Semi-Mathy Games
December 14, 2011 4 Comments
Here are some silly semi-mathy things I’ve done with my students either as bonus problems or fillers. I cannot vouch for their pedagogical value.
- +1 or +3. A bonus question appeared at the end of a test. ”Write Free +1 and you’ll get a bonus point on the test, no questions asked. Or write Go For +3 and if two-thirds of the class does it, all who do will get 3 bonus points. Saying anything out loud voids the bonus for everyone.” I was pretty surprised that in most classes, not enough students went for the +3. One student wrote Free +3 and got nothing…
- Choose A or B. In class, students were given this choice: “Write A and you’ll get a point for everyone in the class who writes A. Write B and you’ll get twice as much as anyone who writes A.” After a long debate, most students picked B. Far fewer students picked B when the choices were revealed publicly instead of privately. (Social commentary followed…)
- The probability you’ll get this question right. Still one of my favorite bonus problems of all time, this came from my wife: “If train A leaves Denver at 50 miles per hour, and train B leaves Chicago at 60 miles per hour, what is the probability that you’ll get this question right?” Students who wrote 1 or 100% were right, students who wrote 0 were wrong, and anything in between was resolved with a coin or random number generator. (There’s a fun discussion over whether a student who writes 0 can be right by being wrong… but if they’re right then they’re wrong…)
- The dollar auction. This one is evil. See http://en.wikipedia.org/wiki/Dollar_auction for a full description. In one class, a student successfully “escaped” by outbidding the other player significantly. In another class, a third student jumped into the auction midstream allowing another to escape. If I were still teaching, I would repeat the process using the bidding systems by Beezid and other “penny auction” sites (http://en.wikipedia.org/wiki/Penny_auction). Hopefully by exploring these auction styles with students they will avoid being scammed for real money later in life.
What else?
About Bowen Kerins
Fun!
Thanks for sharing!
I sometimes use a prisoner’s dilemma type game that I stole from a Yale game theory course:
“At the bottom of your test, write the letter α or β. Extra credit will be determined as follows: I will randomly pair your test with one other person from the class and
1) Give you both 1 point if both tests are marked with a α.
or
2) Give you both 2 points if both tests are marked with a β
3) Give the person who marked β 0 points and the person who marked α 3 points if the tests are marked differently.”
By the way, are you planning on attending ICME in Korea this year?
This seems a little unfair, since your random pairing causes a lot of the variance. I guess I’d have to mark alpha if I didn’t know what I was being compared to, because I’m guaranteed at least 1 point and an “average” of 2 (if I assume everyone else splits 50/50). Meanwhile if I mark beta, my maximum possible is 2 and my “average” is 1.
Another way to do this that doesn’t involve randomness is to compare your test to the majority of the class:
0) You get 0 points if you mark beta and the majority of the class marks alpha
1) You get 1 point if you mark alpha and the majority of the class also marks alpha
2) You get 2 points if you mark beta and the majority of the class also marks beta
3) You get 3 points if you mark alpha and the majority of the class marks beta
This makes the “beta is cooperative” very clear: by marking beta you can give the entire class at least 2 points (if enough people join in).
Never been to ICME, someday perhaps. I’ll be at the AMS/MAA Joint Meetings in Boston this week.
These are fun! For the second game, you wrote, “Far fewer students picked B when the choices were revealed publicly instead of privately.” Not sure I understand how the game would work if choices were made known to everyone.
I agree, I would definitely mark alpha in the Yale game since it has, for reasons you stated, better odds.