Day 1: After going over introductory remarks, I put the students in groups
either randomly or maybe by the brand of calculators they have. I like to
put the HP people together and the TI-85 people together so they can help
each other out on syntax. I give each group a "nice" function, like f(x) =
cos(2x) and a point on the curve near a spot with a horizontal tangent.
(Each group gets a different function and point.) The group's instruction
is: "USING ALGEBRA ONLY find the equation of a line that goes through the
point that appears to be tangent to the curve at that point. When you know
how to do this in general, write down the steps you follow to get what looks
like the tangent line at the point (using algebra only.)" I tell them they
might need to review some formulas from chapter one about lines and slopes.
Day 2: Groups exchange sets of directions. Group 1 -> Group 2 -> Group
3 -> .... ->Group 1. I give each group a new point and curve. This time,
however, the curve has a horizontal tangent, and the point is "near" the
horizontal tangent. Each group has to follow the steps they were given by
the other group to find the equation of a line that appears to be tangent to
the curve at the point they were given. If the set of directions does not
result in a line that appears to be tangent to the curve, the group sends
back the directions for revision. The group that wrote the faulty
directions has to make corrections.
Day 3: Corrected versions are tested. Groups write-up the directions in
final form and illustrate following the steps with several problems. As a
class, we discuss what is involved and compare the sets of directions. The
groups turn in their written directions.
I like this activity because the students scramble to review slope of a
line, point-slope equation of a line, and how solve for y to put an equation
in slope-intercept form. I feel they need to review those topics, and at
the same time learn how to use their book for a resource to refresh their
knowledge. The group activity is a time saver because it saves the time I
used to spend on review of algebra, introduces the concept of a difference
quotient (which now becomes a 5-minute lecture), and introduces intuitively
the concept of the limit as one point moves towards another. (Sometimes
students in their directions have said that the second point must be really,
really, really, really close to the first point.)
Other algebra skills I have students review as they come up--sometimes
mentioned in class, sometimes given as homework as the skill comes up in the
context of calculus.
Martha
-----Original Message-----
From: Jodi Cotten <jcotten@mars.sunyjcc.edu>
To: John M. Flanigan <johnf@HAWAII.EDU>
Cc: Beth Hentges <bhentges@uswest.net>; mathedcc@archives.math.utk.edu
<mathedcc@archives.math.utk.edu>
Date: Monday, March 29, 1999 6:10 PM
Subject: [MATHEDCC] Calculus Review Chapter
>What part, if any, of chapter one in Calculus books do you cover? This
>question has always caused me a great deal ofhought. I know people that
spend
>a month on this chapter, I have ususally spent the first week on it. My
>current train of thought is to not spend anytime on this chapter and then
do
>little 'mini' algebra reviews as needed. I have a hard time wanting to
spend
>anytime on it because students are suppose to be ready for calculus. What
>good does it do the student that is ready to spend any time on this
chapter?
>Just some thoughts I am mulling over. Any words of wisdom from all of you
>experienced Calc teachers?
>
>Jodi Cotten
>Jamestown Community College
>Cattaraugus Campus
>Olean, New York
>
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