Liam: (who had never learned multiplication formally at all) Mom, ask me what anything times anything is.
Me: Uh, okay. What's four times four?
Liam: (pauses for about 15 seconds) 16. (not asking, telling) Ask me something else.
Me: Okay. What's four times eight?
Liam: (again, taking a few moments ~ computing) 32.
And on and on.
So, I ask him how he knows that. Then, he starts to explain his method, which I couldn't repeat to you at all. Whatever's going on up there in his mental computer, I don't get it, but it's his process that he perfected. It's his own.
I told him the process by which I learned to multiply (a room full of 32-plus bored, unhappy children reciting in a dissonant monotone the times table, as dutifully memorized by most of the kids, the rest of the kids improvising by hanging back a little during the recitation to get a clue as to what the number ought to be~~how empowering). Of course, memorizing the times table in that way discouraged anybody considering what these numbers actually meant. All the wonder and joy that I have since discovered about the way numbers work together, all the amazing patterns, well, I didn't get to ponder all that in the school setting. Liam, coming to this through his own method, has the freedom to consider what all these numbers actually mean and their relationships to each other, to make discoveries.
I wanted to pass on to Liam some cool ideas and tricks about multiplication, but he asked me not to. He'd rather make these discoveries himself. I'm positively delighted for him.
2 comments:
Very cool!
I remember standing at my desk, fearful of getting the wrong answer and reciting those damn things over and over, week after week. Totally drained any joy associated with number/math discovery.
Still recovering from that crap 30 years later. I'm so glad my kids won't have that baggage to carry around.:)
Marji ~
As I was laying newspaper out yesterday for my library program (I don't read the newspaper, as I choose *Peace* instead, but I do find interesting articles when I'm laying it out to protect a table from the craft, or making a fire, or changing Nugget's cage...:), I saw an article in the NYTimes about parents who are outraged that they're not teaching *traditional* math in schools anymore.
One parent, whose daughter was a straight A student, was HORRIFIED (::gasp!::) when she realized her 6th grade child didn't know how to do long division. She marched into the school, demanded an explanation and was told, "We don't teach long division anymore. It stifles a child's creativity."
:)
This parent wasn't grinning, however, and she started an organization called *WTM*, which stands for *Where's the Math?*
::sigh::
Poor Kids.
I love watching math unfold in my children's minds. It's one of the greatest gifts of unschooling.
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