Angles of every degree.
Triangles, quadrilaterals, and additional polygons.
Skeletons of solids by means of corks or peas.
6. The law of the mediation of contrasts is shown in the fact that
every line is a connection between opposite points. As in the other
gifts, the law governs the use of the line in the formation of all
outlines of objects and all symmetrical designs.
* * * * *
As we have already noted, the gifts of Froebel are thus far solids,
divided solids, planes and divided planes.
Relation of the Single and Jointed Slats to the other Gifts. How both
are used.
With the single and jointed slats we shall not deal separately, merely
stating that they form a transition between the surface and the line,
having more breadth and relation to the surface itself than to the
edge, but manifestly tending towards the embodied line of which the
little stick given by Froebel is the realization.
The jointed slats, generally ruled in half and quarter inches for
measuring, may be used to show how one form is developed from
another,--for instance, the rhombus from the square, the rhomboid from
the oblong, and they are very useful also for explaining and
illustrating the different kinds of angles, as the opening between the
joints may be made narrower or wider at pleasure.
The disconnected slats are used for the occasional play or exercise of
interlacing, forming a variety of figures, geometrical and artistic,
which hold together when carefully treated.[66]
[66] "The slats form, in some sort, the transition from the
surface-pictures of the laying-tablets to the lineal
representations of the laying-sticks, but have this advantage
over both tablets and sticks, that the forms constructed with
them are not bound down to the surface of the table, but
possess sufficient solidity to bear being removed from
it."--H. Goldammer, _The Kindergarten_, page 155.
Materials of Froebel's Gifts.
As to the unpretentious little sticks themselves, the use of these
bits of waste wood is entirely unique and characteristic. No one else
would have deemed them worthy of a place in school apparatus or among
educational appliances; but Froebel had the eye and mind of a true
philosopher, ever seeing the great in the small,--ever bringing out of
the commonplace material, which lies unused on every hand, all its
inherent possibilities and capabilities of usefulness. Froebel was no
destructive reformer, but the most conservative of philosophers.
How the Stick is to be regarded.
The stick of course is to be regarded in its relation to what comes
before and after it,--as the embodied edge of the cube, as the tablet
was its embodied face. The child should at last identify his stick,
the embodiment of the straight line, with the axis of the sphere, the
edge of the cube, and the side of the square.[67] The sticks and rings
are, properly speaking, one gift, contrasting the curved and straight
lines.
[67] "Just as we obtained the tablets from the cubes, of which
they are the embodied faces, so now we obtain also the
laying-sticks from the cube, whose edges they represent. But
they are contained also in the laying-tablets, for one may
regard the surface as produced by the progressive movement of
a line, and this may be made clear to the child by slicing a
square tablet into a number of sticks."--H. Goldammer, _The
Kindergarten_, page 161.
Method and Manner of Lessons.
Although the stick exercises should make their appearance at least
once every week after their introduction, they may always be varied by
stories, and when occasionally connected with other objects, cut from
paper to illustrate some point, are among the pleasantest and most
fruitful exercises of the kindergarten.
The sticks may be used for teaching number and elementary geometry,
both in the kindergarten and school, or for reviewing and fixing
knowledge already gained in these directions, for practice in the
elements of designing, for giving a correct idea of outlines of
familiar objects, and should constantly serve as an introduction to
drawing and sewing lessons, to which they are the natural prelude.
They should be used strictly after the manner of the other gifts,
beginning with careful dictations, in which the various positions of
one stick should be exhausted before proceeding to a greater number,
with cooperative work, and with free invention. These exercises and
original designs may be put into permanent form in parquetry, which is
furnished for this gift in the various colored papers, as well as for
the tablets. The inventions may also be transferred to paper by
drawing, and to card-board by sewing.
The exercises may continue from the various simple positions which one
stick may assume to really complex dictations requiring from fifteen
to twenty-five sticks, and introducing many difficult positions and
outlines of new geometrical figures.
Forms of Knowledge and Number Work.
When we consider that the length of the sticks varies from one to six
inches, and that the number given to the child is limited only by his
capacity for using them successfully, we can see that the outlines of
all the rectilinear plane figures can easily be made by their use. Of
course in these exercises there must be a great deal of incidental
arithmetic, but the gift may also be used for definite number work,
and is far better adapted to this purpose than any other in the
series, since it presents a number of separate units which may be
grouped or combined to suit any simple arithmetical process.
