While assisting in the classroom this afternoon, I had the opportunity to observe a few students hard at work. They had completely put together a puzzle up-side down, from memory. I asked them what their strategy was, and they simply replied, “we just place the pieces that fit together.” This is a true example of Montessori students hard at work, finding variations and challenging ways to complete a work that’s been done many times before. A camera-worthy moment if I’ve ever seen one.
There is so much to discover using the trinomial cube; a favorite work in our primary community. This blog article, courtesy of the Baan Dek Blog, unfolds all of the intricate details involved in the trinomial cube, and the true beauty behind this awesome mathematical work. Definitely a “must read”!
“There are so many layers to Montessori.
No where is this more apparent than in the simplicity and elegance of the trinomial cube. While the primary aim may seem rather obvious, to build a little puzzle in a box, the secondary aim, an introduction to algebra and preparation for the proof of the formula (a+b+c)3, just blew us away.
The mystery of the material summons our attention. We approach the box with curiosity. We are enchanted by what it promises. We are allured by what might be inside. “What is inside?”, we ask ourselves. With our fingertips, we start to explore.
As we unfold the wooden box and engage, an entirely new world slowly reveals itself. The colors seem to call out to us. Black, red, blue and then yellow. “Why these colors?”, we wonder. Little by little, or more literally, piece by piece, we begin to see more.
“There seems to be an order here.” “Why these shapes?” “What’s going on here?” Then, as if naturally, we begin to form a rough idea of the concept behind the work. “I think I understand what’s happening.” “I can figure this out.”
…While children are inherently captivated by the mathematical precision of this seemingly innocuous puzzle, noting the different heights of the prisms, they are actively working to build a concrete foundation for the abstract nature of the formulation, which they will later expand upon.
…With Montessori, children are constantly working to create the foundations they will need to explore abstractions on their own terms. While many of us encountered this auspicious formula at some point, (a+b+c)3, very few of us had the opportunity to understand and grasp the concept, in such a visceral, hands-on type of way. What’s so key in this process is that it is by discovery alone that children come to unlock the intricate layers.
“ Whereas most of us had to memorize mathematical formulas, eventually solving the problems we faced, children who grow up with Montessori, will understand the problem, before they are faced with the formula. ”
In many respects, they’ll be able to see what it is they are solving…”