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profitably be made use of here by comparing with types selected. The seeds selected as types should be those easily obtained and readily studied by the children, and that present the least complexity to the young mind. The Norway spruce has been selected rather than the pine because its seeds germinate more readily than those of the latter. If, however, the pires are preferred, it must be borne in mind that their cones do not mature till the second aut mn, whereas those of the spruce come to their maturity in one

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The seeds of the spruce are very much like the maple seeds in shape, but grow in a different way. They are placed inside the scales, two in each scale. After the seeds have fallen out they leave a slight hollow which shows just what shape they were. (1) The seed has a wing which covers the seed on one side and on the other it is uncovered. (2)

I split the seed in two and saw the embryo inside (3), and then took the embryo out and put them both under the microscope and I could see the cotyledons quite plainly. (4)

It was about four weeks before any of the spruce seeds were dug up, and when they were, one had the seed on, but it was just ready to fall off. I pulled the seed off and found a milky fluid which the cotyledons feed on. This looked like the fifth drawing.

Another seed had not come off but it was further along than the other, I could see little lines which were the cotyledons. This is shown in the sixth drawing.

The seventh is another of the seeds that was dug up, the ser d had come off because the six cotyledons had eaten up all the food that was in the seed.

The last drawing is the spruce with three cotyledons and it has grown faster than any of the other seeds.

When a plant has more than two cotyledors it is called polycotyledonus, so the spruce is a poly-cotyledonus plant. SALLY P. FLETCHER.

Pleasant St. School,

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After being in the pot about three days, we took one up and were surprised to find a slender root and the beginning of a tiny green sprout.

About a week later, we took up another seed finding that it had grown a great deal.

Four or five roots came from one end of the seed, and from the other came one cotyledon from the top of which grew a slender blade, resembling a blade of grass. We found that the sunflower and oats differed in the number of their cotyledons, the former having two and the latter only one.

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in water till they were swollen, then we took them out and took the shell off of them and took out the seed which we opened and we found the little thing out of which the plant grew.

WILLIAM MITCHELL.

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Grade VI.

How Plants Grow.

The cone (1) of a spruce tree as drawn is brown and scaly. But when they are on the trees they are green. I took a cone and broke off a scale like number two and it had two kinds of hollows in it the shape of the drawing in number three. It had also a little spike-like thing which kept it on the cone.

After looking at the scales, I took the cone and picked from under one of the scales the two little things like number three, and saw that they held the seeds and scattered them.

Then I took a seed which was opened, and found a little stamen looking thing which is called embryo and the white around it is called the albumen.

I saw from under the microscope the embryo had little cracks in it, which after the embryo make cotyledons.

We took up a seed which was one of some that had been about

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TH

MRS. A. A. KNIGHT, Pittsfield. Mass.

dren,- age 12 to 14— were encouraged to prepare cards at home in various inexpensive fashions.

The principal obtained from the school-supplies a large board six feet by three feet. This was covered with flooring paper of a

HE study of tree forms and habits, now taken up as nature work in many grammar schools, is a distinct prelude of botany drill two years later. No people better appreciate this helpful addition to the grammar school programme, than do the teachers of high school botany. No teachers can so see the significance of this movement to nature study, as those who are limited to one term botany in the high school course, and yet are obliged during the short spring term of twelve weeks, to make a class reasonably familiar with structural forms, and go a little into the physiology of plants. For purposes of illustration of what is now done by persistence and by the careful use of odd moments, some work of a grammar school in Pittsfield, Mass., is here displayed. It represents a part of what was achieved in about five weeks. The elm and tulip trees were studied, the elm chiefly. Five or ten minutes was all the time ever available for this pursuit in any one day. The work was taken up directly after calisthenics, or as a brief recess between classes, and although the principal's room is large and extremely well filled, the subject was carried forward informally, and was a really delightful change from the necessarily more mechanical orders of the usual studies.

