Q.E.D.
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Q.E.D.

Math Education Needs Willy Wonka

Time To Bust Through Math Education’s Glass Ceiling

The 1971 movie Willy Wonka and The Chocolate Factory has been one of the most influential things in my life. Its effects have always been fermenting in my mind, creating vivid landscapes of connection in both my personal and professional life. And, this influence is corroborated all over the internet in terms of life lessons that can be learned from this classic film adaptation of Roald Dahl’s 1964 book. This Forbes article is one of my favorites.

In the movie there are literary allusions sprinkled throughout — none of which were in the original book. Shakespeare gets top billing, with 6 quotes. It should be of little surprise that my book Pi of Life: The Hidden Happiness of Mathematics paid homage to this endearing and educational movie.

Last Page of Pi’s Index

In terms of math education, in the broadest strokes, I just think that the experience that students — and teachers — have with mathematics needs to be…weirder. For the most obvious answer is that mathematics is weird. And yes, we are using the word “weird” to mean wonderful, whimsical, and wacky. It’s our moral imperative to share that with our students. But, perhaps we are getting ahead of ourselves.

Do we as math educators see mathematics dripping with those psychedelic colours? Do we as math educators yearn for the most trippy ideas/visions of mathematics. Do we as math educators simply see mathematics as just one more thing to be responsibility delivered in an increasingly weary and anachronistic system?

I believe that the many of the answers to reconstructing the mathematical experience in schools lies — you guessed it — with the magnificently strange Willy Wonka. Gene Wilder’s performance in that film is so riveting and teeming with wisdom, is that he is now overwhelmingly remembered as an actor in that complex role. In the last scene of the movie, Wonka rides in the Wonkavator with Charlie and his grandpa. The fact that the Wonkavator shatters a glass ceiling is a metaphor for another day. But, just prior, Wonka talks about how the mysterious elevator works:

Willy Wonka: “This is the great glass Wonkavator.”
Grandpa Joe: “It’s an elevator.”
Willy Wonka: “It’s a Wonkavator. An elevator can only go up and down, but the Wonkavator can go sideways and slantways and longways and backways…”
Charlie: “And frontways?”
Willy Wonka: “…and squareways and front ways and any other ways that you can think of. It can take you to any room in the whole factory just by pressing one of these buttons. Any of these buttons. Just press a button and, zing, you’re off! And up until now, I’ve pressed them all… except one. This one. Go ahead, Charlie.”
Charlie: “Me? (Wonka nods yes)”

Deliciously embedded in this conversation is the road map for learning mathematics. Our current path is straight, rigid, and always moving in the same, cliched directions of up and forward — here is the question, let’s get some answers; here is the theory, let’s see the application; here are the formulas, use them, etc.

A Wonka road map would be a 360 degree exploration of mathematics — and beyond. It would have the visual sensation of being in his factory, replete with all the strange and colourful rooms. Speaking of which — and the parallel is uncanny — Yayoi Kusama’s brilliant exhibit Infinity Mirrors has made a rare North American stop in Toronto. It is this kind of mesmerizing art that expands the mind that mathematics needs to be. Well, it already is. We just continually fail to harvest these dragon fruits, horned melons, and pitayas — preferring low-hanging fruits of computations, worksheets, tests to be mastered, and grades to be attained.

Otherwise known as Granny Smith apples.

No, these aren’t all classes, but they are the bulk of them. It is quite alright if students find mathematics difficult. It is for everyone. It is not alright for students to find mathematics boring — especially after a dozen years. That is not their fault. It is ours.

Yayoi Kusama
Willy Wonka

The mathematical question that really got me thinking slantways was…Well I don’t want to give you the question. I want to give you the answer — and let’s see if we can reconstruct the question.

What Is The Question?

By the way, I didn’t get all six shapes as the answer. I only got three. I think there is immense value by giving the solution here and begging its question. It is more disarming and there is more compelling, visually stimulating information for all to gaze at. Plus, we want to encourage good solutions and good questions! We don’t have to do this all the time — we don’t even have to do it here — but we need to start playing with mathematics in atypical directions. Especially, if our highest aspirations for our students is to truly love mathematics — and not just hit some benchmarks, which will have little memory and currency years from now.

My daughter came home with some long division homework. It wasn’t division homework. It was a thou shalt take this path homework. One of the questions was 96 divided by 6. Sure, we did the long division. But, I then turned Wonka on her. I showed her some “kooky” ways of doing the question — with my hidden goal of showing her different bases.

When you double in base 2, the answer conveniently hits the target with “one shot”. When you triple in base 3, you have less to work with — we don’t need to triple after 54 — but there is some more figuring out to do. I told my daughter, who is in grade 4, that we are going “shopping” to build up 96. We definitely need a “54”. How many “18's”? One? Two? Three?. She decided to pick up 2 after some thinking. And after that she just needed one “6”. Her total: 9 + 2(3) + 1 = 16.

The great part of taking these strange and twisted paths is that it will be incumbent upon us to take more time to try and learn new mathematical ideas — to install connection and awe. It’s all about the attempt to understand and push ourselves and our students into all the quirky nooks and crannies of mathematics. It is about venturing off the well-marked, safe trails and truly imagine and experience Paul Lockhart’s vision of mathematics: it is an adventure!

Negative Curvature: Looks Wonkaish

As many of you know, The Global Math Project is gathering tremendous momentum, heading towards its second Global Math Week this October. And, once again, Exploding Dots is the centre of attention. Not too ironically, the last island of exploration of this vibrant piece of K-12 connecting mathematics is this one:

Let’s make math weird again. Let’s make math…Wilder;)

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Reimagining the learning and teaching of mathematics

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Sunil Singh

Sunil Singh

Author, porous educator, audiophile.

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