Mathematical Storytelling: Taking The Path Back Home to Imperfection
Chasing Rabbits was my last math book. And this blog, will be my last one regarding mathematics. The reality is, that for me, I have nothing more to write about this subject in a macro, philosophical sphere beyond our own need and desire for wellness. I will still be giving keynotes, workshops, and webinars, but the writing part has been waiting patiently to go to bed — I’ve written over 150 blogs the last few years. Time to shut up!(on math…)
The emergent and dominant theme in math education is now storytelling, which casts a large net on not only how we teach mathematics, but also why we teach mathematics. I am proud to be on the NCTM 2022 Los Angeles Planning Committee. We chose a conference theme which celebrates this.
A slide that has been in many of my presentations has been the one below.
Somewhere in the intersection of the stories of you, mathematics, and your students lies the unvarnished and unflinching truth about how and why we have explored mathematics. It truly has been a global endeavor, spanning thousands of years, with no race, civilization, culture, or hunter-gatherer tribe immune from its magic and mystery. You can’t convey that with bullet points.
You can only convey that with storytelling.
Storytelling also leads us away from the inorganic polymer that has infested math education — over reaching Precision. Without Precision(there is a reason I am capitalizing it), you cannot teach mathematics. However, too much of a good thing can turn out to be toxic. Just like you can overdose on Vitamin C, you can definitely overdose on an unhealthy addiction to Precision.
There are three distinct stages of learning according to Alfred North Whitehead, who wrote the groundbreaking book, Aims of Education(1929) and co-wrote with Bertrand Russell, one of the most important books in history, Principia Mathematica(1910).
Needless say, Whitehead has a background that is impossible to beat.
Generalization is in adulthood. Check. Precision is in youth. Check. Romance is in childhood. Fail.
Precision now occupies the entire domain of K to 12 education, fueled by the beast of high stakes testing and an unrelenting culture of compliance and transactional learning.
The learning of mathematics is dead on arrival in the elementary schools that choose the toxin of Precision over the elixir of Romance. And yet, remarkably, we remain clueless as to the origin of our students experiencing anxiety, apprehension, and trauma with mathematics.
Bypassing the critical first stage of learning yields what it was supposed to, tragically, yield — mathematical dysfunction.
Let me give you an example of how romance might work, even with a complex topic like calculus. Let’s go to a first grade class for this.
Imagine walking into that class and drawing that shape on the board(no axes). Ask students to describe the shape. Maybe some of them tilt their head and say “ a sleeping 8”. I think we would get some fun responses. Maybe one student says it looks like a “ribbon”. You write that on the board.
You also write “Leminscate of Bernoulli”. You tell kids that ribbon in Latin(an old language) is leminscate. You tell them that this shape has another name, but you are a tad embarrassed to share it. Naturally, kids want to know. You write this on the board.
When I was 8 years-old, we moved into our first house in Canada(1972). In my bedroom, on top of the closet was a very dusty grade 12 math book. The cover was gold and black. When I flipped through it, I recognized numbers and operation symbols, but the rest was understandably foreign to me. BUT, I was intrigued by the strange symbols and how they just danced on every page with purpose and meaning that was beyond anything I could imagine.
I was hooked. I was wooed. That was my romantic introduction to mathematics.
I can only imagine the silliest and awkward conversations happening when I write the equation of this curve. But, that is just a nice little digression in this…story. I would ask kids to use their forearms and how me what a horizontal and vertical line would look like. We would do this enough to make it feel like a light, physical activity.
I would then introduce a new word to them — tangent. Maybe I would weave in the game Pin The Tail on the Donkey! What I want the kids to do is to physically locate where the four horizontal tangents would be. This is something they would be able to do, right? I would then start acting real “fussy” and play around with these horizontal tangents, looking at them as if I was hanging a painting on the wall.
I would eventually stop. And we would all agree that these are where the four horizontal tangents are — roughly. The space between our answers and the actual, precise answer is from a pure physical/visual point of view, insignificant.
And yet, in that insignificant space lies the entire K to 12 math curriculum and thousands of years of mathematical development. You tell the kids, lamentably but hopefully, that you will have to wait more than 10 years to find the exact location.(and even then it is no guarantee, as a high level of algebraic creativity will be required).
Storytelling leads us to romance, the messy middle of mathematics, and more importantly, the healthy idea of teaching with imperfection — imperfection with vigor! When you start telling a good yarn about mathematics, you open up the classroom and give permission to chime in about the story. They will invariably ask questions that you do not know the answer to. You shouldn’t have to be burdened by that. You should be thrilled that your students are opening up tiny rabbit holes that they can own — that they can help contribute to the color and texture of the story.
As Dan Finkel says in the most watched TEDx Talk on Mathematics — “You’re Not The Answer Key”.
Mathematical Storytelling relieves you of the false duty of being perfect and precise in everything you teach. The development of mathematics is a story of slow and failure. This is not only a beautiful story. But, it is the only one that is truly ours — and not a manufactured one in the mills of math education.
In the end, the most important story to be written and to unfold, warts and all, is yours.
Thanks for reading. Will still be alive and kicking in math education in 2022, but the pen will be retiring from mathematics. A new venture for it, however, is on the horizon…stay tuned:)
Thank you for reading,