Prisoner’s dilemma

Back to playing games… I have previously played a tournament of the prisoner’s dilemma with some of my pupils.

The basic idea is that of two prisoners who cannot communicate before deciding on their strategy. Do they rat on each other? If only one chooses this strategy, he wins and is set free. If both rat on each other, however, they are both lying and both lose. The rational thing to do is to keep quiet, but this depends on co-operation without the possibility of communication beforehand.

I introduced last year’s class to a set of rules for a simple re-iterated version of the game in one class and then the next time we met, they launched into a full tournament.

• Each pair plays three games and then switches
• I use the following score matrix (about the simplest version of the game)

	Player 2 attacks	Player 2 stays passive
Player 1 attacks	Player 1: 0 points Player 2: 0 points	Player 1: 2 points Player 2: 0 points
Player 1 stays passive	Player 1: 0 points Player 2: 2 points	Player 1: 1 point Player 2: 1 point

After a warm-up round, I had each player decide on a strategy in advance. The strategy could be as simple as ‘always attack’ or as complicated as they could think of, including principles for modifying tactics as the game progressed.

The idea was to play a round and then get them to revise their rules before playing a second round, hoping that they would eventually hit on the fact that they have to trust each other to get anywhere. I blinked here, however. Discussion in the break made me think that they were a long way from understanding this and I broke off the game. Afterwards, I felt that this was a mistake. I should have just let them play several rounds until they finally got the point. Sometimes, as a teacher you have to accept the fact that learning takes time.

This year, I just taught them the game and then launched into it. Again, after the first round, they could adjust their strategy and then we played another round. They hadn’t hit on altruism as a strategy, but they were certainly learning. It seemed as if they weren’t going to hit on it immediately, and they began to complain and get bored, so once again I broke off the game. Still, they had experienced enough of the game that I could riff off this experience. A ‘teachable moment’.

What does this teach? Well, I think this is one of the places where game theory is really useful for analyzing ‘real life’. Think about teaching the Cold War, when the whole world was in effect involved in a giant high-stakes round of the Prisoner’s Dilemma. To a degree, this can give insight into all social life, since all social life depends on counting on other people to mostly do what they are supposed to. We can almost always be exploited, but the cost of always guarding against exploitation by others is too high. We have to mostly count on most people doing what they are supposed to do most of the time, even though they could be rewarded by misusing our trust and a game like this can be a way to simplify and emphasize this for young people.

Photo credits: Peter Bruce, Mike_tn's

Save the Oxford comma!

The utter importance of preserving the final serial comma.

From  Bruce Baugh via Patrick Nielson Hayden via Brad DeLong via Jeff Weintraub via Dan Meyer .

"Among those interviewed were his two ex-wives, Kris Kristofferson and Robert Duvall. "

Verily, the mind boogles. No wonder this one made the rounds.

The best has to be vlorbik's contribution on Dan Meyer's page:

"I'd like to thank my parents, Ayn Rand and God."

Fear - How to teach when fear takes over completely?

 

I’ve been chewing on this topic all summer, but never really get far. Time to post some disjointed thoughts, maybe. In the holidays, I sometimes take the odd summer job - climbing courses for the Norwegian tourist association. Nice to change my office from this:

To this:

So: there's always someone on a climbing course who freaks out. At least on the inside. For this person, their own struggle with fear becomes the main component of the whole course. It often happens on rappel. Halfway down, the student freezes and an instructor often has to go down/up to them and talk them down, even re-rig and take them down physically.

 

These people often take things easier afterwards, dropping out of sessions as much as possible and not covering any optional material. Still, even though they may seem to accomplish less than most, these individuals who struggle with fear may be the ones who walk away with the greatest feeling of accomplishment. That's why I do kind of like beginner courses, even though many instructors look down on them.

 

But what about those who just give in to their fear, or who don't manage to get any further? It happened to me on a course this year: a student just gave in completely to fear each time she attempted something and the course ended without her having achieved anything, really. The question that gnaws me is of course: could I, as a teacher, have done anything differently to help this person?

 

Fear is often an issue when taking the inexperienced outdoors. Heli-ski guides can have trouble because extremely dangerous situations on winter snow can be perceived as harmless by skiers accustomed to managed ski slopes. Rock-climbing instructors can experience the reverse, with students or clients paralyzed by fear in safe situations. This is what happened on my course. We don’t have beginners in dangerous situations, but they may find themselves in unfamiliar situations and ones that look dangerous. Every so often, someone cracks and doesn’t manage to overcome their fear (fear, again, of a safe situation).

