Teacher2Teacher |
Q&A #583 |
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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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