"The teacher must take her materials from the school, and her principles from what she has learnt; and then she must face practically, for herself, the question of this recall. Only her own intelligence can solve the problem, which will be different in every individual case." ~Maria Montessori
I remember Jerry being quite amused that I wanted to be a master trainer yet had no concept or knowledge of Maria's work. I went home to escape winter and I had been reading "The Men of Mathematics" to try and figure out what the hell these guys were thinking, Newton did not develop the calculus to torture high school seniors, and college students. I also read "Innumeracy" by Paulos. He was surprised by this, so he took me down into his basement where he had a library set up and directed me to READ...particularly works by Mario and Maria. It was a large collection of books; I have an affinity for them, so I was quite content to spend hours down there, I found a book on Vedic mathematics, quite a few classics (Socrates, Plato, Aristotle etc) and many more. Jerry was content to have me down there because while I was down there I wasn't bothering him, and occasionally I'd come up with a topic of conversation "worth talking about."
Try to remember my lineage is direct. Me, Jerry. Mario. Maria. I don't recall Jerry (or Maria or Mario) talking about a standard curriculum that was to be applied to every child. Quite the opposite. The teacher was to be trained in such manner that each child's individual interests could be tapped, nurtured and developed. Discovery was directed by the teacher with regard to the child's individual interests.
Therefore lessons were developed for each class and each child in the class on subject matter at hand, in this case math. There was no cookie cutter approach. Even the books he developed were made with the understanding that the student picked where to start and the order. All books were to be completed but how and in what order was up to the individual student. And yes it's a hell of a lot more work, AND the education is far more effective and superior to what currently passes for education in the public school system of the USA. This year's class is not the same as last years class. How is it possible that the lessons would be the same?
"A teacher, by his passive attitude, removes from the children the obstacle that is created by his own activity and authority.". ~Maria Montessori
For example, today we are going to learn trigonometry concepts. The teacher introduces the CONCEPTS then directs the student to discover more and thru socratic method the child discovers axiom and postulate...and the formulas, they aren't hit over the head with them. Once concepts are understood mastery can be attained. Mastery is demonstrated by being able to make up and solve one's own problems. Again: once they understand the concepts all we can do is change the numbers.
"Education is a natural process carried out by the human individual, and is acquired not by listening to words, but by experiences in the environment." ~Maria Montessori
Your job is to create a math rich environment. Place the child in a math rich environment and they will learn math, in their own way and in their own time. This is the education of individuals in groups...how can the lessons be the same, in the same order at the same time. If you were educated in a public school yea verily this is completely foreign to you as everybody pledges allegiance and then opens their text book to page 123, or does the same worksheet in preparation for the standardized test. BTW it has become clear that homeschooled and Montessori students do incredibly well on standardized tests, because again, once the concepts are mastered all the givers of the test can do is change the numbers trying to ascertain if the math is understood or not. This has been circumvented by students and teachers who memorize answers to the test questions, rather than understanding the subject matter well enough to answer any questions. Once they understand addition they can add any two numbers. The principle is the same with regard to "advanced mathematics". The practice is another thing entirely: memorize long enough to take the test.
"Our care of the children should be governed not by the desire to 'make them learn things', but by the endeavor always to keep burning within them the light which is called intelligence." ~Maria Montessori
"The essential thing is to arouse such an interest that it engages the child's whole personality." ~Maria Montessori
Once interest has been pricked discipline and concentration flow as naturally as water downhill, time stands still, and learning takes place.
"The first essential for the child's development is concentration. The child who concentrates is immensely happy." ~Maria Montessori
"Discipline must come through liberty. . . . We do not consider an individual disciplined only when he has been rendered as artificially silent as a mute and as immovable as a paralytic. He is an individual annihilated, not disciplined." ~Maria Montessori
"Teaching is a sacred trust." ~Joyce A. Rogers.