I guess I'm too mathy to call simple problem solving "algebra" in any context, and the counting on the fingers comparison would just have some parents claiming "Junior is doing algebra on his fingers". To me algebra is a
curriculum, that includes some sophistication and depth. FWIW, my daughter's 3rd grade state test results include a
calculus strand. But let's just say she wasn't doing calculus,

. To me "doing algebra" assumes a full curriculum that ends with a mastery of the subject. Otherwise it's too mind boggling for me to think that my own children (all three of them) were really doing algebra as toddlers.