Personally I think you have to take Lockharts Lament with a pinch of salt just like you would any parenting or homeschooling manual. He makes some very good points and if you subscribe to a natural learning, unschooling philosophy he probably really resonates with you.
Like I commented in my previous post I think you can guide and teach providing the building blocks and kids are really capable of figuring plenty out for themselves. Does that mean I am about to stop teaching maths in any formality, certainly not! But I am going to change the way we are doing things.
I will be looking towards more discovery based maths where there is something for the kids to figure out for themselves, Miquon and Montessori maths spring to mind. They encourage the kids to work with the numbers and manipulatives and find the answers and work out things like regrouping and renaming without being explicitly taught. Once they get it I am all for providing the official terminology and notation so they have a written form to go with what they know. Also like I said previously I wont be blindly following a curriculum.
I also think it is great to solve problems in a number of ways. Flossy likes to sometimes use base 5 and sometimes base 10 and it is awesome that she can switch between the two when solving a problem. She just uses whichever seems more comfortable or appropriate at the time. So for an example -
She has 3 different ways she commonly uses to solve this problem
1) 7+7=14 14+1=15
2) 7=5+2 & 8=5+3 5+5+2+3=15
3) 7-2=5 8+2=10 10+5=15
Isn't it awesome that my 5yo Flossy can figure out all the ways to make this happen! She can do that because we have 'played with' numbers since she was very small (being gifted helps too). She doesn't automatically know the answer but she is quick to figure it out. She thinks about it and as she does so I know that she is truly understanding the process. She has the why! We are on the right track, thankgoodness we have only spent 6 months trying to squish into a curriculum, it shouldn't be too hard to get back where we were, enjoying numbers.