I agree completely with Brett and Brian; start with rational exponents and
then go to radical form. Students who learned radicals in high school will
be uncomfortable for a little while but just tell them to change to radical
form and do it that way if they prefer. They will often end up explaining
"their" method to classmates and you won't have much work to do when you
get to radical form! ;-)
There are several advantages to rational exponent form like justifying
fractions as a prereq, allowing them to simplify compound radicals, helping
them understand that the square root of a sum is not the sum of the square
roots (assuming that you beat into their brains the fact that the sum of
squares is not the square of the sum!) and helping them understand why the
powers on variables are cut in half when taking the square root.
Roberta
------------------------
>
>From: jodi <jodi@PRIMENET.COM>
>Date: Fri, 7 Nov 1997 07:51:41 -0700 (MST)
>Subject: [MATHEDCC] Radicals
>
>I am getting ready to start the chapter on radicals in Intermediate Algebra.
>I am going to put aside how I usually teach this chapter and ask for some
>ideas from all of you. This can be such a complicated and nerve wracking
>chapter for them.....and good ideas out there????
>
>Jodi Cotten
>Graduate Student
>Department of Mathematics
>Northern Arizona University
>
>Jodi
>Galations 5:22
>
>"Mathematics is the finest training for the mind." Plato
>
>
>Subject: Re: [MATHEDCC] Radicals
>
>Just a quick general statement. I do very little with radicals. I
>concentrate on converting them to rational exponents. I explain the
>concept, show how to convert to exponentials, and work with them in that
form.
>
>As a college student of the late 60's and early 70's I learned a long time
>ago that radicals should not be allowed on a college campus. They cause
>nothing but trouble. They storm the dean's office, throw bricks through
>windows, organize protest marches, etc. The only thing worse than a radical
>is a radical lurking in the basement. (Think about it :-) )
>
>I would much rather convert all radicals to born again rational expressions.
>Now, rational expressions are much easier to deal with, don't you think?
>
>Bret
>
>On Fri, 7 Nov 1997, jodi wrote:
>
>I simply teach my students to express radicals in the form of their
>exponential brethern. The students already understand exponents so they
>tend to feel little in the way of discomfort (excepting those that didn't
>bother to master exponents when they should have).
>
>Brian Goetz
>Bay de Noc Community College
****************************************************
Roberta S. Lacefield RSLace@mail.way.peachnet.edu
Waycross College http://www.way.peachnet.edu
2001 S. Georgia Pkwy (912) 285-6027
Waycross, GA 31503 Fax: (912) 287 - 4909
****************************************************
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************