1. Why Math Education Needs Puzzles
Scott Kim — Mar 30, 2012 – scottkim.com
NOW WITH
PUZZLES!
Presented at the Gathering 4 Gardner (http://gathering4gardner.com)
2. I design mathematical puzzles
I am a puzzle designer, ambigram artist and math educator. http://scottkim.com
3. “Recreational math should be...regularly
introduced as a way to interest young
students in the wonders of mathematics.”
Martin Gardner wrote a highly influential column called Mathematical Games in Scientific
American Magazine, from 1956 to 1981. By reporting on the playful inventions of
mathematicians all over the world, he single-handedly influenced several generations of
science-loving kids to fall in love with math and pursue mathematical careers.
4. “Recreational math should be...regularly
introduced as a way to interest young
students in the wonders of mathematics.”
In 1995 Gardner wrote an article advocating puzzles and mathematical magic tricks in
classrooms as a way to get kids interested in learning about math. But when he talked with
teachers about this, he got stony silence.
5. Sugar or essential nutrition?
So are puzzles in the classroom just a spoonful of sugar to make the medicine go down? Or
are they something more important, an essential part of a complete mathematical diet?
6. Gabe meets algebra
To answer, I’ll tell you a story. My son Gabe is 13. He’s good at math.
7. Gabe meets algebra
But recently he’s run into his first mathematical stumbling block: algebra.
8. Gabe meets algebra
Why?
For the first time he’s seeing math that makes him panic, and ask in desperation “Why are
we learning this?” He’s drawing a blank, as are many of his classmates.
9. Gabe meets algebra
Why? Algebra =
Language
of Math
So I asked his teacher “Why study algebra?” He answered “algebra is the language of math
(and science). You need to understand algebra to understand higher math.
10. Gabe’s teacher is right. But there’s a problem. If algebra is the language of math...
11. Then why isn’t it taught in a meaningful context, like, say, the physics of roller coasters?
12. Math without meaning
Teaching the mechanics of algebra without simultaneously exposing kids to meaningful
contexts is like...
13. Music
Teaching music by drilling kids in notation and music theory without ever hearing a piece of
music. “Listening to music is for graduate students only.”
14. Sports
Or teaching sports rules and plays without ever stepping onto a playing field. How many
athletes would sit still for that?
15. Language
Or teaching grammar and spelling without ever exposing kids to books. That’s all
backwards — kids learn to read because they love books, not the other way around.
16. No meaning = No understanding
Teaching mechanics without meaning results in students who feel anxious, guess
randomly, cling tightly rote procedures, and quickly forget what they have learned.
17. No meaning = No understanding
Anxious
Teaching mechanics without meaning results in students who feel anxious, guess
randomly, cling tightly rote procedures, and quickly forget what they have learned.
18. No meaning = No understanding
Anxious
Guessing
Teaching mechanics without meaning results in students who feel anxious, guess
randomly, cling tightly rote procedures, and quickly forget what they have learned.
19. No meaning = No understanding
Anxious
Guessing
Inflexible
Teaching mechanics without meaning results in students who feel anxious, guess
randomly, cling tightly rote procedures, and quickly forget what they have learned.
20. No meaning = No understanding
Anxious
Guessing
Inflexible
Forgotten
Teaching mechanics without meaning results in students who feel anxious, guess
randomly, cling tightly rote procedures, and quickly forget what they have learned.
21. Solution: Grammar+Literature
What should math teachers do instead? Take a cue from English teachers, and teach the
grammar of math alongside the literature of math.
22. Puzzles = literature of math
And the literature of math is...puzzles.
By which I mean puzzles, games and other recreational mathematics activities.
23. Like kid’s picture books
Puzzles are analogous to kids picture books — an entertaining way to introduce young kids
to the joys of math without needing to understand abstract symbols.
24. Not just for kids
But puzzles aren’t just for kids. Martin Gardner was the Shakespeare of puzzles,
penning works of recreational mathematics that stir the imaginations of adults.
