One thing that I learned pretty late in the game (too late to be of use to any of mine except my youngest) is that slowing down makes a huge difference in a child's attitude toward math. Early computation is so simple, we are quick to move on the next thing, and we have a tendency to assume that if a child can add 7+2, he is fully ready to understand 7-5, or 17+2. We also associate computational ability with understanding. What I learned to do, with my youngest, is slow down. In the not-so-distant past, it was not assumed that every student needed algebra, and whatever high school students did for math, only some of them did algebra. Now, we expect algebra to be done in grade 8, not 9 (when I was in those grades, advanced students did algebra in grade 8, all others in grade 9), so that the student has time to get to calculus while still in high school. I saw an article not long ago, in which college professors were asking high schools to stop teaching calculus, and to do a better job with with algebra and geometry, so that their students really understood those things and were ready for calculus, which they would prefer to teach themselves. The current STEM trend has us urging "more" instead of "better" on our students--not a classical approach, I don't think.
Now, I never went that far in math myself, and it was a long time ago. But what I found, by slowing down so that my student never moved on until she found problems at the current level *easy* and *intuitive* (not just "doable"), was that she was already more than ready for the next level, and grasped it quickly. But more importantly, to me, was this: she is the first of all my students to ever say the words, "I love math." And if you believe, as I do, that education is the science of relations, of learning to love and care about knowledge, then this was more than a win--it was the only success I ever had.
We are still in the midst--she's in 9th grade--but I decided to have the courage of my convictions. This year, we're finishing up arithmetic, and we going to start geometry with Euclid, and just begin pre-algebra. Next year, we'll work on geometry and algebra simultaneously, with geometry getting the lion's share of attention (I'm following the suggestion in A Liberal Arts Education by Clark and Jain, to let geometry come first). I'm pretty sure we'll finish (by the end of high school) geometry, and algebra I and II, and I'll probably have her do at least 1/2 of a consumer math course for practical knowledge. It's plenty for a high-school transcript, and if she finishes with her love of math intact, that matters to me more than credits on her transcript. She'll be well prepared for whatever higher math she wants to pursue, and there will be plenty of time for it. "Slow down" is now my biggest suggestion for math.