Very little money could be had for this nature study. The chil

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of card board boxes ten and one half by twelve inches bearing their specimens mounted by means of adhesive slips. Of these four cards, one was the colored back of a box cover, with a mat of manila paper. Another presented the inside of a box cover, without a mat, and with the rims of the cover left as a frame. The writer mentions these matters to show how simple may be the means of producing a choice effect. One had its bits of wood specimens grouped around a pretty water color sketch of the elm.

The centre-piece-a miniature tree, with surface and deep roots -was mounted upon plain white cardboard, twenty-two by twentyseven inches, with a one and one-half inch margin outlined in ink. One mount was itself a cross section of elm, of nine inches diameter. On this were rather artistically grouped two dead leaves and eleven specimens illustrating cross and lengthwise sections, outside bark, order of branching, etc.

All this was done in this school with a sharp eye to economy, and with a very slight outlay, the cheapest means of accomplishing results being always preferred.

As has been said, no one knows better than the high schoo teacher what an impulse systematic nature study in grammar schools will give to the botany work of the near future.

were called upon to help in this direction; dirt was begged, bought, everything but stolen.

You would think so simple a thing as planting a seed - any child would be able to do that, yet one little girl put her seeds in the very bottom of the pot and all the dirt on top of them.

The varied experiences of these plants would fill a book, some only spread forth their tender leaves to be the prey of sparrows and cats, others were unfeelingly uprooted by baby brothers and sisters, the young lives of others were prematurely ended by being blown from fire-escapes and window-sills. One child in her great care that the water should not be too cold went to the other extreme got it too hot and scalded the poor plant.

On the last day of June all the plants were brought in and prizes awarded. It was a happy day for all, the plants seemed to enjoy it as much as the children; nasturtiums, sweet alyssum, calendulas, mignonette, morning-glories all in blossom, sweet peas with their curling tendrils, and towering above all, two strong plants of Indian

corn.

Thirty-six girls entered the contest, twenty-six were successful in a greater or less degree. One girl had four pots of thrifty plants, many had two and three. When you consider that the majority of them were raised on window-sills and fire-escapes, and by little girls from ten to twelve who had never planted a seed or tended a plant before, the results were very gratifying.

In "Mosses From An Old Manse" Hawthorne speaks of "the pleasure of planting a seed and nursing it from infancy to maturity" he says, "each individual plant becomes an object of separate interest." Girls especially make good florists because of that strong mother instinct which must always have something to nurse and tend; and the love of flowers is just as strong in the children of the great and crowded city as in their country cousins.

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Happy Contentment.

WR

Grace Carpenter

Nature Work in N. Y. City.

Amateur Florists.

By IDELETTE CARPENTER.

WOULD you imagine that these were prize plants raised for a flower show? The competitors in this show were not skilled florists raising rare and wonderful varieties of roses or orchids to be exhibited in Madison Square Garden: but Puplic School girls who were amateurs truly.

All the plants in this show were raised from seed and grew amid great difficulties. The seeds were planted on Good Friday the 31st of March. As most of the girls lived in flats, tenements or houses where the yards are flagged, to get dirt was no small piece of work. The value of good soil as one of the means of success had been so impressed upon their minds, that parents, friends and neighbors

Editor POPULAR EDUCATOR:

Sunnyview, Or.

Find enclosed 20 cents for the first two copies of your paper. I did not desire a renewal, and someone brought me the two copies from the post office, whereupon I sent you a card asking for a discontinuance of the POPULAR EDUCATOR.

I don't care to read of your little quarrels with other writers and editors, nor of so many new-fangled marches and drills, and other "helps" which teachers, when they read them, think they must use, or they are behind times. Thus many school journals and editors are overstimulating, or rather over-feeding teachers.

One chief cause of failure on the part of many educational system is their trying to do too much.

