Yesterday, we were prompted to describe the Montessori approach to mathematics in a few short paragraphs. This was quite a challenge, one we were up for, and wanted to share with you. Of course, we'd love to hear your ideas, so please feel free to send us your notes! Below, we offer some very basic generalizations, through the specific example of the Pink Tower. There are countless others. Okay, here we go:
If there's one way to describe the Montessori approach to mathematics, it's that the only way to truly understand abstract concepts, is by first developing a concrete appreciation. In a phrase, the only way to achieve the abstract, is through the concrete. Which is to say, before we move on to the abstract, we need to make sure that the children have a solid, tangible grasp of the concepts that they're working on. As adults, we take for granted that children understand concepts, but concepts can be extremely difficult to teach.
From the very first day students enter the Montessori prepared environment, we're busy indirectly laying the foundations for critical and creative mathematical thinking, not only through the way the materials are ordered on the shelves - from left to right, top to bottom, ordered in terms of complexity - but also, through implementing ten units (preparation for the decimal system) in many of the sensorial activities. Later, these concepts will be made more direct or explicit, but only when we're certain that the children are ready for the them.
Take, for instance, the Pink Tower. When the children first engage with this activity, on the surface of things, it's merely a fun, engaging puzzle for them to build. While it teaches volume, visual discrimination, and requires children to carefully position the largest piece to the smallest piece, requiring great manual dexterity and concentration, at this point they are unaware that the blocks are actually the cube root of ten, nine, eight...
Years later, or at a time when the children are ready for more advanced mathematical work, we'll introduce them to square and cube roots. We don't make the direct connection to the Pink Tower, leaving it for the children to explore and discover on their own - which so many of them do! Children will inherently be familiar with the concepts, because they would have been introduced to them many times before.