The use of the didactic math materials developed by Maria Montessori is one of the most recognizable hallmarks of a Montessori education.
This system in which a child is constantly moving objects with his hands and actively exercising his senses, also takes into account a child’s special aptitude for mathematics. When they leave the material, the children very easily reach the point where they wish to write out the operation. They thus carry out an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations. (Montessori, 1967, p. 279)
These materials are distinct in that they guide students to explore mathematical principles independently in a concrete and experiential way. This allows students to utilize all of their senses to internalize math concepts, and ultimately allow them to achieve abstraction. The materials are developmentally appropriate, carefully designed to meet the needs characteristic of the plane of development of the child intended to use them. The materials appear time and again, within the spiraling math curriculum. Upon each appearance, students revisit what they already know, and are provided a reference point for where the new information now ascertained from the material is to be organized.
Golden beads used for introductory lessons in the primary classroom, such as the introduction to place value, are later used by the upper elementary student to understand more complex lessons, such as the first square root lesson. The golden beads are familiar, isolating the difficulty to understanding the new, more advanced concept of what square root means.
The same holds true for the binomial cube; through use of this familiar material, difficulty is isolated when it is used to later demonstrate more complex concepts. In this way, work done at the primary level scaffolds the work done at the upper elementary level. “Children can create mental structures from previously learned material into which new carefully designed material can be assimilated” (Lillard, 2005, p. 236). This is the elegance of the use of the didactic math materials within the Montessori spiralling curriculum and the genius of its design.
Lillard, A.S. (2005). Montessori: The science behind the genius. New York: Oxford University Press.
Montessori, M. (1967). The discovery of the child. New York: Ballantine Books.