I went skiing for the first time on Tuesday. As a native Texan, I’d never really seen the point of putting something slippery on your feet and then stepping on frozen water. But I live in Utah now, so ski I must. It was hard. It’s hard to do something you suck at, and it’s hard to fall down, pick yourself up, and do that thing you suck at again. Not everything in life is a metaphor for teaching or learning mathematics, but this one is. It’s easy for an experienced person in any field to forget how hard it is to suck at it, and math is no different.
Journalist A.K. Whitney is a “math phobe turned math phile,” according to her Twitter bio. Growing up, she enjoyed science, but bad experiences in middle and high school math classes kept her from pursuing a STEM major. A few years ago, she enrolled in a pre-algebra class at a local community college and started her math education basically from scratch. When a friend asked her why, she said, “I got sick of believing I suck at math.” In a series called Mathochism, she writes about her experiences working her way up through calculus. I first encountered the series on Medium, where she is posting an installment every Monday, Wednesday, and Friday, but it is also available on her blog. She also wrote an article for Cosmo about why and how she overcame her fear of math.
Another perspective on learning math as an adult comes from Jennifer Ouellette’s series that eventually spawned The Calculus Diaries. Ouellette is a well-known science writer who focuses on physics, but she had never taken calculus. While she finds conceptual explanations helpful, she writes,
I must confess that on the rare occasions when I’ve bothered to put in the effort to understand a basic euqation or two–and they must be basic, given my functional innumeracy–it has deepened my grasp of the essential concepts in ways I don’t entirely undrstand, yet can’t deny. It’s like some final piece clicked into place that I never even knew was missing.
It’s really interesting to see the points of view of students who start without a strong math background or confidence but genuinely want to learn—and learn to like—the subject. We sometimes assume that students in introductory math courses just want to fulfill a university requirement and don’t really care about learning the material. Those students do exist, and we probably won’t really be able to reach them, but it’s valuable for us to see what makes it easier or harder for a motivated student to make progress. For Whitney, teachers and textbooks are important, but she also writes about broader issues: male dominance in classrooms, our society’s attitude towards women STEM majors, and the myth that you have to be a genius to be good at math.
Her comments about her teachers, from the “dapper professor” of pre-algebra to the “calculus dementor,” are interesting because we get only one side of the story. Sometimes I try to fill in the gaps and figure out what might have been going on from the instructor’s perspective. In a post called Show Your Work, Whitney expresses her frustration at worked examples that skip steps. She writes,
It’s particularly galling when an instructor skips steps on examples in lectures (and so does the book in its ridiculously expensive solutions manual that promises to solve all the odd problems yet leaves out a third of them), then expects me to “show my work,” all my work, and even takes points off for paraphrasing a little on a definition or for not writing f(x) on every step.
I wish I knew specific examples of what steps were omitted and what definitions were paraphrased. I’m sure the instructor thought he or she was doing the examples fully and that his or her rules about how work had to be shown were clear. And what seemed like “paraphrasing a little on a definition” to Whitney may have changed the meaning of the definition. It’s probably impossible to avoid those problems in any class, but it’s good to remember that students who make mistakes like that aren’t being sloppy or lazy. It’s just hard for students to evaluate their own work and understanding.
Unfortunately, Whitney’s calculus class ended on a sour note. But this time, she left with a different attitude than she had in middle school. She writes,
But unlike previous bad experiences, this didn’t sour me on math. Nor did it take away from my interest in learning more calculus, which was actually one of the most satisfying chapters in my short math career.
Yep, I really love calculus.
In 2013, she took a calculus MOOC to solidify and expand on her previous calculus experiences, and for her, it was a good fit. It gave her more motivation than just sitting at home with a calculus book had, but she had the flexibility to choose when to watch lectures or take quizzes. She ended the MOOC on a high note.
At the end, I was tired but very happy. The course confirmed that I really did learn calculus, and that I wasn’t wrong to love it.
And my grade? It doesn’t matter, but I wound up with an 89.3 percent. My B streak continues, and illustrates what I have learned about my math ability: It will never come easily, but I can understand it. I can appreciate it. I can learn it.
I don’t suck at math.