Way back in the day, I persuaded my then-wife to homeschool our children. She was a hard sell, which is another story. But why was I so interested? Why did this matter to me? It comes down to two things. First, from day one, I believed that math and reading classes were a colossal waste of time. The reading primers were silly; it would have been better to let me pick a book from a good library and just read to myself. The math was also slow. I learned more by setting and solving my own problems. By 4th grade, I had already surpassed my teacher’s understanding. She called in the Mother Superior, who studied my work at the blackboard, and said “That boy knows what he is doing. Leave him alone.”
I found out later just how slow the math was, compared to what could have been. One of my grandsons is a 2nd generation home schooler, possibly the smartest kid I have ever met. We had a chat when he was 6 years old. He already knew just about all the arithmetic which the average high school graduate knows, and then some; for instance, he had mastered binary arithmetic. So I asked him to think about adding the numbers from 1 to 100. The obvious way, adding 1, 2, 3, 4 … one at a time, requires 99 additions. I suggested a different method: write the numbers 1 .. 50 as a series from left to right; then from right to left, write 51 to 100, under the top 50 numbers. The 100 falls under the 1; the 51 under the 50. He looks this over, and it is obvious that there are 50 pairs, each adding to 101; he does the multiplication mentally and gives the answer: 5050.
So I ask, what about the even numbers, from 2 to 100? Just the even numbers. He chews on this for a few seconds and replies “2550” – which is also correct. (25 pairs times 102)
The first problem is usually presented in high school, and baffles most students. The second problem will defeat all but the cream from your best math class. For me, that’s a perfect math lesson. If you can convey one interesting idea per day, and it sticks, your child will learn an awful lot of math in a few short years.
But I’ve jumped ahead of the story. What did I know, and when did I know it? Backing up, my math and reading classes were solid proof that I was in the wrong sort of place. My 7th grade teacher was a real smart lady who recognized that I was bored out of my gourd, and arranged for me to take a test with the 8th graders. I was in the uppermost stanine, and my math and reading scores were “12th grade level.” I advanced a grade, a year younger than my new classmates, and was swiftly advised to hide my light under a bushel so they wouldn’t look so bad.
Super genetics? Maybe, maybe not. I like to think I had a simple “secret weapon”; from an early age, I was a bookworm. I read everything, my folks had a fairly decent set of books, I read my older brothers’ textbooks.
I think the tipping point was in Physics class. My teacher looked at my notebook and said “Mac, why aren’t you taking notes?”
With my renowned tact, I replied “You haven’t said anything interesting.” You can imagine how that went over. “WHAT? Please explain.”
I replied “According to Claude Shannon’s Information Theory, the only part of a message worth communicating is that part which is unpredictable. So my rule is: if I know something already, or can quickly derive it from what I already know, it is not interesting. I write down everything else.”
“You already know this stuff?”
“Well, of course I do. Aside from a few formulas, the only thing novel about this course was the use of vectors – I had never heard of them before. That was interesting. I wrote it down and studied it.”
My teachers soon learned that I was not bluffing. I ate encyclopedias for breakfast. I had already read some old books on various sciences before even starting high school. For me, there was hardly anything interesting in that physics class, in the information-theoretic sense. A different student with a different set of prior knowledge would write a different set of notes.
Who reads A Mathematical Theory of Communication for fun? A kid who wants to learn everything he can about computers, that’s who. This was no part of my formal schooling; it was just my crazy hobby – and it led to a long and interesting career.
So that’s my “secret weapon.” I resolved to impart it to my children and anybody else who could use it. Read something interesting, as often as you can, as early as possible. And I resolved to try to keep things interesting; to not repeat the same material ad infinitum. I did not want to waste my children’s time.