Let kids play on mountains

For amusement, late this evening, I took up pen and paper to show my 8-year-old how lines have equations to go with them. You know, simple things like y = x, y = 8-x, y = 5... He patiently helped me identify a few points on each line, and watched me connect them. He was particularly amused  to see the equation approximating the relationship between his age and his younger brother's.

He then asked, what about circles? Do they have equations too? So I showed him x*x + y*y = 4, focusing on the positive quadrant, carelessly mentioning there was something called square-root, and showing him where (sqrt(2), sqrt(2)) was on this circle.  This concept he had never heard of before intrigued him.

He then asked, does every number have square roots? I showed him sqrt(4) as another example. He could then figure out square roots of 0 and 1, whose consistency pleased him.

He then asked, what about negative numbers, do they have square roots too? I didn't launch into a lengthy explanation, but pointed out simply that square-root of -1 is nowhere to be found on the number line he is familiar with.

I was thrilled, of course, at the sheer effortless-ness of this conversation, which took all of ten minutes, and touched on such a wide range of mathematical topics, from analytic geometry to surds to imaginary numbers. But my point is not at all to show off my son as a genius of some sort. Like many kids his age, his biggest interests and activities revolve around video games, spinning tops, cartoons, and hanging out with friends.

I believe what this little incident truly exemplifies is that any kid can make creative jumps and connections and ask great questions quite easily when they're simply curious, when their learning is not being controlled via rigid structures, when it is not boxed into an arbitrarily fixed place and time and dragged in lock-step with everyone else. It helps to have an environment that supports this kind of freedom and stress-free exploration. I am grateful for his amazingly unique school, Play Mountain Place, which lets him follow his own interests at his own pace. Learn more about it at playmountain.org