I travel a lot.
I live in two mathematical worlds. I’ve invested substantial time in both. I have friends in both. I am where I am today because of both.
But the mathematical worlds I visit are quite different.
Math World #1
My first math world is densely populated and diverse. It is held together by the common belief that either you are a Math Person (about 10% of its citizens) or not (about 90% of its citizens).
There are also very strict laws in this world:
Math is a linear progression of skills. You must learn them in order.
Math is either right or wrong. Black or white. No gray.
You must memorize your math facts or you may die (or at least never go very far in math.)
The Ruler of the Math World is the person who is the quickest at computation.
You must practice math. Over and over. If you do not do homework, you may die (or at least not learn math.)
Just memorize the rules. Like 2 negatives = a positive. Never mind that -3 + -3 = -6. Don’t ask questions.
Math must be taught the same way it has always been taught.
Students must pass state tests, therefore, they must practice assessment items over and over.
Never EVER use your fingers to do math.
I am one of the lucky ones in Math World #1. I have been christened a Math Person. It happened in 8th grade. My teacher told me I was Good at Math. He did not know I had not memorized my facts in 3rd grade. He did not know I used my fingers to do math by pulsing them where no one could see. And I did not tell him.
Most people in Math World #1 are not so lucky. They are Not Good at Math. But it’s okay. They have great personalities. I wish I could bring them all to my other mathematical world, but most of them don’t know it exists. If I tell them, they often don’t believe me.
Math World #2
I am not sure when I first discovered Math World #2. For years I did not talk about it, because the people in Math World #1 never mentioned it, so I thought it might not be real.
In Math World #2, you can learn things in any order. You can have several answers to the same question. You can wonder about things. You can be creative. You can be visual.
But the best part is, in Math World #2, everyone is Good at Math. That’s because the people in this world have discovered something. Real math is more than the small part of math the people in Math World #1 know about. Folks in Math World #2 have gone to the edge of the world to discover math is not flat. It is big and glorious.
I try to bring my friends from the first world to visit the second, but the trip is very scary. What if I’m wrong? What if it’s not a real place? What if we make math beautiful, meaningful, sensical, and then it turns out we were wrong, and our students can’t pass the state tests?
The Struggle is Real
Two worlds make a good fantasy story, but this is my real life.
Somehow I survived the boredom of chalkboards full of facts in the 70s. Looking back, I was probably At Risk. I daydreamed a lot in the elementary grades. I was off task. My family moved every year to a new Texas town.
I found greater success in high school, and was accepted into Baylor University. On a whim, I decided to specialize in math as part of my degree in education, which meant I took 24 hours of “hard core” college-level math, which I also survived. For the next 17 years, I taught in the classroom, and for the last 12 years, I’ve worked with math teachers and math curriculum in both Missouri and Texas.
From the beginning, I searched for ways to bring the big and glorious parts of math to students, because I believed in my heart of hearts that I could help them all become Math People if I could help them SEE the math. So I hunted. And created.
And amazingly, I discovered there were others who knew the beautiful side of math. The creative side. The meaningful side. I came across the work of some great thinkers who also wanted to show students the way math could be. Marilyn Burns and Cathy Humphreys. Frances Thompson. Lappan, Fitzgerald, Winter, and Phillips, authors of The Middle Grades Mathematics Project. More recently for me, Jo Boaler. Dan Meyer.
And amazing things happened with my students. The more I sought to show them the beautiful, visual, conversational side of math, the more they engaged. Learned. Retained. But it took work. Persistence. I loved it when I heard, “I never got math before this year.”
Sometimes a student would get mad. “Just tell me how to do it!” But I knew if I did, I’d be sending them away from their own sense-making. So I persevered. But it was scary. Was I really doing them justice? Were they really learning the math they needed? Occasionally the parent of a student with a low grade would tell me NO. Real math was not this creative and beautiful. So I worried.
But time after time, the students did learn. And go on to learn in their next math course. Even if that next teacher did not believe in the side of math I knew and loved.
Much research has been published to support the beautiful side of math. Two especially impactful works for me have been NCTM’s 2014 publication Principles to Actions: Ensuring Mathematical Success for All, and Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching by Jo Boaler and Carol Dweck.
But even with this research, I still see most people living in Math World #1. I want to help them find Math World #2. But it’s scary. Our view of math is ingrained so deeply into each of us, even if it is not the true nature of math.
How can so many people believe math is one thing when it is actually so much more?