There's a really wonderful origin story about the concept of zero. In Architecture as Metaphor, Kojin Karatani, writes: "Zero was invented in India and was originally the name for not moving a bead on an abacus. If it were not for zero, the numbers 205 and 25 would be indistinguishable." That's a pretty powerful thought. We thought we would take this opportunity to further elucidate how the concept of zero is imparted in Montessori.
First, it's important to remember that the way children learn math in Montessori, is through the concrete. Which is to say, we introduce children to the quantity, and then the symbol. For example, when we teach the concept of numbers, children first explore the red rods.
After the red rods have been mastered, we then introduce the number rods, which, as you can see, are differentiated. Again, focusing on the concrete, we later introduce a number to represent each rod. So, for instance, we would place the number 10, next to the number rod that has ten units. We only reach this activity, once we're certain that the student knows the quantity.
So, how do we confirm that children understand the concept of zero? With the spindle boxes, as pictured above. Slowly moving away from the concrete, towards the abstract, there is a box with 10 slots to add spindles. The object of the activity is to place the correct amount of spindles in the appropriately marked box. The first slot, marked 0, will contain no spindles, while the last box, marked 9, will contain 9 spindles. Hence, the child comes to understand that zero demaractes no quantity. While the concept of zero may seem rather obvious to us as adults, it can be an extremely difficult concept to teach children.