We do regular school exercises with the kids each week to teach them basic reading, math, geography, and other concepts. As you remember, Alex learned to read this summer and fall. Now he is working on math.
In the last two weeks, he has learned a few rules for math: numbers stand for things; adding one to a number leads to the next larger number; adding zero to a number leads to the same number; and that sometimes, letters can stand for numbers.
Today we were working on some addition problems, and I introduced the basic algebra concept that "sometimes letters stand for numbers". I wrote the problem, "3+H=6" and asked Alex what number the letter "H" stood for. He looked at it, and said with little hesitation, "3!"
I was amazed - I remember in junior high watching so many kids get paralyzed by seeing letters in math problems. I guess Alex isn't old enough to know to be afraid of that, but in the next five minutes we did a dozen more algebra problems: "4+Z=8", "Q+6=6", "Q+6=7", etc...he got every one right and didn't even hesitate.
It leads me to wonder if we don't underestimate what kids are able to learn. I was telling Alex that other kids won't learn to read until they are seven years old. He wondered how they would be able to wait two more years to read Spider-Man books.