Special methods of instruction

Front matter

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Preface

Special Methods deal with practical classroom work. Logically such methods are expressed in the form of sentences in the imperative mood, each sentence corresponding to a definite situation. General method is somewhat the same saA^e that the sentences correspond only in a general way to a number of definite situations. Neither general nor special methods are directly concerned with aims of education, underlying principles of instruction, historical development, comparative values, and the like. Such aspects belong to the field of the theory of education. The present volume deals with special methods of instruction.

The generous latitude which is allowed, and the universal encouragement of initiative and original work which is given by the Department of Education of New York City have enabled me to try out methods in all the elementary school grades. My thanks are due to the teachers of five schools who have given aid and suggestions. Throughout the book traces are due to long association with such leaders in practical education as Principals S. Badanes, B. Cronson, W. E. Grady, W. F. Kurtz, L. Marks, R. F. McCormack, J. J. 'Regan, J. J. O'Reilly, J. E. Wade, and Superintendents A. W. Edson, E. D. Farrell, H. W. Jameson, W. H. Maxwell, and B. Veit. Suggestions on formal grammar have been given by Principal J. J. O'Reilly, one of the most practical teachers in the City. Dr. S. Badanes has read the proofs and has made corrections in the chapters on arithmetic and on language work. The literature in English and German of which I have made use will be treated critically in a separate pamphlet.

Felix Arnold New York City

Contents

CHAPTER PAGE

I — Visual Appeal — General Directions 1

II — Arithmetic — Visual 5

Chapter I Visual Appeal — General Directions

Properly to present visually the subject matter of any lessons use the following:

Blackboard

Chart

Map

Model

Specimen or Object

Perception Card

Text-book

And if available,

Steroscope Lantern Moving Picture.

I. The Blackboard

1. The blackboard. Have the board, or the part to be cleaned washed down every day. First rub the board down dry, and remove all chalk dust from the trough at the bottom. Then go over the surface with a wet or damp rag. Whenever it seems necessary and at least once a week have the board washed down with ink or ink and water. Use the dregs from three or four inkwells. After the board has been so washed down, have any ink stains or drippings wiped off with a damp rag.

Have the board rubbers or rags cleaned every day. Have them cleaned in the school yard and not in the room, at the windows, on the stairs or against the school walls. Have all the chalk cleared off every afternoon. In the morning have the needed chalk arranged in the trough ready for use.

2. Blackboard work. Use about a third of the board for diagram, drawing, map, calendar, outline, graph, table, list of words, phonograms, dates, etc., which are to be used during the day or during several days. Make your diagram, drawing, etc., either after school sessions or before school sessions. Use white chalk for letters, words or figures. Use yellow, orange, or red crayon for underscoring, boxing, etc.

Use about one third of the board for type problems, type sentences, spelling list, outline in history or geography, etc., which are needed for the day's work. Write such problems, sentences, list, etc., before the children are in the room. Use white chalk for letter, words or figures, and yellow, orange or red crayon for underscoring.

Keep the middle third of the board free for the work of the day. If immediate use calls for it fill this third with the work to be taken up, as problems in arithmetic, sentences in grammar, model for dictation or composition, etc. The specific board work in the different subjects will be taken up under different headings, as, arithmetic, language, etc.

II. The Chart

1. The chart. Make your chart out of white cardboard or out of oak-tag. For more permanent use buy white window shades. So that cardboard charts may last and that they may be properly hung, punch eyelets a few inches from the side and about three quarters of an inch from the top of the chart. To prevent the chart from turning or bending when hung, reinforce the back with a flat stick or slat of wood. Place the slat at the top and back of the cardboard and tack on.

If a shade is used spread glue over the shade three or four inches from the top, roll it tightly round the roller and tack it on with iy 2 or 2 oz. tacks. Mount the shade on a piece of wood about three inches wide and an inch thick.

Colored ink can easily be made. Use any colored powder and mix it with water and mucilage. Add to this one or two drops of ox-gall for a gill of the mixture. Spread the ink with a brush or use a stub pen as with ordinary ink. Use black ink for figures, letters or words.

2. Chart work. Chart work is very useful for visual appeals which are to be made again and again during the term. Make charts for tables, graphs, lists of phonograms, lists of dates, outlines in history or geography, number forms, cross section of maps, letter forms, etc. More specific material will be found under the different chapter headings.

