This thread makes me a little sad, because my mathematical ability is
somewhere around the level of an 8th grader, and I don't think that
will ever change. I care about this issue on behalf of my kids.
I'm 37. When I was in elementary school, the style was 'drill,
drill, drill'. For a while, I thought I was a math whiz, because in
the 100 question multiplication quizzes, I was always the first to
smack my pencil down: done!
In the higher elementary grades, I still got correct answers, but
my teachers chided me for skipping steps. I found this aggravating,
and concluded that I must be really smart (ha). In junior high, math
got more complex. I was bothered that plain old arithmetic did not
make answers just appear in my head without doing the steps. I got
through exponents and factoring, somewhat, but in high school, I found
myself nearly in tears trying to slog through the problems. I
memorized the steps, but I didn't understand them, and I hated those
pencil-and-paper sessions of going through steps I didn't understand.
I eventually quit school at age 16 (not over math).
Fast-forwarding, when my oldest son was in first grade, he had a
homework assignment with simple addition. It showed a picture of 5
pennies, and another picture of 3 pennies, and asked how much were ALL
the pennies. And at the bottom, it said "How did you get your
answer?"
The answer is 'I added 3 to 5', but my son was stressed. He
had added 3 to 5 and gotten 8, and that process was so obvious to him
that he was confused at the question. It was as if he had patted a
kitten, and said 'The kitten is soft...', and then someone asked him
'How do you know the kitten is soft?'
The answer is 'Because I am touching the kitten'. But that
is already obvious, and who would ask such a silly question.... so the
person being asked the silly question wonders if there is something
that he has missed.
These 'show your process' questions are part of the quest for
better math ability in the U.S., I guess, but as a math failure and a
mom, I find them annoying.
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