Sensorial Materials: Geometry
The Sensorial materials may emphasize the development and refinement of the senses, but they are equally powerful tools for supporting the child's mathematical mind. Elegantly constructed, these materials introduce elements of geometry and algebra through hands-on, concrete, didactic exploration.
The child first explores qualities of dimension: height, width and depth. The Pink Tower, Broad Stair, Red Rods, Knobbed and Knobless Cylinder Blocks give children the opportunity to name and classify these qualities and their superlatives. Larger, smaller, deeper, wider, and so on... by moving the apparatus about the room, children have real, physical experiences of the ways to classify dimension and of the real changes that are caused by seemingly minor differences. Simultaneously, each of these materials is based on a system of tenths, with each cylinder, prism or cube proportioned equally to its next largest companion. The cubes of the Pink Tower, for example, range in depth from 1cm^3 to 10cm^3. The second smallest cube is 2cm^3. The third smallest is 3cm^3 and so on, such that the smallest cube is 1/10th the size of the largest. The same structure exists for each of these early Sensorial materials, a quality that children often discover on their own as they realize that they can stair-step the smallest prism up the rest of the Broad Stair, or can create a length comparable to the longest Red Rod by placing the smallest and the second longest next to each other. The curious child given enough time to explore will discover that the cubes of the Pink Tower, when aligned on two edges, create a ledge the perfect size for the smallest cube to slide around. Children allowed to explore these materials together will discover endless combinations and patterns created by the precision of these materials. (Google "Sensorial Grand Array" for some examples!)
Other materials in the Sensorial sequence are more direct. The Geometric Solids introduce the common shapes of geometry in ways the child can compare and manipulate. The Metal Insets allow children to master forming these shapes and to explore mental rotation, symmetry, and scale. The Geometric Cabinet makes these representations more abstract and expands the child's nomenclature. The Constructive Triangles demonstrate the triangular base structure within straight-edged geometric shapes. Meanwhile, the Binomial Cube, Trinomial Cube and Decanomial prepare the child both for the relationships of Geometry and the language of Algebra.
Do children really need to understand Geometry and Algebra in early childhood? Well, probably not in the same way you did when you learned it in school. For young children, these are not lessons in memorizing equations they may not really understand. Instead, these are opportunities to develop their geometric and spatial thinking. Geometric knowledge, in turn, supports the child's mathematical reasoning, understanding of proportion, managing data, problem-solving ability, and processing skills. The enchanting design of the Montessori materials allows these critical skills to develop through child-centered play. Rather than learning not to like Math, learners here experience Math as an elegant language through which they can unlock and describe their world.