One of the most familiar technological tools in the classroom is the last we’ll discuss in this class: the graphing calculator. You are probably already awareÂ of at leastÂ the basic functions of whatever calculator you have used in your own classes, but you might not have thought about the calculator as a pedagogical tool.

I’m of two minds about graphing calculators. On one hand, they are surprisingly powerful machines and, when used the right way, they can help a student understand a concept or an example without being distracted by rote computation. On the other, they’re clunky and old fashioned; we have much more powerful and user-friendly tools available now (for example, the software we’ve discussed in this class).

I found this 20-year-old report from Texas Instruments about the role of the calculator in math education, and figured I would hate-read it while I was procrastinating. After all, the report was put out by the same company that has had a near monopoly on calculators in classrooms for *years*…so it’s not exactly unbiased.Â However, the report discusses the exact same themes we’ve been discussing all semester! Take a look at the five mythsÂ mentioned near the beginning of the report; do they sound familiar? Familiarize yourself with the content of the rest of the report; you could replace the words “graphing calculator” with any other kind of technology essentially throughout the whole piece.

In addition to the benefits of using the calculator as a pedagogical tool, you should become familiar with the pitfalls as well. There is a nice chapter on Lies My Calculator and Computer Told Me from Stewart’s Calculus book. The examples listed in it aren’t the most relevant for us (many of them deal with rounding errors) but the chapter contains a nice quote:

*Computers and calculators are not replacements for mathematical thought. They are just replacements for some kinds of mathematical labor, either numerical or symbolic. There are, and always will be, mathematical problems that canâ€™t be solved by a calculator or computer, regardless of its size and speed. A calculator or computer does stretch the human capacity for handling numbers and symbols, but there is still considerable scope and necessity for â€śthinking before doing.â€ť*

Complete the following exercises:

- Imagine you are trying to help your students understand . Try substituting larger and larger numbers for in your calculator. What do you expect to see? What do you notice?
- Graph the function on your calculator. What behavior do you expect near the -axis? Do you see it on the calculator’s graph? Compare the graph your calculator gives you with the graph Desmos gives you.
- Graph the functions on your calculator. DoÂ you see what you expect to see? Do you notice anything weird? What happens if you graph the same functions on Desmos?
- Graph the function on your calculator in the window for and for . How many roots does it look like there are in ? Change the window to for and then to for with the same -values.Â What has happened to the roots? Try graphing the same function in Desmos.
- In the standard window on your calculator, graph the piecewise defined function if and if . Ask the calculator to tell you the derivative at . Is this what you were expecting? Try graphing the function on Desmos.
- Use the equation solver on your calculator to solve . How many solutions do you expect?

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