Norman Allison Calkins.

# Manual of object-teaching : with illustrative lessons in methods and the science of education online

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Font size WEIGHT OF OBJECTS. 73

The following tables will furnish facts that will aid the teacher
in making experiments, which will lead the pupils to gain much
useful information about the weight of objects :

COMPARATIVE WEIGHTS.
Steam is lighter than gas.

Gas

" air.

Air

" cork.

Cork "

" poplar wood.

Poplar "

" pine wood.

Pine "

" ice.

Ice "

" fresh water.

Fresh water "

" salt water.

Oil "

" water.

LIGHTER THAN WATER.

Steam is

raVo

as heavy as

water.

Air

<t

FO(F

u

M

Cork

II

*

u

((

Poplar

"

f

u

U

Pine

u

1

M

U

Maple

u

f

M

M

Oak

"

T5

U

u

Oil

II

ft

u

u

Ice

M

"

u

HEAVIER THAN WATER.

Milk is about 1^ times as heavy as water.

Coal " 1 "

Brick " 2 " " "

Slate " 2| " " "

Glass " 3 " " "'

Diamond " 3^ " " "

Garnet " 4 "

Cast iron " 7^ " " "

Copper " 8| " " "

Silver " 10J "

Lead " llf " " "

Mercury " 13| " " "

Gold " 19 L " "

Platinum "21 "

MANUAL OF OBJECT-TEACHING.

METRIC MEASURE.

THIS system is now extensively used in eleven countries of the
world, and is being introduced into the United States. Could
all the instruction in school pertaining to the tables of weights
and measures be confined to the metric system, it would save
about one year in the school life of each pupil who completes
an ordinary grammar-school course; and could the power of
habit produced by long use of the present tables be overcome ;
and could the people be induced to make use of these tables in
greater than the saving of time in school. Although so great a
saving of time would be effected by making all our tables of
weights and measures as simple as that of our table of money,
which is part of a metric system, it is not very probable that this
system will come into general use in this country during the
present century.

Its simplicity may be seen in the fact that it is necessary to
remember only three terms as the key, or units in all the measures
and weights by this system, for

All lengths are measured in metres,
capacities " " litres.

' capacities
" weights " grams.

With the metre every possible dimension length, surface, so-
lidity can be measured; with the litre, every possible capacity;
and with the gram, every possible weight.

Parts of each of these three unit measures are represented
by the same terms a tenth, by deci ; a hundredth, by centi ; a
thousandth, by milli.

For representing lengths, capacities, or weights greater than
the unit, each increases by a decimal ratio, as in our money.
Ten units, a hundred units, and a thousand units, of either meas-
ure or weight* would be represented by the same terms, thus :

METBIC NUMBERS. 75

deka signifies ten of the unit; hekto, a hundred of the unit ; kilo,
a thousand of the unit ; and myria, ten thousand of the unit ;
hence ten metres would be called a dekametre ; ten litres, a. deka-
litre; ten grams, a dekagram ; and a hundred metres would be a
hektometre ; a thousand litres would be a kilometre ; ten thousand
grams would be a myriagram.

In the same manner a tenth of a metre would be a decimetre ;
a hundredth of a litre would be a centilitre ; a thousandth of a
gram would be a milligram.

These terms may be abbreviated in use to decim, centim, mil-
lim ; or dekam, hektom, kilom, myriam.

COMPLETE METRIC TABLES.

Dollar is a measure of values. I Litre is a measure of capacities.
Metre " " " " lengths. Gram " " " weights.

Deci means tenth.
Centi " hundredth.
" thousandth.

Deka means ten.
Hekto " hundred.
Kilo " thousand.
Myria means ten thousand.

How to Head Metric Numbers. When we write 9
eagles, 5 dollars, 7 dimes, 5 cents ; we read it, 95 dollars 75 cents.

When we write 7 kilom, 2 hektom, 8 dekam, 6 metres, 8 decim, 5 cen-
tim; we read it, 7 thousc'ind 2 hundred, 88 metres and 35 hundredths.

When we write 8 myriagrams, 5 kilograms, 3 hektograms, C deka-
grams, 4 grams, 5 decigrams; we read it, 85 thousand 3 hundred and
64 grams, and 5 tenths.

For addition or subtraction, write the figures the same as in
United States money.

