Geometry
The experiences with Geometry are similar to other Sensorial Extensions, aiming to introduce children to different areas of the classroom. The purpose of Geometry in the Children’s House is to allow the Absorbent Mind to gain Experiential and Sensorial exposure to each element and for this to be retained in the Mneme before the child analyses it at the Elementary Level.
Before the child enters the Children’s House she will have been indirectly prepared for Geometry lessons by the sight of common geometric shapes in her daily life – windows are rectangular, the mirror is oval balls are spherical, cupboards resemble cuboids. However, the correct terms for these shapes are unlikely to be given, especially with any consistency or clarity – though if parents are made aware they can easily do so.
Often the child’s first explicit experience with Geometry is in the Sensorial Area of the Children’s Home Before this indirect preparations are given in the Exercises of Practical Life, especially folding napkins, which introduces rectangles and triangles, though there are other experiences, like washing the chowki. The first direct materials for the conscious development of Dimension and Form, which are known as the Cylinder Blocks, Pink tower, Brown Stair and Red Rods. These materials prepare the child, trough muscular and visual impressions for arithmetic, and algebra because of they are designed to represent the decimal system. The Geometric Solids introduces three-dimensional shapes encourage the child to connect abstract forms to objects in her daily environments, the Binomial Cube gives the child an impression of Geometric formulas, while the Geometric Cabinet and Cards gives the child an opportunity to study and manipulate ‘materialised abstractions’, laying down kinaesthetic memories for later application. The Stereognostic exercise with the Cabinet gives further opportunities to work with the shapes and all of the above exercises are used as opportunities to give the precise language needed to crystallise abstract qualities and communicate ideas abut them. The Constructive Triangles are another type of analytical Geometric experimentation; the discoveries of new shapes within known ones indirectly prepares for theoretical work with shapes (e.g. area, perimeter, Pythagorus) and the associated terminology. The Binomial and Trinomial Cubes and the Sensorial Decanomial Square are very closely related to both Geometry and Algebra.
The Nomenclature Cards for parts of a triangle, circle and square build on this as do the Small Metal Insets (divided triangles and squares) which allow children to identify similarities, differences between shapes, build on their vocabulary and identify identical matches using tools, rather than tracing. Children also produce booklets in which their Geometric Explorations are conveyed through illustrations and, when they are able, writing.
Children are familiar with Geometry in Art when they fold and cut paper, complete needlework and notice patterns in their free expression, coloured inks, designs and patterns can be used deliberately to link art to shape, using tessellation, mirroring and rotation. The Graded Geometric Figures bring together Geometry with Art; a vital link, often missing in other forms styles of teaching Maths, paving the way for Physics and Philosophy. Children the age of five children are shown technical skills; how to use protractors to draw and measure angles, the Montessori Protractor to calculate fractions and shown methods to calculate height, length, circumference, weight and capacity, to use metric and decimal units, calculate the time in hours and days and later on the Calendar.
Language Cards of Geometry
Material Description:
One definition set of each of the following
- Polygons
- Squares
- Quadrilaterals
- Triangles
- Parts of a triangle
- Parts of a circle
- Parts of a square
- Different types of angles
- Different types of lines
How to make:
Decorate the isolated part of the figure, which is made out of paper
Presentation:
- Present with the correct vocabulary in the ‘Three Period Lesson’, through games and by encouraging children to make and draw the figures themselves with geometric instruments
- The children learn the names and shapes and make their own designs, booklets, drawings and any further work they choose to clarify their understanding.
- Allow the child to decorate her booklet
- Full Definition Set I
- Definition split into parts
- Later, when they can read, encourage the child to write her own definitions using a good dictionary for reference
- The definition set is given, preferably after the child has written her own.
Criteria of Perfection (Control of error):
- The cards and booklets themselves
Direct Aim:
- To prepare the child for further work with Geometry and enrich vocabulary
Age at Presentation:
Five and a half to six and a half years