Flow

I must have three unfinished blogposts to get through, but this is what I keep coming back to this week.

Natasha Lewis Harrington is a doctoral psychology student who writes about my favorite game (Magic: the Gathering) in her spare time. Sometimes she crosses the stream to great effect. Like this week, when she wrote about why this game is so good at encouraging creativity among players. It's applying the work of (let me copy and paste here) Mihaly Csikzentmihalyi (specifically Creativity: Flow and the Psychology of Discovery and Invention [Google book preview]) to the question of how can we learn to engage more. I think it's well readable by non-Magic players, so please do peruse.

Here's the quick take:

(The little bit of art is from Flickr, Paolo Colacino who does what he calls generative art. Quite neat.)

Csikzentmihalyi has a TED talk about leaving boredom:


Why is this gripping me so? Because of the divide between math as taught and math as it could be.

Math, as it is often taught, violates all three of these principles. (1) We tell you the problems to do, (3) we insist on solo mastery and uniformity of method.

Wait, that's only two.

I'm wondering if I have, in my need to change (1) and (3), more than occasionally neglected (2). Is that the procedural knowledge which I de-emphasize?  I usually do that in an attempt to get the pendulum swinging in the other direction, but in doing so am I denying needed support?

Maybe not. Maybe Learning the System in mathematics is not the procedural stuff. Maybe it's the processes, hidden behind the procedural emphasis. (The processes now appearing with their new band, the Standards for Mathematical Practice.)

Of course, there's hope. Teachers like Fawn Nguyen, Michael Pershan and Andrew Stadel are knocking this engagement issue out of the park on all three principles.

But, as Dave Coffey has cautioned, and convinced me, we need to teach our students to take control of their own engagement. So when they leave Jim Pai's classroom, they can be engaged the next year, too.

That's empowerment, and that's what I want for my students.

Game Design: 6-10

Mark Rosewater, head designer for Magic: the Gathering, has up the 2nd part of his intro to game design article, so it must be time for my 2nd part of my commentary thinking about educational games.

The first five principles were:

1. Goal(s). Easiest part for educational games.
2. Rules.  
3. Interaction. 
4. Catch-Up. Most subtle, maybe because so many games lack this.
5. Inertia. Hard for teachers.

The second five:

6. Surprise. The game should have some unpredictability for players.

To me, this connects strongly to Interaction and Catch-Up. One way to get surprise is hidden information - which often can contribute to interaction amongst players.  Information can be hidden from both or the players can hide it from each other. The new game Flip Out has a good element of this with two sided cards of which each player sees different sides. A benefit for math and literacy is that this makes inference a part of the game.

The other easy way to add surprise is random events - which can contribute to making catch up possible.  The only thing that makes Monopoly playable is the dice rolling.  In Euchre, no matter how good you are, you need cards to play. The math benefit is the addition of probability, even if informal, to game play. It's no surprise that the two most common game pieces are dice and cards.

7. Strategy.

Interesting to me that this is so low on the list, which makes me wonder what he was ordering them to achieve.

by mhuang @ Flickr

This is the biggest add-on for educational games over other activities. The problem solving inherent in any game with strategy is such fantastic grist for mathematics.  Mathematicians often see math as a game because of this strong connection. How do we achieve a result with allowable moves? Using games with K-12 students,asking for their strategies always makes for an amazing summary and unearths most of the math content of the games. It also helps build Inertia as then students are more interested in playing again, trying our others' strategies or designing ways to beat them.

There's a natural tension between Surprise and Strategy.  If things are too random, strategy loses all impact. If things aren't random at all, it is chess or go.  Both great games, obviously, but also both games that struggle with Catch-Up and Inertia for many players. Plug for Magic: the balance of these two elements is a large part of what makes the game so bloody amazing. Also applies to Bridge, to a lesser extent. (Yes, I'm claiming Magic > Bridge.)

8. Fun.

I struggle with this. Because I find interaction, surprise and strategy so engaging, I love games in general. I'll play anything. But what makes a game fun to kids is often a surprise to me. It's not uncommon for me to take a game to kids, and let them add the context. I wrote about this a bit with my Division into Decimals game.  Games like Decimal Point Pickle and Power Up had this in spades. Probably this is the difference between a game being good, and the game being a smash hit.

