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be systematic in the teacher's mind and follow a plan. It should begin with the observation and retracing of the reading-lesson, and end with free production in other subjects. Each subject furnishes a special opportunity. Arithmetic and place-lessons furnish good opportunity for description ; stories for narration; general lessons for logical exposition, i. e., an enumeration of classes, kinds, forms, etc. The oral forms should precede written, and imitative reproduction precede free production.

PRIMARY READING.

DESPITE progress, primary reading continues to be the worst taught of primary subjects. Why? Because teachers are lacking in definite aim. They have gathered up an apron full of devices and gone to the school-room expecting success to come from applying these one after another without any system. But success lingers and they wonder why their pet “methods" do not succeed. The reason is not far away. They have no good general plan. They have begun building before they have decided whether the outcome shall be a garden-wall, a cow-house, or a front-porch. What then should be the aim of the teacher of primary reading? First, to awaken interest and keep it awake; second, to have a variety that will prevent the pupil from tiring of any one thing before another is introduced; third, sufficient repetition to insure the imprint of words and sentences beyond forgetfulness; and fourth, a proper connection between reading and the other work of the school-number, place, general lessons, etc.

The idea must be learned before the word, if it is not already familiar. A good First Reader is made up of ideas and oral words already well-known.

The problem, then, is the learning, in the shortest and best way, of the written word and its association with idea and spoken word. The first thing to be done is to get the child to look at the word carefully, to see all its parts and to compare it with other words before his eyes. Thus if the word being learned is chair, it should be compared with air, chain, hair, etc., nearly like it in form. The test for the completeness of this step is the ability to distinguish chair by the eye with great quickness, when mixed up with other forms. By one device or another the eye must be kept busy with it until this end is reached. The next thing in order is to impress the word on the memory by impressing it further on the eye, ear, understanding, etc. The means of doing this are comparison and contrast of form and meaning, speaking and writing, and other forms of building up and tearing down the word. The test is the ability to remember it quickly and readily, and of course to recognize and write it. The last part of the work is the use of the word with other words of the reading lesson. These must be recognized singly before they are to be attempted together. The, dog, is, and black, must be learned before The dog is black. Connected words also need drill.

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ARE "TIMES" AND "CONTAINED TIMES

LOGICALLY CORRECT.

In such expressions as “3 times 4 are (or equal) 12” and “4 is contained 3 times in 12," two questions have been raised; First. Are times and contained times correct? Second. Whether correct or not, should we supplant them by others more easily understood, especially by primary children ? Certain critics and progressionists impeach the logical correctness of the expressions. There are two different sects of these reformers of arithmetical nomenclature. Each looks at the language of number through a lens of its own make. The first would say “3 fours are 12,” “there are 3 fours in 12,” or “12 may be divided into 3 parts or groups of 4 each,” etc. This is not new until such expressions as “ 3 four dollars are 12 dollars” is reached. This means that three numbers of the value of four units each equal one number of 12 units, or it means that the number 12 (a complex unit) may be considered as made up of 3 parts, each of which has the numerical value of 4 units. That these fours are dollars has nothing to do with the relations between the 4's and 12. Number is a relation of ideas and objects entirely independent of and distinct from other qualities and relations. For the reason that, in considering number, we do not, at any time, consider the

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other attributes of objects, and sometimes ignore them entirely, some numbers are called abstract, and, indeed, it is held by some that all number is abstract.

When we say

4 horses," we are utterly indifferent to any attribute, except numerical relation. They may be 4 toy horses worth 5 cents a piece, or they may be four Maud S's worth $20,000 a piece. What then is gained by discarding times and contained times? .4 times 3 ” means the application of the idea three to some larger conception 4 times in succession, the relation being that of whole and part. If these ideas are pictured (they may or may not be pictured definitely) there will of course be other qualities connected with numerical relation. This gives rise to the claim of other mathematicians that all number is concrete. Numbers are originally formed in the mind by constructing a series of ones, twos, threes, fours, etc. Thus the mind can not put 7 and 5 together and make 12, without first putting 1 and 1 and 1 and 1 and 1 to 7 and getting 8, 9, 10, 11 and 12 respectively. So before the child can find 6 twos in 12, he must have made 12 up of twos; the same is true of threes, fours, sixes, etc. This fact is at the bottom of the use of times and contained times. Number, as has been pointed out in this department before, must pass through four stages: (1) Numbered objects (particular present things); (2) concrete ideas of particular things (things themselves absent); (3) abstract ideas of particular things (no definite pictures of definite objects); (4) dealing with symbols (letters, words, figures) without any conscious use of their ideas.

