# Best Uses of Graphing Calculators

With the recent announcement of the Casio Prizm, graphing calculators have been getting publicity they don't normally see. Gizmodo, Wired, Mashable, and many of the other major tech sites/blogs have run articles on the Prizm, and I've noticed a common theme in the comments on those articles. A number of people are questioning graphing calculator use. I'm somewhat used to this. On my Youtube channel, I get these same questions and comments, and on rare occasions they even come from parents of my students.

The conversation is almost always initiated by an engineer, computer scientist, businessman, recent college grad or someone else who was highly successful in their own math education, and likely even uses math in their career. The objections aren't always the same, but they tend to fall into one of two almost opposite groups:

## The calculator is too advanced

I never had a graphing calculator, and I was an A student in math all the way through (calculus or another advanced math course). Why does my kid even need a TI-89 Titanium? They can solve the problems without one. The calculator does practically all the work for you.

## The calculator isn't advanced enough

Why should they need to learn how to use a graphing calculator? In the real world, people use computers. The capabilities of a TI-Nspire are weak compared to the software that gets used in the work place.

I the first objection more often, but they're definitely both out there. I'd like to take the rest of this article to respond to those arguments. I think anybody who thinks that the graphing calculator is on it's way out is out of touch with what goes on (for better or worse) in a high school classroom. I have no doubt that things will change, but we're still a long way from the death of the graphing calculator. As I see it, here are some of the most important uses of graphing calculators.

## Graphing calculators make math dynamic and visual

Graphing calculators allow teachers to promote thought provoking activities . The examples of this are too numerous to list, but imagine the parabola y=x2 . Now add a leading coefficient of 1/3, 1/2,1, 2, 3, 4, and so on. If you are already very familiar with the effect a leading coefficient has on a parabola, you are probably envisioning an animated parabola, with its "arms" getting closer together.

But for a student new to parabolas, this may not be the case. I can tell you from personal experience that I can ask a class to graphing all 6 of those parabolas by hand, place them side by side, ask them to think about what is happening, and (after probably the 30 minutes this activity would take to accomplish with beginning algebra students), only about half the class will truly have the mental picture or animation that I am trying to help them see. The rest will simply wonder why we spent so much time graphing parabolas by hand, even with significant guidance.

On the other hand, just about every graphing calculator on the market has some sort of app that allows you to set up a parameter "a" in front of the parabola and animate the graph. In the course of 5 minutes, I'll be able to help far more students understand than I would have gotten in 30 minutes. You also have to understand that the point of an activity like this was not to graph by hand (even though that is an important skill). Graphing calculators often allow me to spend the time on the part of the activity that is actually important and not waste time on tedious skills that the class mastered long ago (even though they remain tedious long after they are mastered).

There are a ton of examples I could give here, but let me focus in on just one.  Optimization story problems, or problems where you have to find a maximum or minimum, can be solved using first semester calculus techniques. For many years, that is the first exposure students had to this type of problem. That no longer needs to be the case. In fact, with a graphing calculator, there's really no reason a second year algebra student couldn't work these kinds of problems. Students can focus on how to write a function that models a real situation and then use the graphing calculator to find the maximum or minimum.

## Graphing calculators are cheaper than computers (and ipads and iphones)

Admittedly, there are things you can do on a computer that you can't do on a TI-Nspire. In the real world, you are likely to use Microsoft Excel (at a minimum, and something far more powerful for hardcore statistical analysis) to do data analysis. That said, we're not yet at a point, where kids are going to carry around a laptop with them at school both due to size and expense.

As much as Google would like Android to be the next educational tool, the whole category of iPhones, iPads, and Android devices is a long way from having acceptance in the educational community. Most schools are still banning anything with wireless capabilities, and I can tell you firsthand with good reason. The lure of texting, games, and more during class is just too strong for most kids, never mind the fact that they are banned from important tests such as the ACT, SAT, and AP tests due to the obvious cheating capabilities a wireless device introduces.  There is still something to be said for a dedicated mathematics device, designed for educational purposes, for around \$100.

Long term, I think the survival of the graphing calculator niche will involve Texas Instruments, Casio, and HP building an iPad/iPod type of device. It won't be easy, though, because to infiltrate the market, such a device will have to: 1) have some built in limitations to prevent it from making cheating easy or having too many irresistibly fun, non-academic uses, and 2) get the approval of the folks at ACT and SAT, who so far, haven't exactly been about change in this area.

## Graphing calculators mean teachers can ask hard questions

If you took calculus prior to the graphing calculator revolution, you probably are familiar with tests that allowed you to leave your answer in a non-simplified or non-decimal form. In fact, there are still professors that give tests this way because they've been doing it for 20 years or more. This is definitely appropriate in certain situation.  However, for certain story problems, why wouldn't I want a decimal solution.

There are other times, where an intercept is difficult to obtain without a graphing calculator. Maybe it would require repeated iterations of Newton's method. That's great if you're testing Newton's method, but if it's one step of a larger problem, why wouldn't you want students to have access to that intercept in a matter of seconds? There are numerous examples like this.