VISUAL APPEAL

III. The Map

1. Flat maps. Maps are usually supplied by the school authorities. For purposes of instruction better maps can be made by the class teacher. Make the map on the blackboard, or for more permanent use, on a shade or cardboard.

In drawing a map first sketch the outline lightly with white crayon or, for shade work, with charcoal. Fill in what is to be the specific object of the lesson, as, rivers, mountains, products, special divisions, etc. If necessary draw a water line. Now fill in the outline with a firm hand. Use white chalk for printed matter, for rivers, etc., blue crayon for water line, brown or purple for highlands, and green for lowlands. Railroads and steamship routes may be indicated with firm red lines. Ocean currents may be marked with firm blue lines. The colors may be used solidly or may be indicated by line work. Solid coloring should be very light. For the different kinds of maps read the chapter on geography.

2. Relief maps. Very durable and effective relief maps are made out of papier mache. Have a board made from 3 to 5 feet long and from 2 to 3 feet wide. To prevent warping or curving have the ends of the board paneled and the back braced with cross pieces. Outline in pencil the map to be made and coat with glue the part of the board to be covered with papier mache.

To make the needed papier mache tear newspapers into small pieces and let them soak in water over night. Squeeze the paper into a massy pulp and let a pupil pound it with a stone till the pulp is of the consistency of clay or putty. Mix with the pulp some white photo or flour paste. The papier mache' will then be ready for use.

Squeeze out any water that may be in the pulp. Spread it evenly over the board, closely following the outline. Roughly put in mache' for the highlands. Use the fingers to even out the highlands, valleys, lowlands, river beds, etc., so that the map assumes a more finished form.

Let the map become hard. Paint the map white and the. background some other color, as blue or green. When the paint is hard shellac the entire surface. The map will then be water proof and can be washed. Different colors can be used according to the kind of map made. All colors should be fairly light.

IV. Perception Cards

Perception cards are made out of oak-tag or card board. Backs of pads may be used. Cut up the cardboard into cards about 9 or 10 inches long and about 5 or 6 inches wide. For tables, phonograms, etc., place the basic element on the large card, and the variable elements on movable cards about 3 inches wide. Use twine to fasten the movable cards.

Other materials for visual appeal, as, models, text-books, etc., need no special description. Their use will be indicated under the different subject headings.

V. General Suggestions

Whatever is basically visual should be presented visually, and not verbally or orally. For example, the map itself should be drawn for the pupils. No verbal description should take its place. Not the rule for an example, but a type example should be worked out. Not a definition of a noun but a series of nouns should be illustrated and listed.

Whatever visual work is to be presented should be carefully prepared before the pupils enter the room. With the blackboard filled with work, charts ready and perception cards arranged and near at hand, the teacher can proceed with an air of certainty and assurance which both impels attention and secures good discipline. With definite work before him the pupil more readily settles down to class work and more quickly loses the harum-scarum images and notions of the home and the street.

Whatever material is used should be neat and clean. In fact it should be the best that the teacher can present. No slipshod work should be tolerated. Such signs of carelessness as dirty, torn maps or charts, grey blackboards, miserable, scrawlly writing, or indistinct figures should not be allowed. No pupil who is unable to write large and distinctly should be permitted to write instead of the teacher. Such excuses as, 'I can't draw,' 'That's the way I always write,' and the like, should be translated into their real meaning, 'I am not fit to teach.' It requires but little practice for any teacher to attain skill in blackboard work, and in the construction of models, charts, etc. In fact such work, as in the case of kindergarten teachers, should be required of all normal pupils and of all pupil-teachers.

Chapter II Arithmetic — Visual

I. The Number Four

1. Counting. Call on four pupils, all boys or all girls. Slowly explain and question as follows : I want four boys to stand.

No, not so many. Four — one, two, tbree four. Jobn, Henry, James, William. Stand up and step before the class.

This is John. (Mark on the board). This is Henry. (Another mark). This is James. This is William. One, two, three, four.

Look at the boys. One, two, three, four. Look at the marks on the board. One, two, three, four.

How many marks are there? Count them with me as I point.

