I use both. When students only see slope as the change in y divided by the
change in x, they have more difficulty intepreting the kinds of slopes they
get from doing line regressions on real data, therefore they do not
recognize m = .0013, for example, in an equation of the form, y = mx + b,
as a slope. Without rewriting a slope in decimal form, as a ratio of the
change in y to 1 unit change in x, they have a more difficult time
determining which slope/rate is steeper/greater. On the other hand,
students can get the beginning concept of slope possibly easier by the
definition of change in y divided by the change in x.
I also have students write ratios, not only as (the number of gidgets) to
(the number of widgets) but also as (the number of gidgets) to (1 widget).
I think this helps students read and understand newspapers or magazines that
report that some study found that 1.3 adults to 1 child, preferred a
particular product. Without the recognition that 4:3 is about the same as
1.3:1, students have little foundation for understanding what might be meant
by 1.3 adults.
Martha
-----Original Message-----
From: Syrilda Miller <symiller@eclipse.net>
To: mathedcc@archives.math.utk.edu <mathedcc@archives.math.utk.edu>
Date: Saturday, September 26, 1998 2:25 PM
Subject: [MATHEDCC] calculus:def of slope
>I have been looking at applets on several web sites to use in teaching
>my calculus class. Some define slope in a slightly different way than I
>normally do. This has made me curious about what other teachers on
>this list use.
> I define slope as the change in y divided by the change in x. (In
>various circumstances I use several other common forms as well.) Do
>any of you say " the change in y when the change in x is 1" Now, of
>course this is the same numerical value that my definition would give.
>I can see both advantages and problems with each version. I plan to
>continue using my original version, but if I see that many of you use
>the "change in y when the change in x is one" version, I will add that
>to my repertoire.
>
> If you are curious about the sites I have seen, here are some:
>
>1. http://www.ies.co.jp/math/java/heihen/heihen.html
>
>2.
>http://www.univie.ac.at/future.media/moe/galerie/geom1/geom1.html#anstieg
>
>The second site is part of a really terrific site :
>http://www.univie.ac.at/future.media/moe/galerie.html
>(If you go there let me know if you have a problem seeing all of their
>page. I loose about 15% of the right hand side or the bottom. I wrote
>to them but their suggestion for correcting the difficulty didn't help.)
>
>Syrilda
>
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