Developed in the early nineteen hundreds by Maria Montessori, the first woman to graduate from medical school in Italy, the Montessori approach to education is based on one pretty big principle: Kids learn according to their own pace, rhythm, and capabilities during periods when their brains are particularly receptive to learning. (She originally developed her methods to fit the educational needs of children with disabilities.)
Above all, Dr. Montessori believed that children weren't just little adults but that they had their own, unique developmental patterns. Therefore, they should be educated in a way that might be different than the way adults traditionally thought about education. She believed that children are dynamic, they learn about the world through their senses, they learn what interests them, they repeat activities, and, in many situations, they can teach themselves.
So how do the kids in these programs learn? Well, it's a very hands-on approach, as they use all kinds of materials that stimulate their senses. Children are encouraged to order things from smallest to largest, lightest to heaviest, palest to darkest. In one "work," the child orders blocks with different grades of sandpaper on them from smoothest to roughest. In another, different temperature water is added to small metal bottles, and the child orders them from coolest to warmest. The teacher acts more as an observer than an instructor (which is in line with what we've discussed about how smart parents watch for patterns and interest levels in their own children). The result is that students learn through discovery -- often at times when they're by themselves.