Through The Looking Glass: An Alternative Perspective of Mathematics Through Storytelling
The last chapter that I have to write for Chasing Rabbits: A Curious Guide to a Lifetime of Mathematical Wellness is the penultimate one, Chapter 8: Through The Looking Glass.
My writing process is scribbled and scattered, much like my life. So, it’s not a surprise that the 9 chapters in my next book were written completely out of order. You wouldn’t know that by reading the book. So, strangely, my disorder serves up order.
The chapter in question that needs my final attention is about looking at mathematics through an entirely different lens. If traditional math problems can be seen as going from A to B. I show why it can be B to A. Maybe A to C then to B. Or, just A to where ever or whenever.
I do this by taking 10 math problems and getting a bit “Wonka” with them — going backways, frontways, and slantways. In essence, what I am really doing is making my own narrative for math problems. I am showering standard problems with color that might not have been there otherwise.
Starting off with math problems that have a story already embedded is a great idea, as it allows a wider range of emotionality to come into the problem.
Let me show you an example I just did with my 6th Grade Math Recess class that I stream at Dexter Learning. My students are starting algebra.
Let me share with you two screen shots. Would you have guessed this as the order?
In mathematics, the trajectory has generally been theory then application. Personally, I think more curiosity and binding of the two comes out when we start with a problem — especially one that we cannot solve because we are missing some tools.
The Camel and the Bananas problem sets itself up perfectly for taking the road not taken.
You have 3000 bananas to transport to a town 1000 km away. The camel can only carry 1000 bananas at maximum and it will eat 1 banana for every km it walks. The natural first trial of loading up your camel and going to town results not only in the disappointing answer of no bananas transported, it opens the problem for humor!
My students inquired about having two camels, flying the bananas over, and even bringing in a gorilla because they are stronger. That argument was “shot down” because we all know gorillas might require more than 1 banana/km.
Humor. It organically entered the question and disarmed the challenging mathematics that lay ahead — way ahead.
After some back and forth, students thought of creating a drop off point. The halfway mark created the same problem as going all the way.
(Insert lots of humming and hawing)
It was then suggested to drop them off 200 km away. Sure enough, a tidy pile 600 bananas could be created with one trip. The intrigue was building. Students were beginning to believe that, yes indeed, bananas could be transported!
And, that’s when I cut the cord…
The mathematics needed to solve the problem, algebra, hasn’t been taught. The kids had some correct early strategy — and enthusiasm. The emotions to this problem were all over the map, but everyone wanted to know how this story would end. So, I started at the beginning.
Once we catch up again to the camel and the bananas, which will have been waiting patiently for a couple of weeks, students will appreciate not only the answer to the problem, but the quirky and whimsical path that we took there.
Through the looking glass. It’s time we make mathematics a weird and quirky adventure.