\$386 25 m.386 25 #.386 25

27 10 27 10 27 20

148 75 148 75 148 75

54 30 54 30 54 30

\$616 50 m.616 50 #.616 50

and fifty cents; six hundred sixteen metres and fifty hundredths;
six hundred sixteen grams and fifty hundredths.

Subtraction, multiplication, and division in the metric system
would be performed the same as in United States money.

The abbreviations are simple, m., L, g., for metre, litre, gram; d., c.,

76 MANUAL OF OBJECT-TEACHING.

for deci, centi; d., h., &., T., for deka, hekto, kilo, myria; dm. for deci-
metre; Dm. for dekametre.

Values Of Metric Quantities. A metre is one ten-mill-
ionth of the distance from the equator to the pole, or nearly 40
inches.

A litre is a cubic tenth metre (decimetre), and is about equal to
our quart.

A gram is the weight of a cubic hundredth metre (centimetre), of
water ; and is about -fa of an ounce.

Four steps equal about three metres.

The width of the hand is a decimetre ; and the width of a finger
two centimetres.

Our nickel Jive -cent coin weighs Jive grams; its diameter is two
centimetres.

Our three-dollar gold coin weighs Jive grams; and two silver dimes
weigh nearly five grams.

Our gold dollar equals more than Jive francs of the French money,
or 5.1826 francs.

In the use of the metric system, carpets would be measured by
metres ; long distances by kilometres ; short lengths by decimetres, as
lengths from four inches to the length of the metre ; and lengths
less than four inches by centimetres, or millimetres.

Measure liquids, small fruits, etc., by litres; fruits and vegetables
in quantities larger than our peck by dekalitres, or hectolitres; wines
and other liquids in large quantities like our barrel, in hectolitres.

Weigh medicines and small articles by grams; sugar, flour, coal,
hay, by kilograms. A. thousand kilograms is about one ton.

Measure surfaces by square metres, square centimetres, etc. Meas-
ure solids, as wood, etc., by cubic metres, cubic centimetres, etc.

METHODS FOR ELEMENTARY LESSONS IN FORM. 77

FOEM.

TEACHERS learn by experience that success in training
pupils to understand a subject depends very much upon
ability to present the lessons in different ways ; and upon
furnishing something for the pupils to do by way of
showing that they understand each fact stated, and notice
each step taken. Those who teach large classes especially
need to be familiar with a great variety of methods for
bringing the same subjects before their pupils, to keep up
the interest of each until all understand the lesson.

For the purpose of adding to the variety of methods of
teaching Form, as given in the Primary Object Lessons,
the following suggestions are presented. These methods
are not intended as substitutes for those in that book, but
as additions thereto ; and while intended partly as ways
for reviewing those lessons, their chief purpose is to fur-
nish a greater variety in the modes of teaching Form. A
in a large class shall be constantly supplied, during the
entire exercise, with something to do.

Lines. Having given the pupils ideas about kinds and po-
sitions of lines, place in the hands of each pupil two small splint-
like sticks of equal length such as are used for lighting lamps.

1. If the class is composed of quite young pupils, let their
first exercise be the holding of splints in imitation of the teacher,
as she represents the position and gives its name, somewhat as f ol-

78 MANUAL OF OBJECT-TEACHING.

lows, viz. : " vertical position ;" " horizontal position ;" " oblique
position;" " perpendicular position ;" " parallel position."

2. As the second step the teacher may draw lines on the black-
board representing each of the positions illustrated before, and
request the pupils to name it when drawn, and represent it with
the splints.

3. For a third step the teacher may name the positions with-
out representing them by lines, and require the pupils to represent
each with splints, as the name is given.

Angles. Having given one or two lessons on angles, as
described in the Primary Object Lessons, distribute the splints,
giving two to each pupil. Let all the pupils imitate the teacher
as she represents each angle with splints, and names it.

Next draw each angle on the blackboard, and request the pupils
to name them, as drawn ; also represent them with the splints,
held by the thumb and forefinger, at the angle.

For a change in the exercise the teacher may name each angle,
and all the pupils represent it with splints or with their fingers.

Plane Forms. When the pupils have had lessons on the
square and oUong, provide them with each shape cut from strong-
paper manilla paper is best for this purpose.

First. The teacher may hold up one of these forms, and re-
quest ail the pupils to hold up a like shape and to give its name.
The teacher may hold up the other form, and the pupils do as
before.

Second. The teacher may name each form, and request all
the pupils to hold it np as the name is given.

