## MEDU2010 Technology in Math Education

### Fall 2017 - Professor Kate Poirier

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 aware of at least 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).

In addition to the benefits of using the calculator as a pedagogical tool (see the graphing calculators homework), 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 can’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 “thinking before doing.”

For project #3, choose one of the following exercises. (Comment on this post to indicate which exercise you have selected—do not choose an exercise that has already been selected by someone else.) Prepare a short lesson introducing the topic and explaining the issue the calculator encounters in this case. Your presentation must include the use of the virtual TI calculator (available on our classrooms’ desktop). You may also include hand-drawn graphs and/or Desmos graphs if they are relevant for your topic. In addition to your presentation, include a post on your ePortfolio outlining your presentation. Include screenshots or photographs of the graphing calculator.

1. Imagine you are trying to help your students understand $\lim_{n \to \infty} (1+ \frac{1}{n})^n$. Try substituting larger and larger numbers for $n$ in your calculator. What do you expect to see? What do you notice?
2. Graph the function $f(x)=\sqrt{4-\ln(x)}$ on your calculator. What behavior do you expect near the $y$-axis? Do you see it on the calculator’s graph? Compare the graph your calculator gives you with the graph Desmos gives you.
3. Graph the functions $f(x) = \sin(10x), g(x)=\sin(100x), h(x)=\sin(1000x)$ on your calculator. Do you see what you expect to see? Do you notice anything weird? What happens if you graph the same functions on Desmos?
4. Graph the function $f(x) = \sin(\ln(x))$ on your calculator in the window $[0,1]$ for $x$ and $[-1,1]$ for $y$. How many roots does it look like there are in $[0,1]$? Change the window to $[0,0.1]$ for $x$ and then to $[0,0.01]$ for $x$ with the same $y$-values. What has happened to the roots? Try graphing the same function in Desmos.
5. In the standard window on your calculator, graph the piecewise defined function $f(x)= 3x - 2$ if $x < 1.5$ and $x^2$ if $x \geq 1.5$. Ask the calculator to tell you the derivative at $x=1.5$. Is this what you were expecting? Try graphing the function on Desmos.
6. Use the equation solver on your calculator to solve $\frac{\sin(x)}{x} = \frac{1}{x}$. How many solutions do you expect?

## Due date: Tuesday, November 28

1. I chose number 2

2. I choose number 5

3. Here’s a link for a 90-day free trial for a TI-84 emulator that you can install on your home computer, if you like. It’s available for Windows and for Mac (the first two items on the list)

https://education.ti.com/en/software/details/en/FFEA90EE7F9B4C24A6EC427622C77D09/sda-ti-smartview-ti-84-plus

4. Ichoose #6

5. I choose number 6 for the project which is sin(x)/x =1/x

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