AND IDEA.

IN E. E. White's excellent article on "Numbers and their Expression," in the March number of the Journal, he attacks the fundamental error in teaching primary number, viz., failure to distinguish between expression and thing expressed. There is another distinction equally important, namely, that between idea and object. Except in the use of numbered objects, in the first stage of primary number, or in the use of illustrations, we deal with our ideas of objects, and not with the objects themselves. Ideas then are our "numbers." It is this fact which is at the bottom of the claim of some mathematicians that all number is abstract-an abstraction from objects themselves. Take Prof. White's definition of a fraction and that of decimal fraction: "A fraction is one or more of the equal parts of a unit; and a decimal fraction is one or more of the decimal parts of a unit." Mathematically there is no such thing as the division of an objectunit into equal parts, any more than there is a perfect material sphere. We can form the idea equal parts, as we can form the idea perfect sphere, but we can not realize either. But what of it? Much. If we are dealing with ideas in all number-teaching, an understanding of the kinds of ideas and how they are formed will relieve us of the necessity of doing the work hap-hazzard. The kinds are:

I.

Numbered objects (sense-perception).

2. Pictured ideas of individual objects (imagination).

3. Abstract numbers-unpictured, (product of generalizing faculty).

4. Symbols (sense and memory).

The first, second and fourth are concrete; the third, "abstract." The mind learns numbers in the order named. First it deals with numbered objects. The child should be kept upon these until it can readily illustrate any number or process. Numbered objects should then be dropped. Next, the mind deals with pictured ideas of objects. The test of work needed is ability to handle them readily. When the pupil can deal easily with fifteen houses, horses, etc., he is ready to be put at unpictured fifteen, or as Prof. White would say, the fifteenness of the number. But,

finally, the mind discards this and deals with the symbol "15." It does not trouble itself in ordinary computation to go through the process of thinking fifteen. If a skilled accountant sees "" and "8", he thinks the character "15". This is a simple act of automatic memory.

ONE of the best thinkers on educational subjects in the country says with reference to the question as to whether or not the mind is an organism: "Am glad to read your protest against the mind an organism. An organism is of course higher than an inorganic [body]; but it is not the ne plus ultra. Mind is higher than an organism. * * * Death belongs to all organisms."

HON. Leroy D. Brown, of Ohio, as chairman of a committee appointed to consider the terminology of schools and schoolwork, presented a report at the Washington meeting of superintendents, February, in favor of the naming "Primary School", "Intermediate School", and "High School", instead of the present naming, "Primary School", "Grammar School" and "High School", employed in many places. The committee advises that all blanks, reports and school-names should be made to conform as rapidly as possible to the new naming. Schoolofficers are everywhere requested to coöperate in making the change of name. The nomenclature "Primary School", "Grammar School" and "High School" is both misleading and incorrect. A uniformity of terms is desirable, along with a naming that will state the facts. The committee considered the possibility of changing "High School" to some term less objectionable, but decided that it is too firmly rooted in use. The desire for sets of names that are logical and uniform is a hopeful sign and deserves encouragement. We hope the report of this com

mittee will receive the attention it deserves from Indiana schoolofficers.

BACKING one's cart to mill is neither a very graceful nor a very profitable mode of taking grain to the hopper, and yet this is exactly what teaching formulas in arithmetic means. It is putting

the cart before the horse. The formula is properly the last thing to be made, not bolted, by memory, whole. Thousands of schools, however, reverse the operation and put the formula, which expresses a process, first, and like the makers of the "Old BlueBack" spelling book, trust to Providence to supply the ideas that should precede and underlie the formula. There is a fatal facility acquired by children for the mere time of instruction, which is made the justification of those teachers who teach formulas. They take refuge behind that mothers' apron of shallowness, from the accusers of Socrates to the present, and say that teaching formulas is the "only practical" or the "most practical" method. To come to the point so that it will not be misunderstood: the formula Multiplicand+ Multiplier Product or any other should be made when the pupil thoroughly understands and can perform all phases of the process--if he should have it at all. The practice of furnishing cases, explanations, definitions, etc., ready-made, needs only to be understood to be condemned.

