We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
This Irish group, The High Kings, sing The Fields Of Glory, not allowed to be embedded but watchable at Youtube. It was said that "The Battle of Waterloo was won on the playing fields of Eton."
As I've participated in and coached individual and team sports, I've watched how they build the best traits of character. Here's a review of a critique of not enough engaging young people's imagination beyond the rote.
I commented on another thread about this, but rote learning of certain subjects was the daily fare around our home when the kids were starting their educational journey. There is no substitute for rote learning arithmetic tables, certain geometrical and trigonometrical theorems and some grammatical/spelling concepts. On the other hand, we always encouraged their music, sports activities and reading. A couple were much more sports oriented, the others more towards drama and music so the concentrations changed as the children grew but they all learned to love to read and that, I think anyway, made the difference.
Summer was their time - as long as they didn't try and kill themselves, anything and everything was game. We left them alone to do as they wished with two rules - tell us where you're going and you'd better damn well be there if we check up.
So I guess the upshot of this is we used a combination of the two approaches - seemed to work well. :>)
Tom ... I agree with you 100% about rote learning of certain basics, whether mathematical or language/spelling concepts, economics and historical facts. Once you know certain things, like the need for parallel construction in English sentences, the use and misuse of punctuation like commas, how to decline verbs properly, as well as all of those mathematical concepts you mentioned, you take possession of that skill-set and are empowered by it. And since many of today's teachers think rote learning is just dumb, the only place your darling kids are going to learn these things is from you.
Teachers who refuse to teach rote learning are the ones who are dumb. They use the time we used to use for that to inculcate half-baked political ideas in the young minds before them.