When a square is more than a square

While we've spoken of the long bead chains before, I wanted to focus on a specific point of interest. Each colored bead represents a certain number and a certain set of that number. When placed in a long chain, children are able to count them, identifying important numbers within the set. So in the Long bead chain of 5 (light blue in color) it has number tags for each set of 5 (5, 10, 15, 20, etc). There are larger tags for each square of 5 (that is, each set of 25). When a square tag is placed on each squared number, a square bead is placed as well.

To think that Maria Montessori thought about the concept of squared numbers and considered a means to make it as concrete as possible! To think there are children all over the world who are learning a mathematical concept that they can feel in their hands before ever knowing how to connect it to an algebraic equation. It's quite baffling. What beautiful things God makes, both concepts and man to understand them.