Anyone remember Piaget's experiments on children in the "preoperational stage" (2-6) where he theorized that children of this age couldn't yet understand quantity?
The idea of "number conservation" - that is, that the actual number or quantity stays the same even if the items are rearranged, spread apart, or moved - was something that Piaget believed was too advanced for a child until about the age of seven.
Hunter hasn't really ever had a problem with this since, ever since he was pretty young we were doing the Doman math program. But today's little episode reminded me of good old Piaget and the later debunking of this particular theory of young children, while Hunter and I were doing a little math with today's lunch.
You see, it's true that most little kids without much math instruction will tell you there are "more" marbles if you spread them apart and make the pile "bigger", even though you didn't add any actual marbles. However, more recent experiments to mimic Piaget's original show that little kids do indeed have more math smarts than once thought. One experiment, not listed in the above link, showed that when the set of rearranged objects was something desirable (say, M&M candies instead of marbles), little kids would consistently pick the pile that had more actual candies versus the pile that was just spread out more. Maybe we were just asking the question wrong.
Hunter wasn't picking from a pile of candies, but he reminded me of that little experiment today when we were playing around with our lunch, finding the possible dividends for the number six.
We made six hard boiled eggs to eat, three for him and three for me. "What's six divided by two?" I enquired.
"Three" he figures.
"Ok, well what would we do if we wanted to divide these six eggs for three people?"
After staring at the three bowls and thinking for quite some time about his much beloved eggs, he finally offers,
"Cook some more eggs."
Guess when it's something you want, the math doesn't matter so much, does it?
"And he took unto him all these, and divided them in the midst, and laid each piece one against another..."Hunter is 5 years, 1 month old