A child can learn basic concepts of math in two ways. He can learn by using concrete materials during the years when he enjoys manipulating equipment or he can learn through abstract methods at an older age. There are two characteristics of the math area that are the most important differences between Montessori Math and other curriculum. The depth and the complexity of the materials, and Montessori’s concept of abstract vs. memorization are the most important differences. The prepared environment and presentation of the materials lead the child to discover important facts, create formulas and problems and come up with critical thinking solutions.