You're a teacher in a public school. You give your 3rd graders a
worksheet of 50 two digit addition questions, e.g. 43+25. The
kid gets 90% of them right. Pass or fail? Now it's reading
comprehension time, you give the kid this: He gets them all
right. So? The math example, above, is real, and real(ly) scary.
+ 2 4 So the kid had done an entire worksheet of these. But what
was hidden from view was that the kid had absolutely no idea he
was adding 2 digit numbers. He had memorized the mechanics of
the process and nothing else. So when he was asked, "if you have
45 beads, and a friend gives you 24 beads, how many beads to you
have?" he didn't know to put the numbers on top of each other
like the worksheet; what he did was say the number 45 and then
start counting on his fingers, 46, 47, 48, 49.... and of course
he ran out of fingers and had no idea when to stop, so he
guessed. The problem is that as long as he completed the
worksheet, you wouldn't know there was a problem with doing math
until it was way too la