I am forever indebted to my trainers for their instance on essential components of a Montessori education. The glare of the white hot light of the lessons, the classroom management, the observation, and the teacher preparation was at times overwhelming. I had heard all of this before in my 3 to 6 training. It was what I had seen done to varying degrees in places at which I had served children.
What was a new piece of the puzzle of the Montessori Education was the reflective moments. Once a committed Montessori mom told me how frustrated she had become at a very senior Montessori teacher, “She says the materials teach. That is great. When do I see understanding!” I sat back and made soothing sounds and assured her it would work. I didn’t have any answers.
My trainers provided me with the answer. An answer that I had not often seen employed. It is the reflective statement. The process was neglected in the boys. It was painful for them to begin to reflect on a lesson’s main point and put it into their own words. They were used to the lesson ending with, “Go do 5 problems.” I was now telling them, “Write down in your journal the definition of the relationship between the legs and the base of the triangle.” That was hard. Supper hard.
Today it became apparent again. LR has been doing square rooting of binomial and trinomial numbers for over a year. I had had a sense that he didn’t have the principals ground into his mind. He could do the work with only a minor bit of trouble, but he couldn’t manipulate it to serve him later in higher math. Although I’m not concerned that he can’t do higher math with it right now – he is only 11, I am concerned that he didn’t understand what was meant by the idea of square rooting.
The pain of it became obvious today when he couldn’t locate a calculator with a “root” button. I mentioned that that shouldn’t stop him from finding out the radicaland. Go do it. He stared at me. Then said that he didn’t know how to figure that out. He had been provided with the proper information and had been doing square roots for over a year. I wouldn’t let him not sweat through this. Being able to put it in his own words as opposed to me handing it to him is a gift in Montessori.
LR did sweat. He toiled for 20 minutes and came up with various theories. None of which worked. Finally I asked him to think it through in a very simple root – 9. Ahhhhh. The light bulb went off. He was so proud of himself. He set off to check his work. He knew how it went together now. Step one in understanding complete.