Pointing to a row of marks ask, How many marks ?
Then point to the figure opposite, and ask, What figure ?

It is, of course, a very simple thing to teach the writing of num. bers up to nine.

Let us see now how to teach the writing of numbers above nine in an intelligent way, by the aid of the Numeral Frame.

How many balls on this wire ?
Ten balls.
That is, here is once ten, pointing to the row of balls on one wire.
I will now write the figures for ten.

You see I write the figure one, and then put the zero on the right of it, to show that the figure one is to stand for once ten balls, and not for one single ball.

You may count ten.
Make ten horizontal straight marks on your slates.
What figures stand for ten ?
Figure one and zero on the right of it.
Hold up the right hand.
How many balls on this wire ?
Ten balls.
And how many on this ?
Ten balls.
How many on both ?

Twenty balls [this had been previously well learned in the counting exercises).

Twenty are how many tens ?
Twenty are two tens.

I will make the figures for twenty. I make the figure two, and then put a zero at the right of it, to show that the figure two stands for two tens, or twice ten balls, and not for two balls.

What stands for twenty ? The figure two, and a zero at the right of it. What does the figure two stand for when there is a zero at the right of it?

The figure two stands for two tens, or twenty, when it has a zero at the right of it.

How many are twice ten ?
Twice ten are twenty.

So proceed with the tens up to a hundred. Thus it is seen that the writing of tens by the help of the Numeral Frame is a very simple process. The child easily comprehends that a figure with a zero at the right of it does not stand for so many units, but so many tens, or the balls on so many wires. Only one more step is necessary in order to understand fully how to write all numbers below a hundred. Let us see how the pupils may be led to take this step.

How many balls on this wire ?
Ten balls.
What figures stand for ten ?
The figure one with a zero at the right of it.

Here are ten balls on this wire, and I pass out one on the next wire.

Ten and one are how many ?
Ten and one are eleven.
I will write the figures for ten and one, or eleven.

I write the figure one for once ten balls, and the figure one at the right of it for one ball.

What figures stand for eleven ?
The figure one, and the figure one on the right of it.
What does this figure stand for?
It stands for once ten.
And this ?
It stands for one.
How many are ten and one ?

Ten and one are eleven. .
Write the figures for eleven.

I now pass out two balls on the second wire. The balls on the first wire and two more are how many ?

Count, ten, eleven, twelve.
Ten balls and two balls are twelve balls.

I will make the figures for ten and two, or twelve. I make the figure one for the ten, and then put the figure two at the right for the two.

Write the figures for twelve.

Thus proceed to one hundred. While learning by this method the Arabic notation of numbers to one hundred, much knowledge of numbers will be incidentally acquired. Besides, it cannot fail to be interesting, because it can be understood.

It is important that the tables in addition, subtraction, multiplication and division should be thoroughly committed to memory, so that the results of the operations which they involve may be given without stopping to make the calculation. But the minds of the pupils should be prepared for this at each step by numerous exercises in calculation upon sensible objects, and upon practical questions, such as are found in the text of the primary arithmetic.

TEACH SUBJECTS AND AWAKEN THOUGHTS.

[From the Annual Report of the School Committee of Providence.]

THERE can be no equality in our schools so long as teachers differ so widely in talent, in attainment, in spirit, in methods, in energy, in devotion, in government, and in professional skill. Teachers must and should differ in methods of teaching and influen. cing children. To this there can be no objection, provided their methods are right in themselves, and tend to secure the end to be accomplished. That teacher is censurable, who, with the means at command, falls into a thoughtless routine, and contents himself with simply keeping school, hearing lessons, and dismissing. Any lack of earnestness on the part of the teacher is instantly felt throughout the whole school. He who would attract the attention of children must present something to command attention; he must awaken curiosity, and then promptly satisfy the cravings of excited interest. In this respect there is a wide difference among our teachers. That teacher is not eminently qualified for the work who cannot, on occasion, stand before a class, without text-book or notes, and discuss in a clear and consecutive manner any of the topics that are to occupy the attention of the children. Such is not the habit of some of our teachers. Too often do they sit inactively at the desk, content to put, in consecutive order, the questions of the text-book, and receive from the children the abstract answers which follow, — making here and there, if need be, a verbal correction. It is no wonder that such a school falls into a thoughtless way of reading, studying, and reciting. Exclusively oral instruction is undesirable, and equally so is an exclusive use of the text-book. A proper mixture of the two is the true desideratum. A teacher who cannot stand before a class with a bit of lioen cloth, and trace its history back through the several processes, from its present state to the sowing of the flax-seed eliciting all the children's knowledge upon the subject as he goes, is not in command of an awakened school. We have those who teach subjects rather than books, and who use books in order to teach subjects; and, it is to be feared, those who teach books and not subjects, — words and not thoughts. Hence the great disparity so often observed in our classes in geography. Let anyone who desires a confirmation of these statements enter some of our Grammar or Intermediate Schools at any hour, and call for a class in geography. He will see the whole class, without book, or question, or hint from the teacher, produce in outline upon the black-boards well proportioned maps of any country whose geography they have studied, and that with a promptness truly surprising; and at the call of the teacher, or otherwise, these outlines will be filled with accurate locations of the principal rivers, mountains, lakes, towns, and other prominent features. All this is done with such a promptness and accuracy as to show that the pupils are relying upon their own conceptions of these features, and not upon the statements of any text-book. Let him pass from this to another, where the teacher has not acquired experience and skill, or has no power to teach independently of the book, or is not animated with the true spirit of the teacher, and he will find a class going through the process of

text-book questions, — a kind of exercise which may go on for weeks with scarcely a conception of magnitude, form, relative position, or locality. And yet, with industry and perseverance, a class may be made to repeat whole pages with fluency and accuracy. So far as language can indicate it, the pupil may seem to understand geography. Indeed, a cursory examination may secure for such a teacher the customary report, —“in a satisfactory condition.” Yet this school never thrives. It lacks animation, and the reason is obvious. There ought to be a wide disparity between this and the former school.

In no study is this difference more striking than in the ordinary reading lessons. The best teachers, as well as the poorest, must go through the mechanical process of teaching the children to pronounce the words from their printed forms. While the whole attention is given to this, one word is as good as another. No idea is necessarily associated with it. Unless great pains are taken, the children will fall into a settled labit of pronouncing words without attaching to them any thought whatever. Reading thus becomes monotonous and lifeless. In the hands of an unskilful teacher, it remains so. The only steps towards an improvement consist in the enforcement of certain rules for the articulation of the syllables, or the pitch and modulation of the voice. Far otherwise is it with one whose motto it is, to “Teach subjects and awaken thoughts." The lesson is never left until the scene depicted is spread before the eye of the mind, and the entire mental picture is realized. In possession of this, the child reads in those natural tones of voice which express his own thoughts and feelings. The same difference of method prevails in every study, and hence the great disparity so often reported by our superintendent.