A Different Perspective: Mathochism and the Calculus Diaries

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.

Find x. Image: Aaron Rotenberg, via Wikimedia Commons.

Find x. Image: Aaron Rotenberg, via Wikimedia Commons.

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.

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1 Response to A Different Perspective: Mathochism and the Calculus Diaries

  1. Avatar Zor Shekhtman says:

    I believe our high school educational system completely missed on its extremely important goal – development of students’ minds. Instead, it concentrates on jamming as much information as possible into students’ brains. The difference between these two is comparable to the difference between an author of a novel and its reader. The “standard” approach to a high school education is to produce “readers” – people who can absorb someone else’ ideas. Granted, society need such people, they keep it running. But we also need “writers”, generators of ideas, those who move a society forward, and that’s where the current educational system in most high schools falls short.

    I was educated in the Soviet Union, lived for 30 years there (less than half of my life) and was very lucky to have brilliant math teacher at high school. The I have graduated from Moscow University as a mathematician in time when its Department of Mathematics was one of the best in the world. My view on how to teach math is certainly influenced by my personal experience. Working with computers in the financial industry, I always felt that rigorous math education helped me in all aspects of real life, not related to mathematics. So, my criticism of the current approach to math education in high schools as a process to accumulate information was multiplied by my personal very different educational experience that, in my view, provided much better and useful results.
    That’s why I decided to start my Web site UNIZOR.COM where I present math as it was presented to me – based on logic, rigorous proofs, solving numerous problems, axiomatic approach etc.

    After writing the software needed to drive the Web site I started video-recording the lectures, developing exams, advancing functionality of the site. There are more than 450 lectures already there (June, 2015). Many topics (but not all yet) are supplemented with exams. So, there is plenty of work to do, and subjects like Algebra, Geometry and Trigonometry are relatively complete.

    I was comparing my site with many others (like Khan Academy that has a very large audience) and can definitely state that mine is more challenging, oriented on more advanced students and presents more for an inquisitive mind. In addition, it has a functional part, it is not just a set of videos, but rather a process where a parent or a supervisor can enroll a student or a group of students into different topics, then students learn the material on their own by listening to lectures and solving problems, after which the students can go through the exam, results of which become known to a parent or a supervisor. A combination of advanced educational material and an educational process makes the site rather unique.

    I do not think that our established educational system will change soon. So, for those with desire to know, who decides that development of their mind using the art of mathematics as a tool is an important aspect of their education, Internet is the best way to go. My site, UNIZOR.COM, as well as many others might provide the venue.

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