Train up your child in the way he should go.
If you have a deep understanding about something, you can teach it to your eleven year old. This is true of any topic – economics, physics, math – anything. In fact, if you’re unable to break it down to an eleven year old’s level, you might not have the grasp you think you do.
Calculus segments the area under a curve into many small rectangles. If the rectangle is very thin, you can approximate the curve segment as flat. Fourth graders learn the area of a rectangle is width x height so we can easily compute this. As the segments get increasingly thinner, the rectangle approximation becomes better. Integral calculus is the mathematics of adding up the areas of an infinite number of infinitely thin rectangles to find the area under a curve. Don’t focus on teaching the mechanics of an integral, focus on the why! Why does an engineer or scientist need calculus? Why do I need to find the area under a curve? The mechanics will come later – focus on the motivation first. Said differently, emphasize the vision today, and the tactics will develop over many tomorrows.
Recently, my eleven year old son, Christopher, was in my office laying on the sofa talking with me while I paid bills. He asked me about time travel and I knew I had to stop what I was doing and seize the opportunity (sorry bills!). Proverbs 22:6 states “Train up a child in the way he should go, and when he is old he will not depart from it.” Christopher is exacting. He loves anything having to do with robots, time travel and building his own Lego creations. I opened my book to share the Twin Paradox (p. 218) and he was thrilled to see his name in the story. I told him that if he traveled in a spaceship at 80% the speed of light for several years and returned to earth he would be younger than his twin sister, Sofia. Time slows down as you approach the speed of light because nothing can exceed the speed of light – this is time dilation from Einstein’s special theory of relativity. The lesson lasted a half hour – longer than I expected. Even if he doesn’t remember everything about special relativity, he is enriched to have some insight into time travel and is less likely to be intimidated in science class because he hears this stuff at home.
The next time he brings up robots, I will teach him about AI and how machine learning will produce robots that learn and emulate human thinking. In the future, we will need algorithm and code developers for all the robots. After all, who will train them in the way they should go?