Sunday, May 2, 2010

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!

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!


  1. Did you hear about Saito's recent DQ and suspension? Apparently, he won't be inducted into the hall-of-fame now.

  2. Very sad story. He has been such a great player, and seemingly good guy. Hopefully his story isn't finished and there's a redemption ending.

  3. The Guillaumes, too! Weird stuff goes on at the top...