The ability to evaluate inverse trigonometric functions correctly is a fundamental and critical skill that a student needs for Calculus. For whatever reason, many Precalculus students struggle to master this skill and many who do master it do not retain it by the time they take Calculus. I decided to step outside the box and have my students play a game that would force them to make more sense of the range of answers that can be found when evaluating inverse trig functions.

I had read on some math blogs about teachers using the card game War to help students evaluate logarithmic functions and so I thought I could make this work for my situation. War is a card game in which each player gets half of the deck of cards. For each turn, the players each flip a card. The player with the higher valued card wins both cards. The player with the most cards at the end wins the game. I adapted the game with homemade cards that had all the inverse trigonometric functions that use angles found on the unit circle. I prepared a visual aid that diagramed the allowed range of answers for the six functions. I divided the students into groups of three: two players and a referee. I explained the rules and then let them play.

It was slow at first while they got used to the rules and got comfortable with evaluating the functions. I circulated the room, checking in with students and responding to questions. It was very apparent to me just how many students really didn’t understand what they were doing. Group by group, I responded to their questions. As soon as one in the group understood, I would leave that person to explain to the others. Slowly but surely, they started to “get” it.

While I doubt that anyone would claim that this was a particularly fun game, I had many students tell me on their way out how much this helped them gain confidence with these functions. While I was circulating around the room I also witnessed many “aha” moments where students for the first time seemed to grasp the purpose of evaluating these functions. I’m not sure how I will be able to assess how well this extra day and extra activity really served to improve their understanding and retention of the subject, but subjectively I conclude that this was definitely time well spent.