I hope this hastily written note will not offend you, gentlemen, but start you thinking anew on this line. Hundreds of our teachers, who are led along by their noses, are stuffing themselves and their pupils, and mental dyspepsia is the inevitable outcome. The paper has its merits and I shall not enumerate them, but I feel it my duty to point out a few things that might be bettered. As a rule people are too modest to tell another of his faults, but too free in exaggerating them behind his back.

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Nature Drawing.

Hints for Grammar Grade Teachers.

By A. B C.

HE subject of drawing as it is studied now in the public schools is divided into three heads, geometrical, decorative and pictorial drawing.

Just how much time to give to each of these divisions is now an important question in the minds of those specially interested in the subject.

A great deal depends upon the needs and circumstances of different classes and different places. What would be good for one place may not be needed in another.

The pictorial part of the work is often found to be the last subject to be studied in a course prepared by special instructors.

This, it seems, is hardly right, for if we say that "drawing is a language" and should be used in every possible case as a second means of expression, then should we not do everything we can to help the pupil in seeing and expressing his idea in the most comprehensive way.

To a child an oblong may be his picture of a cylinder, but he soon realizes that No. 2, means more than No. 1. If this is so, why spend so much time the first of the year (in grammar grades) upon the facts of form?

Why not take the two together? The child must know the facts first, but it is often found that his thoughts have been kept so long on these, that when the appearance is taken up it is very hard to get him to see and draw an object correctly as it appears.

To lead a child to draw what he sees and not what he knows is one of the hardest steps in the whole subject of drawing.

This is noticed now more than ever as so much drawing is done in illustrating the different nature studies, as botany, geology, zoology, etc., where the child has to sketch right from the speci

mens.

The pupils seem to prefer to draw a leaf as though it were pressed (No. 3.), instead of studying it carefully, getting its varied curves, (No. 4.)

It is a familiar sight to see a child try to flatten a specimen in botany given him to draw.

Realizing the difficulty existing, an experiment was tried the

first of the school year which was very successful, and which could even now be an assistance to many.

Simple dried autumn leaves, just as they had fallen on the ground, were used for specimens in the drawing lesson.

The pupils enjoyed studying them, trying to get into their drawing the dried, withered character of the leaf.

We started first with a simple e'm leaf which had folded upon the mid-rib, (No 5.) Then we tried apple (No. 6), pear (No. 7), and chestnut (No. 8).

It was not long before the pupils were brave enough to try an oak (No. 9), and maple (No. 10', starting first with simple speci

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We had not gone far with this work before I realized that we were getting more than was anticipated. The pupils not only enjoyed the work but derived a great deal of good from studying the simple and beautiful curves found in " a common brown leaf."

From these leaves we gathered many helpful thoughts for every day life, for we could not but help notice what beautiful shapes they had taken before bidding us good-bye, forever.

After the leaf work we started on model drawing, and it was then that we realized what a help the work before had been in opening the eyes of the pupils.

ARITHMETIC.

Misconceptions in Number Teaching.

By J. A. MCLELLAN, LL.D., Author of " Applied Psychology."

N view of the conflicting opinions which have been recently advanced in the POPULAR EDUCATOR by different writers, the following remarks may not be out of place.

1. A number is not a thing, any more than the perception of color is a thing. It is due to the mind in action—that is, to the separating and combining analysis and synthesis (activity of the mind.) In primary work we use things, and perform acts with things to enable the child to see the relations which make number. But neither the things nor the acts with the things are numbers. The group of dollar symbols, in Jan. issue, e.g., may be formed by three physical acts: we put down a first group of four things, then a second group of four things, and finally a third group of four things. But no one will say that these physical acts are the idea twelve. The things are used -put together and taken apart,— physical combination and separation — to help the mind's process of thinking the whole into parts, and the parts into the whole. When we say that $4 is taken three times to make $12, we do not mean merely the physical action. That is simply a means to the mental process; we mean that in forming the idea twelve as made up of three equal units, there are three related mental acts; exactly as in forming the idea of three with reference to any unit whatever. This is the idea of times; it is abstract and essential to any and every idea of number.

