Sunday, April 29, 2012

Keeping math contests in perspective

It is sometimes easy to lose sight of the fact that math contests are meant to be fun and engaging, but not ultimate ends in and of themselves.

 The main value of math contests is not to be found in the honors and awards (which are very nice, of course, but somewhat beside the point). The main value of math contests is to be found in wonderful mathematics it can draw students into discovering. Not only do they discover mathematics, but they can also discover the joys of working hard towards shared goals with a community of kindred spirits.

 Math contests are a little bit like mountain climbing. The views from the top are nice, but even spectacular views do not justify the extreme efforts it can take to get there. What can justify those mountain-climbing efforts are the joys of the journey, especially if shared along with others, and the beautiful things you can learn about the natural world and the power within yourselves as you help one another to discover hidden potentials and problem solving abilities within you that you did not know existed.

Just as you should "stop and smell the flowers" as you climb the mountain, so too should you remember to "savor the problems" you encounter in math competitions. By construction, those contest problems have already been solved, but reflecting on them after the contests are over may inspire you to create new and fresh ones of your own devising--or you may discover exciting new ways to solve old problems.

 A recently revived discussion on the Art of Problem Solving discussion forums reminded me of a remarkable essay written three years ago by a student on his contest experiences, which has resonated with many readers. The essay is very moving, thoughtful, and beautifully written. Both the essay (linked in the first post on the thread) and the discussion which followed it are readings that I would highly recommend to students, parents, and math teachers and coaches.

I would also recommend reading an inspiring speech given by our alumna speaker at Math Prize for Girls last fall, which also addresses these issues, and gives some excellent advice well worth bearing in mind for making the most of your math contest adventures.

You may also want to explore the links to the authors' blogs, which discuss some of the wonderful mathematics they have been inspired to learn and share with others. There is more recommended reading on these topics here. Some of our older alumni may also find useful advice and insights in a similar vein here.

Monday, April 23, 2012

Drawing new circles

The folks at the First Unitarian Society of Schenectady celebrate this poem:
He drew a circle that shut me out 
Heretic, rebel, a thing to flout.
But Love and I had the wit to win: 
We drew a circle that took him in! 
— "Outwitted" — Edwin Markham
This poem resonates with me in many ways, but today I want to focus on the way it connects to my vision for guerrilla math circles.

Many people feel "shut out" of the mathematical community.  They see math as a superpower that others have but that they hopelessly lack.  They can't imagine math as a joyful and empowering activity, as hard yet rewarding work.  They see the world as divided into non-intersecting circles of "People who can do math," and "People who can't do math."  They place themselves squarely in the latter and can't imagine that they could ever find joy and empowerment in visiting the other circle.  They may even be inclined to disparage or make fun of others who claim to enjoy math.

Can we find a way to draw math circles in a way that draws those folks in? I think we can.  That is where my concept of "Guerrilla Math Circles" come in.

To be continued ...

Guerrilla Math Circles, Math Super Powers, Math as Performance Art, and Math for the 99%?

I love the dual messages encoded in the T-shirt logo design above:

  • Math is a superpower!
  • Share with it with everybody!
    (∀ is a mathematical symbol that means "for all.")
If you also love this logo (designed by mathematician Cindy Traub of the always awesome St. Mary's College math department), please go here to vote for it.  If the design wins the contest, then mathematicians from all over the country attending this summer's Math Fest will get t-shirts with this logo, and I think it would be outstanding to have this message spread far and wide.

Mathbabe has been blogging about how math is a superpower, and that wonderfully evocative and inspirational phrase has been reverberating around in my head ever since I encountered it for the first time on her blog.

Those messages especially reverberated in my head last weekend, when I was in Washington, DC helping out at the Julia Robinson Math Festival held at the Smithsonian during the Math Circles on the Road event.  

You will have to forgive me--my head is truly exploding with all the inspiration and ideas I brought away from that experience, so this post (and most likely my next few posts) will be rambling all over the place as I share them.   A giant brainstorm hit me at the end of the weekend, a new concept I will call "Guerrilla Math Circles," which I will explain in a later post.   I will get there...I promise.

The event at the Smithsonian was really wonderful, with 60 enthusiastic math circle leaders from all over the country (including Elizabeth Parizh and myself from Albany Area Math Circle) helping to run free and fun public math circle demonstration activities for hundreds of enthusiastic participants.

