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.

Dylan Wiliam

I’ve been told that computers are about to revolutionize our classrooms for the last 30 years. And I’m still waiting.

 

Dylan Wiliam

The internet can still be fun

Every time I go to cut my RSS-feed from the Guardian's technology blogs, then they rake up stuff like The David Cameron anecdote generator. Interestingly enough, the generator itself is blocked at my workplace. I'm going to try not to think too hard about what damage the county authorities believe this could be doing to the next generation of citizens.

I also learned from the Guardian about Gamestation's changing their terms and conditions to include ownership of their customers' souls. It's not boring out there yet.

Does God exist?

…a post title a bit more in keeping with the blog’s title, perhaps. This blog is about belief, in the end, but it’s not always so obvious.

A little while back I was invited to the library at lunch to debate the existence of God. Amazing that at least 70 pupils showed up in their lunch break to hear such a debate. Here’s a answer to those who wonder if today’s youth are totally shallow.

Not quite satisfied with the debate. We should have agreed on more in advance, as my opponent’s approach was almost poetic and rather hard to attack. We only got going once the audience got involved, so we should have started with questions more quickly.

Worksheet > Exam 2

Well, our input to a working group at another school was pretty one-way. We went, we talked about living with computers in the classroom and then we came home. God only knows what they made of it all. Nice contrast between me and my boss, who is more of a gung-ho Web 2.0 educator than I am. I talked mostly about furniture, but in the context of all the other stuff that regularly comes up here.

Back to worksheets and exams. There is a tremendous culture of what I call ‘worksheet’-type questions here, particularly in English class. What was the name of the main character? What happened to him when he was eight? And so on.

Compare that to a typical exam question: “Rewrite the following paragraph to avoid its monotonous and awkward style.” Quite a typical exam question. There is also a part b here: “Explain how your version differs from the original using appropriate terminology.” Now, these are very typical exam questions. Here, they could be used in the year 12 English exam. I find these quite good questions. They demand concrete skills and they enable those pupils who have learned something to demonstrate those skills. They let the examiner differentiate between candidates quite easily without recourse to the dreaded multiple choice or to extremely subjective grading.

Trouble is, many of the pupils being prepared for this exam are being subjected to a strict regimen of short stories and worksheets. It’s no wonder that so many schools do so poorly on this exam – reading tons of short stories and doing worksheets is not a good preparation because the exam demands specific skills and knowledge. Worksheets demand knowledge of specific short stories which can’t be tested on the exam in the absence of a national reading list. This kind of teaching also chases pupils to SparkNotes and the like, and that’s really not building any skills.

Leadership in the digital classroom

I’ll get back to worksheets and exams in a moment. Firstly, leadership in the digital classroom. My boss is visiting a school tomorrow to talk about teachers as leaders in the classroom and I’m going along for the ride. We’re visiting a school that has a focus on ‘the teacher as leader’ and we, I suppose, represent a digital school.

What to share? Well, you have a few hours. What do you suggest I say?

Here are some of my initial thoughts:

• Stand at the back of a room full of teachers. What do you see? Facebook, email, newspapers. Are we expecting behaviour from children and youth that we cannot expect from adults? There was an interesting post a while back on 1:1 Schools pointing out that we often try to get the kids to learn things that most adults don’t know. It’s a very interesting point to make about school, but schools are also often very focused on behaviour and we seem to have the behavioural equivalent here. My pupils are sometimes confused when I berate them for answering the telephone during class. “But the teachers do it!” Humn….


• Leadership in the digital classroom has to rest on three pillars:




1. The technical. The endless proxy war, the American-style filter war, our own experience with LANschool – these things can make one think that there are no technical solutions. Giving computers to pupils and then trying to control them with filters or piggy-back systems can seem like a losing battle. A few pupils spend lots of time figuring out hacks that then spread. What one needs are simple steering or filtering tools that are robust and that form a part of a wider strategy.


2. The cultural. One has to build up a culture in school that regards class time as working time and the computer as a tool for work. You can’t avoid frequent and difficult conversations with pupils. It helps if the whole faculty is on board here.


