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What is the teaching concept behind the Montessori materials?

The child spontaneously teaches himself by working with materials and activities that he chooses—work that match his interest and abilities. The teaching materials are designed to lead the child unconsciously from the simple to the complex, from concrete perception to abstract conception. The materials are self-corrective, allowing the child to find the answer for himself.  Each piece of material is specifically constructed to entice the child and engage him through hands-on participation.  Concepts are broken down into small parts that isolate difficulty, yet solve “the problem of the match” where there is always something familiar, yet something more challenging and interesting in the work itself as it builds upon previous exercises. This programmed learning approach insures that the child will experience success. Lessons are presented in a systematic way known as the “Three Period Lesson.”  Materials are presented and demonstrated for the child to then practice and ultimately internalize the specific concept or understanding.  The cycle of “competence breeding confidence” motivates the child’s desire to learn and work in later life.
What is the teaching concept behind the Montessori materials?