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

4 thoughts on “Teaching Calculus with a Game”

  1. tom says:

    I’d love to play this game. Where can I download it or access it?

    1. Bernard says:

      Thank you for your interest in playing the game. Since we usually transfer the intellectual property of the prototypes we develop to our clients, we wouldn’t be able to share it without their explicit permission. We will make sure to ask and in case we obtained the permission I will post a link here.

  2. Y. Acebo says:

    Would it be possible for a teacher to have access to this game for a PreCalculus class? Thank you.

    1. Bernard says:

      Thank you for your interest in this project! I sent you an email – I will ask our client, since they own the intellectual property.

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