Representing the line as it does, it has less bodily substance than
any previous gift, and hence comes nearest to the numerical symbols,
as the next step to using a line would obviously be making one. It
also offers very much the same materials for calculation as were used
by the race in its childhood, and hence fits in with the inherited
instincts of the undeveloped human being.[68]
[68] "Each following generation and each following individual
man is to pass through the whole earlier development and
cultivation of the human race,--and he does pass it;
otherwise he would not understand the world past and
present,--but not by the dead way of imitation, of copying,
but by the living way of individual, free, active development
and cultivation."--Friedrich Froebel, _Education of Man_,
page 11.
Who has not seen him arranging twigs and branches in his play,
counting them over and over or simulating the process, and delighting
to divide them into groups? So the cave-dweller used them, doubtless,
not in play, but in serious earnest, for some such purpose as keeping
tally of the wild beasts he had killed, or the number of his enemies
vanquished.
"With a few packets of Froebel's sticks," as has been very well said,
"the child is provided with an excellent calculating machine." The use
of this machine in the primary school in word making as well as in
number work is practically unlimited; but in the kindergarten it may
very well give a clear, practical understanding of the first four
rules of arithmetic,--an understanding which will be based on personal
activity and experience.[69]
[69] "Thus the child's sphere of knowledge, the world of his
life, is again extended by the observation and recognition,
by the development and cultivation, of the capacity of
number; and an essential need of his inner nature, a certain
yearning of his spirit, are thereby satisfied.... The
knowledge of the relations of quantity extraordinarily
heightens the life of the child."--Friedrich Froebel,
_Education of Man_, page 45.
Evolution of the Kindergarten Stick.
It is well by way of prelude to the first few lessons to draw from the
children the origin and history of the tiny bit of wood given them for
their play, and they will henceforth regard it in a new light and
treat it with greater respect and care.
Let us trace it carefully from its baby beginnings in the seed, its
germination and growth, the influences which surround and foster it
from day to day, its steady increase in size and strength, its
downward grasp and its upward reach, the hardening of the tender stem
and slender cylindrical trunk into the massive oak or pine, the growth
of its tough, strong garment of bark, its winter times of rest and
spring times of renewal, until from the tender green twig so frail and
pliant it has become too large to clasp with the arms, and high enough
to swing its dry leaves into the church tower.
Then let us follow out its usefulness; for instance, we might first
paint a glowing word-picture of the logging-camp, the chopping and
hewing and felling, the life of the busy woodcutter in the leafy woods
in autumn, or in the dense forests in winter time, when the snow, cold
and white and dazzling, covers the ground with its fleecy carpet.
Again, let us depict the road and the busy teamsters driving their
yokes of strong oxen with their heavy loads of logs to the towns and
cities where they are to be sold. A scene, a perfect word-picture,
should be painted of everything concerning the trip,--the crunching of
the oxen's hoofs on the pressed snow, the creaking of the heavy truck
as its runners slip along the smooth surface, the breath of the men
and animals rising like steam into the clear, cold air. All these
things rise in image before the child's eye and are not soon
forgotten, you may be sure. The work and life of the river-drivers
might also be described, and their manner of floating the logs down
river in springtime when the water is high and the current strong.
Then perhaps the children will help to tell us about the mill of which
they doubtless know something,--where the sawmills are built, how the
water helps in turning the great wheel, the buzzing and hissing of the
big saws, and the way in which they quickly make boards of the long,
strong logs. This and much more may be said, and if it is well said,
no child can ever look at the tiny stick afterwards and entirely
forget the charm which once surrounded it.[70]
[70] "These terse graphic descriptions of objects will be
found very serviceable in sharpening and intensifying the
powers of observation, as well as securing clearness,
distinctness, accuracy, and life in verbal description. Here
the pupil learns practically to give due prominence to
essentials, and to appreciate the full value of accessories;
to look for and discover the fundamental ideas of which
things are the modified, adorned, garbled, or stunted
expression; to seek and find the very soul of things."--W. N.
Hailmann, _Primary Helps_, page 17.
Group Work with Sticks.
