"The awakening mind of the child ... is led from the material
body and its regular division to the contemplation of the
surface, from this to the contemplation of the line and to
the point made visible." FRIEDRICH FROEBEL.
"And it is precisely thus that the first artistic work of
primeval man occurs; he begins by the forming of simple rows,
as strings of beads, or of shells, for instance."
H. POESCHE.
"For the last step in this analysis the child receives small
lentil seeds or pebbles--concrete points, so to speak--with
which he constructs the most wonderful pictures."
W. N. HAILMANN.
1. The point made concrete, which forms the tenth and last of
Froebel's gifts, is represented by many natural objects, by beans,
lentils, pebbles, shells, leaves, and buds of flowers, by seeds of
various kinds, as well as by tiny spheres of clay and bits of wood
and cork.
2. We have been moving by gradual analysis from the solid through
the divided solid, the plane and the line, and thus have reached in
logical sequence the point, into a series of which the line may be
resolved.
3. The point which was visible in the preceding gifts, but inseparable
from them, now in the tenth gift has an existence of its own.
Although it is an imaginary quantity having neither length, breadth,
nor thickness, yet it is here illustrated by tangible objects which
the child can handle. By its very lack of individuality, it lends
itself to many charming plays and transformations.
4. By the use of the point the child learns practically the
composition of the line, that its direction is determined by two
points, that the shortest distance between two points is a straight
line, and that a curved line is one which changes its direction at
every point. The gift closes the series of objects obtained by
analysis from the solid, and prepares for the occupations which are
developed by synthesis from the point.
5. The outlines of all geometrical plane figures both rectilinear and
curvilinear may be illustrated with the point as well as straight and
curved lines and angles of every degree.
6. The law of mediation of contrasts is no longer illustrated in the
gift itself, but simply governs the use of the material. All lines and
outlines of planes made with a series of dots show its workings, and
the symmetrical figures, as we have noted from the first, owe to it
their very existence.
Meeting-Place of Gifts and Occupations.
When we begin upon a consideration of the tenth gift, the last link in
the chain of objects which Froebel devised to "produce an all-sided
development of the child," we see at once that the meeting-place of
gift and occupation has been reached. The two series are now in fact
so nearly one that the point is much more often used for occupation
work than as a gift. This convergence of the series in regard to their
practical use was first noted in the tablets, and has grown more and
more marked with each succeeding object.
Though the point is in truth the last step which the child takes in
the sequence of gifts as he journeys toward the abstract, yet we are
met at once in practice by the apparently inconsistent fact that it is
one of the first presented in the kindergarten. This can only be
explained by the statement that it is in truth quite as much of an
occupation as a gift, and is used in the former sense among the
child's first work-materials as a preparation for later point-_making_
(perforating), and as an exercise in eye-training and accuracy of
measurement. It is not an occupation, of course, for the reason that
permanent results cannot be produced with it, and because no
transformation of its material is possible.
The Point as a Gift.
Before the child completes his kindergarten course, however, he should
certainly be led to an intellectual perception of the interrelation
of the gifts and their gradual development from solid to point, for
their orderly progression according to law, though it be but dimly
apprehended, will be most useful and strengthening to the mind. To
discern the logical order of a single series of objects is a step
toward the comprehension of world-order in mature life.[78]
[78] "This coming-out of the child from the outer and
superficial and his entrance into the inner view of things,
which, because it is inner, leads to recognition, insight,
and consciousness,--this coming-out of the child from the
house-order to the higher world-order makes the boy a
scholar."--Friedrich Froebel, _Education of Man_, page 79.
The mind in later childhood should be what Froebel describes his own
to have been. "I often felt," he says, "as if my mind were a smooth,
still pool scarce a handbreadth over, or even a single water-drop, in
which surrounding things were clearly mirrored, while the blue vault
of the sky was seen as well, reaching far away and above."
When the derivation of plane and of straight and curved line and their
place in the gifts are clearly understood by the child, there will be
no difficulty in gaining an equally clear apprehension of the point
and its position in the series. This may be done somewhat as follows.
When the children are playing with blocks on some occasion, we may
direct the conversation to the essential characteristics of the cube,
its faces, edges, and corners. Do they remember which one of their
playthings is like the face of the cube; do they remember cutting clay
tablets from the clay blocks?
It is most unlikely that this experiment will have been forgotten, but
if it has been, it may be easily repeated. Speak next of the edges of
the cube, and let the children recall the derivation of the stick.
That portion of the cube not yet discussed will now be seized upon by
the children, and they will ask if any of their playthings are like
the cube's corners. Can they think of anything; shall we not try to
make something?
Now the clay appears, cubes are quickly fashioned, and each child is
allowed to cut off the eight corners of his block. He has no sooner
done this than he sees the nearest approach we can make to a point,
and proceeds to make a design from them while he recalls the beans,
shells, lentils, etc., he has used before in a similar way.