There was a strong theme of "math as performance art" running through many of the sessions, including the one that Elizabeth and I helped Anna Burago to run, along with Ashley Reiter Ahlin, Berhrooz Parmani, Yulin Qing, and Jack Reynolds.   We engaged a group of students (around 8 or 9 years old) in acting out mathematical logic problems set on an island inhabited by Knights (who always tell the truth), Liars (who always lie), and Tourists (who can go either way.)  Simple props (leis for the tourists and pennants bearing a K or an L for the knights and liars) added greatly to the engagement of the event.  (The kids loved waving the pennants--and it was a really nice way to get their heads inside the logic exercise.  We had originally intended to use paper hats bearing K or L, but after consideration of hygiene/sanitation issues that could arise from switching hats around, we decided to go with pennants instead.  Props to my ever-resourceful 80-year-old problem-solving mother for suggesting that chopsticks leftover from takeout orders work much better than drinking straws for constructing inexpensive pennants!  The kids loved waving the pennants around so much that drinking straws would have quickly drooped.)

Another great session I had the chance to observe also involved math as performance art.  Blake Thornton of the Washington University in St. Louis Math Circle adapted an idea from Terry Tao's blog into a great session on the Island of the Blue and Brown Eyes.  (Again, it was fascinating to see what a difference the use of a simple but concrete prop made with the young children, who were acting out the roles of islanders trying to reason through a problem of inferring their own "eye-colors" based on their observations of the "eye-colors" they observed on the other islanders along with a remark made by a clueless tourist who did not understand the island's taboo against discussing eye color.  In the first run of this activity, Blake and his assistants gave each child an index card that told the child how many of the other islanders in the room had blue eyes, and how many of the other islanders had brown eyes.  In the second run of the activity, Blake and his assistants asked all the children to close their eyes as they placed a colored sticker on each child's forehead to designate that child's "eye color".  When the children were told to open their eyes, they could then immediately observe the eye color of all the other islanders.  This very simple expedient worked *much* better for the students involved, and I was really impressed at the way the children were then able to reason through the problems presented to them.)

I also got the chance to observe a Math Wrangle organized by Tatiana Shubin from the San Jose Math Circle.   The wrangle involved six very impressive young members of the Fairfax Math Circle, who wore awesome t-shirts bearing a translation of a famous quote from Georg Cantor as they wrangled in front of an adult audience awed by their poise in presenting their mathematical reasoning.

Their shirts said:  "The essence of mathematics of mathematics is its freedom."

Freedom...yes, freedom and free were more words that reverberated in my head last weekend.  Math is free--you can do it with scratching in the sand or dirt (as Archimedes did) or even just in your head (as prisoners of war have done in order to maintain their sanity) or with the simplest of materials such as stones or paper and string or colored sidewalk chalk.

And I was troubled by that message.


Turnout at the free math festival and at the nearby free Math Alive! exhibit at the Smithsonian was excellent.  It was a beautiful spring day with a Cherry Blossom Parade that had brought huge crowds downtown.  

There were thousands of children eagerly passing through the Math Alive! exhibits, with hundreds of them checking into our math festival and staying to participate in an activity or game with us.

So why was I troubled?

Because, among the hundreds of students that I personally observed passing through the festival and the museum that day I did not see a single African-American child visit our festival--and this in a city where the overwhelming majority of public school students are African-American and where the black-white educational gap is the greatest in the country.   (I did hear a report from other attendees that they did see a few African-American students attending, but there was general agreement that they were very few in number.)

We were at the Smithsonian in a FREE math festival, held in a FREE museum, on a national mall surrounded by monuments and memorials in the capital of a country that cherishes FREEDOM.  Our society is far from perfect, and yet it represents a beacon of freedom and opportunity to the entire world.    The free museums of the Smithsonian and our free-to-the-public math festival were emblematic of that freedom.

The newest memorial celebrating freedom near the national mall just opened last fall, the Martin Luther King Memorial.  For me, it brought back many memories of my childhood growing up in Washington, DC in the 1960s.  I spent much of the summer of 1963 at my grandmother's apartment, where she was dying of cancer, and tenderly cared for by a much-beloved African-American woman.   I still remember us sitting together in the living room as we watched the black-and-white television in awe of the vast crowds assembled on the mall downtown and heard Martin Luther King's powerful words reverberate:   "Free at last!  Free at last!  Thank God Almighty, we are free at last!"  

I too have a dream.  And it began to take concrete shape last weekend as I contemplated all these memories that reverberated in my head last weekend in Washington, DC.

To be continued....