3. The practical. There will always be a need for ‘eyeballing’. If your pupils are working on screens in class time, you need to be able to see them, and you need to be able to get to them quickly. How are you going to give help and guidance if you can’t get to them and see their work? This is where furniture comes in.


• The standard line is often: clear tasks, short deadlines, imposed collaboration. If pupils are going to work on computers, then they should have something clear and specific that they are expected to produce, an explicit and limited time to do it in and ideally this should not be ‘meaningless’ work, but something that is immediately useful for others. This makes some sense, but I think it underestimates the distractive power of computers. Vast amounts of money are spent on training our students to expect entertainment and that’s what you as a teacher in a digital classroom are up against.

Feedback, anyone?

Worksheet > Exam 1

I was substituting for a colleague a while back and in one of the breaks started talking to some of the pupils. One of them confided to me that he had never read any of the books they had studied in school. “Thank God for Spark Notes” he said.

This reminds me of an essay from the exams I marked last year:

I must admit I am not a very big book-reader, in fact... I don’t think I have ever successfully finished a single book in my entire life. It’s hard to understand, but it’s true. The school projects I have had when we were supposed to review a book, they were all lies. When I reviewed “The Da Vinci Code”, “Harry Potter and the Philosophers Stone”, “Atonement” ect. I had just watched the movies and based them upon that. However, I have read the beginning of some books and I have watched a lot of films in my time. (Anonymous pupil)

Moments like these cut to the heart of the matter for me. How is it at all possible for students to replace reading a book with reading a plot summary? They seem to be equating reading a book with knowledge of its plot. Huh? Are we in schools treating ‘reading books’ as synonymous with ‘finding out what happens’?

Yup.

Consider the following questions from one of the textbooks on my desk to the short story ‘Snow’ by Julia Alvarez:

• Where does the family live during their first year in New York?
• What impression do you get of the Sisters of Charity?
• Who was Yolanda’s favorite?
• Where was Yolanda seated in the classroom?
• Why was she put there?

Etc, etc. Typical worksheet stuff, right? Now, what exactly is being trained by setting questions like this?

Nothing. There is no skill or important knowledge base that is being pushed here. Such questions are merely control. They also fill the time, keep the students doing something and thus make us teachers feel useful. But – we can’t hide from the fact that this type of work tends to kill interest in something that is intrinsically interesting. It also teaches pupils to equate ‘reading’ with ‘finding out what happens’. Set questions like this and you chase the pupils to SparkNotes. Consider the questions above – if your goal is to answer them, then it’s actually more effective to read the notes than to read the story.

Think about that for a moment. If you are a teacher who sets worksheet-type questions for your class and you find out that they have answered them by reading the notes, how do you react? Shouldn’t they be praised for finding a more efficient way to get the task done?

So, OK, worksheets are out. What do you ask about literature? There are two questions about literature (or film) that I tend to use in my classes:

• Did you like it? (and why?)
• How does it work?*

These questions are not more easily answered by reading the notes. They correspond roughly to the two mains types of writing about literature and film: criticism/review and academic literary analysis, so they get kids working in real-world genres, not the made-up school-only genres we often get them producing in. Answering such questions well involves important skills.

I’ll post this now and get back soon to part two, which is to consider this line of thinking and ‘worksheet teaching’ in the light of final exams.

* There are, of course, a couple of other interesting questions about film and literature:

• How is this work situated in history? (how can we see it as a product of its time and what effect has it had on the world?)
• What does this work teach us about the world/ society/ life/ ourselves?

…but I rarely get there with teenagers.

Playing games

I used to be a middle school teacher (8-10) and I was known for using games a lot in class. For some reason, the games didn’t accompany me on my switch to senior secondary school (year 12). Maybe I’m afraid that it will be harder to get older kids to play. Maybe I’ve become less playful myself.

