l 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.
Woo hoo! Buying sticky notes for Christmas is less expensive than a new baseball glove. haha :)
ReplyDeleteYour analytical son asked me a question in music class last week that took me three tries to answer. I presented the answer in two rather musical ways and finally used the game of golf to answer his question.
ReplyDeleteWe were looking at a note tree (which is basically a math lesson in fractions) whereby the whole note is divided into two equal parts to make two half notes; two half notes are divided into two equal parts to make four quarter notes, etc. He couldn't understand why the note values decreased as you moved down the tree.
I asked him if he was familiar with the game of golf and how to score it. He said, "yes - lower is higher." The light bulb finally came on! The farther we move down on the note tree, the greater the number of notes are required to balance the equation.
The kid is a walking genius!
I can attest to C. not getting enough math. We went from the small whiteboards to the front white board for him to work out problems. I have to take out the calculator to check out his answers!! What a great kid to have around the classroom. MM
ReplyDeleteI love the way C is taking what he knows and generalizing it. How exciting that Math is matching outside play and video games for his attention! WOW!
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