The sticks are especially serviceable for group work of various kinds,
either at the long or square tables. As the children have now an
abundance of material they can make all the objects, perhaps, which
may be mentioned in a story the kindergartner tells. If it is about
the origin of Thanksgiving Day, for instance, Abby, who sits at one
end of the line, may make a picture of the Mayflower, and John, her
neighbor, make the Speedwell. The next child may construct a cradle
for Oceanus, the little Pilgrim baby born on shipboard; the next use
his material for the Indian huts the settlers saw after landing; and
so on, each child making a different object, which remains upon his
table until the close of the story. When this is completed, it will
have been fully illustrated by the children with their sticks, and
they will be delighted to inspect the different pictures which they
will plainly see are much more varied and beautiful than any one of
them could have made alone. Thus the value of cooperation will be
plainly shown, without a word from the kindergartner.[71]
[71] "In this group work it is desirable that the common
aims should be fully within the comprehension of each little
worker, yet sufficiently beyond his powers of execution and
endurance to make him sensible of the need of assistance. The
former secures the possibility of individual enjoyment, and
hence the only reliable incentive to persistence; the latter
insures free subordination to the will of the whole, the
essential condition of success."--W. N. Hailmann, _Primary
Helps_, page 18.
Forms of Life.
As to Life forms in general, their number is practically unlimited,
though as they are only line-pictures, and heavy lines at that, they
are not as real as those made in the Building Gifts. They are easily
made, however, and the veriest baby in the kindergarten who handles
the sticks as a prelude to his drawing exercises invents with them all
sorts of rude forms which he calls by appropriate names.
The question of color as it enters into these forms needs, perhaps, a
moment's consideration here. As the gift includes both white and
colored sticks, would it not be well to use the former for all
dictations in Life forms, reserving the brilliant hues for the forms
of symmetry whose charms they would greatly enhance?
Connection of other Objects with Stick Dictations.
We may sometimes connect simple, inexpensive objects with stick
dictations, with a view to making them more realistic and delightful.
When the little ones are just getting the various positions and
corresponding terms into their minds, and when therefore it is
advisable to keep them amused and happy with one to three sticks as
long as possible,--that is, until the fundamental principles have
become very familiar,--these objects are most invaluable.
Innumerable lessons may be practiced with one stick only, calling it
at last a whipstock and giving it a bit of curly paper for a lash. Far
from being an instrument of punishment, it makes every child laugh
with the glee of possession.
With two sticks laid horizontally we may give a little paper
horse-car, or when one is vertical and the other runs horizontally
across its end, we may call it a candlestick and snip a half-circle of
paper into the semblance of a flame. The effect is electrical, though
the light be only one candle-power.
And so on, _ad infinitum_; it is enough to give the hint for the play.
We can cut little paper birds for the bird-cages, tumblers for the
rude little tables, green leaves for the trees, etc., making the stick
exercise, even in its first more difficult details, a time of great
satisfaction and gladness.
Complete sets of these card-board objects, one for each child, should
always be kept on hand; if well made they will last a year.
Forms of Beauty.
Enough has already been said of the possibilities of the sticks to
show that they are most valuable for symmetrical forms. They may be
combined with the tablets, and thus very pretty effects be made, and
when four children unite their material at the group work tables, the
dictations and inventions produced are of course very large, and may
be really beautiful if constructed on artistic principles.
Border work may be very fully carried out with the sticks, and another
charming feature of the gift is the way in which it lends itself to
the making of snow crystals. These are symmetrical combinations and
modifications of familiar geometrical forms around the hexagon. Mr. W.
N. Hailmann says regarding them: "At first, it is best to give each
child only six or twelve sticks, and to dictate the central figure (a
hexagon or hexagonal star) verbally or by means of a drawing on the
blackboard. They may then receive a number of additional sticks, and
let the central figure grow, all obeying the teacher's dictation, or
each following his own inventive genius."[72]
[72] "These forms are invaluable even as _silent_ teachers
of geometrical and numerical relations. Used judiciously
in conversational lessons, leading to partial or complete
analysis of the figures in spoken or written descriptions,
their teaching power is inexhaustible."--W. N. Hailmann's
_Primary Helps_, page 21.