Last week, I pulled myself together and played one of my favorites. The Market. Manipulative, lots of fun. Goes like this:

Pupils are told that they are going to play at ‘a market’. They are divided into 3 groups and everyone is given trading cards. There are three types, e.g. red, white and green. The most scarce (I used green) are also the goal of the game. Everyone tries to accumulate green cards. The groups are unequal and the largest group is given primarily the most common ‘base’ type – red. This group should actually be a majority. The next largest group gets more cards per player. They get reds too, and more whites, but still few greens. The smallest group gets a few reds, some whites and also the most green. Ideally, the teacher glosses over the inequality of the groups as much as possible by dealing out quickly and putting emphasis on the rules of play. No attention is given to the fact that the players are not given equal cards. (Put the red cards on top of the pile for each player).

Play occurs in rounds of about 5 minutes. Everyone trades individually. The ideal is to gather ‘sets’ of one red, one white and one green card. At the end of each round, each set ‘generates’ a new green card. During the round, the players trade with each other. At the end of each round, the group that has the highest combined score gets to agree on a new rule for the game. The teacher (the ‘referee’ ) can also come with new rules, usually rules that are only valid for one round. For instance, to stimulate activity in the first round, 3 reds can also ‘generate’ a green. To dampen ‘inflation’, the referee can create tax rules to siphon off green cards. Tax rules can also help level the playing field by being weighted instead of flat, but be warned that this can stimulate solidarity amongst the ‘rich’ group. If play goes on for a while, a rule will be needed for the conversion of green cards into white.

The idea is that the different colour cards represent different types of resources, say red for labour, white for knowledge or human capital and green for material capital. Profit requires combining different types of resources and profit can then itself be re-invested and form the basis of more growth.

The point of the game is what happens. These kinds of things tend to happen:

• Most players increase their holdings.
• The rich group wins.
• Group solidarity forms, especially amongst the ‘poor’, and slowest for the ‘middle class’. In my class last week, pupils quickly got into their roles and began throwing out unfavorable characterizations of the other groups.
• The ‘poor’ or ‘working class’ tend to gravitate towards group play, but this requires internal leadership (or heavy hinting from the teacher).
• Pupils quickly get into the game and get surprisingly emotionally involved. All manner of underhanded tricks appear, cheating, intimidation, brinksmanship, etc.

The game is intended as a quick ‘Marxism light’ – demonstrating the functioning of class in industrial society, but my pupils pointed out that it could be any market system – modern world trade, for example. If people play rationally, then everyone tends to get richer, but while the poor get a bit richer, the rich get much richer, so it’s a good point.

It’s also interesting from a psychological point of view: how quickly groups form and how they relate to competing groups. My pupils last week from the winning group had a typical reaction: they were disappointed when they learned that I knew in advance that they would win. Even when it became clear that they had started with an advantage, they still liked to think that they somehow ‘deserved’ their position.

Endless fuel for classroom discussion here.

Picture credit: http://www.flickr.com/photos/artemuestra/ / CC BY-SA 2.0'>Reuters / Micheal Caronna

Mistaking access to information for learning

OK – the party line goes something like this:

‘Before’, information was scarce, so it made sense to crowd people into rooms where they all faced the front so that one expert could enlighten them.

‘Now’, information is readily available, so that this structure is obsolete.

The trouble with this analysis is that it starts with a false picture of the past. Most of what has ever been taught in schools has not been information that is particularly hard to come by.

Nothing I teach has ever been a secret. Most of what I teach is fairly simple, conceptually, and very easy to look up.

So, why do they pay me?

Because learning new stuff is difficult.

Skinner’s famous axiom was that (since we can’t see inside people’s heads) the only way to tell if someone has learned something is that they show new behaviour. Unfortunately, getting humans to act in new ways is difficult. Very difficult.

I feel left out of the party. The information revolution is supposed to be transforming schooling. “Pupils now have all the information in the world in their pockets and can find the answer to any question in seconds.” True, but irrelevant. This does not transform school, because school has never been about digging around for scarce information. This does not transform the role of the teacher, because the role of the teacher never has been the sole point of access to important but inaccessible information.

Information has become much easier to access in the last few years, but that ease of access has meant nothing for my teaching because scarcity of information has never been the issue. The difficulty of learning is the issue and sometimes I feel that all the digital revolution has given me are a bunch of shiny new toys that don’t even work half the time and distract my pupils when they do.

(Part 4 in the series Sick of Gurus)