25. But teachers resist puzzles
Unfortunately merely giving puzzles to teachers fails miserably. When toy maker Thinkfun
introduced their Game Club classroom packs, a few teachers knew just how to use them.
But most teachers balked. And for good reason: conventional curriculum does not support
puzzles, and teachers raised on bad math education have trouble connecting puzzles and
math. There’s a vicious cycle: bad math education creates teachers, administrators, parents
and policy makers don’t understand math, which creates more bad math education.
26. So try a different approach
To get out of our rut, we need to take a different approach. Here are some current
approaches to popularizing math that bypass traditional curriculum. From left to right we
have the Flatland movie (http://flatlandthemovie.com), Vi Hart’s viral math videos on
YouTube (http://vihart.com), the Museum of Mathematics in New York City (http://
momath.org), and Karl Schaffer’s dance performance The Daughters of Hypatia, celebrating
women mathematicians through the ages (http://mathdance.org).
27. 1. Learning resources
Here are some of the actions I plan to take to get puzzles into math education.
1. Compile resources for teachers, listing puzzles for every mathematical topics.
28. 2. Weekly YouTube puzzle
2. Start a puzzle puzzle channel on YouTube, where I post a puzzle of the week. The best
part will be video responses where kids explain their solutions. Shown here is Vi Hart’s
YouTube channel.
29. 3. Recreational math eBooks
3. Produce recreational math books, eBooks and apps that present recreational math to a
younger audience using today’s interactive media.
30. 4. National puzzle competition
4. Launch a national puzzle competition, that engages students of all levels in solving,
presenting, and inventing mathematical puzzles. Two efforts that are already doing this are
the national Maths Week in Ireland (http://www.mathsweek.ie), and Math Fair out of
University of Calgary, which features student-made puzzles presented in a science-fair-like
setting (http://mathfair.org).
31. Pass it on
By making recreational mathematics part of the math curriculum, we will stop the vicious
cycle of math illiteracy, and passed on the legacy of Martin Gardner to the next generation.
32. Thank you
scottkim.com
pinterest.com/scottekim/cool-math-education
Editor's Notes
Presented at the Gathering 4 Gardner (http://gathering4gardner.com), March 30, 2012, Atlanta Georgia.\n
About me. I design puzzles for books, toys, and videogames. I also do mathematical art and dance. My passion for math education runs through all my work.\n
Martin Gardner wrote a highly influential column called Mathematical Games in Scientific American Magazine, from 1956 to 1981. By reporting on the playful inventions of mathematicians all over the world, he single-handedly influenced several generations of science-loving kids to fall in love with math and pursue mathematical careers.\n
Gardner advocated using puzzles and mathematical magic tricks in classrooms as a way to get kids interested in learning about various mathematical topics. But he reports that when he talked with teachers about this, he got stony silence.\n
So are puzzles in the classroom just a spoonful of sugar to make the medicine go down? Or are they something more important, an essential part of a complete mathematical diet?\n
To answer, I’ll tell you a story. My son Gabe is 13. He’s good at math.\n
But recently he’s encountered his first stumbling block: algebra.\n
For the first time he’s running into math that makes him panic, and ask in desperation “Why are we learning this?” He’s drawing a blank, as are many of his classmates.\n
I asked his teacher how he would answer the question “Why study algebra?” He answered that algebra is the language of math (and science). Mastering algebra is essential if you want to understand higher math.\n
Gabe’s teacher is right. But there’s a problem. If algebra is the language of math...\n
Then why isn’t it taught in the context of compelling applications, like the physics of roller coasters?\n
Teaching the mechanics of algebra without simultaneously exposing kids to meaningful contexts is like...\n
Teaching musical notation and theory without ever hearing a piece of music. “Listening to music is for graduate students only.”\n
Or teaching sports rules and plays without ever stepping onto a playing field. How many athletes would sit still for that?\n
Or teaching grammar and spelling without ever exposing kids to books. Teaching grammar without meaning is all backwards — kids learn to read because there are books they love, not the other way around.\n
Teaching mechanics without meaning results in students who feel anxious, start guessing randomly, cling tightly rote procedures, and quickly forget what they have learned without ever understanding it.\n
