Calculus Wars

Calculus Wars is a series of small serious games illustrating concepts from first-year calculus. The first entry in the series is Calculus Wars Episode i^4: The Quadratic Evasion, which covers Taylor series. In the game, the student flies a small helicopter, while a tank shoots projectiles at the helicopter. The tank targets the player using Taylor series– switching from a 0-th order prediction of the player’s future position to a 1st order prediction, and then a second order one.

These slides give an introduction to the game.

Calculus Wars
Curated by Jason Jason
Episode i^4 of Calculus Wars is designed to teach students about Taylor series using the example of a tank shooting a (slow) projectile at a moving helicopter.
Episode i^4 of Calculus Wars is designed to teach students about Taylor series using the example of a tank shooting a (slow) projectile at a moving helicopter.
The tank is controlled by the computer, the helicopter by the student.
The tank is controlled by the computer, the helicopter by the student.
The game is written in the Unity engine, so it compiles on Mac, Windows, and Linux.
The game is written in the Unity engine, so it compiles on Mac, Windows, and Linux.
intro_credits_shot
intro_credits_shot
The instructions for the student are very simple.
The instructions for the student are very simple.
At first, the tank fires directly at the player with no further explanation.
At first, the tank fires directly at the player with no further explanation.
After dodging several shots, the student gets a visual explanation.
After dodging several shots, the student gets a visual explanation.
The tank’s solution remains on screen until it hits or misses.
The tank’s solution remains on screen until it hits or misses.
The next level uses velocity and position to aim the tank’s shells.
The next level uses velocity and position to aim the tank’s shells.
This is harder to dodge.
This is harder to dodge.
A hit causes the helicopter to tumble…
A hit causes the helicopter to tumble…
…landing with a fireball…
…landing with a fireball…
..and a cloud of smoke.
..and a cloud of smoke.
Targeting mode 2 uses position, velocity, and acceleration to aim.
Targeting mode 2 uses position, velocity, and acceleration to aim.
You have to think in order to survive!
You have to think in order to survive!
credits_shot
credits_shot

How do I use this in class?

There are two ways to use this in class. The first is to introduce the game as an in-class activity, played on the classroom pc or laptop using the LCD projector. You can let the students play, and then add your own explanation of what’s going on after they try it for a while. This is a good introduction to linear approximation in a real-world context: the important lesson to convey to your students is that we rarely know the formula for functions whose values we want to predict.

The second way to use this is to give your students the assignment of downloading the game to their computers and figuring out a way to defeat it. They should then write a short reflection on the strategy they used. Of course, several strategies will immediately occur to the seasoned calculus teacher once you know what’s going on. My advice is not to give your students any advice on how to solve the problem. The act of formulating a game strategy based on math is the most valuable part of this activity for them.

How to play

The easiest way to play the game is to use the HTML5 version. This should just open in your browser and play (I’ve just tested in the current Safari, and it worked nicely). If you want to download a version to use offline, try the versions below. The Mac version seems to be quite stable. The Windows version is currently suffering from some bugs. I don’t know about the Linux version.

Windows version

Mac version

Linux version

Feedback

Right now, the game is ready for playtesting and the files above should be playable versions of the complete game. I welcome your feedback (both game-wise and teaching-wise). If there’s interest, the distribution build will include a system for you to verify that students actually completed the game which is integrated into the WebWork homework system. I’m very open to integrating the game with other LMS systems or course homework systems (Mooculus?), but you’ll have to work with me on access to your particular system.

Support

nsf1This project was supported by a generous seed grant from the UGA Office of STEM Education. This material is based upon work supported by the National Science Foundation under Grant Number (DUE-12-45540) Motivating First-Year Calculus with Robotics (MYFCR). The game is (presumably) copyrighted by the University of Georgia.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.