This is a great calculus game that I saw demonstrated at the MAA/AMS joint conference in Boston in January. It was created by Teena Carroll of Saint Norbert College.
Students are in groups of 4, each with a post-it note. On the post it note, each student draws an arc that goes from one corner of the post-it to the opposite corner:
Student 1 is then asked to position their post it so that is is concave up and increasing, student 2 so it is concave down and decreasing, student three so that it is concave up and decreasing, and student 4 so that it is concrete down and decreasing.
The group then links their post-its together on the wall, in any order, and identifies points of discontinuity and inflection points.
I’m not teaching calculus this semester, so I played this game with a student I am tutoring. I was wowed at the way the game teases out the difference between concave up (positive second derivative) and increasing (positive first derivative). I’m looking forward to playing it with a whole calculus class!
Finally, I wonder if this is a game, really, or is it art? Or is it not art, but just great math? Whatever it is, it’s certainly a lot of fun and a great learning tool.
See the game video: https://www.youtube.com/watch?v=LYGwaI-haOM
NIU-Torcs is an example of a college-level mathematics game that allows for deeper learning within the game. Brianno Coller and colleagues developed the game through an NSF grant to help their mechanical engineering students learn numerical methods (Coller & Scott 2009). Students begin the game by learning how to code acceleration and steering using the programming language C++. They then move to making the car move fast without skidding off the road, by calculating numerical roots, solving systems of linear equations, and doing curve fitting and simple optimization. The authors report that students are motivated to keep trying far more than when given these types of problems as meaningless homework exercises. Concept maps produced by the students in both the game-based and traditional classes showed that although measures of low-level knowledge were statistically identical, students in the game-based class had much greater levels of deep thinking, which included being able to compare and contrast methods and link concepts together. In addition, student attitudes about the class had changed – they were more engaged, and more able to recognize the value of the mathematics they were doing.