Change this by asking the pupils to hold up a form that has
two equal long sides, and point to these sides. Then ask them to
hold np the form that has four equal sides; then the one that
has two equal short sides. Let them count the right angles of
each form.

Square and Rhomb. Give an exercise with the square
and rhomb, as with the square and oblong. Request the pupils

METHODS FOR ELEMENTARY LESSONS IN FORM. 79

to find wherein the square and rhomb are alike ; also wherein
each differs from the other.

Rhomb and Rhomboid. Give each pupil a paper rhomb
and rhomboid, and proceed as with the last two exercises.

Triangles. Triangles may next be taken ; using the right-
angled, acute-angled, and obtuse-angled triangles. When tjie pu-
pils can readily state and point out the distinguishing parts of
each of these triangles, give a similar exercise with equilateral,
isosceles, and scalene triangles.

These exercises may be changed by requesting the pupils to
fold or cut pieces of paper at home to represent the forms of a
lesson, after the school exercise has been had. The paper forms
thus made should be brought to school the next day for the
teacher to examine ; and the best forms may be shown to the
class and commended ; while the poorer ones may be used for
pointing out the mistakes made. But this should be done with-
out allowing the pupils to know whose form is criticised.

Circles, etc. Provide forms of paper representing circles,
semicircles, rings, crescents, ovals, and ellipses, and give exercises
similar to those with the square, rhomb, etc. Lead the pupils to
notice the difference between the semicircle and the crescent;
also between the oval and the ellipse.

Polygons. During a later stage of instruction, similar ex-
ercises may be given with the polygons pentagon, hexagon, hep-
tagon, octagon, etc.

Folding Squares. Give each pupil a paper square, and
request the class to fold the paper so as to make an oblong;
then to fold it again, so as to make a small square.
. Next, having unfolded the papers, let them fold the square so
as to make right-angled triangles. Then let them tell how it was
folded, as, " Folding a square through its centre from corner to
corner will make a right-angled triangle."

80 MANUAL OF OBJECT-TEACHIXG.

Then let them fold this triangle again, and make a smaller
right-angled triangle. Lead pupils to notice that in the folding
of the triangle it is " folded from the middle of the long side to
its opposite corner."

Folding an Oblong. In a similar manner teach the pu-
pils to fold oblongs into other oblongs, also into squares and into
triangles.

Folding Rhombs. Let the pupils fold a rhomb through
its centre and the nearest opposite corners, and make equilateral
triangles.

Folding Equilateral Triangles. Fold the equilateral
triangle from the middle of one side to its opposite corner, and
make right-angled triangles.

Let the pupils also fold rhomboids, and notice what kind of

Folding Circles. First fold circles so as to make semicir-
cles ; next fold into quadrants. Let the pupils notice how many

Fold the circles into six equal parts call these sectors ; let the
pupils compare the shape and size of these with quadrants.

Fold the circle into eight equal parts ; count the sectors ; com-

Request the pupils to cut and fold these forms at home.

REVIEWING LESSONS IN FORM. 81

REVIEWING FORM LESSONS.

GOOD methods of teaching provide for reviews of each
subject taught, to gather up and fasten the important
facts in the pupil's mind. The real progress of the learn-
er can be determined only by such a review as will show
what the pupil retains of the subject, and what mental
powers have been strengthened by his attention to that
subject.

In conducting the review the intelligent teacher will
use such methods of testing the amount of knowledge
acquired, and the learner's ability to think upon the sub-
ject, as will prevent the giving of answers in formal,
'memorized phrases.

The review should not attempt to cover the minute
particulars embraced in the processes of instruction, but
aim rather to ascertain what essential facts have been se-
cured by the pupil ; and thus prepare for extending the
instruction upon the same or a kindred subject.

It is very important that the review should be as brief
and comprehensive as the circumstances will permit, with
due attention to the essential facts. The review should
take place as each successive stage of the subject, or
period of instruction, is completed.

For the further illustration of this matter it is proposed,
in this connection, that a review be had of the lessons
which are outlined in the Primary Object Lessons under
the head of Form,' and that this review shall be prepara-
tory to subsequent and advanced lessons upon the same
subject.

