Some recent examples of Andy's insights
In the car one day, on the way to the playground, Andy said, I know what 9x9 is!
Yeah, it's 81! You know how I figured that out? 9 times 3 is 27, then 27 + 27 is 54, and 27 more is 81!
So, he didn't just memorize the times tables, or the trick that in multiples of nine, the digits in the answer add up to 9. He understands that 9 units of 9 is the same as 3 units of 9 added up three times!
And why did he figure this out? Just because was curious and confident that his understanding of math -- as he comes across it in everyday life -- would be enough to figure out the answer to his random wondering.
On paper, in a math class, what he did in his head would look like this: 3(9X3) and they'd call it something like pre-algebra, and to someone like me as a student it would have looked very scary, because when I was taught math in school it was arcane and took many steps to reach the answer. And even tho I knew what the right answer was, I could never make their way work. Andy doesn't need to work it out 'the right way' -- his own methods work fine.
His favorite math fact in recent weeks has been 100 x 100. His method, as he'll tell anyone who will listen, is that since 100 x 10 is 1,000 you just do that math 9 more times for 9,000, add it and you get 10,000. The really cool part is he can do it faster in his head than he could on paper and this way, it's always available to him.
Gotta love math that happens for its own joy!
On another day…… Andy explains global warming
Recently the topic of global warming came up and Dan asked what it is. Before I could answer, Andy said, "I know -- let me tell him!" Here it is:"Global warming is when the planet gets too warm, and it causes the ice in places like Antartica and the North Pole to melt, which enhances (one of his new favorite words) the oceans and makes the water higher, so someday the coasts will be flooded. It's caused by all the stuff we put in the air."All this gleaned just from what he hears around him, since it's not something I ever explained to him. Recently, he explained to his grandparents why we don't shop at Walmart -- honestly, I'm afraid to hear what he may have said, or what they thought, since he tends to mix up all my politics and commentary in a very confusing way.....