A lot of people see math as just a set of facts to memorize. So they think that a kid who does long division in 2nd grade has been coached to memorize facts and algorithms. They don't know how to tell if a kid understands what he's doing because they don't even realize there is anything to understand.
Last year, I helped DD's third grade teacher teach long division. Of course the teacher knows the algorithm and can DO long division, but she doesn't really understand it. That makes it tough to teach other than saying, "This is how you do it. Copy what I do."
