Cabinet of Geometrical Plane Figures

MATERIAL I - THE PRESENTATION TRAY:

This is a strong wooden tray containing three square of plain
wood, and three wooden frames with insets of a square (sides 10 cm),
a circle (diameter 10 cm), and an equilateral triangle (sides
10 cm). Each inset and the bottom of the tray are painted blue.
The rest of the wood is finished with a clear, colorless varnish.
 

MATERIAL II - THE CABINET

The cabinet has five drawers. All the insets of the cabinet are
blue, and the bottom of each drawer is light grey-blue.
All the rest of the wood is lightly varnished. Each figure in the
presentation tray and the cabinet has a small knob in the center
to hold it by.

Drawer 1 - Six Circles

There are six circles, each inset in a square wooden frame and arranged in
order of size. They have diameters of 10 cm, 9 cm, 8 cm, 7 cm, 6
cm, 5 cm, respectively. Thus, they vary in size in a regular way
with 1 cm difference in diameter between any two in succession.

Drawer 2 - Six Rectangles

There are six cut-out rectangles kept in order of size, each in a square
wooden frame. The rectangles are 10x10 cm., 9 x 10 cm., 8 x 10 cm.,
7 x 10 cm., 6 x 10 cm., and 5 x 10 cm., respectively. Thus, they also
vary in a regular way with 1 cm. difference on one side between
each in succession.
 

Drawer 3 - Six Triangles

There are six different triangles inset in square frames. Three scalene
triangles (no equal sides) in one row, and three isosceles triangles
(two equal sides) in the other row. Triangles are classified by their
sides and their angles. All triangles have at least two acute angles.
They are named by the third angle.
Counting the equilateral triangle in presentation tray, there are
seven triangles in all.

Drawer 4 - Six Polygons

The six polygons all inscribe within the10 cm. diameter circle.
A Pentagon (5 sides and 5 angles)
A Hexagon (6 sides and 6 angles)
A Heptagon (7 sides and 7 angles)
An Octagon (8 sides and 8 angles)
A Nonagon (9 sides and 9 angles)
A Decagon (10 sides and 10 angles)
 
Polygon means many angles

Drawer 5 - Four Quadrilaterals and the Ellipse and Oval

This drawer contains the other four quadrilaterals - the
parallelogram, the rhombus, the trapezoid, and the right-angled trapezoid. (The
square and the rectangle are in drawer 2.) It also contains two curved
figures - the ellipse and oval.
 
With this drawer all the possible regular quadrilaterals are in
the cabinet.
 
  • Square - all sides are equal and all angles are right angles.
  • Rectangle - opposite sides are equal and parallel, angles are right angles.
  • Parallelogram - opposite sides are equal and parallel (the square, rectangle, and rhombus are all parallelograms).
  • Rhombus - all four sides are equal (equilateral parallelogram) but the angles are not right angles.
  • Trapezoid - two sides parallel. (In countries other than the U.S. this is called trapezium.)
  • Trapezium - no two sides are parallel (not in the Neinhuis cabinet).
  • Oval - egg shaped (from ovum meaning an egg).
  • Ellipse - A symmetrical plane figure bounded by a single curved line every point of which is not equally distant from the point at the center when viewing 1/2 of the symmetrical plane.
    •  
    Thus, the cabinet contains all the regular plane figures and
    enables the child to classify every plane shape he sees in the
    environment.

    PURPOSE:

    1) A visual and tactile study of the full classification of the
    regular plan shapes as a foundation for the later study of
    geometry
    2) To learn the words which will be needed and which will allow the
    child to express himself
    3) To make the child aware of shapes in the environment and to get him
    to observe the environment with intelligence
    4) Perfection of movement of the hands
    5) Indirect preparation for writing as the child is feeling the
    curves and straight lines similar to the ones which compose the
    letters of the alphabet and his hand is being trained

    PRESENTATION:

    The Presentation Tray
     
    The presentation tray is placed in front of the child on a table.
    The teacher sits beside the child. The teacher removes each inset
    in turn and places it on the blank square above or below the space
    from which is was taken out. The teacher pauses after removing the
    inset to let the child observe the fact that the space left by a
    figure is the same shape as the figure itself. The fact that the
    bottom of the drawer is the same color as the figures helps make
    this more apparent.
     
    The teacher takes one figure, holding it by its knob, and with the
    tips of the first two fingers of her dominant hand she traces
    exactly around the circumference of the figure. Then, she also
    traces around the circumference of the space left by the figure.
    She then replaces the figure in its socket. The teacher repeats
    this with each figure in turn.
     
    At any point in the demonstration, the child may join in using the
    material as demonstrated, or he may be invited to use the material
    himself when the demonstration is over.
     
    The exact feeling of the contours is difficult and most children
    need to be given exact demonstrations several times. The teacher
    does not interrupt the child when he is working but, instead,
    gives him a lesson another day before he begins to use the
    material, stressing the handling of the material at that time. The
    figure is held still and the fingers move around it.
     
    Before giving a lesson the teacher must herself practice with the
    material until her own movements are perfect.

    PRACTICE:

    The child uses the material as demonstrated.

    EXTENSION:

    When the children have had the material to work with for some time
    the teacher may, after school, prepare the tray for the next day
    by varying the figures with three other contrasting figures from
    the cabinet. For example, the teacher might remove the circle,
    square, and equilateral triangle and put an ellipse, a rectangle,
    and a polygon in the tray. Over a period of time the children
    become familiar with all the figures in the cabinet because the
    teacher changes the figures in the tray from time to time. The
    cabinet is kept in a stock cupboard outside the classroom during
    the period that the figures are being introduced in the
    presentation tray.

    LANGUAGE:

    When a child knows any figures well, their names may be taught
    using the three period lesson.

    PRESENTATION:

    The Cabinet
     
    Place the cabinet in the room. Once the cabinet has been brought
    into the classroom all the figures must be kept in their right places
    in the cabinet. It is no longer possible to vary the figures in the tray.
     
    The teacher takes a drawer (e.g. of circles) from the cabinet and
    places it on the table in front of the child. She removes the
    insets, placing them in a mixed order on the table to one side of
    the drawer. She picks up a figure, feels around it, then feels
    around the sockets until she has decided where the circle fits;
    she then replaces it and takes another. The child joins in as soon
    as he understands the exercise; then the teacher can leave him to
    work alone.
     
    When one tray has been introduced to a child, he may help himself
    to any tray and do the exercise in this way.

    OBSERVATION:

    The teacher must be aware that the child may use the cabinet in a
    free way. She must watch before deciding to interrupt him.
    Children may spin the circle around, they may discover that a
    square will fit into its socket in four positions, that the
    rectangle must be rotated through 180 degrees, etc. They are
    gaining valuable knowledge when they experiment in this way.
     
    The figures may be compared and some geometrical deductions made.
    For example, the polygons may be inscribed in the largest circle.
    It can be clearly seen when doing this that the more sides a
    figure has the nearer it is to the area of a circle.

    CONTROL OF ERROR:

    Many figures will not fit into the wrong sockets. In the case of
    the circles or the rectangles, if a mistake is made, there will
    always be one figure at the end which will not fit into the last
    socket.
     

     

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