The objection 10 times arises in the first two of these stages. If we picture "3 times 4 are 12,"

0000, we are told that we can not find the times, but that the child readily finds four or a group. Each one of the “groups” is one time the application of the idea four. The child can not go into any of this explanation, but he can see that one of the series above is a time as readily as he can see it a four or a group.

The other sect of nomenclaturists substitute of for times and contained times. They would say "3 of 4 are 12," meaning " 3 times 4 are 12," or would say “4 of 12 are 3,” meaning "4 is contained 3 times in 12."

times in 12.” Of means group of each. There are

0000

0000

serious objections to a new language unless there is real need for it. From anything we have been able to see, neither of the new sets of expressions is able to show any good reason for its exist

Besides, these new expressions emphasize the wrong side of number-teaching. The failure has not been greater to have these expressions 'understood than any of the others of arithmetic-children have not understood any of them.

ence.

S. S. P.

PRIMARY DEPARTMENT.

(This Department is conducted by HOWARD Saxdison, Professor of Methods in the

State Normal School.]

SPELLING-FIRST GRADE.

F

JOR two months the child is occupied in learning words as wholes, and in this time he should not be called upon to

separate words into parts, i. e., to name the letters which compose them. He should, however, be ready at any time to write the name of an object, when the object is presented. (The word having been taught, of course.)

At the beginning of the third month go back to the first word presented and teach the names of the letters. Supposing the first word to have been cat, when c, a and t are learned, bat is easily learned, for a and t are old friends, and b alone is new. The same is true of mat, rat, hat. This fact is a strong argument in favor of teaching words in groups.

The child should be able to write every word he knows. If he can read from the board "See my red ball," he should be able to write the sentence from dictation. It follows, therefore, that the spelling lesson proper should be written. The preparation for this lesson may be the copying of words or sentences from the board. Then, having had all work erased from board and slates, dictate short sentences. Examine each slate carefully, correcting all mistakes in capitalization and punctuation. This exercise, if continued daily for six months, will produce valuable results.

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SECOND GRADE.

ous.

Two new words may be learned each day by second grade pupils, and the teacher should take good care in dictating sentences, to review each day the words learned on the day previ

Two new words may seem a small number, but at that rate the pupil will learn four hundred in the course of the year. Each word learned should be learned thoroughly. The pupil should know its written and printed forms, and should be able to use it correctly in a sentence, with proper capitals and punctuation marks.

After the preparation for the lesson, work should be erased from slate and board, and sentences formed by the teacher or pupils should be written on the slates. The slates should be examined daily with care, that no bad habits of penmanship be allowed to strengthen.

FANNIE S. BURT.

NUMBER WORK-THIRD YEAR.

The work in the Third Year should be concrete to a consid. erable degree. Among the materials which will assist in making the work concrete may be mentioned :

One hundred one-inch wooden cubes, which may be obtained from any carpenter for twenty or twenty-five cents; a box of educational toy money, price twenty-five cents; a box of wooden splints, which cost five cents for twenty-five hundred, or a box; a box of elastic bands; a quire of printer's paper cut into two or fourinch squares will last one or two terms and will cost twenty cents.

Toy money and splints are valuable in teaching the three kinds of ones necessary to be known in this grade, i. e., a one one or a unit; ten ones, or one ten, ten tens, or one hundred. By view. ing one cent as representing one one; a dime, or ten cents, as representing one ten; one dollar, or ten ten-cents as one hundred, the work, will become simple and interesting, hence easily comprehended. Splints are valuable because they furnish means for individual work.

Illustration : (On the table are a box of elastic bands and a pile of splints for each child.)

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