Shack Attack

Game Theory for Middle School Day 2: Chicken and Commitment

Chicken is a discoordination game, in which each player gets his highest payoff from making the move that the other player does not make.

We start, of course, with a video:

Then I go on to help the students build a payoff matrix. This is a good time to reiterate that payoffs are ordinal and approximate (the order from least to greatest is more important than the exact amounts). Notes:

• The negative payoff from both guys swerving comes from the broken tractors and humiliation in front of their friends. You can make (and discuss) assumptions that adjust this payoff, but it should generally be worse than steady/swerve but better than steady/steady.
• 13 year olds are little lawyers- they love to find loopholes and call you on them. It helps to teach these kids the word abstraction early in the unit: I explain that in order to just focus on the math and the theory, we're going to create a simple model of a complex situation.

Discussion questions:

• If you know the other person is going to swerve, what should you do? If you know they are going to hold steady? What should you do?
• What should you do if you don't know what the other person is doing? Depending on the class level, you can introduce the idea of risk-loving, risk-neutral, and risk averse personalities. The former would hold steady, while the latter two would swerve.
• What if you had the choice of swerving left or right? How would that change the matrix?

Then we get to the fun part: commitment devices, reputation, and meta-gaming. Given a scenario like chicken, what could each player do to convince the other one that he was going to hold steady? I love kids' answers to this- a few needed a little guidance, but all of these were independently generated at least once:

• "He should just text while he's driving so he can't see the road. Then he won't know when to swerve so the other guy will just swerve."
• "He should be drunk."
• "He should be a badass so everybody knows he won't back down."
• "He should rip off the steering wheel! Beast!"

Explain to the students that these are commitment devices- strategies we can use that commit us to a choice for us down the road (heh), forcing the other person to make their choice based on the one we committed to. If they're reasonably sure we'll hold steady, they will swerve. 

Next: Cuban Missile Crisis! Start by showing the clip below from 13 Days:

 

Then, as usual, make a matrix:

Discussion questions:

• Wait, this really happened? The US and Russia played a game of chicken with nukes?
• What would you do in the USA's position? The USSR position?
• What commitment devices could the countries have used ahead of time to ensure they won the game?

Extension exercises and questions:

• Draw a payoff matrix for chicken with options to swerve left or right.
• Is tic-tac-toe a game of chicken? Is it a discoordination game? Why or why not?
• Can you think of any coordination games, where both players need to do the same thing to win?

Game Theory for Middle School Day 1: Payoff Matrices and Rock Paper Scissors

I majored in Economics with a focus on game theory, so I like to share it with my kids. I usually spend anywhere from a day to a week on the subject, depending on the students' engagement. Because Econ often seems dry to younger kids, I like to jump them right into the middle, and deal with terminology later on  in the unit. For today, the objective is mainly to understand how situations can be reflected in a payoff matrix.

1) Have the kids play rock-paper-scissors.

2) Ask what strategies they use to win (eg "play what would beat the winning move from the last throw."  Ask their friends what they would do if their opponent was using a particular strategy. Introduce simultaneous vs. turn based games. Discuss how much RPS would suck as a turn-based game.

3) Construct RPS payoff matrix. Fill in a few squares; have them do the rest.

4) Play videos:

 

Discussion questions:

-How good are these guys? Is this a real game?

-Who's paying for the $50,000 cash prize? (students will notice the heavy Bud Light signage all over the stage)

-Does the cash prize make sense, given what other pro athletes are paid?

 

I like to have them generate their own payoff matrix or decision tree for the game, but if they need a static visual aid, here's a good one:

Discussion questions:

-Is this game as balanced as normal RPS? Why or why not? Do you think it would be more fun? Why or why not?

-Is this game easier or harder to create strategies for than normal RPS?

-What would a payoff matrix for this game look like?

If there's time in the period, we spend it talking about random situations in life we could model with payoff matrices. I also try to get them thinking about the complexity of games like chess, and why can't solve those on paper.

 

 

Nostesia: Bad Schools Are Nothing New

Jamie Voller:

I know of no college or university in the country that doesn’t have to offer most or all of its freshmen courses in remedial English, beginning mathematics, beginning science and beginning foreign languages. Consequently, we give two or three years of college [courses] and the rest is high school work.

