Why Math Education Needs Puzzles

Scott Kim, scott@scottkim.com

http://pinterest/scottekim/cool-math-education

http://www.slideshare.net/scottekim/why-math-education-needs-puzzles-12495813

 

I wrote this paper for the biannual Gathering 4 Gardner in April 2012, honoring math & science writer Martin Gardner, whose writing about recreational mathematics have inspired millions.

 


Gardner on recreational math

Martin Gardner wrote a highly influential column called Mathematical Games in Scientific American Magazine, from 1956 to 1981. By reporting on the newest mathematical discoveries from all over the world, Gardner influenced several generations of science-loving kids to fall in love with math, and pursue mathematical careers.

In a 1998 article reflecting on his career [1], Gardner writes that "recreational math should beÉregularly introduced as a way to interest young students in the wonders of mathematics." He goes on to describe puzzles and magic tricks that excite student curiosity about various mathematical topics. Sounds like a good idea. But when Gardner tried to convince educators to incorporate recreational mathematics in their curriculum, he reports that Ňmovement in this direction has been glacial.Ó

I would like to melt the ice. I believe puzzles can be a potent solution to the widespread problem of mathematical illiteracy: students who know how to perform mathematical procedures but donŐt understand what they are doing. In this paper I will show how we can harness the power of recreational mathematics to radically improve math education.

 

Gabe meets algebra

My son Gabe is in seventh grade. HeŐs good at math. But recently he encountered his first stumbling block: algebra. For the first time heŐs seeing math that doesnŐt make sense to him, and causes him to ask ŇWhy are we learning this?Ó HeŐs drawing a blank, as are many of his classmates.

So I asked his teacher why students should study algebra. He answered that algebra is the language of mathematics. You need to know algebra to do higher mathematics, science, and engineering.

I agree. Learning to make sense of algebraic expressions is like learning to read. At first you have to sound out each letter, then put letters together to make words, and words together to make sentences. But eventually the process becomes automatic and you stop seeing letters and start reading ideas. And reading expressions is essential for mathematical literacy.

But thereŐs a problem. If algebra is the language of mathematics, then why isnŐt it taught in a meaningful context? Algebra is usually taught as an abstract set of rules, with only occasional, highly contrived examples of how it might be used. No wonder students feel bewildered.

Now itŐs true that sometimes you just have to buckle down and learn a rote technique— you have to learn your ABCŐs before you can read. But the extreme emphasis on rote learning in math class is a set-up for failure.

 

Grammar without meaning

To dramatize how truly bizarre conventional math education is, imagine how other subjects would look if they were taught in the same way as math. Paul Lockhart [2] and Tristan Needham [3] have written similar critiques.

If music were taught the way math is taught, you would study notation and music theory. You would be tested on chord naming and proper voice leading. Never would you hear a whole piece of music, except, perhaps, in graduate school. You would have no idea that music was anything more than marks on paper.

If sports were taught the way math is taught, you would study rules and strategy. You would be tested on history and player statistics. Never would you step onto a playing field, except, perhaps, in graduate school. You would have no experience of sports as a physical activity.

Finally, if English were taught the way math is taught, you would study the mechanics of grammar and spelling. You would be tested on conjugation and sentence construction. Never would you read a book except, perhaps, in graduate school. You would have no idea that words had meaning.

Teaching mechanics without meaning leads to predictably dismal results: students feel anxious, guess randomly, cling tightly to rote procedures, and quickly forget what they have learned.

ThatŐs all backwards. Kids learn to read because thereŐs something they want to read. Mechanics and meaning go together. In math, as with English, we should teach literature in parallel with grammar.

 

Puzzles are the literature of math

But what is the literature of mathematics? What are the creative mathematical works that can excite kidsŐ imaginations?

First of all there are storybooks that involve math. Young adult novels like The Phantom Tollbooth [4], and A Wrinkle in Time [5] put mathematical ideas into dramatic situations. The classic novel Flatland uses the geometry of 2, 3 and 4 dimensions to tell a tale of social narrow-mindedness [6]. And picture books like How Much is a Million? [7] give numbers visual meaning. Those books can and should be woven into mathematics education.

Then there are games and sports. When kids play games like Yahtzee or Connect 4, they develop number sense and logical thinking skills. Sports like baseball require counting and statistics. Computer games like Tetris exercise geometric thinking.

Finally there is recreational mathematics — fun puzzles like Tangrams [8] and Rush Hour [9]. Children learn through play, and recreational math is mathematical play.

Of course recreational math isnŐt just for kids. Martin Gardner — the Shakespeare of recreational mathematics — wrote essays that stir the imaginations of adults.

