A few of the principles and philosophies of the Montessori Method are following the child (observing their interests), prepared environment (order & beauty), control of error (successful learning), isolated quality (color, shape, etc), freedom within limits (choice), and independence (not helping a child do something they can do themselves). I love all of these and am constantly trying to encourage the students in these areas.
All of the materials in a traditional Montessori school are designed to be self-teaching. Children learn to solve problems, see natural connections in knowledge, learn skills related to practical living, and therefore, expand their imaginative thinking.