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.