subject? What word qualifies the object? What words extend the predicate?

Observation.-Proceeding in this way, the pupil will be taught the art of composition. But in all this there is comparatively little knowledge of parsing required.

ARITHMETIC.

All the junior classes, in an elementary school, should be taught arithmetic on the collective system. The synthetic method of demonstration, first explained, at least in this country, in the writer's treatise on the Principles of Arithmetic, is certainly the best adapted for elementary instruction. The suggestive method of interrogation is most generally applicable to the teaching of demonstrative arithmetic.

In teaching common or slate arithmetic, the following general rules should be observed:

1. All the demonstrations should be given distinctly upon the black-board.

2. The essential data of the question (not the whole question) should be written, in a proper order, on the black-board, especially when the question contains three or more data.

3. The teacher should fully explain every step of the process as he writes it down. It is a bad plan to work out the whole question, and then to proceed with the explanation.

4. The pupils should take a part in the investigation. The master should require them, time after time, to tell him what quantities he must write down, at the different steps of the investigation.

Let us take a few examples of this method of teaching arithmetic.

1. Lesson on the Addition of Fractions.

Let it be required to add one-half and three-fourths together.

Here, before we can add these fractions together, we must bring them to the same part of unity, or, to speak

more simply, we must bring them to bits of the same size. Let us suppose that we have to find how much the half of a loaf added to the three quarters of a loaf will make. What do I take as the unit here? (Ans. A loaf.) Now, how do we get the half of a loaf? (Ans. By cutting it into two equal parts.) How do we get the three-fourths of the loaf. (Ans. By cutting the loaf into four equal parts, and taking three of them.) Now, how should you put the half bits into quarter bits? (Ans. By cutting each half into two equal bits, for then we should have the whole loaf cut into four equal bits.) Very well. Now, how many fourths will there be in one half. (Ans. Two fourths.) So that you have to put together, or add, two fourths and three fourths. What will they make? (Ans. Five fourths.) But I want you to give me the sum in mixed numbers. How many whole loaves would you have in five quarter loaves? (Ans. One and a quarter more.) That is to say, the sum of one half and three quarters will be equal to one and a quarter.

I am going to show you how to do this question in another way.

or 1.

B

or 1.

Let a stick or a line (A B) be divided on the upper side into two equal parts, and the bottom side into four equal parts. What will each of the upper parts be called? What will each of the bottom parts be called? Look at the figure, and tell me how many fourths there are in each half. And so on, as before.

The teacher should also do the same thing by the division of a space.

2. A Lesson on Rule of Three.

Let it be required to find the cost of 9 books, when the cost of a dozen is 8s. 1d.

Let us first write the essential data of the question on the black-board.

DATA.

Cost of 12 is 8s. 1d.- the cost of 9 is required.

SOLUTION TO BE WRITTEN ON THE BLACK BOARD.

After the teacher has written down the language, "Cost 12 books" he asks the class- "What shall I put this equal to ?" After he has received the answer, he fills it in, and then asks "Why is it equal to 88. 1d.?" "How many books have we to find the cost of ?" "Now if we can get the cost of 36 books, we may readily get the cost of 9, as you will see, when we proceed with the solution." After writing down "Cost 36 books =” he asks,- "Will the cost of 36 books be more or less than the cost of 12 books?" 66 Why?" "You are quite right, three times the number of books will cost three times as much." "Now having got the cost of 36 books, how are we to get the cost of 9?" Exactly so, fourth the number will of course cost one-fourth the price." And so on.

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The more advanced boys should be sometimes called upon to give a demonstration on the black-board.

MENTAL ARITHMETIC.

This subject should be taught on the collective system, in connection with the method of interrogation. The boys prepared with an answer to the question proposed by the master, should hold up their hands, and the master must then call upon some boy to give the answer; and so on to the other artifices described in connection with the subject of collective teaching. Young children should be practised, for some time, in mental calculation, before they are taught anything relative to the symbols and notation of numbers. Strokes, counters, balls, &c., should be taken as the representatives of numbers, and all the

leading properties and operations of arithmetic should be demonstrated by the use of these objects, before any technical modes of calculation are attempted. All the processes should be thoroughly demonstrative, and no rules should be laid down independently of the investigations. All tricks and clap-traps of mental calculation should be conscientiously avoided. The boy called upon to give the answer should give the process of investigation.

GEOGRAPHY.

Geography may be thoroughly taught, to large classes, on the collective system. The method of suggestive interrogation, followed by or accompanied with catechetical examination, seems well adapted for teaching this subject to all classes in an elementary school. No branch of geography should be taught without the aid of a map. Every collective lesson on geography should be given in connection with a large map, which should be suspended directly before the class. When any country, or city, or river, or mountain, is spoken of, its place upon the map should be pointed out, and its relative bearings, boundaries, or extent should be fully explained. Physical geography and history should always be taught in connection with descriptive geography. (See p. 194.)

If a teacher can sketch well, he should draw his own maps upon the black-board-First, tracing the outline of the country, he mentions the various kingdoms or seas whose boundaries his chalk is tracing; second, with a few jottings of his chalk he marks out the principal mountain ranges, forming the great ridges or apexes of the watersheds ; third, he traces the rivers winding their way from their mountain source or sources to the great reservoirs of the waters of the globe. He pauses for a moment to review his work,- he has sketched out the works of nature as the hand of the Creator has left them; now he has to begin to sketch the works of art and civilisation - he has to people the wilderness, and to trace the progressive steps of civilisation; upon the banks of the tidal rivers, he marks the site of the great mercantile

cities; on the shores of the mountain streams he plants the names of the oldest industrial cities; on the coal fields he places those mighty manufacturing cities which have almost sprung into existence since the discovery of the steam-engine that mightiest monarch of civilisation and power, which seems to control the destinies of the world; last of all, he marks the sites of those large towns which form the market places of the rural population. We said that the work was progressive,- every fresh touch of the chalk is associated with some new idea, and every fresh idea has its appropriate association with some line or mark upon the board; the sketch goes on,—it

becomes more and more finished;— the skeleton becomes lined with sinews, then clothed with flesh and blood; every fresh step towards completion excites new interest in the minds of the boys, they wonder how a few jottings can call up the idea of a mountain range, or how a winding line can call up the idea of the course of the sparkling river, or how the little mark put for the mountain city should awaken, in their imaginations, the sound of the flip flap, flap flip, of water mills, and the busy hum of industry; they wonder, but they know not, that the visible picture which their master has drawn, with his chalk, would be dull and lifeless, without the living moral picture with which it is associated. Such a lesson is complete in its parts and perfect as a whole. It is a complete exemplification of what has been called the constructive method of teaching.

Map drawing is an excellent means of teaching geography. This exercise, as we before observed, should be set apart for home lessons.

DRAWING.

Collective teaching, combined with the system of home studies, is best adapted for giving lessons on this important branch of school education. As this truly useful branch of knowledge does not appear to have received that amount of attention, in our schools generally, which its utility demands, we shall enter more fully into