Tuesday, 19 May 2009
Math and Understanding
The hard part in evaluating students is to figure out when they really "get it." When they actually understand. The kid who makes the mistake in the picture above, almost understands canceling in simplification. The hard part is to find out just what it means to understand.
For example, kids, and teachers, all agree that if x=y and a=b and none of those are zero, then :
1) x+a = y + b
2) x-a = y - b
3) x(a) = y(b)
and the one I used in class today to find the exponential curve through two points...
4) x/a = y/b...
If you disagree, say so now, because this is where it gets fun....
If you think your students really understand this idea, give them the following problem:
32 ounces = 2 pounds; 8 ounces = 1/2 pound
so 32*8 = 2(1/2) or
256 ounces = 1 pound....
If they can explain what happened, I think they understand.