Unexpected Things in Home Schooling, Particularly in Math
Homeschooling Ben and Lily this year, I’ve been teaching math, programming,and business so far, and helping my wife with the other subjects. One thing that strikes me is how much incidental material I have to teach— and that this might be the most important part of the teaching. We have Word Books where the children write down hard-to-understand or hard-to-spell words that come up, for example. Reading a short Holmes legal opinion brings up a lot of new words. Today in math we added Cylinder and Corollary. Vite and Allez and Tres Bien came up because the kids are taking some time off to go cheer their old classmates at the school Jog-a-thon, and will miss their French period. And in math, where I am teaching probability, we haven’t gotten past the first 5 pages of the book because there’s so much that ought to be nailed down first— subscripts, long division, decimal points in arithmetic, repeating decimals, the idea of a proof, variables, random variables, numerator vs. denominator, solving an equation for one unknown, lemmas, how to describe assumptions, notation, the random number function in Excel, diffusion processes (at the simplest level!), graphing, functions… This way, though, only what’s useful is taught. There’s none of this “What does ‘divisor’ mean?” stuff. Now that I look at it, they’ve been hit with a lot of material. I should do a review of all of these concepts. They’ll be getting repeated practice on them during the year.
I’ll add while I’m at it that probability and statistics is turning out to be a very good subject to teach, though I would now structure it differently. What’s nice is that you can have them do mathematically precise proofs of the probability of different outcomes (say, of 2 flips of a coin), and then have them do experiments and see how the results match up with the theoretical probabilities, and how that changes as sample size changes or in repetition of experiments. This will naturally lead to the topic of statistical significance. It also teaches the importance of good and careful notation, record-keeping, and framing of propositions and hypotheses.