Everything you know about childrenŐs books applies equally well to mathematical games. We read books to our kids at bedtime as a warm family activity that promotes reading. You can also tell number stories to your kids, such as the ones on the site Bedtime Math (bedtimemathproblem.org). And you can play mathematical games together as a family, thanks to the Family Math books from the Equals program at the Lawrence Hall of Science. [10].

 

But teachers resist puzzles

If puzzles are mathematical literature, then puzzles should be part of the mathematical curriculum. Introducing puzzles into schools is a good idea, but simply giving puzzles to teachers does not work well in practice.

Consider ThinkFun, the premiere maker of mathematical puzzle toys for older kids. ThinkFun CEO Bill Ritchie started their Game Club (thinkfun.com/teachers) in 2007 to equip teachers with low-cost puzzles and teaching materials that teach problem solving skills to students through puzzles.

A few teachers who already understood the value of puzzles enthusiastically jumped on board. But most teachers resisted. And for good reason: Puzzles do not fit the standard mathematical curriculum.

Teachers are under tremendous pressure to cover state-mandated topics within tightly constrained time periods. Teachers donŐt have time for puzzles. And even if they had the time, teachers are not trained to know what to do with puzzles in their classrooms.

Changing math education is hard because we are all caught in a vicious cycle. Bad math education creates teachers, parents, administrators and policy makers who cling tightly to the math education they know, even though it didnŐt work, which creates more bad math education. Without a model for a workable alternative,

 

So letŐs bypass schools

ThinkFun has not given up on education, and neither should we. To get puzzles into math education, we need to take a different approach. Here are some recent projects that bypass schools entirely, and take mathematics directly to the public in the form of entertainment.

Flatland: The Movie is a beautifully scripted and animated 30-minute adaptation of Edwin A. AbbottŐs classic mathematical fairy tale.

Mathemusician Vi Hart creates short stream-of-conscousness films for the web that present artistic / mathematical ideas in an irreverent, spontaneous and wholly personal manner. Her videos have gone viral, especially with young women.

The Museum of Mathematics in New York City (momath.org) will be the first museum of its kind in the United States when it opens later in 2012. It strives to present the wonders of mathematics in an exciting, visual, interactive format that will change the public understanding and perception of mathematics.

Mathematician-dancer Karl Schaffer creates dance performances that are equal parts math, dance, and theater. In his most recent work, The Daughters of Hypatia, four female dancers tell and dance the history of women mathematicians through the ages.

 

And pass on GardnerŐs legacy

All of us who attend the biannual Gathering 4 Gardner have been deeply affected by Martin GardnerŐs writings. We all understand that math is a joyous, creative, exciting endeavor. But GardnerŐs writings are known only by an elite, older crowd.

I think the mission of G4G should be to pass the joy of mathematical games on to the next generation, and reach a much wider audience. That means taking the wonderful ideas in recreational math and presenting them in a more accessible form. Here are specific actions I want us to take to get puzzles into math education.

1. Create a mathematical puzzle exhibit that can appear in science museums, that lets visitors get their hands on a variety of classic puzzles.

2. Compile puzzles resources for math teachers: for every mathematical topic, make available puzzles that can be used to introduce, teach, and enrich that topic.

3. Start a problem of the week channel on YouTube, where a new mathematical puzzle is posted every week. Each puzzle includes 3 difficulty levels, and encourages viewers to post their own video responses explaining their solutions.

4. Produce recreational math books, eBooks and apps aimed at kids.

5. Launch a national puzzle competition that engages students in solving, presenting, and inventing mathematical puzzles. An organization already doing this at a local level is Math Fair out of University of Calgary (mathfair.org).

6. Start a national math week (or month), with public festivals everywhere. Ireland is already doing this with their the national Maths Week (www.mathsweek.ie).


References

1.      Martin Gardner, ŇA Quarter-Century of Recreational MathematicsÓ, Scientific American, August 1998, pp. 68–75.

2.      Paul LockhartŐs, A MathematicianŐs Lament, Bellevue Literary Press, 2009.

3.      Tristan Needham, Visual Complex Analysis, Oxford University Press, 1999.

4.      Norton Juster, The Phantom Tollbooth, Random House, 1961.

5.      Madeleine LŐEngle, A Wrinkle in Time, Farrar, Straus and Giroux, 2012. Originally published 1962.

6.      Edwin A. Abbott,Flatland, Dover Publications. Originally published 1884.

7.     David Schwartz, Steven Kellogg, How Much is a Million? Perfection Learning, 1997.

8.      Tangrams, Smart/Tangoes USA.

9.      Rush Hour, ThinkFun.

10.  Jean Stenmark, Virgina Thompson, Ruth Cossey, Marilyn Hill, Family Math, Lawrence Hall of Science 1986.