“You have twenty seconds to name as many animals as you can. For example: cat, dog. Go!” Looking up at the ceiling, I don’t know why I am in this room, or why this lady is asking me questions. Finally I know what I want to say. “Hippopotamus,” I declare. But the time ticks on. Just before time runs out, I land upon the animal that I find the most complex. “Human!” I declare triumphantly. “I’m a human. I’m an animal!"
“Time’s up,” she calls, disappointed that I only named two animals. At four years old, my responses were clearly not what was wanted from me. But reflecting on that experience has helped me land on an insight that has shaped my passion for teaching: we, as humans, are deeply complex, and my goal as a teacher is to fully embrace the imaginations and complexities of each person in my class, both allowing and encouraging my students to do the same.
In the middle of second grade, we were carefully practicing our letters while our teacher was lurking behind us, going from chair to chair and peering over our work. Suddenly, she stopped at Harrison, snatched the paper away from him, held it up, and asked, “Who can tell me what is wrong with Harrison’s letters?” After a moment of silence, the teacher laughed, and said, “These letters are midgets! We need normal-sized letters, Harrison!” Harrison managed a smile before sneaking further down into his chair. From then on, my goal was to stay invisible. I decided to keep my complexity hidden, as exposing my weaknesses could lead to ridicule.
That goal persisted through high school. I started each class with the goal to stay invisible. The teachers had to show me that I would not be shamed if I messed up. Of all the wonderful teachers I had, my high school mathematics teacher showed that best. We walked in on the first day of class, and he wrote “3x7=7x3”. He then counted out both ways of doing the multiplication: 7, 14, 21, and then 3, 6, 9, 12, 15, 18, 21.
“Isn’t it miraculous that we arrive at the same answer?” He asked, excitedly. He proceeded to give an intuitive argument for why they are the same, and he ended his first day with a lesson that stuck with me: mathematics is not a set of rules that you accept, but rather an amazing set of patterns that you can see if you look at it the right way.
When teaching exponents, he asked us to write down as many possible meanings for “two to the power of negative three.” Candy was on the line, but it was not for the group who got it right; it was for the group with the longest list of meanings. The goal was not to be perfect, but rather to have the confidence to write all creative answers, even the “wrong” ones, on paper. We were to embrace the creativity and complexity of mathematics by embracing our own creative, complex minds.
I fell in love with mathematics that year. Mathematics, I learned, was about taking risks unabashedly. I also fell in love with teaching that year. My teacher made each class a challenging game, and he listened to every voice as one about to make a novel discovery. He helped me not only understand the beauty of mathematics, but also made me feel that I could do mathematics.
These experiences help explain my passion for teaching and, in particular, teaching mathematics. Students think in different, creative ways, and we can learn from them if we listen. Shame is a powerful emotion, and teachers can be a particularly powerful force, either allowing shame to fester in the minds of students, or cultivating students’ belief in themselves. And finally, mathematics is a creative, challenging, and fun process that we all can do. Showing students that we care about their ideas, cultivating students’ belief in themselves, and ultimately creating a space for students to engage in creative mathematics is what teaching is about for me.