It is well here to suggest making the bits of clay into tiny oblate
spheroids, and laying them away to dry so that we may make a group
work invention of them to-morrow. Better still, however, is the
instant introduction of sticks or wires to connect with the clay
points, and thus form at once the skeleton of the solid, which will
give an ineffaceable impression of the relation of point and line to
each other.
Pleasure of Child in Point-laying and Stringing.
The pleasure the child finds in point-laying is not confined to the
kindergarten, for playing with beads and pin-heads is an ordinary
nursery occupation in all countries, and which of us cannot recall
long happy hours on the seashore, or by the brookside, when we
gathered and sorted shells and smooth glistening pebbles, and laid
them in rows and patterns? The mere handling of a great store of these
gave a Midas-like delight, and what primitive artistic pleasure we
felt as we arranged them according to the principle of repetition to
border our garden-beds or to inclose our miniature parks and
playgrounds.
The same joy is felt in plucking, arranging, and stringing rose-hips,
the seeds of the ailantus, the nasturtium, the pumpkin, or the
"cheeses" of the mallow and wild geranium.
Miscellaneous Materials.
It will commonly be found that the child enjoys tenfold more the
objects for point-work which he finds himself than the more perfect
school-materials. Imagine the joy, for instance, of a bevy of
kindergarten children set free on Pescadero Beach (California), and
allowed to ramble up and down its shining sands to pick up the
wonderful Pescadero pebbles. What colors of dull red and amber, of
pink and palest green, what opaline lights, and smooth, glimmering
surfaces! "Busy work" with such materials would be worth while
indeed,--yet easy to obtain as they are, they are almost never seen
in use.
Smooth, white pebbles, washed entirely clean and sorted according to
size, are not uncommonly seen in the kindergartens, however, and are
especially useful in the sand-table, and if these and the shining
cream-colored shells could be found by the children themselves, their
pleasure in them would be immensely increased. That this is true is
proved by the experience of many teachers with seed-work. One of our
own brood of kindergartners once had a birthday melon party for one of
her children. The melons were brought to the kindergarten room and
there divided, the small host serving his guests himself. Great
interest was immediately shown in the jet-black seeds of the
water-melon in contrast with the smaller light-colored seeds of the
musk-melon, and unanimous appeals were made to the kindergartner that
they might be saved and used for inventions. This was done, and they
were always called for afterwards in point-work, rather than the
beans, or vegetable and wooden lentils.
In those kindergartens where the seeds of all fruits are saved by the
children at lunch hour, it is also noted that the collection thus made
is always the object of universal interest and preference.
Use of the Gift.
One of the first uses of the point may be in following the outline of
some form of life which the kindergartner has drawn in white or
colored chalk on the child's table. This is much more fascinating work
than the placing of seeds one space apart, three in a row, etc., for
the latter belongs to the "knowledge-acquiring side of the game,"
which, as Froebel says, is the "quickly tiring side, only to be given
quite casually at first, and as chance may provide suitable openings
for it."
The forms drawn in chalk may very well be of curving outlines of
vegetables, fruits, leaves, and flowers to connect with the study of
the first gift, and may include any other simple appropriate object
which the kindergartner is capable of drawing.
The more advanced child can of course make his own Life forms without
the aid of drawing, and if he is given different sizes and kinds of
shells, seeds, or pebbles, often arranges them with great ability to
imitate the shading of the object.
The beginning of the forms of knowledge is in placing the points in
regular order on the squared tables at the intersection of vertical
and horizontal lines. Next, the child lays one space vertical lines,
three points in a line, then two space lines with five points, then
horizontal lines, angles, parallelograms, borders, etc., following out
the school of linear drawing, and in this way progresses in an orderly
manner to the designing of symmetrical forms. Curved lines of course
are quite as easily represented as the straight, and really beautiful
designs are often made by the children with them.
Tenth Gift Parquetry.
Tiny circles and squares of colored paper corresponding to the wooden
lentils are also to be had with this gift, and afford a means of
preserving the designs in permanent form. They are so small, however,
as to give occasion for considerable patience in pasting them, and are
rather difficult to arrange with regularity without first drawing the
design. It is doubtful, in our opinion, if they may be considered to
be of any particular educational benefit, if indeed they are not a
positive harm to the child in that they require a too minute and
long-sustained use of the finer muscles.
Objections to the Gift.
These strictures on the tenth gift parquetry bring us naturally to the
criticisms lately made by eminent authorities upon some of the Froebel
materials. The objection that many of them require too minute handling
and too close attention on the part of children of the kindergarten
age seems, as far as the gifts are concerned, to hold especial weight
in regard to point-work.[79]
[79] The development of motor-ability in children and its
furtherance or arrest by the kindergarten materials concerns
the occupations more particularly, and as such will receive
full consideration in a later volume.
