Here is a great primer on Montessori for ages 3-6.
The actual Philosophy is much deeper, bordering on the mystical, but this gets you oriented with the classroom.
"Children are allowed to continue with a piece of work for as long as they desire. They choose activities that interest them and practice them until they feel a sense of Mastery. Then they move on." ~6:30
7:40 "Part of becoming Independent Learners is taking responsibility for oneself, and the classroom environment."
3:00 "As the child becomes comfortable with the basics, the materials becoming increasingly abstract and complex, helping the learner to understand first the patterns of addition, subtraction building from this foundation to the complexities of squaring and square root, cubing and cube roots."
3:40 "The materials provide a method for the students to check their own work, as well as, to visualize the problem in 3 dimensions.
What I want to study is the cutting edge human/childhood Developmental Science, Montessori and similar alternative educational philosophies, and the 12 Archetypes in the Enlightened Child book.
So I can develop materials that Leverage a child's developmental capabilities to learn Life Success Principles as enjoyably and early as possible.
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