So I just re-read - and really read for the first time in years, Lockhart's article A Mathematicians Lament, which he has also published as a small book. The online pdf is here: http://www.maa.org/devlin/LockhartsLament.pdf
After reading this I am starting to understand the people who believe unschooling is best done ALL the way. Can't just say, well we only do writing or math practice for a little while, the rest of the time is free. It's the presentation of math or writing or whatever for that "little while" that can make so much difference. And then the writing and math will be free too.
My dd LOVES math and sees it everywhere - when listening to music,when looking at jewelry, she just picks up on the patterns and makes comparisons using terms from math. She can't necessarily "do" what one might expect from someone of her age - this is getting more so now that she is almost 10 and the "expectations" are rising rapidly. So I have been trying to ensure that she can do various things and have been pretty happy that she has gone through the Singapore Math book, though lately it has become more of a chore and I don't like that. But at least it is helpful to learn the skills ... or so I thought.
Now after reading Lockhart's article, and seeing that he says so emphatically what I have long believed and observed, I am wondering if I am taking the beauty, the art, the struggle and the epiphany away. Taking away the chance to discover and to be amazed.
Sure, she can master the skills ... but are we cutting out the mathematical experience in the process?
This may not make sense if you haven't read the article ... I will try to come back with some relevant quotes, but it would of course be better just to read the article.