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mathematics. In the first place it is an absolute science,every statement is capable of proof, from the assertion that twice two are four to the minimum line. Every number bears a certain set of relations to every other existing number. Hence knowledge is accurate and inaccuracy is a falsehood on the face of it, and capable of demonstration.

Let us see what difficulties the child encounters and what he has to learn. He is taught first to count to ten with objects, talks of ten and all preceding numbers and verifies his knowledge with objects, learns the signs of representation, combines the numbers within the limits and puts the result into written expression. He knows that 2 stands for that number of objects, that + means to put into one group and to separate into two. For the learning of these arbitrary signs only sufficient time must be given to impress them on the memory, or you find yourself in difficulty in some other place. That done, extension of knowledge for a few years means repetition of the same principles under different conditions. Memory is strengthened but not depended on, for the child is to be required to prove every statement with objects. Reason is not yet developed,- let the eyes see, the ears hear, and the fingers enumerate every given requirement. Then the visible sign. Call on memory for nothing but the arbitrary sign to represent the verified statement. Do not permit a child to say two and two are four unless he can prove it. Then clinch the fact with numberless illustrations which the child himself is to make. Assume the character of doubting Thomas and he will be anxious to convince you, himself and his companions that there is no doubt about the matter.

Now the time will surely come when he can conceive the numbers abstractly, but never carry him to the point of not feel. ing the obligation of proof. Teach him to be as careful of representation as of thought; that the signs used, though arbitrary, are absolute and almost universal in their significance. He knows that if he means 3, 7 will not convey the idea of three to others; that he would as well tell you he had eight cents when he had but five as to represent it in figures. The child will say he “forgot," "made a mistake," or "didn't think.” He would

never think of offering such an excuse for a verbal, and ought he to be allowed to make such a one for a written falsehood ? We are presuming that the child has been carefully and accu. rately taught. He knows what the result of the calculation should be and the written expression of it. Here is the point, he is morally responsible for every statement within his knowledge. Hold him to it. Culpable carelessness degenerates into a tendency to plausible explanations of false accounts. The old adage, “Figgers never lie,” may be read to mean that the mak. ers of figgers' are responsible. Inaccuracy ought not to be permitted. The child ought not to feel that an incorrect answer is possible, that he is held for results within his knowledge, that “I didn't think” can no more be accepted for a wrong calcula. tion than for asserting that it was night at mid-day.

In this place we must be careful how far the child's knowledge extends; a requirement beyond that is a positive injury, for it induces the expedient of 'guessing,' that can not be too strongly reprehended. Numbers are truthful, and in our dealings with them is involved the integrity of the character.

In some processes of reasoning the mind may fail to see true relations, but, given the right process the answer follows as a certain result. In taking up new work with advanced classes the question must be carefully reasoned, process accurately taught, results never considered. To teach them an incorrect answer is impossible from correct reasoning.

Aside from a moral standpoint the world calls false accounts dishonest, in school it may have been a “mistake." Calculations in a class on a promissory note may vary according to the accuracy of its individual members and seemingly no great harm done except to strengthen the feeling of indifference, but if in business the maker of the note differs from the holder he might justly be accused of wishing to turn it to his own advantage. The pupil who contends for the merit of making but one mistake while his class mate makes two, stands not on his own intrinsic value, but views himself relatively and is satisfied with being a point better than his neighbor instead of aiming at perfection. He resorts to expedient, nothing is absolutely pure bnt only less adulterated than the next. He spends at least enough energy to cover up and make appear accurate to have made it so twice over from the beginning. The world has not time to investigate, unless he owes it money, and what matters the disapproval of his own soul ?

These are the capabilities of numbers in developing the integrity of the character, some of the causes of unintentional falsification, and some of the methods by which a truer sense of their importance may be reached.

We have a two-fold purpose in all our teaching, -fitting for eternity and for practical life, where, though the fine surface may be soiled the grain is uninjured and what a man is he remains—then if knowing the evil he remains unsullied, the Beautiful is his relaxation, the Good his consolation, and the True the active principle of an undaunted soul.

AN OLD SONG ANALYZED.

You all know the old familiar song :

Sing a song of sixpence,
A pocket full of rye,
Four-and-lwenty blackbirds

Baked in a pie," etc.-
but have you ever read what it is meant for ?