In this gift, as well as in the seventh, the child's imitative and
inventive powers are obviously more greatly taxed than in the others,
and the danger will be, if he is not well trained, that, as he
apparently can do anything with the material, he will end by doing
nothing. The greater the freedom given to the child, the greater the
necessity of teaching him to use that liberty in and through the law,
and not to abuse it by failing to reach with its aid the highest ends.
Connection of Sticks with Drawing.
We may make the laying of one-inch sticks in vertical and horizontal
positions, in angles and squares, a prelude to the drawing of similar
lines; and the copying of stick dictations, either from the table, or
from memory, into drawing, is a most excellent exercise, calling into
requisition great correctness and good judgment, besides an unusual
amount of calculation, since the stick dictation will be on a scale of
one inch, and the drawing on a scale of one fourth inch, reducing the
original design to one in miniature. The child will almost always
begin by attempting to make the picture exactly like his model in size
without counting the inches and trying to make it mathematically
correct; but after the idea is carefully explained and fully
illustrated, he will have no further difficulty excepting, perhaps,
with the more complicated figures containing slanting lines.
Ambidexterity.
We should encourage in all possible ways the use of both hands in all
the exercises with gifts and occupations, not only that one may be as
skillful as the other, but also to avoid a one-sided position of the
body which frequently leads to curvature of the spine. The well-known
physiologist, Professor Brown-Sequard, insists on the equal use of
both hands, in order to induce the necessary equal flow of blood to
the brain. Through the effect of our irregular and abnormal
development, the cause of which is the too persistent use of the right
hand, one lobe of our brains and one side of our bodies are in a
neglected and weakened condition, and the evils resulting from this
weakness are many and widespread. Dr. Daniel Wilson says: "In the
majority of cases the defect, though it cannot be wholly overcome, may
be in great part cured by early training, which will strengthen at
once both the body and mind."[73]
[73] "Whenever the early and persistent cultivation of the
full use of both hands has been accomplished, the result is
greater efficiency, without any corresponding awkwardness or
defect. In certain arts and professions, both hands are
necessarily called into play. The skillful surgeon finds an
enormous advantage in being able to transfer his instrument
from one hand to the other. The dentist has to multiply
instruments to make up for the lack of such acquired power.
The fencer who can transfer his weapon to the left hand
places his adversary at a disadvantage. The lumberer finds it
indispensable, in the operation of his woodcraft, to learn to
chop timber right-and-left-handed; and the carpenter may be
frequently seen using the saw and hammer in either hand, and
thereby not only resting his arm, but greatly facilitating
his work. In all the fine arts the mastery of both hands is
advantageous. The sculptor, the carver, the draughtsman, the
engraver, the cameo-cutter, each has recourse at times to the
left hand for special manipulative dexterity; the pianist
depends little less on the left hand than on the right; and
as for the organist, with the numerous pedals and stops of
the modern grand organ, a quadrumanous musician would still
find reason to envy the ampler scope which a Briareus could
command."--Dr. Daniel Wilson, _Left-Handedness. A Hint for
Educators_.
Abuse of Eighth Gift.
No materials of the kindergarten (save the beans, lentils, etc., which
serve to represent the point) have been so over-used and so abused as
the sticks. When no other work was prepared for the children, when
helpers were few, and it was desirable to give something which needed
no supervision, when inexperienced students were to take charge of
classes, when the kindergartner was weary and wanted a quiet moment to
rest, when everybody was in a hurry, when the weather was very cold,
or oppressively warm, when there was a torrent of rain, or had been a
long drought, the sticks were hastily brought forth from the closet
and as hastily thrust upon the children. These small sufferers, being
thus provided with work-materials in which it was obvious that
superior grown people took no interest, immediately lost interest
themselves. In riotous kindergartens the sticks were broken, poked
into pockets, and thrown on the floor; in the orderly ones they were
gazed at apathetically, no one deeming it worth while to stir a hand
to arrange them, save under pressure. Sticks had been presented so
often and in so tiresome a manner that they produced a kind of mental
atrophy in the child,--they were arresting his development instead of
forwarding it.
Such an abuse of material is entirely unnecessary in the kindergarten,
where so many ways are provided of presenting the same truths in all
sorts of different and charming guises. It is unnecessary and most
unfortunate, for it has frequently thrown undeserved contempt on an
innocent and attractive gift, which, when properly treated, is one of
the most pleasing and useful which Froebel has bequeathed to us.