To some extent I think the last two principles are really subcategories of this one. Did they get pulled out to make ten or - more likely - is there something I'm missing that makes them truly distinct?

9. Flavor.


10. Hook.

Flavor is about the context and setting for your game, which heavily influences the fun aspect for players, in my experience. At least on entry, and Mark connects this to the barrier or entry cost to your game. The other principles determine long term fun. In our house, this gets us to play a game fr the first time, but won't sustain interest. One neat point he makes about flavor, though, is how it can influence design. My youth Bible study is making a return of the Lord card game based on the 10 bridesmaids parable. (Yes, really.) But the context for the game is inspiring a four horseman of the apocalypse feature that will definitely add interest to the game. Probably shouldn't have shared this story.

The idea of constructive flavor reminds me of my colleague Jacqui Melinn talking about integrated units.  A marine biology integrated unit is not when you put your math practice problems on a whale-themed sheet, it's when your questions about whales require math to think about and solve. Good flavor isn't an add on, but supports the game mechanics. For a math game, this gets at the structure of the game supporting the mathematical objective. Cheap flavor is the hallmark of flashcard/drill math games. "Look you're doing lots of multiplication, but it's on a baseball diamond!"

Hook is what gets people to try your game. This is less important in educational games to me as we have a built-in market (students), but I'm also not trying to sell my games to a publisher. (So maybe my hook is that my games are free?)  However it does remind me of Dan Meyer talking about a hook for a lesson, and could well be linked to engagement. I just don't know how to tease it out from flavor and fun. Maybe hook is a measure of whether the game has things that make you wonder?

My Nine
Looking over the list, I think I'd order them more like the following to get at my process.

1. Goal(s). Design starts with objectives.
2. Structure. (Not in his list!) What is the essential nature of your set of learning objectives and how can that show up in the game?
3. Strategy. These three have to go into the primary design phase as well, or the game will just not have them.
4. Interaction.
5. Surprise.
6. Catch-Up. As you start to playtest, these two are important to attend to for good design.
   
7. Inertia.
8. Rules. For me this comes late; kind of a synthesis step as you think about how to communicate the game. It will often result in design revision, though.
9. Context: Fun-Flavor-Hook. To me this can't really be evaluated fully till you're out with the intended audience. You need a first take on this before that, but should be open to major changes in this area.

Boy, I enjoyed these two articles. Thanks, Mark, for  writing them, and giving us fledgling designers something to think about. Note that Mark has a Tumblr where he answers many questions and gives the behind the scenes story at Wizards of the Coast. I asked, for example, about the order of his list, and he wrote: "I left it up to my subconscious. That was the order that felt organically correct. I’ll be honest, that I can’t exactly explain why."

Images: All Magic: the Gathering stuff is very heavily (c)'d by Hasbro.

Concentration Against Opposition

Hosting the Play Date
I am hosting the Math Teacher's at Play this month.  Please submit your own blog if you have something to share.  But also consider submitting something you've found valuable at someone else's blog.  It's the same form for either, and it just takes a second.  The link can always be found at the bottom of the right side column here.

Complex Instruction
I've shared before how NRICH is probably my favorite source for rich problems.  They also share bits of scholarly writing, host discussions and contribute in other ways to the math ed community.  This month, they've posted a wealth of resources on problem selection for group environments, leaning heavily on Jo Boaler's work with several of her articles or chapters; Dr. Boaler calls it complex instruction.  Take a look!


Concentration
Last and most oddly, I wanted to share some quotes from a Japanese gamer.  I play this game called Magic the Gathering, which is really the best strategy game ever invented.  (With the possible exception of global thermonuclear war, but you know the only way to win that...)  Players construct their own (or copy someone else's) deck of cards, and then face off against one or more other players.  It has a pro tour, and a small number of players who actually make their living playing.  The best analogy I've heard for it is a chess game with modifiable board, rules and pieces.  Each year the game expands and changes, yet remains simple enough for interested people to pick it up.  It has probability situations that will break your brain.  Frankly, it's amazing that I've gone this long without geeking out about it in this blog.

