Tex, I love the story of your DS and his giant. I don't know what to say, with respect to resizing, though. Are you saying your DS is tinkering with the concept of conservatism? Are you familiar with that classic test with the glasses of water?
Never heard of it. And google's letting me down on this one.
It's simple. You take two glasses, one squat, one tall and thin. You half fill one with water, then pour it into the other glass and ask them if there's more or less. From what I just read they shouldn't be able to say it's the same until age 7? Can that be right?
That must be why this sort of thing is my DD's favorite ATM, it must be very new to her to understand it. I'm interested to test her with the conservation of area tomorrow. Hopefully she fails. (ETA: I'm relieved, she failed)(ETA#2: now she passes. Oh hell)
By six or seven, most children develop the ability to conserve number, length, and liquid volume. Conservation refers to the idea that a quantity remains the same despite changes in appearance. If you show a child four marbles in a row, then spread them out, the preoperational child will focus on the spread, and tend to believe that there are now more marbles than before.
Or if you have two five inch sticks laid parallel to each other, then move one of them a little, she may believe that the moved stick is now longer than the other.
The concrete operations child, on the other hand, will know that there are still four marbles, and that the stick doesn�t change length even though it now extends beyond the other. And he will know that you have to look at more than just the height of the milk in the glass: If you pour the mild from the short, fat glass into the tall, skinny glass, he will tell you that there is the same amount of milk as before, despite the dramatic increase in mild-level!
By seven or eight years old, children develop conservation of substance: If I take a ball of clay and roll it into a long thin rod, or even split it into ten little pieces, the child knows that there is still the same amount of clay. And he will know that, if you rolled it all back into a single ball, it would look quite the same as it did -- a feature known as reversibility.
By nine or ten, the last of the conservation tests is mastered: conservation of area. If you take four one-inch square pieces of felt, and lay them on a six-by-six cloth together in the center, the child who conserves will know that they take up just as much room as the same squares spread out in the corners, or, for that matter, anywhere at all.
This discussion is really fascinating, and ties into something I was thinking about a few weeks ago. Until you have these developmental stages, you can't do certain types of math. Like area is usually fourth grade, because it's kind of pointless to teach if they think it's fluid.
