On Doug Noon’s Borderland blog, high school teacher Karl Fisch defends the use of conceptually-oriented math programs like Everyday Math in elementary schools. In doing so, he makes a distinction between arithmetic and mathematics:
But, as a high school teacher, I think it's just as important for students to understand multiplication and division. In my experience, many students who know their facts don't have a clue what multiplication and division is. I believe part of the reason that programs like EDM were developed were to attempt to address these very issues. Teachers were sending their kids forward thinking that they knew mathematics, when they really just knew arithmetic (and even "knew" is probably too strong).
Noon, a 6th grade teacher frustrated with his schools’ use of a conceptually-based math program, retorts that basic math facts are central to mathematical understanding:
[Students] need to know the multiplication facts to simplify fractions and find common denominators. They need to know the facts in order to think mathematically. But [in programs like EDM] the facts are not stressed. So I back up, I and stress them because I know that later on, teachers will not want to spend time doing that. The rest of that suff about "conceptually-based" algorithms is all hoo-haw because the whole point of an algorithm is to take the thought-work out of calculating. And where is all the conceptual understanding with the 'lattice method', which ignores place value altogether? None, n-o-n-e of the kids who use those alternate calculation methods have ever shown me that they have any understanding whatsoever about what they are doing.
A version of this news article first appeared in the Teaching Now blog.