Honors PreCalculus
I visited an honors precalculus class at Fairfax High today, so I could get a feel for some more accelerated math. It's the course Tricia Colclaser teaches when she's not teaching Algebra II.
The class is a little larger, with 30 students, and it moves fast. The students worked their way through a lesson on analyzing and graphing rational functions. Some things were familiar to a recent Algebra II student, ie. they factored lots of polynomials. But most of the lesson was over my head.
Starting with the vocabulary. The class discussed "asymptotes," which apparently come in three varieties: "horizontal," "vertical" and "oblique." They also talked about "removable discontinuity" not to be mistaken with "nonremovable discontinuity," and  my favorite  "holes."
I learned another new term called "synthetic division," and the skill itself, which is a nifty alternative to long division (aka real division???).
"Are your heads spinning?" Colclaser asked her students, as she quizzed them on the coordinates of holes and the equations of vertical and horizontal asymptotes for a particular function.
Mine was.
It's likely that once upon a time, I used these words in sentences to express some kind of mathematical thought. Example: "I drew my asymptote the wrong way!" or "That's a strange asymptote!" But they are lost, checked out, spending a leisurely afternoon at the beach with all the dative verbs I learned in Germany.
To test your own working knowledge or memory of these concepts (the math ones, I mean), I have obtained some homework problems that Colclaser handed out. She wanted to give her students something that was "harder" than anything they would find in the text book, she said.
Check back for the Friday Quiz. That gives you two days to brush up!
By
Michael Alison Chandler

March 4, 2009; 1:54 PM ET
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Next: Friday Quiz
Posted by: fahdp  March 4, 2009 5:38 PM  Report abuse
I'm glad to see you refer to using words to describe mathematical thought. I have often asked student in my own math classes to learn the language of math, hoping they would see the efficiency and gracefullness of using that language. It's analogous to the medical language doctors use to communicate with each other. It's more efficient as it allows complicated concepts to be described with fewer words. I'm looking forward to Friday's quiz!
Posted by: Cfhoag  March 4, 2009 6:46 PM  Report abuse
My daughter had it last year as a sophomore, and is taking AP Calc this year. Sadly I haven't been able to help her these last two years. I look at her homework and the problems are a half a page.
Posted by: crazyeagle  March 5, 2009 8:39 AM  Report abuse
Wow, Trish Colclaser sounds like an awesome teacher! Jan Lynch, Garden City, New York
Posted by: jlynch3  March 5, 2009 9:05 AM  Report abuse
Sometimes I think it would be refreshing to have a math class taught just like an Italian class or a French class.
If you trip over math vocabulary, you are always going to have a hard time. Might as well become fluent!
The terms you mentioned are familiar to me. What has me really flummoxed is the way math uses the word 'unique', for example. Or 'indefinite'. Words you thought you knew...
Posted by: KathyWi  March 5, 2009 2:23 PM  Report abuse
All of these terms are covered in the Algebra II curriculum in PG county... hmm.
Posted by: someguy100  March 5, 2009 9:14 PM  Report abuse
It does sound like the Algebra II I taught last year.
The concept of "removable discontinuity" is one that, as a mathematician, drives me nuts. At least the way it is taught in HS.
If a function appears to be noncontinuous in one form but when simplified becomes continuous then you always had a continuous function. What got drilled into me thirty years ago while getting my degree was to always simplify functions as a first action.
Posted by: ggartner  March 6, 2009 7:04 AM  Report abuse
Careful with removing those discontinuities  that's how people wind up proving things like 1 = 2!
Posted by: tomsing  March 6, 2009 8:54 AM  Report abuse
Sorry to be fussy about a previous post, but a function either is or is not continuous, regardless of how it is written. Rewriting enables you to take a limit that you would otherwise not have been able to take. It does not change the function itself (after all, the limit and the value of the function are not necessarily the same thing).
Posted by: DDunn1  March 11, 2009 12:48 PM  Report abuse
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i hate to be a geek, but all of those terms sound familiar.