from Karen A:
M, our 8th grader, is in Algebra this year. M tends to get math conceptually. However, we have noticed several problems, which can sometimes be the difference between an A and a B for her.
One, she doesn't always know the material as well as she thinks she does. Two, she doesn't always pay close enough attention to detail. As a result, on quizzes and tests, those factors can mean the difference between an A and a B.
Let me note that her teacher is doing a nice job of teaching and the text itself is fine. Plus, there are online practice quizzes available (in addition to the daily homework, which the teacher goes over every day in class).
M had a test this week on Factoring and she needed to get an A on the test in order to get an A for the quarter. So, she was motivated! She started preparing for the test several days ahead of schedule by taking online quizzes.
The night before the test she worked all of the problems on the Review sheet. She had several equations to memorize and she came up with the following poem as a memory device:
"When factoring the difference of squares, write the answer in plus or minus pairs."
Her older sister coached her on paying attention to detail; especially in noting plusses and minuses within the equations.
M then came up with a list of five things that she absolutely needed to remember; she wrote them down and then memorized them. One of these was a reminder to be sure and read the question carefully, so that she knew what the question was asking for.
In short, she was well-prepared and as a result, she was the first one finished. Instead of handing in her paper, she went back through each problem, carefully checking for possible errors (and she caught several minor mistakes). She was the last person to hand in her test.
The result? She scored 100% on the test. Afterwards, she said, "I like math; I enjoy solving equations."
What is the takeaway? There are several, at least in my mind. First, I think she is finally starting to understand that having a conceptual understanding is not enough; she has to know the material thoroughly (and this requires hard work and practice). Two, she has to pay attention to detail (the old pencil and paper thing). Three, "rote" knowledge of arithmetic is essential so that the brain is freed up to do the next level of skills required.
Fourth, there is a tremendous amount of memory work required and that is essential (at least in my mind) for success in Algebra.
This story is a keeper.
ReplyDeleteIn particular, it illustrates why “rote” should not be considered a four-letter word by my school administrators.
absolutely
ReplyDeleteAlso, having a big arithmetic brain isn't enough either. My math kid is hitting his first bumps in the road because he resists solving algebraically when he can just "move numbers around" in his head (so says his algebra teacher.)
ReplyDeleteShe said that he can get away with that for awhile, but eventually he won't be able to.
There is so much algebra for him to remember in a very flexible way that he is starting to have too much in his working memory. He's gotten away with this for years, but now he is in a fast moving rigorous course and his easy going way isn't coming through for him.
It's some of the same problems your child is having (small mistakes, details being missed), but some procedures aren't locked in solidly enough and he's starting to fall apart a bit.
The detailed memory work involved is tremendous and difficult, particularly when no one mentions that this is the way it's going to be. (except his parents.)
It's been a bit of a shock for him to realize that he has to work differently than ever before.