In order to suggest methods by which teachers may
determine whether the pupils have obtained real knowl-

4*

82 MANUAL OF OBJECT-TEACHING.

edge concerning the object or lesson, or have learned only
words about it, the following questions and directions are
presented as suggestive of a modc'of testing the result
of the instruction ; but these are not given for the teach-
er to follow literally. In every instance the questions
or the directions should be adapted by the teacher to the
condition and circumstances of the pupil, and be sug-
gested chiefly by his previous answer to a question or
by his statement upon the subject under consideration.

REVIEW EXERCISES.

Lines, and their Positions. Hold a string so as to rep-
resent a straight line.

Hold a string so as to represent a curved line.

Draw straight and curved lines on your slate.

What kind of line does the cord represent when it is wound
around a top ?

Place a string on the table so that it will represent a spiral line.

In what position is the kite string when the kite is high in the
air?

Hold two pencils so as to represent parallel lines.

Draw vertical, oblique, and horizontal parallel lines on your slate.

Hold one pencil perpendicular to another pencil.

Hold a pencil perpendicular to the side of the desk.

Angles. Take two pencils and represent an acute angle; a
right angle; an obtuse angle.

If you should cut a circular pie into four equal parts, what angles
would be formed ?

If a pie be cut into three equal pieces, what kind of angle would
each piece have ?

If a pie be cut into six equal pieces, what kind of angle would
each piece have ?

If one boy had a piece of pie with an obtuse angle, another a
piece with a right angle, and another a piece with an acute angle,
which boy would have the largest piece of pie, and which the
smallest piece ?

Plane Forms. How many lines must you make in drawing
a square ?

KEVIEW EXERCISES. 83

How many lines in a triangle ?
How many lines in an oblong ?
Could you make an oblong with four equal sides ?

Triangles. When all the sides of a triangle are equal, what is
the name of it ?

How many right angles can a triangle have ?

How many obtuse angles can a triangle have ?

If a triangle has one right angle, or one obtuse angle, what must
the other two triangles be ?

How many acute angles must each triangle have ?

How many acute angles has a right-angled triangle ?

How many acute angles has an acute-angled triangle ?

How many has an isosceles triangle ? '

What kind of angles has a scalene triangle ?

How would you cut a square in half so as to make two triangles ?

Rhomb. If you should draw a plane figure with four equal
sids, two acute, and two obtuse angles, what woul d be its shape ?
Where is the difference between a square and a rhomb ?

Polygons. What kind of angles do pentagons, hexagons, hep-
tagons, octagons, etc., have ?

Oval. What is the difference between an oval and an ellipse ?
How could a hard-boiled egg be cut so as to represent an oval ?
Try it at home.

Circle. How could a boiled egg be cut so as to represent a
circle ?

How could you cut a circle from an apple ? Try it.

If you cut a circle in half, what will be the shape of each part?

What have you eaten that had the shape of a circle ? of a square ?
of an oblong ?

Solids. Could you make a cube of an apple ? of a piece of
cake ? of a slice of bread ?

How would you make it ?

[Ans. Cut it so that it would have six equal square sides.]

Did you ever eat a cube ? What was it made of? What would
you like to have a cube made of if you must eat it ?

If you should cut a slice from the side of a cube, what would be
the shape of the slice ?

84 MANUAL OF OBJECT-TEACHING.

Did you ever eat a sphere ? What was it rnade of ?

Did you ever eat a cylinder ?

Could you make a cone of something good to eat ?

Did you ever eat anything of the shape of an ovoid?

Could you cut a square prism from a slice of bread-and-butter ?

Could you make a pyramid from a potato ? What is the shape
of the sides of all pyramids ?

Could you make a sphere from a hard-boiled egg ? How would
you make a hemisphere from an orange ? How many hemispheres
could you make from a very large orange ?

If you break a cylindrical stick of candy in half, what will be the
shape of each piece?

What shape are the sides of all prisms ?

What shape must the base of a cube have ?

Can a cylinder have a square base ?

If a prism has six equal oblong sides, what must be the shape of
its ends ?

The foregoing questions and directions will suggest
many others for reviews. The questions for this purpose
should be so formed as to lead the pupils to discover new
facts and relations in the lessons on Form.

Point. Make a small dot on your slate. You may call that dot
a point. Has the point length ? Has the point breadth ? Has the
point thickness ?

A point has neither length, breadth, nor thickness. It has position
only. A point has no magnitude or dimension.

Line. Make two points on your slate. Draw a line from one
point to the other. Has the line length ? Has the line breadth ?
Has the line thickness ?

