Montessori Monday: The Binomial Cube
Algebra? In preschool? Why not? As a field of mathematics, algebra addresses concepts that apply regardless of the individual quantities involved. Likewise, early childhood development is focused on understanding which experiences can be generalized and which ones are unique. It's a perfect match.
Of course, the children exploring the Binomial Cube don't think about it in such high falutin' ways. In our classrooms, algebraic equations are represented in seemingly simple, concrete block puzzles. The Binomial Cube, constructed of six prisms and two cubes, represents the algebraic equation (a+b)^3. The cube is built by placing each of the eight blocks into the proportions of a new cube, as children rely on the colors of the prism faces and their own alignment of the sides of the new cube to complete the puzzle. For small children, this is a curious and engaging challenge: can they build the cube correctly so that the puzzle box closes? For older children, the process of learning the names of each prism and the concrete appreciation of what we mean when we say "cube (a number)" inspires endless additional extensions. For adults. it may be the first time they've seen an algebraic equation represented concretely.
The Binomial Cube is exemplary of a basic premise of Montessori education: children are capable of understanding and mastering concepts far beyond what we typically expect in preschool settings, if those concepts are presented in a developmentally appropriate way.
By translating the algebraic equation into a beautiful, self-correcting, didactic exercise, Montessori makes this seemingly complex concept simple enough for a very young child to understand.