My Automathography

I’m taking Justin Lanier’s smOOC called Math is Personal, and one of our first assignments is to write our “automathography”. So here’s mine. Enjoy!

Mary’s Automathography

I love math, but I didn’t fall in love with it until college. I was good at math in high school, but I was good at all my classes, so nothing stood out about math in particular. I definitely had a fear of getting the wrong answer in math class, and I was happy to just follow the procedures given to me by my teachers. At this point in my life, I don’t think I understood what mathematics actually was. I won the conference quiz bowl in math my senior year, and it was great to get that recognition, but I graduated high school thinking I would study chemistry in college.

I soon discovered that I did not enjoy working in the lab, but that I did enjoy my math courses, so I ended up majoring in math. I went to a huge university (40,000+ undergraduates), so my first two years of math classes consisted of lectures with 300 students. Despite this, I found myself completely inspired by the professors. I was enamored with how passionate and genuine they seemed. In other subjects, I felt like the professors and TAs were egotistical or arrogant. In contrast, everyone in the math department seemed friendly and easy going. I’ll always remember when one of my calculus professors introduced Euler’s identity. His voice wavered, and I thought he might even cry when he described how this one equation related the most important numbers in mathematics.

Even those first few years of college, I was still focused on answer-getting. This quickly changed when I started taking courses like Real Analysis and Modern Algebra. In these classes, I was finally challenged to think for myself. There were no recipes to follow, and it was completely up to me to decide how to prove or demonstrate something. It was both terrifying and liberating. Math became a creative endeavor for me, and I loved it. I truly came to understand and appreciate Georg Cantor’s quote: “The essence of mathematics is its freedom.”

Besides the creative aspect of math, I also thrived on its collaborative aspect. Getting to know the other students in my classes was so much fun, and struggling with them on math problems late into the night will always be one of my favorite college memories. I also always appreciated how there wasn’t a competitive atmosphere in math, compared with most of the science classes I took. Simply put, I learned so much from doing and talking math with my peers. I became more confident and began to embody the mathematical habits of mind.

In particular, I will never forget the group I worked with in Real Analysis. The professor assigned problems every class which were due the following class (this course required more of my time than any other), so the five of us would get together almost every day, sometimes for several hours, to struggle through them. We would meet in the student union in the evenings, staying later than everyone else and having conversations about math or maybe not about math. Before class, we would meet in the math library to share any last minute insights, often getting looks from others for being too loud. Naturally, a strong bond formed between the five of us. On weekends (or Thursdays, or whenever we could no longer stand to stare at our papers) we would go out and get drinks together.

The experiences I had in classes like Real Analysis really transformed my idea of math. I learned the value of productive struggle and collaboration. I learned how to be creative in math and make it my own. I really felt mathematically strong at the end of it all.

Fast forward to the present- five years after that Real Analysis class. I am now about to start my first-year teaching high school math. I hope I don’t suck.


Filed under culture, fun, productive struggle

11 responses to “My Automathography

  1. Jasmine

    Mary, thank you for sharing! Your description of the collaboration within your department sounds very much like my experience. I also had fantastic professors who helped me to see that math is amazing and creates a lovely way to view the world. I hope that this class allows some space for that collaborative work on math with other inspired folks.

    That’s so exciting that you are entering your first year teaching! Which classes will you be teaching?

  2. Hi Jasmine! Thanks for commenting. I am also looking forward to the conversations and collaboration. I was given a couple different schedules to choose from, and I got my first pick: Geometry and a class called Functions, Statistics, and Trigonometry (FST). FST is kind of like the second half of an extended Algebra 2 class. Should be fun!

  3. Hi Mary! I enjoyed reading your automathography. Your Real Analysis class sounded like my experience in Geometry. If only we were allowed to collaborate and work that way in high school it might not have taken us until college to really appreciate math!
    Good luck with your new teaching career! When do you start?

    • I agree- I hope to incorporate collaboration as much as possible this year. I want to hear lots and lots of math conversations. Thanks for the luck! The kids come September 2, so I’ve still got a bit of time to get prepared.

  4. Analysis was the class that got me, too. I wouldn’t be half the teacher I am without the experience of struggling and collaborating I had in that class. Interesting that you had the same experience! What about the class do you think makes that so?

  5. Thanks for sharing your math journey, Mary!

    If not any of your classes (in particular), what did you like—really like—when you were in high school? What were the big pieces in your identity?

    I similarly did well in all of my classes in high school. I think the relationships I had with my math teachers—and their earnestness—made a difference for me. Also, the fact that there were opportunities to do math extracurriculars. But while I liked math a lot, I still thought of myself as a generalist. In some ways, I still do. But I identify much more strongly as a mathematician now. How has this evolved for you?

    What caused your fear of wrong answers in math class, do you think? And from what direction—were you worried about what your teacher would think, or your peers, or yourself, or…?

    What did you not like about working in a lab? How was/is math different from this?

    I’ve also encountered this with math folks—their passion and genuineness. What exactly is it, and where does it come from? Why are math people so lovely? I’d like to know. I mean, lots of non-math-identifying people are awesome, too. Additionally, I think mathy people tend towards humility, and playfulness, and a love for ideas.

    In your upper-level math courses, were there any problems or proofs that you were particular proud of solving, or that posed challenges that felt important and empoweringly frustrating at the time? Also, what was the terror of this experience? What was the liberation of it?

