Oh, my goodness. How do you teach a child whose mind works so much differently than yours? Sometimes when he is thinking, I wish I could take a magnifying glass and see what is going on in there. His mind works with such different gears than anything I’ve ever seen. It frustrates me to no end, but is also holds endless fascination for me. Ever since he was little he sees things that the rest of us don’t. If he shares his thoughts, then “aha!” we cry as we view for just an instant what he sees all the time.
I should have known how frustrating this would be way back when I tried to show him the idea of subtraction using grid paper. I tried to adapt to his visualization by using manipulatives. I cut out the number of squares in a long series to represent the first number, cut out another line of blocks to represent the other, and then place them one atop the other to show the difference between the two (like
Cuisenaire rods). We would then cut the longer one so that the two rods were the same length and then count up the number of boxes in the cut off piece and there was the answer along with a visual representation of difference. But no, he had some way that he knew how to work it. He had no interest in looking at it the traditional way. I cannot even begin to show you his process because I still don’t understand it.
Today is this same battle just with a different part of math. He is working on division. The book has recommended that he round the divisor so that he can best begin to estimate his answer. Of course that just helps you to come up with a guess. You still have to multiply by the divisor and subtract, but he thinks it’s easier to multiply his guess by the approximation he used, calculate the difference between the approximation and the real divisor, multiply that by the guessed number, and then add or subtract as necessary to come up with the remainder. Gee, I wonder why he is frustrated . . .that is an awful lot to keep in your brain. I can’t seem to get him to understand that writing down the process of math is not cheating. I tried to show him that while this strategy may work with 628 / 23, it would be very difficult when we got to 6457 / 432 and that we were really focusing on the process of division not necessarily just the product (or in this case quotient). No, he insists that his way is better. After watching him struggle, I finally insisted that he did it the proper way and he completed the entire set of problems in just a couple of minutes. Of course I will admit that the most frustrating part is when he gets it right with his way of thinking and his explanation, while it may be the longest possible way to come to a solution, is correct.
Of course to compound the issue, he has to think – outloud. Now I don’t mean adding or subtracting outload. He has to hum or bang his pen or play with the walkie-talkies. He has to think with noise while I’m trying to type and the repetitious noise makes my brain want to explode. While I think silence does the same to his. He doesn’t like others to make noise, but he can sing an opera as he solves his problems. It is funny how we all have our different styles of learning. Clearly ours don’t line up that well. But on the otherhand, I cannot imagine what would happen to this child in public school.
“Genius . . . is the capacity to see ten things where the ordinary man sees one.” -Ezra Pound