Most people agree that this is a perfect example of the declining quality of our schools. The problem with the argument, however, is that Professor Greene uttered this statement about the poor quality of high school graduates in March 1946. And when he spoke, he became part of a long line of complainants. Thirty-eight years prior, a 1908 Carnegie report discovered that large percentages of America’s high school graduates were being admitted to elite colleges with “conditions,” i.e., in need of remediation. Further back, in 1900, when only the top 2 percent of high school graduates went on to college (compared to 62 percent today), 378 of America’s 450 colleges reported that incoming freshman needed remedial work. Eighty-four percent!

The full post is well worth a read. What it's missing, though, is perspective on the nature of work in the past compared to the present. Yes, schools may have sucked in 1946, but even after going through a remedial English class in college, virtually any graduate was assured a stable, well-paying job. A bachelor's degree was a ticket to the middle class, and even without one, any hardworking, moderately competent adult could secure a full-time job (unemployment was generally under 4% from 1945 through 1960, and sometimes dropped below 3%).

Things have changed- a B.A. won't get you a job without good problem-solving skills, decent writing, and aggressive hunting, and tutition rates and student loan regulation make college a dangerous gamble for some. Bad schools may be nothing new, but we have never needed to work on them more than we do today.

 

Year-End Goals for My Class: Two Key Mindsets

My Program Director Master of Teacher Leadership Development Teach for America mentor guy Nate has us doing some soul-searching and visioning for our classrooms. It's refreshing and inspiring- a far cry from last year, where I felt like I was searching for perfect systems, rushing to hit objectives on time, and lowering the bar for my kids and I.

Today I decided that if my kids only remember two things about my class, I want them to be:

1) Problems need to be solved, you have the tools you need to solve them, and time's a wastin. Why? Because life is made of problems, and the more you solve, the better you get. 

2) To master anything, you need to practice it a lot.

These two mindsets matter more to me than the Algebra curriculum- if they internalize both of them, they will be set up for success with any teacher down the road, in any subject. 

Below are good but not critical mindsets:

"Math is fun"

"Mr. Shackelford is a good teacher"

"I'm good at math"

"I will use my Algebra skills later in life."

Yeah, I'd like my kids to have them, but if I have a class of problem-solvers who know the value of practice, their attitudes toward math and school will turn around just fine.

Non-Food Rewards for Students: My Class Point Reward Chart

I could pretend I don't like food rewards because it promotes a mentality that you "earn" junk calories, but my real gripe with them is the hassle. I hate arranging the pickup/delivery, coordinating with different classes on their lunch periods (they won't deliver pizza at 9AM), begging families for side dishes, and keeping my classroom clean and grease-free. At the end of the day, I'm left asking "Yeah, the kids seemed to like their two slices of Dominos, but was that worth $200?" (I have 160 kids, and that's including tax, tip, and some soda. It was a once-a-year-thing). 

Here's my new reward chart (each of these should happen once or twice over the year):

1) YouTube day (100 points): for a large part of the period, we watch a carefully curated playlist of interesting, funny, or just plain cool videos. I let students submit suggestions in advance, so I can review them and decide whether they fit.

2) MythBusters (200 points) one episode takes about a full period. It's educational, but also well-done and entertaining. The most popular episodes are the ones with explosions.

3) Class outside (500 points): one day last year during standardized testing, I took the kids outside during a break for about 10 minutes. I jogged them down the block to the park next door, and they ran around, frolicked, and played on the equipment. When we came back in, there was a giant smile on each one's face, and one actually called it the best class we had ever had. Kids are kids. Let them be kids.

4) Teach Mr. Shack a dance (1000 points): This is my favorite. The class picks any sort of dance (past candidates have been the dougy, ballet, the moonwalk, and breakdancing), and on some Friday, a few representatives teach it to me and I perform it (usually badly) in front of the class. It's funny, can't be bought anywhere else, and hey, I even get to learn something.

I've been trying to think of other rewards at smaller point increments- maybe problems taken off the homework, or music during the Do Now or during practice time. However, I adjust homework and play music so much I fear it would break their pavlovian reward circuit.