=

"How cultivate the memory?" has long been a stock question at institutes and teachers' meetings. Is it not about time to retire it with that other venerable old chestnut, "How to prevent whispering." The memory doesn't need cultivation. It will take care of itself. If the subject is thoroughly taught it will be remembered. Drill, everlasting drill, on a few knick-knacks of a subject may fix them in the verbal (local) memory, but what of it? How much is such knowledge really worth? Drill is a poor pony, ridden to death. That which has to be rubbed in, by sheer repetition of verbal forms is more useless, so far as any real effect on our lives, actions, and character is concerned, than so much old junk to one who is not a junk-dealer. We need to master the subjects well for ourselves and then study how to have the pupil master it for himself. This done, all that is needed will

be remembered.

ONE of the straws at the recent superintendents' convention, at Washington, was the unanimity with which that body seconded a suggestion, by Hon. M. A. Newell, of Maryland, that normal

schools should establish a department for the training of superintendents. Come to think of it, what is more patent! If the training of the subordinate who deals with forty childrea is important, how much more so is that of the superintendent who directs not only that teacher, but perhaps scores or hundreds of others! Hitherto it has been assumed that the wisdom stored in superintendents' heads was God-given and did not need training, while that under the teacher's hat-band was of the earth earthy and hence needs normal schools, institutes, reading circles, etc., to train it for its work. If a teacher needs professional training, why not a superintendent? Or, shall we go back to that good oldfashioned argument that so long made academic scholarship the only training required of the teacher, viz., that experience is the only school to make superintendents. We need not get confused on this question. The art of superintendence is learned by experience. But there may be instruction in that knowing which precedes doing.

Superintendents have themselves made good progress to be able, in so representative a body, to see that special instruction is needed for their duties, and that superintendents' sense is acquired in the same way as teachers' sense.

THE SCHOOL ROOM.

[This Department is conducted by Gво. F. BASS, Supervising Prin. Indianapolis schools.]

T

HIS is an old maxim. It is much talked about in iustitutes

and other teachers' meetings. It is often written about in It is sometimes used in school with very

school papers.

small pupils who are just beginning to learn to read.

Institute instructors generally take the picture of a cat (and say that the real cat would be better) and show how they would get the pupils to become possessors of the idea cat. After this is done, they say they are ready to show the printed word cat.

This, when well done, makes an admirable lesson in the institute and in the school. Sometimes, however, in the school

some little embryo senator sees the point too soon and says, "I can spell cat, c-a-t. I can write it on the board, too; papa told me how." This spoils the plan. The senator is told in a very stern manner to take his seat and keep still. Lesson No. I in squelching. Nothing like this ever happens in an institute. But the question we are getting ready to ask is, Why do tcachers who believe, preach and teach "ideas before words" have, or allow pupils to learn the definition of subject, predicate, phrase, etc., before they know the thing when they see it; before they know any of its general characteristics? Why do they! Why not bring in the subject as they do the cat? Why not examine it as closely as they do the cat? Why can not the pupils be led to see that the word used as subject names or denotes an object? Also, that it denotes the object about which an assertion is made? To decide whether a word does this he must use his common (cat) sense. This then will assist in training him up in the way he should go, and when he gets old he will be able to go it.

Please remember the cat work in all the work you do. Stick to the old maxim until the words and ideas have been associated with each other so often that either one suggests the other. In case a boy gets ahead of your nice little plan "take your hat off to him" and thank him.

LANGUAGE LESSONS.

(FOR SECOND READER PUPILS.)

THE SENTENCE.-A child who is able to take up the Second Reader knows many sentences, both oral and printed. He may not know that they are called sentences. He probably could not tell what a sentence is, but he can use one to tell what he thinks. He can ask more questions than any philosopher can answer. He knows the difference between a question and an answer; between a command and an exclamation, when he hears them; but he is not familiar with the written form. He can express his thoughts with the vocal organs, but not with the pen. We give him language lessons that he may learn to express himself as readily with the pen as with his tongue.