 

What happens here? My thinking is that this may be a product of our modern, protected lifestyle. This lifestyle can result in a very limited play of emotions, and when different emotions finally occur, the flood of feelings can be so overwhelming, unfamiliar, and awful, that the individual looses the ability to decide on their own actions. Fear, to take my example here.

 

Fear is not itself a negative thing. It keeps us alive. Our feelings connect us to our lives and help us navigate through them and fear is the most fundamental. I believe that fear is the primeval emotion – all animals must feel some kind of fear. Not all organisms seem to feel contentment or love, but everything avoids what is dangerous to it. Fear is directly connected to an organism’s survival, so it isn’t surprising that fear is a powerful emotion with somatic effects.

 

My wife thinks that many of us are unable to distinguish between our emotions and ourselves, especially in these moments of powerful feeling. Myself, when I am afraid, I am able to look at my fear a bit from the outside and think about whether or not I am reacting to something real about my present situation or if my situation is simply provoking old emotions. An inability to  do this may result in an inability to function when powerful emotion takes over. This seems to be what happened to a couple of my students this summer. Unable to distinguish between themselves and their fear, they have no opportunity to function when they are afraid. Some really absurd situations result. This summer, one woman sat whimpering on a ledge despite being fully secure when another young woman who was full of excitement at something she had just done skipped by her unsecured on the same ledge, smiling and chattering. I frequently see small children waltz up climbing routes chattering to their parents, while on the next route a frightened adult student cowers, completely paralyzed by fear.

 

Well – is there anything to learn from this? Does any of this have relevance for the classroom? I think so, because many pupils struggle with fear in the classroom. Many educators think of the fear that pupils fear in the classroom as something different than the fear one feels in a ‘dangerous’ situation, but I feel my experiences as a climbing instructor challenges this thinking. One can’t make a distinction between rational and irrational fear. Fear is always ‘real’ to the one who feels it, and fear on a climbing route may be far less rational than the fear of one’s classmates. The key is the relationship the student has to his or her own emotions and their ability to not be taken over by fear but to let other parts of themselves decide on their course of action.

 

So how can we as educators help students overcome by fear? My thinking above would seem to hint that these are complex issues rooted in the student’s life experience, so the help we can offer is limited, especially in the case of weekend courses. Being supportive (eye contact!) and challenging  at the same time seems to help, and so does breaking things down into one task at a time. Present a frightened person with simply the next step they have to do, not the whole project.

 

Since I believe that the problem may be rooted in the student’s relationship to their own emotions, the teacher / instructor can help by trying to make the student aware that they are not the same as their emotional reactions, but that these things are simply a healthy part of them. This is a long journey for some people and we have to have realistic expectations about what we can accomplish with people in the time we have available.

Death by blogging / Podcast

A few of my pupils looked disturbed as a mentioned the class blog. "Not another blog! I've already lost track of all the blogs I'm supposed to write." Humn. Maybe we're overdoing it a tad...

 

I was able to inform them that, this time, this was a teacher-run class blog, not an individual blog. At the moment, it's basically a podcast. Each class, a new student is assigned to sum up the day's work and submit their summation to me as an mp3 file.

 

I save the mp3 on a free, open web archive. At the moment, I'm using the Internet Archive, which is sort of awkward to use, but works well once you've finally uploaded your file. It saves your file and generates a URL for it.

 

The blog has link fields enabled, meaning that the title of the blog post is itself a link, in this case to the audio file submitted by my student. In Blogger, it’s simple to set this – you just check a box in the ‘settings’ tab. 

 

When I set this up, Blogger’s built-in feed was inadequate (don’t know if they’ve improved it), so I used Feed Burner to burn a feed for the blog. Feed Burner, now owned by Google, works well for podcasting. All my pupils have to do is open the blog once, click on subscribe, and they then get the podcasts automatically sent to their service (they’re teenagers, so almost all of them use iTunes) every week. The ones who synchronize their iPod with their computer get the podcast automatically on their iPod as well.

 

I was a bit disorganized last time I did this, but now that I’m a bit slicker, I’m excited to let this run for a few months and then get the pupil’s feedback on this.

Close those machines!

This year's leader for our student council came to our last staff meeting to introduce herself. She began by asking all the teachers to close their laptops. At the end of her short presentation, she couldn't help but comment with a smile that not all the teachers had done as she had asked.

