The mom of a five-year-old learner told me the learner was adding hundreds in the car. He said adding 500 + 500 wasn't any more complicated than adding 5 + 5. She asked where he learned this, and he said he taught himself. 

Montessori materials provide a hands-on way for learners to experience our base-ten number system and in effect, teach themselves through their own physical actions and critical thinking. The self-directed discovery that opens the door to critical thinking at a young age leads to a strong math foundation. One that will not collapse later on in elementary and beyond when concepts and critical thinking become necessary.

This kind of learning is in contrast to being instructed to memorize steps to produce rote calculations. The memorization of steps as instructed provides a shortcut to better-standardized test scores but is a fragile foundation to build on.

As always, in-depth discovery trumps spoon-fed memorization in the long run. Not to mention the self-confidence learners gain from knowing they can figure things out independently. This leads to gains in more than just math. 

How many ways can you show twenty-three?