Of course some people do give reasons why play is useful. In these two papers, I’m building on some insights found in a 1933 paper by Lev Vygotsky entitled Play and its role in the Mental Development of the Child. (Vygotsky, you may well know, is one of my current heroes.) I remind the reader that in play, you can find all sorts of higher-order thinking skills taking place. Imaginary play is a very natural, distilled, abstractly difficult thing to do. Yet kids seem to do it on their own anyway, and before they even step foot in a classroom. If taught effectively, I think play is a useful vehicle for transfer of skills and tons of that ever-so-hot interdisciplinary work that goes on nowadays. (Wait until I get my genetic algorithmic music up and running.)

Journal 4: Methodological Doubt, Belief, and the Structure of Play

Reflection Paper 2: Decision-making as Game: A Mode of Prediction and Solution

Peter Elbow introduced concepts of methodological doubt and belief in his book Embracing Contraries: Explorations in Learning and Teaching. They’re central to his believing game and doubting game. Traditionally, doubt has been used as the primary tool in critical thinking. This unbalanced attention really makes a lot of analysis blind to new insights that can be gleaned from a moment of pure, suspended disbelief. (My ego won’t let me pass up an opportunity to say that both games show up automatically in my coffee mug model of classroom education.)

In my first paper I remark that all games require its participants to engage in the believing game—they have to believe that the rules imposed by the game are real and that the game itself is real. There are no consequences in any game if you don’t except them. You can always pick up the ball with your hands in soccer, unless you firmly believe that you can’t. For this reason, we might frame any situation as a game.

In the second paper, I extend my ideas to show that framing a situation as a game can greatly improve your power to predict behavior and arrive at winning strategies by simply considering the acceptable moves in your game. To illustrate my point, I work through a problem of the type sometimes given in consulting or computer science job interviews. The example shows, additionally, how mathematical reasoning (which I believe is no different than plain, old, vanilla reasoning) can be used to solve a problem without once using “math.”

As always, please comment freely. I’d love to get some feedback on this stuff.

Technorati Tags: vygotsky, play, imagination, games, rules, prediction, decision-making, higher-order knowledge, belief, doubt, mathematical reasoning, education, learning, solution finding, transfer, cognition, thinking, critical thinking, creativity, soccer, peter elbow, epistemology, coffee mug model

I’m not going to give some holier-than-thou exegesis of social ills or anything like that. There are too many others out there who’ve already done that for me. Besides that’s not how I roll. I’m going to leave up to you, the informed reader, to decide how you feel. I just want to situate his comments so that we’re in a better position to judge it. To begin, though, here’s what the AP reported Hardaway said:

You know, I hate gay people, so I let it be known. I don’t like gay people and I don’t like to be around gay people. I’m homophobic. I don’t like it. It shouldn’t be in the world or in the United States.

The fact that Hardaway is commenting on gays is almost irrelevant. Let’s see how his words sound when we make a few substitutions.

You know, I hate black people, so I let it be known. I don’t like black people and I don’t like to be around black people. I’m blackophobic. I don’t like it. It shouldn’t be in the world or in the United States.

Now how about another go at it?

You know, I hate blue-eyed people, so I let it be known. I don’t like blue-eyed people and I don’t like to be around blue-eyed people. I’m blue-eyedophobic. I don’t like it. It shouldn’t be in the world or in the United States.

That could be funnier. Let’s fill in something outrageous.

You know, I hate iguanas and carrot cake, so I let it be known. I don’t like iguanas and carrot cake and I don’t like to be around iguanas and carrot cake. I’m iguana-and-carrot-cake-ophobic. I don’t like it. It shouldn’t be in the world or in the United States.

Now, let’s try just one more time. Then you can go back to work.

You know, I hate dignity, so I let it be known. I don’t like dignity and I don’t like to be around dignity. I’m dignophobic. I don’t like it. It shouldn’t be in the world or in the United States.

That’s it. Mull over what you’ve read, and report back on what you’ve learned from it.

Technorati Tags:tim hardaway, homophobia, society, hatred, racism, carrot cake, iguanas, basketball, miami, mad libs

In the meantime, I took this quiz on the NOVA website about that silly E=mc^2 equation that everyone talks about. I was tricked by one of the questions.

Einstein appears to be the theme today. I met with Professor Strain to talk about possible final paper topics. After rejecting his initial offer (a proof of the previously thought impossible global solution to the vaccuum field equations by wave coordinates; they were thought — reasonably, it seems —, to diverge at inifinity.), we mulled over a casuality theorem due to Jacobi fields, or applications of PDE to mean curvature, finally arriving at the Hamiltonian formulation of GR. This is something that I really ought to understand. ADM mass, a quantity I now know and love, was originally proposed as a good definition of total mass because of its appearance by variational techniques. When explaining it, I like to use the nonlinearity of the field equations to eek out the self-interaction of gravitation. (This amounts to linearizing the theory and noting that these equations obey a linearized Bianchi identity, suggesting a conserved quantity.) I don’t know the calculus of variations, and, as a geometer, I should. And since I want to go into GR, this couldn’t make more sense.

Also, it seems, as my grandmother mentioned to me today, that Newton was an alchemist! I can’t but believe she’ll soon be concocting her own Philosopher’s Stone before long.

And mom, dad, and Janice, you can, if you want, purchase the complete DVD set of Sportsnight for me for Christmas.

For today is a holiday.

Thankfully, I’ve stopped drinking coffee before it became a habbit. You see, I try never to touch the stuff. And so, when I do, it does a number on me. You can ask some pre-law non-resident tutor Amy. I ran into her last night in the dining hall a full two hours after I had but one single cup of coffee. (The redundancy was for emphasis.)

By that time, of course, the effects of the drug had dissipated. On my way to section — I had stopped by the dining hall for cookies and coffee on my way to music section — I fantasized about what would happen should I continue drinking coffee. I would purchase a lizard, I thought. Frank — as that is what I called the lizard in my head at the time, though I noted carefully and to myself, that his name would depend essentially on his temperment and to call him Frank without regard to his personality would be unfair. For simplicity, I draw upon the stereotype that all lizards are called Frank. At least the hypothetical ones are, in much the same way humans use John or Bob as a common enough name when describing some abstract, fairly anonymous man. This stereotype, regarding the name Frank, is particularly less well-known in human spheres simply, I believe, very few of us speak any of the varieties of lizard; and few of them, human. So, you, kind reader, will excuse my use of the name Frank — he would sit upon my shoulder and sip my coffee. But, as my tastes are well set in their place, and for a generic lizard, as Frank is, we would almost certainly disagree on the ratio of sugar and cream to coffee. Being a lizard, he would demand more sugar. Lizards, you well know, have an insatiable sweet tooth. Between the caffeine and the fights with Frank, I’d lose too much sleep, never finish my thesis, and be forced, by a hypothetical lizard no less, into the navy for the next five years, never to rise above the rank of lieutenant junior grade.

Instead, I’ve turned to my collection of hats. For they and I bicker far less. Today my grey tuque and I purchased a very nice new set of jammers. They are navy blue with a yellow stripe down either side. You will note their accidental but happy coordination with my goggles.

The jammers wear like the skin of a seal that I onced clubbed and skinned while on a trip to a reservation in northern Oregon when visiting a friend who worked on a reservation investigating native forms of art, specifically vase painting, but also sculpture. When I swim in them I feel agile, and breathless, and deft. It’s like a good novel. But underwater and not on the back cover, breathless is a desperate adjective. I swam at the MAC, not having the patience to try out my new suit in at the Blodgett. The warmer water and heavy chlorination makes for dry skin. Even if that skin happens to have come from a seal.