Chasing Rabbits: A Curious Guide to a Lifetime of Mathematical Wellness
This is a draft of The Introduction that will appear in the book Chasing Rabbits: A Curious Guide to a Lifetime of Mathematical Wellness
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24 is a factor of 288.
What a perfectly odd way to start a book. Stating a wholly benign math fact to get your attention. If I can be even more ludicrous, let me state that 24 is also a factor of 24. Ho hum, it is also a factor of 48. If you think I am going to mention 72 or 96 next, you would be wrong. Those numbers are not interesting…
“The cure for boredom is curiosity. There is no cure for curiosity” — Dorothy Parker
In a couple of sentences involving very accessible mathematics, you should be curious as to what is really going on with 24 as a factor of numbers in a paragraph that had equal parts of boring clarity and equal parts cryptic mystery. It seems like the nonsense conversations one would find in Alice in Wonderland. Except, there is no nonsense going on — I have only chosen to come at this cool mathematical idea through a more cloaked and untraveled path.
288 isn’t the interesting number. It is its neighbor on the floor above, 289. Similarly, so are 25 and 49. Do you recognize these numbers now? Squares, right! It’s actually more interesting than that. These are prime squares and every prime square(except 4 and 9)is always one number more from having 24 its factor (will be proven in detail later in the book). What is just as interesting is that I learned this nifty pattern in primes in late 2020.
The most important words in the title of the book are mathematical wellness. And, how we get there is by chasing ideas, problems, conundrums, puzzles, and stories of mathematics with unbridled thirst — curiosity. For not just for today but for a lifetime. It’s all about the mathematics. As such, it should have been no surprise as that is how this book began — and will subsequently end. Every morsel of mathematics you chomp on in the following 300 pages is a healthy bite of something contemporary or historical. But, the mathematics doesn’t sit in isolation from the continuum of life. The call to rehumanize mathematics is also a call to center our own lives with humanness — something which feels especially more adrift for the mentally, physically, and emotionally taxed classroom teacher.
We as front-line guardians of education are not as well as we need to be. And, across the compromised hand that the pandemic dealt the whole world in early 2020 with regards to the loss of our physical classrooms, our weakened state of care, concern, and compassion through the technological divide that left many of our students isolated, disconnected, and emotionally fragile.
This includes my own kids. Both hate remote learning, and they feel frustrated not being able to rightfully articulate that ham fisting the worst ideas of 20th century math education through fiber optic cables for unhealthy chunks of time is tantamount to torture. My own 12 year-old daughter, Raya, told me that she would rather be attacked by a bear than do online learning. Yes. I didn’t know whether to laugh or cry.
Wellness isn’t an option in our stressed and socially compressed lives. The equanimity and balance that has defined wellness has gone from recommended to required. It is not only part of a 4.5 trillion dollar economy in the United States, but a large non-profit group called The Global Wellness Institute(globalwellnessinstitute.org) has framed its call to contribute to this needed cause with a word that needs to sit in our discussions of math education.
Resetting. Everyone. Unfortunately, for the better part of its history, education, rooted in post-industrialization of dehumanizing checkpoints, performance markers, and output of production, has kept an almost impervious, bureaucratic barrier to holistic changes needed.
The pandemic punched holes through these walls with no uncertain force.
The infrastructure, laden with inert administrative detail, was now totally on fire or taking on water. Choose your metaphor of destruction. Asking teachers to teach in this environment has been like asking teachers to run into a burning house and rescue a VHS player that doesn’t even belong to them.
Math anxiety didn’t exist before education. Frustration, confusion, darkness, incorrectness, and failure did. But, not math anxiety. That is a synthetic, toxic polymer of education. Never mind anxiety being a block to understanding mathematics, it is just such an unhealthy thing for a child to be burdened be. But, as we will discover in this book, anxiety is a late diagnosis of the real problem — alienation.
A common slogan used in math education is that it is important for students to “overcome their fear of math”. Pretty sure fear was not a word that existed in the vocabulary of anyone who fell into the magical and psychedelic rabbit holes of mathematics. Linking mathematics to an accessible and equitable wellness might seem like a stretch in the largely grey narrative of education, but outside that world, it is how it has, at least implicitly, been championed.
Now, with the current state of our world and the rise of mental health issues, it is high time to make mathematical wellness explicit with some of the recognizable pillars of general wellness.
Mathematics is connected to all of them. Even the ones that might not seem like they might be— Physical and Environmental — are. One of the things that should be encouraged in at least high school math classes is that students go outside for a walk, especially if they are stumped on a mathematical idea. For the simple reason of being outside and getting some needed fresh air, exercise, and head-clearing time. This is something that James Tanton would recommend to his students often when he taught high school. Now, long healthy hikes in his home of Phoenix, Arizona is part of his routine. And, having our students understand a topic like data science is imperative to nurturing interest and concern in the environment, and they being future custodians of our planet.
The other four pillars are detailed fixtures in this book, which have marinated in my life as a math educator. But, they really aren’t pillars, more like paint blotches that have bled into one another.
And now, they are leaving this permanent stain that makes mathematics a cherished and emotionally indistinguishable part of my life like music, sports, travel, cooking, baking, writing, film, art, friends, family, and my kids.
The great mathematician Paul Erdos once said that “mathematics is the only infinite human activity”, implying that we will never be able to find out everything there is about mathematics. Given the fact that there are around 500 unproven ideas in mathematics waiting for some kind of closure to the truth or falsehood, Erdos might be correct. Answers in mathematics are wonderful, but can be elusive — and might cause some stress if we only focus only on that.
The entire history of mathematics, from every tribe, civilization, culture, and race, has given us the primer to participate in the wondrous and mysterious entanglements of mathematics. Be curious. Be creative. Be imaginative. Be hopeful.
Be well.
If you are reading this book, you are a mathematician. With that comes a characteristic, perhaps dormant, that we must recognize and value if wellness as a moral compass for math education is to exist and blossom.
It is impossible to be a mathematician without being a poet in soul.
Sofia Kovalevskaya
Let’s go chase some rabbits, tripping and tumbling in our pursuits, dreaming of our adventures, and desiring more mathematics than this fragile life — even more so now — can possibly give us. After all, we are all poets in soul.
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Anticipated release date of September 2021