I've pondered this before: lots of teachers (myself included) spend lots of time managing student computer use. Some of us spend a lot of time lamenting the poor spirit shown by students sitting in the classroom doing something other than what they should be doing. But - adults seem to be exactly the same.

What conclusion can we draw here?

GPS and ugly shoes: Tech and mental flabbiness

I’ve been on holiday recently, and once again borrowed my Father-in-law’s GPS for the car. It gets me thinking. The GPS is fun to use, and sometimes quite useful, but it can also get one into trouble since it replaces part of the thinking process without thinking itself.

We humans are actually quite good at orienting ourselves in space, extrapolating from incomplete information and reassessing based on observations. It’s probably healthy to stretch this capacity once in a while. The trouble with the GPS is that one quickly gets a far more passive attitude to navigation.

I think of the parallel to the physical world. It’s natural for us humans to find ways of saving energy and making jobs easier. Cars, elevators, wood-splitting machines – thousands of inventions make our lives easier. The trouble is that our bodies are adapted to an active lifestyle and all these inventions actually make us sick. Obesity and other effects of a sedentary lifestyle such as back problems have become major health issues in the western world. There is a growing awareness that we need to be far more physically active than we are, but so far this has mostly extended to filling up our free time with compensatory exercise. We drive to work, sit at our desks and then use the exercise room on our break. A bit absurd?

A new trend is slowly appearing however, based on trying to adapt our everyday life to our needs. I have, for instance, become one of those people who wear those silly-looking shoes designed to simulate walking on a soft, uneven surface.   We are poorly adapted for the hard, flat floors that I walk on all day long, so the idea is that by simulating the kind of surface we are adapted to walk on (soft, uneven), we can avoid some of the health problems of modern life. In this case, poor posture, reduced balance, short hamstrings, etc. These shoes are also harder to walk on, removing some of the ease of the modern lifestyle and re-inserting more physical work into daily routine.

Now, the GPS makes me wonder if we have started doing the same thing to our minds that we have done to our bodies: our brains, like our bodies, need exercise, and we are increasingly getting machines to do the tedious work of thinking for us. How does this affect us? I was helping a year nine student with a math problem a while back and part of the path to the solution required him to find 3 times 49. To my surprise (and dismay), he reached for his calculator.

Now, I’ve thought about this and anyone who uses a calculator to find the product of 3 and 49 is …well, damaged by access to calculators. For any normal person, multiplying 3 by 50 and then subtracting 3 is much, much faster than doing the work with a calculator, so dependency on calculators is actually slowing this person down. There are other issues here, however. This student didn’t even consider for a moment an alternative to his calculator, so it seems that calculator use has encouraged a passive attitude to numbers. Math is the subject that is most often a problem for schoolkids, so I wonder if we aren’t worsening the situation by teaching them dependency on pacifying tools.

I don’t mean to be a Luddite. We have become capable of so much more by ‘extending our brains’ onto external aids. Think of how much more we can do with just a pencil and a piece of paper than without. I’m a better shopper when I use a shopping list. Although I could practice mnemonics to use instead of my list, I prefer to use my brain power on other things. There is an urban myth about Albert Einstein not knowing his own telephone number. He had it written down if he needed it and could free brain space for more important things.

Whether this story is true or not, there is a point here. Tools make us capable of more, amplifying muscle or brain power and taking over mundane, repetitive tasks so that we can focus on the big stuff. To get back to the navigation example: I can navigate without a compass, but I’m much, much better if I have a compass. Isn’t the GPS just another step up? To think of my physical parallel: I live in an apartment building and wouldn’t want to get rid of my elevator. When my fridge dies, I don’t want to haul it down the stairs. The trick is to not take the elevator when I don’t have a fridge to carry. Walk to the store, bicycle to work, etc.  These things get talked about all the time. Do we need to start talking about the mental equivalents?



(I seem to remember reading a similar piece a while back, also taking a GPS as a point of departure. Can anyone remember seeing it?)
Photo credit: mraoch, Inky Bob

Does this blog exist?

Bogus question - yes it does. I've just been too busy with other things to spend enough time on it. First with exams (more on exams soon - I've been thinking a great deal about exams lately). And I've been on vacation (this is the house we rented). If you're not the least bit envious, then you haven't studied the picture closely enough.



I'll get back to classrooms and computers soon enough, but first, a little reflection on ugly shoes, mental flabbiness, GPS and ...fear.