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No textbooks, no grades ! Someone explain this to me because it does not make any sense!
Montessorians see text books as limiting. "It is the third day of the fourth month so everybody turn to page 64." Instead we believe in giving children the information they need in a multitude of ways. We teach them the concepts through manipulating objects, color, movement, matching, comparing, researching and so on.
Additionally we feel that simply going to a text book for information doesn't teach a child how to learn. When they are older and have a question, but aren't in a classroom setting, children who are taught to rely on textbooks won't know how or where to get the answer. But a child who is taught to use the library, the internet, newspapers, as well as to gather information from their surroundings, use prior knowledge, analyze and extrapolate will.
As far as grades go, in Montessori we work towards mastery- the complete understanding of a concept. In a grade focused classroom people often work on learning tricks to pass the test. This may get them a good grade, but they often have very little understanding of the concept. In the future, when the concept is studied in more depth, they can't relate or apply their knowledge to the new concept.
For example, when focusing purely on getting children to pass a test on adding fractions with like denominators, a teacher might say something like, " Add the top number, keep the bottom number". This little trick works like magic and they get a great grade on the fractions part of the test. But the next year when learning to add fractions with different denominators they are floundering.
Another problem with being grade orientated is that some children will do enough just to slide by. "Well I passed." Is what I usually hear from them. When we focus on mastering a topic instead of just getting a grade, these children have no way to "just squeak by".
The lack of grades can also refer to the fact that children in a Montessori classroom aren't limited to the work for the grade in which they are in. A Child's progress is not dictated by a textbook or a grade level, but by their own innate ability.