Last weekend, as an evening of theater came to a close, an image proving the Pythagorean Theorem appeared. I was reminded immediately of the Montessori material used in upper elementary classrooms. Though this character in “The Curious Incident of the Dog in the Night-Time” was demonstrating his acute mathematical abilities, I again considered how much Dr. Montessori knew about how children learn. She developed a system to make concepts accessible to children and lay the foundation for the more complex mathematics they will encounter as they move on to middle and high school.

These particular materials help children prove the Pythagorean Theorem, which states that given a right-angle triangle, the sum of the squares formed on the short legs equals the square formed on the hypotenuse.

Manipulating these materials demonstrates this and gives children visual and kinesthetic ways to see the theorem in action. They explore it much like we might explore a puzzle; they can see that the pieces “fit.” One side squared plus the other side squared equals the third side…the squares are right there; children can see them, count them and physically move them. They don’t need to be advanced mathematicians to do this work, nor do they need to be able to write the algebraic expression to prove it. Instead they have the opportunity to explore it, manipulate it and see for themselves how to make sense of this idea and store it away for future use. The wonder of Montessori!