I let my 8 year old use a calculator if doing a calculation by hand won't teach him anything. So, if he understands a concept completely, I don't force him to calculate by hand.
A good example of this is exponents. If he has to figure out 8^4, I prefer to let him type 8*8*8*8 on a calculator to having him laboriously go through each calculation.
I also don't always insist on absolute mastery of something before moving forward. So when he knew ~2/3 of the 0-10 times tables, we moved to long division. He memorized the remaining multiplication facts by applying them in division. The new subject matter kept his interest up and he simultaneously acquired the remaining old subject matter.
I'm more cautious with algebra, though. We do a lot of reviewing so that I ensure he retains concepts.
Val