A line has neither breadth nor thickness. It has length only. A line
is a magnitude of one dimension.

Surface. Make four points on your slate to represent the four
corners of a square. Draw lines so as to connect these dots. Move

your finger from one side to the other of this square ; move it from
the top to the bottom of the square. That part within these lines
is the surface. Has the surface length ? Has the surface breadth ?
Has the surface thickness ?

A surface has length and breadth. It has no thickness. A surface is
a magnitude of two dimensions.

Figure. A. form that is represented by a plane surface is called
a figure. The size and shape of a figure are determined by lines.

Boundary. How many straight lines form the sides of this
square? How many straight lines has the triangle? How many
lines has the circle ?

The lines that form the sides of plane Jigures are the BOUNDARIES
of those figures.

The boundaries of a triangle, a square, or rhomb are called its
sides. The boundary of a circle is its circumference.

How many boundaries has a triangle ? How many has a square ?
How many has a rhomb ? How many has a pentagon ? How many
has an octagon ?

Linear Figures. Figures that are bounded by lines are
called linear figures. AVhat is the least number of lines that will
bound a linear figure ? What kind of line must be used ?

What is the least number of straight. lines that will bound a linear
figure ?

What linear figures are bounded by two lines? (Semicircle, seg-
ment, crescent.) Represent a figure bounded by two lines.

Make three different figures, each bounded by one line, and write
the name of each figure in it. ( Circle, oval, ellipse.)

Make a figure bounded by two curved lines, and write its name.

Quadrilateral. Figures that have four sides or boundaries are
called quadrilaterals; as square, rhomboid, trapezium, trapezoid, etc.*

Parallelogram, Figures that have their opposite sides paral-
lel are culled parallelograms; as, squares, oblongs, rhombs, rhomboids.

Polygon. Figures that have more than four sides are called
polygons^ Regular polygons have equal sides, and equal angles.
Make six kinds of quadrilaterals, and write the name of each.

* See Primary Object Lessons, pp. 97, 99, 101, 103. t Ibid., pp. 103, 104, 105.

86 MANUAL OF OBJECT-TEACHING.

Make four kinds of parallelograms, and write the name of each.

Make six differing figures each bounded by three lines, and write
their names.

When may we call a plane figure with two equal acute, and two
equal obtuse angles a rhomb ?

What form may be produced from a rhomb by so changing its
angles as to make them all equal ?

How many squares can you draw around a single square, so that
one side of each shall be bounded by one of the sides of the single
square ? Try it.

How many squares can you place around one square, so that it
shall be touched by each square ?

Diagram. When a piaffe form is spoken of with regard to its
shape, it is called & figure. When several lines are arranged so as to
represent two or more combined figures for the purpose of illustra-
tion, it is called a diagram.

Draw a figure on your slate.

Draw a diagram on your slate.

Circle and its Parts.* Direct the pupils to draw six cir-
cles on their slates with a string and pencil. Write above them the
name of the figures ; and write around the first circle the name of
the boundary, and in the circle the name of the point in the middle.

Divide the second circle into two equal parts, and write the name
of the parts on one of them.

Divide the third circle into four equal parts, and write the name
of the parts on two of them.

Draw a line on the fourth circle to represent the greatest distance
across it, and write the name of it on the line ; also,
draw another line half the distance across the circle,
and write its name on it.

Draw lines in the fifth circle to represent a sector(l)
and a segment^), and write the name in each.
Draw lines on the sixth circle to represent a chord(S) and an ?r(4),
and write the name by each. Lead the pupils to notice
the differences between a sector and a segment; also be-
3 tween a chord and an arc, and to point out each.

Request the pupils to state what is represented in
each circle. Lead them to notice that all the diame-
ters of the same circle are equal ; that all the radii of the same cir-

* See Primary Object Lessons, pp. 106, 108, 111-114.

cle are equal ; and that the radius is always half of the
diameter.

Lead them also to notice that the chord of the arc of
a sextant of any circle equals the radius of that circle.
The dotted lines represent the chord of the arc, in this
cut. Let the pupils prove this equality with a pair of compasses.

Sextant. Draw a circle and divide it into six equal parts, or
sectors. Each of these parts may be called a sextant.

If a circle be divided into eight equal parts or sectors, each part
may be called an octant.

Tangent. Draw a circle; then draw a straight X^^V*

line so that it will pass the circle, just touching its cir- / \