As it is once again math competition season in my part of the world, I thought it would be nice to do a post on graphing calculators and mathematics competitions. While I realize this post may only appeal to a small segments of my readers, it is something I’m passionate about, and it may be helpful for new math team coaches out there.

I do feel as though I can speak from a position of some authority on this subject. I have coached the math team at my school for 8 years now, this being my sixth as the head coach. When I took over the head coaching role of the team in 2007, we had not won a regional in 15 years and never brought home a trophy from the Illinois state championships. This coming weekend, we are hoping to win a 5th straight regional title and we are in search of our 4th consecutive top 3 state finish, last year having narrowly missed winning it all at state and finishing second.

While there are many factors that have led to this massive change of fortune, graphing calculator use and training has been a major component. When I took over the team, I found a closet full of TI-92’s collecting dust in a cabinet. Immediately, I started handing them out to the kids and training them on them. Five years later, we have re-retired the TI-92’s and compete with TI-Nspire CAS’s. The kids are extremely proficient with them, and it is a significant advantage over schools that send their students into the competitions either without graphing calculators or completely untrained on how to use them (and I would say the majority of teams fall into one of these two categories).

In addition to the state math team competition series, I have also coached students in other mathematics competitions such as AMC, Purple Comet, and WYSE (Worldwide Youth in Science and Engineering), so I’m familiar with a variety of competitions. Let me give a few pieces of advice about graphing calculator use in mathematics competitions.

## Know the Rules

Before you jump into the competitions, take a few minutes to familiarize yourself with the rules of the game. Everything else in your graphing calculator strategy will be dictated by the competition’s rules. You can often find them on the sponsoring body’s website, and if not, a competition director will surely be happy to answer your questions.

Most competitions will fall into one of three categories:

- No calculators of any type allowed–time to move from this article if that’s the case.
- No CAS calculators allowed–probably ACT legal calculators.
- CAS calculators allowed–probably SAT legal calculators, although some competitions such as ours in Illinois are fine with the TI-92/TI-Voyage.

## Make a Wise Decision on a Team Calculator

If feasible, I think it is wise to get as many of the students working on the same calculator. If you have a little bit of team cohesiveness, they’ll probably be discussing problems from time to time. Our kids are constantly sharing tricks they’ve learned on the calculator with each other, something that’s made easier by the fact that they are all working on the same device.

Your main decision has to be whether you are going to use a CAS calculator or not, something that the exam rules may dictate for you. If you have the freedom to use a CAS calculator, take a look at past competition exams. In most cases, it’ll probably be to your advantage to have a CAS, but clever test writers can negate that advantage. If there were no budget constraints, my choices for a competition calculator would boil down to two: the Casio Prizm as a non-CAS, and the TI-Nspire CAS for a CAS calculator. Both are very easy to use and very powerful. I’d choose the Prizm over the TI-84 because of greater power in certain graph features, with conic sections, and it’s ability to simplify radicals and do exact trig values, features that are handy under the time constraints of a competition.

## Know Your Calculator’s Capabilities

Despite my top choices for a competition calculator, there are many other choices out there that would make good competition calculators: the TI-84, TI-89 Titanium, TI-Voyage 200, TI-Nspire, and Casio 9860 GII would all be among them. The key thing is that you have to know your calculator’s capabilities inside and out. In math competitions, speed is critical. I wouldn’t waste time on solving a system of linear equations with a matrix and the Gauss Jordan method on a TI-Nspire because it’s got a linear solver that’s faster and would make sense even to a freshman. Do you understand how to find the determinant of a matrix with a variable in it on a TI-89? If not, neither will your students. Every nuance you pick up is something you’ll have the chance to pass along to your students, and trust me, the kind of student that competes on a math team is a sponge for those kinds of calculator tricks.

## Train Your Students

I can’t understate this one enough. The kids won’t know how to take advantage of the calculators if you don’t do some coaching. When I first got started, we did an hour long training session for all the kids on how to use the calculators. Nowadays, the returning players bring so much knowledge to the team already that we only give intensive training to new players, mainly freshmen. Everything else is done in one on one sessions as calculator appropriate problems crop up via practice exams.

You don’t have to show them everything in their first year. We make sure all new players know how to use the algebra features of the TI-Nspire CAS, including solve, factor, expand, etc. As they get older, we add in features like matrix operations, combinatorics, calculus features, etc. Once they are trained, it’ll save you a ton of time on working through solutions with them. For example, my kids know that if I’m working through a solution with them, if we can get to the point where we’ve got the same number of equations and unknowns, the explanation is over. No matter how difficult the equations would normally be to solve by hand, they are comfortable with my expectation that they need to know how to solve those equations with their CAS.

## Have Fun

I know some people buy into the notion that math team kids already work hard, so being a part of the team should just be silly time. I believe kids love being a part of something excellent, so we train hard, and they do love it. My coaching staff and the kids believe in having plenty of time for laughing and joking, but we also believe in doing math team to succeed, much the same as we would for an athletic team. Trust me, there is absolutely room for both. Your students will thank you for making the effort to both have fun and challenge them mathematically.

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