Category Archives: Math Games

University of Pennsylvania offering online course in gamification

Ken Werbach, associate professor of legal studies and business ethics at the Wharton School of the University of Pennsylvania, is offering a free online course on gamification. The course examines the use of digital game design to solve business problems. He provides dozens of examples of companies using game elements to promote customer-engagement, enhance employee-productivity, encourage sustainable behaviour change in areas such as health and wellness, and create a better environment in the workplace. Anyone can register for free at


University of Pennsylvania offering online course in gamification – Times Of India.

More news from the algebra front lines…. (a failed game)

Today in my remedial algebra class, I thought I would make an inequalities game. I had this great idea that I would put up on the board a whole bunch of inequalities, and each group would add or subtract or multiply or divide different things to these inequalities, and we would see if the result came out still true, or false.

(For example, it’s true that 2 < 4, and if you add 5 to both sides of this, you get a still true statement, 7 < 9, or if you multiply both sides by 2, it’s still true, 4 < 8, BUT, if you multiply both sides by a negative number, like -2, it’s not still true:   -4 < -8 is NOT true. Which leads to rules about how you solve inequalities.)

So… the first problem was that only about a third of the class was there on time…. So I went over inequalities and how to graph them for a bit first, vamping…..

Once more students had arrived, I put them in 6 groups, and put 6 TRUE inequalities on the board, like this:

Group 1: 2 < 4         Group 2: 5 < 8       Group 3: -2 < 5   etc.

I was going to ask each group to do different things to their inequality — one group would add a number to both sides, another would multiply both sides by a number AND ONE GROUP would multiply both sides by a negative, and they would be the mystery group where it would turn out that this gives a false result!!


Never under estimate the degree to which following directions is difficult, especially in a remedial class. I put the problems up for each group and I could tell pretty quickly that most students were baffled.

SO… I had them all do more or less the same thing each round — first I had them all add or subtract the same number to both side of the inequality, then we discussed it, then I had each group multiply both sides of their inequality by 2, and we discussed it… and then I had each multiply by -2, and we discussed it.  The last one — multiplying both sides by a negative — results in a statement that is NOT TRUE.

And then we went over the results: adding or subtracting by the same number — results in a true statement. Multiplying by a positive, results in a true statement.  Multiplying by a negative number…NO! The statement turns out false… this lead us to how to solve inequalities.

Well, so the game failed… but the experiment worked out! They were asking questions, arguing with me, protesting, working problems, THINKING. It was pretty awesome, actually. Good class!

Calculus: Art on the Wall Game (Teena Carroll, Saint Norbert College)

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.