Teaching mechanics without meaning results in students who feel anxious, start guessing randomly, cling tightly rote procedures, and quickly forget what they have learned without ever understanding it.\n
Teaching mechanics without meaning results in students who feel anxious, start guessing randomly, cling tightly rote procedures, and quickly forget what they have learned without ever understanding it.\n
Teaching mechanics without meaning results in students who feel anxious, start guessing randomly, cling tightly rote procedures, and quickly forget what they have learned without ever understanding it.\n
What should math teachers do instead? Take a cue from English teachers, and teach the grammar of math alongside the literature of math.\n
And the literature of math is...puzzles. By which I mean puzzles, games and other recreational mathematics activities.\n
Colorful puzzles like pentominoes, are analogous to kids picture books — an entertaining way to introduce young kids to the joys of math without needing to understand symbols.\n
Of course recreational math isn’t just for kids. Martin Gardner was the Shakespeare of recreational mathematics, penning works of imagination that resonate with adults.\n
If puzzles are the literature of mathematics, then presumably we should give puzzles to teachers and tell them to add them to their curriculum. Unfortunately this front-door approach fails miserably. When educational publisher Key Curriculum Press introduced their problem solving curriculum “Crossing the River”, or smart toy maker Thinkfun introduced their Game Club classroom packs, a few enthusiastic teachers knew just how to use them. But the vast majority of teachers balk. And for good reason: they have their hands full covering the state-mandated curriculum, conventional curriculum does not support this sort of material, and most math teachers lack the training to know what to do with puzzles. There’s a chicken and egg problem: bad math education creates teachers, administrators, parents and policy makers don’t understand math, which creates more bad math education.\n
To get out of our rut, we need to take a different approach. Here are a few of the wonderful backdoor approaches to math education that are starting to take hold now. From left to right we have the Flatland movie (http://flatlandthemovie.com), Vi Hart’s viral math videos on YouTube (http://vihart.com), the Museum of Mathematics in New York City (http://momath.org), and Karl Schaffer’s dance performance The Daughters of Hypatia, celebrating women mathematicians through the ages (http://mathdance.org). All of these productions sidestep traditional educational institutions and go straight to kids, parents and teachers by offering entertaining and enriching experiences. You’re having so much fun you don’t realize you’re doing math...at least not boring classroom math.\n
Here are some of the actions I plan to take to get puzzles into math education. The first step is to compile puzzles resources for teachers. For every mathematical topic, make available puzzles that can be used to introduce, practice, and enrich that topic. Shown above are teacher materials supporting the Tangram puzzle, already commonly used in elementary schools for teaching fractions, geometry, and symmetry.\n
I also want to start a puzzle channel on YouTube, where I post a puzzle of the week. Teachers already know and understand how to incorporate weekly puzzles, so this is a great way to get a toehold into schools. Every week I will present a different mathematical puzzle in a 1-2 minute video. The best part will be the video responses from kids, explaining how they solved the puzzle, and offering their ideas for ways to extend the puzzles. Shown above is Vi Hart’s YouTube channel.\n
I then want to produce recreational math books, eBooks and apps aimed at kids. Essentially I want to take the work Martin Gardner has already done, and present it to a younger audience using today’s interactive media. Shown above is the innovative iBook Life, by E. O. Wilson, to which I have added some puzzle pieces.\n
Finally I would like to launch a national puzzle competition, that engages students from say 5th through 12th grade in solving, presenting, and inventing mathematical puzzles. My goal is to find ways for every student to succeed, not just the mathematical elite. Two efforts that are already doing this are the national Maths Week in Ireland (http://www.mathsweek.ie), and Math Fair out of University of Calgary (student-made puzzles presented in a science-fair-like setting; http://mathfair.org).\n
And if we succeed in introducing recreational mathematics to young people, we will have stopped the vicious cycle of math illiteracy, and passed on the legacy of Martin Gardner, so important to all of us, to the next generation.\n
