Monday, October 01, 2007

Tricks Are For Kids



I've been reading a lot of math blogs lately and one thing I have come across quite a bit is that people are opposed to math tricks. Maybe I am misinterpreting the expression math tricks, but I always thought they were good. They were little ways of making a complicated example easier.

My AP calculus students are bright kids but have never been taught some of the little tricks to make their lives easier. For example, we were writing the equation of a tangent line last week. The slopes all came out to be fractions. The kids did not know an easy way to change the format and avoid working with fractions. They never knew that tanx/sinx can be rewritten (sin x/cos x) (1/sin x) instead of working with the complex fractions. They don't know the special triangles and insist on getting sin 45 from their calculator instead of figuring it out.. It never occurred to them to use the graphs of the trig functions to get the values of quadrantal angles instead of relying on a calculator.

Tricks don't replace knowledge. Tricks are part of knowledge and they make expanding knowledge easier.

6 comments:

Jackie said...

Hmm, I don't think of the examples you listed as tricks. I think of them as understanding. I'm interested to hear what others have to say.

Pissed Off said...

maybe not tricks, but shortcuts. the kids just don't know them.

JUSTICE not "just us" said...

In my school "tricks" are what dazzles the adminstration not conveying a deep undertanding of subject matter because there is no respect for scholarship. In fact the people that observe you often don't know the subject matter.

I think i will devote a post on the fraudalent observation system we have.

Thanks I think teacher blogs should be looking at what is going on in the front lines--the classrooms.

Anonymous said...

"tanx/sinx can be rewritten (sin x/cos x) (1/cos x)"

I think a correction would be nice.

Pissed Off said...

thanks!

Sarah Rainsberger said...

Funny, I think I was reading one of those very same blogs this morning. The comment I posted there was:

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@pisani - The problem is not that tricks are in use, it’s that they are sometimes the ONLY thing in use! I think it’s neat to point out patterns, but only AFTER the theory is understood. Since there’s usually not time for both, you’ll find that teachers tend to do one or the other.

I hardly consider FOIL a “trick” though, because it’s limited to one specific case. And believe me, it takes just as long to “teach” them FOIL as it does to teach “distributive multiplying” so why bother?

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I agree with the commenter who said that perhaps what you're describing with the equivalent form of the trig expression isn't so much a "trick" as a reminder that previously acquired knowledge is admissible in later math questions. Most kids are compartmentalizing their knowledge way too much, probably because they're taught in units, and chapters -- often at the mercy of disorganized textbook with an ineffective sequence. Not every teacher has the time, energy, experience and/or freedom to re-sequence.

If, for example, teachers would/could teach graphs of trig functions before solving trig equations, then students could easily remember things like sin90 or cos270 with a quick, rough sketch. But, how many times have I had to tutor kids in solving trigonometric equations only to learn that they hadn't seen the graphs of sinx and cosx yet? Makes it a little difficult for them to remember why there are sometimes 3 roots between 0 and 360 degrees, but yet sometimes only 1 root, when usually, they're taught to look for 2 roots. Not to mention the fact that they have to whip out a calculator to solve cosx=0, and heaven forbid they hit the wrong button, because they'll never know it!