Wednesday, November 3, 2010
A Young Mathematician at Work
Sauntering under the coffee table, wiggling under the couch cushions, holding tightly to the cup holders, and peeking out from the glove box. I've been discovering sticky notes, fluttering like butterflies, all over my house and car. They are the workings of one inquisitive third grader who instead of absently disappearing into game play with his PSP, ipod, or iphone, instead opts to pick up a pencil and scour for a sticky note. He writes himself problems like 283x32, and proceeds to solve, not in conventional ways, but in creative thought provoking ways demonstrating his conceptual understanding and number sense.
My son's solving frenzy started after his first multiplication lesson in his third grade classroom. In the lesson, the class discussed things that typically can be found in groups like eggs and soda cans, and then they discussed the idea of groups of things. He took his knowledge, and his understanding of repeated addition and applied the two. Not to a typical third grade problem like 5X4 or 3x6, but immediately to larger numbers. He could do this because the concept remains the same and he was able to generalize his understanding.
The first problem I watched him solve was 237x13. He wrote it down on the white board in my office and proceeded, to my disbelief, to get the right answer. He added 13 groups of 237 using a doubling repeated addition approach. I then walked next door to chat to a colleague and returned to find not only had he solved the multiplication problem, but a division problem, as well. When I asked him how he knew division, he responded, "It's 'groups of' only backward."
In the division problem, you can see that he thought of groups of 20. How many groups of 20 will it take to get to 240? He has his groups numbered at the top to show 12. Quite impressive.
I'm thrilled, not only because my son is solving math problems in ways that demonstrate his ever growing knowledge of numbers but because he is easily able to generalize his knowledge, a key component of learning. I truly believe the reason he is able to do this is because he's grown up in a school where the curriculum tools are conceptually focused and full of problem solving situations. He hasn't been exposed to rote memorization or a sets of procedures, rather he's been taught to think. And, for that, I am grateful.