Here's a philosophical question, Kriston, which is:
How do you do math, which ostensibly builds on skills (and isn't lateral thinking, my DD's strong suit) if you let the kids guide you. For example, she loves geometry, but still needs boring memorization in basic skills, she lost some due to constant pull out attempts by our "resource teacher". If geometry needs any boring calculuations, she freezes. Can you get to pre algebra or cool geometry without first doing the basics that lead to it, or am I a totally outdated, in the box thinker on this?
Funny you should ask...
We skipped all the "boring memorization" in multiplication and went straight to geometry for a while last year. I figured that he was not even 7 yet, and while he understood the concept of multiplication and could perform well on problems if given enough time, he just was't ready to sit down and memorize the facts. I preferred to give him concepts and keep his interest level high rather than drill him and kill his love of learning and math. He was very visual and loved puzzles and logic and shapes, so it just made sense to me, even though high school geometry and all the angle and plane stuff was not the norm to do with a 6yo!
Then this year, we did a lot of things that required that he knew his facts if he wanted to do them well and/or quickly--games, activities, etc. We did a little drill work, but not much AT ALL. Mostly we just used the very rare drill or timed test to reinforce what he had learned.
It was painless! He learned his times tables pretty thoroughly that way, too.
Is that right for your child? I don't know. A 9yo is different than a 6yo. Our DS was ahead, so it didn't really matter if he didn't have automatic recall of facts right then. It might matter more for your DD.
Just don't mistake arithmetic for math. That's like thinking that knowing your colors is art. It's just not all there is to it. Slipping fact-learning into conceptual stuff that appeals to them can be a lot more effective.
Please note that what I'm describing is a controversial approach, and I know that. Some people really think that facts MUST be memorized before kids advance. I'm something of an "off-roader" in math.

But I think that if you keep the kids interested and you give them math to do that is conceptual but requires that they use their facts, they'll learn the facts when it's worth their time to do it.
Finally, BTW, I would say that though math is usually taught in terms of "first you learn step one, then step two, then step three," most (a fair amount? Not sure of how much of a case I want to state there...) of it doesn't really have to work that way. DS7 (then 6yo) did just fine with high school level geometry (just adapted to be light on the proofs) last year, LONG before it usually occurs it the normal math sequence. Just because the standard path goes a certain way doesn't mean that that's the only way to learn math.
Of course, YMMV...
