Maria Montessori believed that the hand was the direct link to the mind, so she chose to concretely teach form. Once the child can feel and understand three-dimensional objects, he can then move to more abstract two-dimensional, or plane shapes. Later he will create shapes out of smaller triangles and through work with the metal insets.
Geometric Solids
The geometric solids are three-dimensional representations of shapes. They include cube, rectangular prism, cylinder, cone, triangular prism, ovoid, ellipsoid, square-based pyramid, triangular-based pyramid, and sphere. The cube and rectangular prism are familiar because the child has worked with the Pink Tower (Pink Cubes) and the Broad Stair (Brown Prisms). He will also recognize shapes like cylinder, cone, ovoid, and sphere from his environment.
Children are encouraged to use both hands to feel all facets of each solid. They may play guessing games with the solid inside a bag. They may be blindfolded and use their hands to “see” what the form is. Another favorite game is “Which one is missing?” in which one of the solids is hidden and the child has to guess which one it is.
After the solids are introduced, the child will later match the solids to their bases. For example, the cube will match up to a square, whereas the rectangular prism matches both a square and a rectangle and the cone matches a circle.
Geometric Cabinet
The Geometric Cabinet consists of the plane, or two-dimensional, shapes. The initial tray introduces the basic shapes of square, triangle, and circle. The remaining six trays teach other curved and straight-edged shapes. The child learns to identify different forms of the basic shapes as well as other quadrilaterals and polygons.
In the initial presentations, each tray is introduced one at a time and the shapes are named. The child uses the first two fingers of his dominant hand to trace the edge of each shape in order to truly understand what it is. In subsequent lessons the child matches the shapes to cards. The first set of cards is a solid shape. The second set is a thick outline of each shape. The third set is a thin outline of each shape.
Constructive Triangles
With the constructive triangle boxes, the child recreates the plane shapes using smaller triangles. The triangles are color-coded by shape created, and have thick black lines that indicate where they are to join each other.
The introductory triangles are a set of blue triangles that allow for free exploration. Next comes the Triangle Box in which the child creates larger triangles from the smaller ones. In the remaining boxes, the Large and Small Hexagon Boxes and the Rectangle Box, the child creates other plane shapes. Another box of blue triangles matches the Rectangle Box so that those shapes can be made without the control of the color-coding and black lines.
Metal Insets
Plane shapes are also taught in the metal insets. As children learn how to control their pencils while tracing around the various shapes, they also learn to name all of them. This is the most abstract way the child is guided in his work with the various shapes, other than trying to draw them free-hand.
In the Sensorial area, Montessori starts the child with concrete representations of shapes through the three-dimensional Geometric Solids. She then moves to the abstract by introducing the plane shapes in the Geometric Cabinet, then having the child create them through the Constructive Triangles and Metal Insets.
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