Call on a number of pupils one at a time to count the boys and the marks as you point. Point to John, and pass to William. Point to William and pass to John. Begin indiscriminately with the other pupils, Henry or James. Group the pupils and direct as. follows:

John and Henry, move over.

Now we have, One, two, One. two.

Altogether, One, two — three, four.

James, step closer to Henry.

Now we have. One, two, three — one.

Look at the lines on the board as I draw them.

Count them.

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Make use of other objects in the room, as books, pencils, papers, panels in the door, window panes, walls of the room, corners of the desk, etc. Have the pupils recognize and pick out four of a kind. Question them as follows :

How many pencils have I in niy hand ? Count them.

Harry, get me four pieces of paper. Hold them up.

Count them — John. William. Joseph. Frederick.

I want some others to count. No, not the class. Hold up hands.

Now point out four panes of glass.

Come up and touch four desks.

Show me four panels in the door. Count them.

Make four white marks on the board.

Get four pencils. Hold them up.

Call on individual pupils to point out, count, hold up, etc. Give the same question or task to several pupils. Pass rapidly round the class and throw questions repeatedly at parts of the class which seem to pay less attention than needed.

In the above presentation, actual objects in the classroom are used. Follow up the work by representative objects and blackboard work. Draw simple figures on the board, using four strokes for each figure. Pause after each stroke and count as you make the stroke. Use figures similar to the following :

Line ivorlc.

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Animals.

Leaves, objects, etc.

2. Measuring. Let pupils pace a short distance. Direct them as follows:

Who can walk from here to the door?

Take four steps — One, two, three, four.

Who else can do this? Try it, John. William, count.

Draw a line on the board, four feet long. Use colored crayon. Measure the line with a foot rule. Direct as follows:

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See how many times I mark off. Count.

Who can mark off? Try it. John. Henry. Rose.

Who can count as I point? William, Mary.

Who can draw a line as big as this one?

Who is about as big as this line?

Come up, Harry. Now count. Just four feet. Call upon a number of individual pupils. As you measure, have some pupil count for the class. Arrange squares in rows as follows :

Point to each square, and have the pupils count. Show a gallon measure, and alongside of it a quart measure. Pour four quarts of water into the gallon measure. Use glass measures if possible. Count slowly as you pour — One, two, three, four. Let the pupils count. Use the gill and the pint in this manner. Draw the measures on the board as follows :

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Call upon individual pupils to note the number, count, etc.

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3. Number forms. Mark four dots on the board. Make the dots two inches wide, place them two inches apart, as follows :

Have the pupils look at the dots and tell how many. Let individual pupils count the dots. Have them close eyes, and locate four dots by pointing in the air with their fingers. Direct them as follows :

Close eyes. Try to see the dots. Point them out.

Ready — One, two, three, four.

Now begin at the other side — One, two, three, four.

Open eyes. Look at the board. Close eyes. Point.

Now all point at the door.

Point to the ceiling — One, two, three, four.

4. Number machines. For classroom use, the number machine should be of a good, wholesome size, about three feet square, with balls two inches in diameter. The following machines explain themselves : Tillich Blocks Number steps. Russian machine

II. Addition and Subteaction — No Carrying

1. Counting. Direct the class as follows :

I want three boys to stand. John, William, Henry, come

here.

How many boys are there? Count them.

Come, James. How many now ? Count, them.

Now, count as I point. One, two, three, four. Three and one make how many? Count.

John, sit down. Now, how many?

Pass the same questions to a number of individual pupils. Do not let the class answer in chorus. Insist on rapid, individual answering. Take four books, or pencils, or papers, etc., and proceed as follows :

How many pencils have I? Count them.

I give this one to John. How many are left ?

How many did I have? What did I give?

One from four equals how many ?

Four less one equals how many?

Take away one from four. Count the ones left.

What is the remainder?

Take away two from four, add two and two, and question as above. Draw four cherries (or other simple objects), on the board, thus:

Rub one off, thus

Draw it on again. Rub off some other one, as the second or third one. Let the pupils count as you draw. Repeat this process with other drawings, as the petals of a flower, steps in a stair, spokes of a wheel, etc.

2. Ratio and measuring. Direct the class as follows :

Who can take a big, long, step ? Come up and try, Henry. Can you step from here to the wall? Is your step long

enough?