We need not consider here the physio-psychological tests lately made
of the early motor-ability of children and the results which these
have shown, but simply concern ourselves with what we have seen and
noted many times in daily kindergarten practice. Is it not true that
the laying of beans and lentils one inch apart on the tables, for
instance, is an occupation which requires very delicate handling on
account of the smallness of the object, its easy mobility, and the
exactness required to place it precisely at the crossing-point of
vertical and horizontal lines? Is it not true that such work requires
considerable effort from the kindergartner to make it interesting to
the child? Is it not true that there is a cramp of the fingers, shown
by a slight trembling, in getting hold of the tiny object and placing
it, a cramp of the eye in foreseeing and following the movement, and a
cramp of the body accompanying the tension of hand and arm? If all
these observations are correct, or measurably so, if they hold with a
majority of children, then point-laying as an occupation clearly needs
considerable modification in the kindergarten.
What are then the objections to the point as illustrated in bean,
coffee-berry, seed, and wooden lentil? In a word, that when
represented as above, it becomes too small and too mobile. The
difficulty of using these materials is immensely increased by the fact
that a slight movement of the child's table will send them all on the
floor, while even an ill-timed cough or sneeze, or puff of wind, will
blow them out of position. Point-laying is quite difficult enough for
the child's small powers under the best conditions, and need not be
made more so by undue mobility in the materials with which it is
carried on. This criticism would not hold of course as against large
shells or pebbles or as against Miss Marwedel's hemispheres and
ellipsoids.
How these Objections may be obviated.
The only good reason for using the small materials to which the
preceding objections have been made is a very good one, viz., that if
we are to take any concrete object to represent the point, it should
be as small as possible, since the point is in reality an intangible
something, having no one of the three dimensions. This reasoning seems
to be logical enough, and it is surely equally so, to insist that the
child shall at some time derive his own points from the cube and make
them as small as possible, that he may the better understand their
relation to line, plane, and solid. When once this relation is
understood, however, and before it is suggested to his mind, why may
he not use the larger materials, even though they do not illustrate
the point as perfectly? Any lack in perfect representation would
probably be more than compensated by the removal of the strain on the
accessory muscles and the gain in artistic development. This latter
point, indeed, needs special consideration, for there seems no doubt
that the continued use of such small objects for design leads to
accuracy and prettiness rather than breadth and power.
The Marwedel Materials.
If we throw out all the smaller materials used for point-laying, and
it seems advisable so to do, we still have left smooth pebbles from
one half to three fourths of an inch in diameter, and shells of any
univalve, such as the "money-cowry" (_cyproea moneta_). These should
be polished, as free from convolutions as possible, and not less than
half an inch in diameter. To these we may add Miss Emma Marwedel's
wooden ellipsoids and hemispheres, already mentioned, which are
satisfactory in size, and add the delights of color.[80]
[80] _Marwedel's Materials for Child-Culture_. D. C. Heath &
Co.
The hemispheres, which are about one half inch in diameter, come in
eight colors and also in the natural wood, are pierced for stringing,
and are similar to ordinary button-moulds, having of course one flat
side.
The ellipsoids in the six rainbow hues, black gray, brown, and wood
colors, resemble elliptical shells, having one flat side, are also
pierced for stringing, and vary in length from three fourths of to
something over an inch, being nearly an inch wide, perhaps, and a half
inch thick.
The children are invariably delighted with both hemispheres and
ellipsoids, and need no stimulus from the kindergartner in their use.
Mind-Pictures.
In some of Miss Marwedel's pamphlets on the use of these materials,
she speaks of the mind-pictures which can be made with them, and which
are of course quite possible with any of the other gifts. These
mind-pictures, showing form and number groups, are drawn by the
kindergartner on the blackboard, where they are left a second and then
erased. They are then copied from memory, and the results compared,
described, and criticised by the children. This constitutes a valuable
mental exercise, and if the tests are simple at first and made
gradually more difficult will be most valuable in increasing the
memory-span as well as in developing language power.
Abuse of the Gift.
If some of the materials used in the kindergarten are unwisely chosen,
and if this objection applies in the gifts, especially to the point,
then the kindergartner has been, and still is, unnecessarily
increasing her sum of error, for no one of the connected series of
objects (save the stick) is commonly so forced upon the child. It is
somewhat unusual for this reason to find a whole class of children
really enjoying point-work, though several conscientious and
industrious members of the group may be toiling away with praiseworthy
diligence.
Sometimes the children's feeling toward the gift goes beyond
indifference and passes into active dislike, but in either attitude of
mind the beans, lentils, etc., are likely to be mistreated.
It is not that the work with them is not in itself pleasing to the
child, but that it has been forced upon him _ad nauseam_, and that the
kindergartner has lacked interest in presenting it. His own interest
has in consequence gradually died out, and when once the fire is cold,
who shall light it again?
That there is no need of this abuse of the gift is clear enough, and
it can only come from entire lack of originality in using Froebel's
materials, or from a mental or physical inertia on the part of the
kindergartner, which causes her to prefer giving out such work as
needs neither preparation nor previous thought.