The author, Tomaharu Saito, is one of the best players ever.  He is known for his concentration, and wrote an article on how to learn to concentrate.  I love when people share their understanding on how to learn, and really feel like that the best reason to teach math (for most students) is that it is such a good context to learn how to learn.  The full article is here; selected quotes below.

I decided to write an article that would always be helpful to players, one whose ideas would not fade with time or format changes.

One of the best reasons to write!  That's one of the reasons I like so much for my students to write.  But then we need to give them ways and opportunities to share.  I'm still working on that.

In order to show 100% of your ability, concentration is crucial.  Frankly, as far as concentration is concerned, each person is different. And I feel like there are some people, although it may be only a handful, who can concentrate extremely well without training.
However, this does not mean that most players are naturally sufficiently focused. I think that time spent training concentration can affect one’s ability to refocus when their concentration is broken. This will boost your deck’s power, and is itself a way of taking countermeasures against weaker decks.

One of the things I am currently struggling with as a teacher is how to develop and support my students in becoming long thinkers, better able to apply themselves to significant problems, and to persevere through being stuck.  This feels relevant.

When practicing concentration, I find it particularly effective to pretend I am playing in a real event and focus accordingly. If my only goal were to boost my concentration, it would be good to always play as though I were in a tournament, but I also like to watch deck development, tune my build, learn match-up odds, and work on other goals which can capture my attention and cause a distraction. Because this can also lower my efficiency, I have found it is not a good idea to always split my focus. It is for this reason that I make time to challenge myself to work on concentration.

Remembering overall purpose, creating authentic conditions, assessing barriers to improvement.  Choosing to challenge yourself.  My teaching question is how to create purpose like that within the classroom.  You wouldn't do this for an exercise.  It needs to be relevant to your life.

Also after reading a book or watching movies or television, make sure you are able to explain the subject to a third party. This is always effective in improving awareness. When it comes to explaining the subject to someone else after reading or watching, you need to have watched it carefully and tried to concentrate in order to pin down the main point.

This is transfer!  He's talking about applying concentration in another circumstance.  The point about awareness in relation to concentration is new to me, but makes sense.

There are various methods for training your concentration, but there are none that allow you to master the skill in a short period of time. There is a feeling that steadily bit by bit the skill increases, so persist in your attempts. 

Also, one characteristic of concentration ability is that it is greatly affected by your every day life. In particular, people who stay up late should be attentive to this. If an individual does not spend enough time in sunlight various problems can ensue, and concentration ability is no exception.

Clearly true.  He's talking about life long learning, and how lifestyle impinges on performance.

Indeed, circumstances where concentration is broken and misplays are made are frequent, and naturally they make winning more difficult. I recommend self-confidence, but you can also learn my own method for recovering concentration.

Have you heard of the Saito Slap?  If there is bothersome noise around me, I will slap my cheek hard to recover my concentration.

He's not kidding.  He's not recommending everyone slap themselves, but instead talks about the usefulness of a routine that you can rely on, that by training triggers a response.  I think about that in my prayer life, but haven't thought about it for teaching.

What are the times when it is easy to break concentration? When you recognize the times when it is easy for problems to arise, it becomes easier to cope with them.

• The moment you think you’ve won
• When you’ve lost a previous game due to a play error
• When you’ve lost a previous round due to a play error
• When you’ve lost a previous game due to a poor draw, mana troubles, etc.
• When you’ve lost a previous round due to a poor draw, mana troubles, etc.
• After some kind of trouble occurs
• When something causes you to become irritated
• When you think about things other than the match

Perfect for an anchor chart!  I love the idea of thinking about ways you get stuck or when you give up on problems or...  What would this list look like in math class?

Magic is a wonderful game. Right now, I am betting my livelihood on it, but even misplays and losses do not cost me my life. I don’t let other people get to me.

If you relax a little, you can move forward.

That deserves an amen for brother Tomaharu.

Now to get more people to reflect metacognitively on their passions!