2. On the other hand young teachers must guard against being deceived by a barren manipulation of symbols. Thus, some of our instructors tell us that $12 ÷ 3 is impossible, because 3 cannot be taken from $12; but that 12 ÷ 3 (abstract numbers) is a perfectly valid operation, because we have 12-39, 9-36, etc. But the idea of the division of 12 by 3 does not give us the idea of the quotient 4. These relations must be supplied first of all by intuitions, i.e. by acts with things. What are the intuitions, the actions with things, that lead to the conception of these relations? Of course in division, as well as in all other mathematical processes, we operate with the pure number symbols and then make the implied concrete applications, i.e. interpret the results. But these symbols must have definite meanings to begin with. Not only so. These symbols and the operations in which they are involved in any problem, must be capable of interpretation at any and every step. So, when in any division problem, I am told that 12-9 = 3, etc., I am not satisfied. I demand an interpretation of this step. I must have a concrete illustration of this abstraction. And if no interpretation is forthcoming, I protest against the substitution of empty abstractions and sounding symbols, for clear and definite ideas. Some begin with the concrete (things) and stay there; others begin with the ab tract and stay there. The true way is from the concrete (things) to the abstract, and from the abstract back again to the concrete.

3. This brings me to notice the assertion criticized in my November article on division, viz : that the divisor can never be an abstract number. It was shown in that article (see page 105) that the divisor may be an abstract number, and that every step in such division is capable of a common-sense explanation. The vice of most primary methods in number is that they have little or no continuity with the child's already acquired experiences; they do not bring into clear and definite consciousness what the child has long been unconsciously doing for himself. When a philosopher tells us that $12÷4 is impossible — but that the operation must be purely abstract, he violates this continuity; he makes the abstract

prec de the concrete; he implicitly teaches that the child cannot distribute 12 things into four equal groups, till he has been taught the process of abstract division! But the child has actually done the thing again and again. He does as the savage does and as the race did before number symbols were invented. His practical solution of the problem prepares him for the arithmetical solution, if the things that nature has joined together are not put asunder by the arbitrary decree of the empiricist. The child is required to distribute a group of things say $12) into four equal groups; what does he do? He places one thing in each of four places, then another of the things in each of the four places, and so on until all the things are distributed. That is, he takes one of the things four times, then another of them four times, and so on. Finally he counts the number of things in one of his equal groups, and his problem is solved. My division by an abstract divisor, (page 105 November POPULAR EDUCATOR) exactly represents by symbols the "talking" operation by which the child distributes the things into a number of equal groups.

These simple examples (see page 105, November number) are typical of both the thought and the process in all division. Take an example with larger numbers $9356 × 687 = $6427572. (a) Given the product and the multiplicand to find the MULTI

PLIER.

$9356 $6427572(600 $5613600 $813972( 80 $748480

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To say that these two operations are not correlative is to make the boldest of bold assertions; is to assert that the number of groups can be found without their value, and conversely; is to assert that $4 X 3 $12, and not = $3 X 4; is to assert that in finding the number of things in the following group there is no relation between the column and the row, - that the row can be found without the column, and the column without the row.

4. The symbols and operations in elementary mathematics should be consistent with what the student is to meet with in his subsequent course. We have then $4 × 3: = $12, and therefore $12 $4 = 3, an admittedly easy and valid operation; but $12 ÷ 4 = $3, an alleged impossible operation, having no relation, of course, with the former. But the student is soon to learn that a xb = c, and that therefore c÷ab; and also c÷b = a; and both inferences must be valid, both necessary, both universal; or all mathematical reasoning falls to the ground.

THE POPULAR EDUCATOR ARITHMETIC is of exceeding value because of its large number of very practical problems. The e problems are such as ch ldren can understand because they are based on every-day transactions, expressed in every-day language. This book ought to be popular. Pa.

L. O. FOOSE, Supt. of Schools, Harrisburg,

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