My 11 year old was asked to describe what he could about the relationships between 1/a and 1/b if a < b (a, b are Natural numbers) and a/b and b/a.
He explained to me that 1/a > 1/b since it had a smaller denominator.
Why?
Well because if the denominator is larger, it's broken up into smaller pieces.
OK, so what about a/b and b/a?
a/b is a proper fraction and b/a is an improper fraction.
Then which one's bigger?
b/a.
Why?
*thinks for a moment*
Because b/a will have a whole number and a/b won't.
Then what can you tell me about all improper fractions?
*looks confused*
I get up and motion for Dawson to do the same.
If I'm 0 and you're 1, where would the proper fractions be?
*points between us*
Here.
Then where are the improper fractions?
*points away from me*
There.
Then what can you tell me about all improper fractions?
They're all bigger than 1.
Then what can you tell me about all proper...
They're all between 0 and 1.
There you go.
So do I have to do this problem?
Didn't you just do it?
Well yeah, but I didn't write it down.
Will writing it down help you understand it better?
Not really.
*Looking my son in the eyes*
*Smiles*
Cool.
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6 comments:
What about having him explain it to someone else? Do you think that would serve to cement his understanding of it even further?
Okay, you just cemented the need for at least one round of conferring as assessment in my classroom this year.
I know you made the right call on writing it down, because if he had seemed a little shaky you totally would have made him write it down. In the process of writing it down, he would have had to think through his reasoning again.
Chris
I suppose the more he explained it, the better. Problem would be finding someone who'd understand his explanation.
hillby
I did much more in the way of conversing with my students on an indicidual basis this last year and found it to be very telling. Kids can learn to manipulate the symbols but had to really dig to express their understanding verbally.
What I find very impressive about this story is the relationship of trust you have with your kid. It would seem to take a lot to be able to talk your kid about something such as math, to reach a point where they are confused, and to have them not want to walk away in the it's-my-prerogative-because-I-am-a-kid-and-I-am-impatient sort of way.
I wonder: Is this relationship what enables you to homeschool, or is this relationship a result of homeschooling?
What a great question. At this point I'd have to say the conversation was a result of homeschooling. My son(s) is/are very stubborn and when he was in school, the last thing he wanted to do was talk about math. He'd take the I already have a teacher attitude very quickly. Now that I'm his math
teacher, that's changing.
We talk a lot in our family, so that helps. But talking about math is a new thing for us.
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