How many steps must you take? Count them.

Take three steps. How many more must you take to reach

the wall?

Let a number of pupils take steps and pace short distances, as, from desk to wall, seat to door, etc Call upon pupils to count as the pacing is done. Draw a four-foot line on the board, thus :

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Explain and question as follows :

Which line is longer? Point to it.

Which line is shorter. Point to it.

Count the parts in the line as I point.

How much longer is this line ? Count as I point.

Now I add to the short line. How many parts?

Count — One and three? One, two, three, four.

Three and one ? Count.

Three from four? One from four?

Let pupils use the foot rule and rule off a four-foot line, a three-foot line, a two-foot line, and a foot line. Let them count the parts in each. Deal with the following figures in the same

manuer: . I

How mauy squares in the first row? In the second row?

Which is bigger? How T much bigger?

Which is smaller? How much smaller?

How many more in this row? Count as I point.

How many less in this row ? Count.

Make use of different measures, as, gallon-quart, pint-gill, etc. Let the pupils tell how many quarts you pour into the gallon measure, how many you take out, how many are left, etc.

3. Number forms. Draw the following on the board :

Rub off one unit. Replace it. Call upon pupils to give the number of dots left after you have rubbed one off, and after you have replaced it. Draw the following number forms on the board and indicate addition or subtraction:

4 take away 1 4 less 1

4 — 1

4 — ? = 1

4 take away 2 4 less 2 r.

4 take away 3

4 less 3

4 — 3

4 — ? = 3

4 — 2

4 — ? = 2

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Question pupils, passing the same question indiscriminately to a number of pupils. Pupils who fail should be made to count the units. After such counting, repeat the question and ask for the answer. Repeated failure should be corrected by repeated counting.

Begin with a number which is capable of analysis, and which correlates readily with the pupil's environment, as, two, three, or four. Nothing, and one, are abstractions which should be reached slowly and which should come out of the analysis suggested. After one, two, three and four, have been studied in the manner suggested, pass to five. Then take up ten, and analyse out of this the following, in the order given : Six, nine, eight and seven. Then go on to twenty, thirty, etc., up to one hundred.

III. Addition and Subtraction — Carrying, Borrowing

1. Counting. Arrange a series of dots on the board as follows:

Question and direct, thus:

Count up to the line. (Nine). Count past the line.

(Fourteen).

How many dots after the line ? (Five) Before ? (Nine) . Nine and five ? Count them.

Five and nine? Count.

Write the figures on the board as follows :

9 and 5 9 5 5 and 9 Add 5 and 9.

With the addition of 5 and 9 take up the correlated subtraction. Eub off dots and question the pupils, thus :

Count the dots.

Count them now. (With 5 rubbed off).

Count them now. (With 5 added).

How many did I rub off ?

How many left ? Count them.

Five from fourteen"

If I take away 5 how many left?

14 less 5? 14 — 5 equals?

Subtract 5 from 14. Count those left.

Vary the subtrahend by making it 6, 7, 8, etc. Return to the diagram again and again and test the result by having the pupils count.

After 14, take 24. Analyse the number as follows:

— 9 = — 9 — _9

10+5

If the children have difficulty in understanding the example, illustrate it by two rows of dots, thus :

Let the pupils give the answers of series of examples like the following :

9 19 29 39 49 59 69 79 89 99

9 19 29 39 49 59 69 79 89 99

5 15 25 35 45 55 65 75 85 95

5 15 25 35 45 55 65 75 85 95

If pupils do not seem to get the answer return to the visual presentation. If, for example, 25 + 9 presents too great a difficulty, simplify the 25, and arrange a series of dots as above.

2. Ratio and measuring. Draw a number of squares on the board, thus:

Compare the two areas and question as follows :

Which row is bigger?

How much bigger is it?

How much smaller is this row?

Call the squares, square feet.

How many square feet in this row? In this?

How much smaller is this row?

How much larger is this row ?

How many square feet must be added to this row to make

it 14 square feet?

How many square feet must be taken away to make 9

square feet? 14 square feet less 9 square feet equals ? Count them. Take away 5 square feet from ]4 square feet.

Arrange the squares as follows: