Montessori Moments

In a Montessori environment students are active participants in their own learning. They are given the freedom to explore their interests and at the elementary level often choose to work collaboratively. Our classrooms bear witness to countless “Montessori moments” each day and while we as educators never take them for granted, it is easy to overlook all that is being gifted to the children each day.

So what do active participants in their own learning, exercising their freedom to work collaboratively and exploring their own interests while using the Montessori didactic materials to aid conceptual understanding, look like?

It looks like this!

Students learning

Two Lower Elementary students who had recently been given a lesson on how to divide using a double digit divisor approached their guide one morning. They were working to complete their morning math warm up (known in Lower Elementary as “math vitamin”), and asked if they could try dividing with a triple digit divisor.

They decided to create the same triple digit division problem and work together, assuring the guide they could be responsible work partners. The students set about solving the problem using the “Stamp Game”, which they had previously used for double digit division. They completed their problem and checked their own work by multiplying their answer by their divisor. They discovered their answer was not correct and after checking with the guide to ensure this was the case they returned to the material to try again. There was discussion about counting more carefully and where the mistake possibly occurred. The students devised a plan to have one child do the exchanging of the stamps and the other to do the sharing, but the subsequent checking of their work showed their answer was still incorrect.

At this point in the morning the math warm up is usually complete and the students expressed concern about not being finished. The guide reassured them that it was fine to keep working and to take their time to work carefully. About ten minutes later the students bounded across the room proclaiming their success! They proudly read their correct answer to the guide, the smiles on their faces showing the confidence they had gained and their total delight.

The next morning the same two students approached their guide again….

Students solving a math problem

This time the students chose to work with a different material, the Racks and Tubes, and success was found on the first try!

Visit here for a glossary of Montessori vocabulary.

Math Materials We Use

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.

References:

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.

Math materials
Math materials
Math materials
Math materials
Math materials