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This idea of mastering a skill without the assistance of materials is what we refer to as abstraction. The materials are symbolic or representative of something else (a number, perhaps), and that symbolism changes over time until children are ready to let go of the materials and find solutions on paper or even in their heads. What do we mean by concrete? The children are able to hold a material in their hands.

This is no different when it comes to math. Much of the Montessori curriculum is based on giving children exposure to concrete materials first, then giving them incremental opportunities to work to more abstract concepts. While they look quite different than what we used growing up (pencil and paper?) there are intentional reasons for these methods. But what, exactly, does that look like? And how does it change as they get older? Montessori math materials are nothing short of amazing.

You know their teachers are guiding them to learn early math skills. You know your four year old loves their classroom and their work.

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