The four-and-twenty blackbirds represent the twenty-four hours. The bottom of the pie is the world, while the top crust is the sky that overarches it. The opening of the pie is the day. dawn, when the birds begin to sing, and surely such a sight is fit for a king.

The king, who is represented as sitting in his parlor counting out his money, is the sun, while the gold pieces that slip through his fingers, as he counts them, are the golden sunshine.

The queen, who sits in the dark kitchen, is the moon, and the honey with which she regales herself is the moonlight.

The industrious maid, who is in the garden at work before the king (the sun) has risen, is day.dawn, and the clothes she hangs out are the clouds, while the bird, which so tragically ends the song by “nipping off her nose,” is the hour of sunset So we have the whole day, if not in a nut-shell, in a pie.— Illinois School Journal.

DEPARTMENT OF PEDAGOGY.

[This Department is conducted by S. S. PARR, Principal De Pauw Normal School.]

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HOW TEACH GEOGRAPHY?

N a previous article, we sketched an outline of the nature of

geography, in its logical relations of idea to idea and condi

tion to condition and of the chronological development of the subject in a growing mind. The former article was an attempt to give the necessary succession of ideas in the subject, first, in the adult and relatively mature mind and, then, in the growing and relatively immature mind.

Such an outline may, by some, be thought only a glittering generality. They do not see how, by its possession, they are nearer successful work. To such we respectfully cite the architect's rough draft as an example of a useful appliance of similar nature, One may think he might build a house without any such draft; but he is mistaken. The building of a cabin or a corncrib involves all the steps of the most costly mansion. The elaborateness and finish of the steps form the difference. The simile is closer than the first hurried look would indicate. As the rough draft is a necessary step to a symmetrical and economically arranged house, so the outline is necessary to economic and systematic teaching

We may even go much farther and say that every teacher makes some such outline. In the minds of some, it is very foggy and obscure. Perhaps it is only a poor starved dozen or so of book definitions; a hazy idea that Kokomo, Kalamazoo, Oshkosh and Skaneateles are towns somewhere this side of the Zuyder Zee. But it is there! The proper thing is to put out this little imp of darkness, lean and unfavored as he is, and put in an outline of the nature of the subject that has some marrow to its bones and some juice in its tissues. When the teacher has staked off his ground and fully possessed himself of it, he is ready to ask the all-important question cui bonofor what end?

THE PURPOSE OF GEOGRAPHY, It is useless to argue the necessity of breathing. People can not help some kind of breathing. But no such absurdity attaches to arguing for pure air and plenty of it. No teacher ever taught geography without some kind of purpose, if only to kill twenty minutes of time. Very many think their skirts are clear in this world and the next, if the pupil can rattle off the language of his book. The only faculty that haunts them is the ghost of memory. At this they are continually throwing the black beans of memorized statements.

The purpose is double and not double. We might say it is to teach a certain set of geographical ideas and to train the mind. The two aims are one and the same. Well taught ideas give culture and good culture finds its possessor with a well organized and digested set of ideas. Assuming, then, these two aims to be one, let us inquire what ideas the pupil should gain from this subject.

Geography is the only subject that photographs the entire life of this busy hive we call the earth. Civilization, which is the outer life of man, is to be viewed in relation to the life of nature, that is, plants and animals. All life is to be held up to the earth as the great fountain of which this life has sprung. It is the only subject that trains one to use his personal experience of trees, plants, brooks, hills, clouds, weather, and the whole round of animals and his experience of men and human affairs to explain and comprehend countries and continents, governments and peoples his eye hath not seen. The big round globe is a hive of busy life which every intelligent person must interpret, as a whole, using what his five senses and his inner lamp of the sout (consciousness) give, as the basis for this interpretation. No other subject exercises the imagination in constructing man and nature in collossal aggregates. History and the social sciences deal chiefly with man, and secondarily with his other half in nature. The natural sciences deal first hand with mother nature and second hand with man. It is reserved for geography to hold one of these in her right hand and the other in her left and trace the interwoven threads of relation.

The judgment is cultivated by tracing the connections of the giant parts of the earth in their relation of cause and effect, pur

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