Teaching Calculus with a Game

Gaining an intuitive understanding about mathematical functions and how their shape is affected by parameters in these functions proves to be a tricky subject to learn. Dr. Brett Smith and Dr. Jim Rolf at Yale University’s Department of Mathematics approached us to create a prototype of their idea for incoming undergraduate students to reinforce basic knowledge of calculus in a class setting.

Bernard and Brett presenting Cartes at the Math Club at Wesleyan University

Cartes is an artillery-style game, in which two people battle each other using function graphs. Remember the classic board game, Battleship? Think of that concept, but players must graph functions to eliminate the opponent on a gridded playing field adhering to Cartesian coordinate space.

In the beginning of the game, players take turns placing traps on the grid, in a color specific to that player (player one is red, player two is blue). Next, players take turns shooting functions through the grid, eliminating traps. Traps are destroyed when they are hit with by a function, which players can craft from a deck of cards and then deploy on the grid.

By substituting 1+a into sin(x), and adjusting the value of ‘a‘ with a slider on a card, the wave in this example could be aligned to take out three of the red player’s “traps”.

The game concludes when one, or both players lose all of their traps, or one of the players runs out of time on the clock, similar to chess rules.

Check out the video below to see the gameplay in action:

Dr. Brett Smith giving us a quick overview on the gameplay of Cartes

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