From: Claudia (for Teacher2Teacher Service)
Date: Sep 18, 1998 at 20:36:27
Subject: Re: Algebra II

You are VERY right, they are difficult to teach because students have a
difficult time.

I try several different things.  I use colored chalks and pencils and treat
the situation like a color by number. If the problem specifies x<2, then we
graph one part in one color and the other in another.  I have used dotted
lines in part and erased.  I have used the analogy such as looking through a
camera lens to view only a certain part of the picture.  You can bring in a
real camera or use a video camera and try that.(this also helps with the
WINDOW idea on the graphing calculator).

Most recently, though, I begin with a lesson in Boolean logic for the
calculator.  I ask if they knew that the calculator can tell them when
something is true or false?   The calculator returns a 1 if the statement is
true and 0 if it is false.  I explain that that is the basis for most
switches on a computer.  The switch has a 0 and 1 on it rather than "OFF" and
"ON".  We take some examples.

Then we move to piecewise functions.  If I want to graph  x+2, when
x<0....the calculator will use a value of 1 for x<0 when it is true and
supply a 0 when it is false.  That is why I enter y=(x+2)/(x<0) in my
graphing calculator.  What happens when the calculator divides by zero????
The graph is undefined (does not exist)....so nothing shows on the
calculator screen.  I know it takes time. But usually, after this occurs,
most students get a better picture.

 -Claudia, for the Teacher2Teacher service

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