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."
Wow. Quite enlightening. Thanks Cathy.
This explains a lot to me about why so many US kids have trouble with algebra. Let's face it: Algebra I is not so tough. But if the kids never really understood what they were doing in 3rd+ grade, it makes perfect sense that they can't apply concepts of division, fractions, and signs in algebra.
Your posting gives me better understanding of why "math facts" drills are so pointless. They aren't just dull; they also allow the schools to pretend that the kids are learning something when they're just memorizing basic facts without understanding how to apply ideas.
I've been thrilled to watch my eldest son blossom as he comes to understand the different ideas behind a fraction (eg it signifies a portion of something or one number divided by another, etc) and apply the ideas in algebra. A while back I wrote out 2x = 4 and asked him to solve it stepwise. He drew a line under 2 and 4 and wrote 2 under each line and then solved it properly. I was so proud of him....
Schools should be able to teach this stuff. It's not rocket science.
Val
