kitchen table math, the sequel: boiling it down

## Saturday, March 24, 2007

### boiling it down

What is sorely missing is critical thinking about "critical thinking."

Instructivist said...

Thanks for highliting this important message, Catherine. (grin)

In a less grandiose and pretentious way, critical thinking is taking place all the time when solving problems in areas like math.

Take, for example, circle problems. When calculating the circumference, students must analize what the problem is asking for, what data is given (radius or diameter), which formula to select, and hopefully advance to an understanding that pi is a ratio (C/d). This is all fairly simple and modest, but my experience has shown me that it incomprehensibly represents a huge challenge to some students.

Karen A said...

I concur! A math story to share . . .

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.

Karen A said...

I should also note that M went to Kumon for 2 1/2 years because we didn't think she was learning the arithmetic she would need in order to be successful in Algebra!

Karen A said...

And finally. . .

I just read the following on gapingvoid.com, and it was in a post about titled, "How to be Creative."

"Being good at anything is like figure skating--the definition of being good at it is being able to make it look easy. But it never is. That's what the stupidly wrong people conveniently forget."

Catherine Johnson said...

oh I love that! (on how to be creative)