    The relationships you built with peers seem like an important part of your positive math experiences. How will you help your students to have the same?

    For you, how is math creative? Related: what do you create when you do math? And finally: what role will creativity play in your classroom, and how will you talk about this with your students (if at all)?

    What have your biggest math experiences been in the five years since you took Real Analysis? What do you know about yourself and what do you know about math that you didn’t know when you were in the midst of that course? (Or it’s immediate “aftermath”.)

    And lastly: I’m sure you won’t suck. And you’ll get better every day—even if it doesn’t always feel like—from here on out. It’s the best. 😀

    Thanks again for sharing!

    • Justin! Thanks for reading and asking these great questions!

      Gosh, I don’t really think I had much of an identity in HS. I cared about getting good grades, having friends, and getting attention from members of the opposite sex. I went to a small HS, was pretty involved in a variety of things, and enjoyed school. I was voted “10-pound brain” and “Most likely to be late to their own funeral” if that tells you anything.

      I definitely identify more strongly as a mathematician now than I did in HS. I also have way, way, way more confidence in my abilities now.

      Getting the “smart” label early on probably made me fear a wrong answer. Getting a wrong answer would make me feel like I wasn’t living up to my name or something. Oh, so there you go, I guess “smart” was a big part of my identity in school.

      Working in the lab? I felt really isolated and bored when I just sat in a dark room by myself watching cells divide under the microscope. The whole experiment and data collection part seemed time-consuming and tedious when what I really preferred was the analysis and conclusion part. Actually, my favorite part of the experience was the weekly lab meeting.

      I think math people have to be humble because math is hard. Not that other subjects aren’t hard, but sometimes you just have no idea what to do with a problem or are completely lost on a concept, and there’s definitely no BSing in math. I also agree that math people are very open to ideas, and they don’t often jump to conclusions, which is rather nice.

      Hmmm, I can’t really think of any particular problems or proofs that stand out from my upper level math classes, but I felt good anytime I figured something out. In my Real Analysis class, no one ever really spoke except for the professor. He was a tiny old man but I think most of us were a little intimidated. One time he asked a question, and I actually knew the answer, so I just answered it out loud. For the rest of that lecture, whenever that particular theorem or whatever it was came up, he gestured toward me and I would repeat what I said before. It’s a silly memory, but I’ll probably never forget it. The one day I spoke in Real Analysis.

      The thinking for myself thing was both the terrifying and the liberating part. I wasn’t used to not having a recipe to follow, but it was exciting to come up with my own unique solutions.

      One week down of my first year teaching, and I’m trying to incorporate lots of group work. The hard part is getting students to share and listen to each other’s ideas, particularly if the students are on different social levels. Also, they tune out when a peer is talking and only think what I, the teacher, says is valuable. So I’m working on establishing group work norms and doing getting to know you activities to build classroom community, but I need to try more things like sentence starters so the kids know what to say to each other when they’re doing math.

      How is math creative? Well, I like to visualize math and I like math art. Those visualizations are created in my own head and then I try to put them on paper. I also like that there are multiple solution paths, and I get to create my own. I get to do whatever I want as long as I can justify it. Creativity is kind of like the freedom to do what you want. I like that there’s a lot of freedom/choice in math. I’m teaching geometry this year, and I love constructions and transformations and all that good stuff, so hopefully we’ll be doing some math art projects. With my seniors in FST, I want to emphasize that they need to come up with THEIR solution path. The way they do it might be different than me and that’s just fine!

      Since college, I haven’t had too many personal math experiences. I learned (and am still learning every day) how to teach math. I definitely want to spend more time doing math for fun. For me. Lastly, I continue to gain more confidence in my abilities as a mathematician and a teacher.

      Phew! That was a lot of introspection. Thanks for the prompting. 🙂

  6. I enjoyed reading this, I come at math from a different perspective in that I was able to do it, but didn’t understand why it might be useful. Physics provided a contextual framework for me to understand, and it was what allowed me to view math through a lens that my brain could make sense of things. Classes like real and complex analysis, were quickly more interesting when I viewed them from this lens. Modern Algebra and other proof based courses were a hug struggle for me, in that constructing proofs is my weakest area, reading them and comprehending them is fine, but creating them is a very difficult thing for me. I am wondering how your experiences in math have translated to you as a teacher?

    • That’s a good question, Miah. I know that I definitely value group work and the productive struggle. I can mindlessly follow someone’s steps, but I don’t think I really understand something unless I struggle with it for a bit and talk about it with others. So this year I’m working really hard to incorporate group work and investigative activities. I do still have to be mindful of explaining things clearly though and not just hope that everyone learned everything that I wanted them to on their own. I also don’t want them to get frustrated if they’re not getting it or aren’t used to this type of learning. So I guess I’m working on balancing student discovery with explanations from me.

      • That balance is a tough one to maintain. As you see students working through this piece while allowing them to struggle and talk to one another, in what ways are you attempting to maintain that balance?

        In your own math experience, what balance worked best for you? Is there a time when you experienced the perfect balance or an imperfect one? What might have been some of the reasons for this experience on either side (meaning a perfect balance or an imperfect one)?

        How might you use your answers from above to help guide your instruction? Are there other voices or resources available to you that would help you with this struggle?

        In what ways would the your students show you that everyone has understood, and is not just mindlessly follow someone the work of someone else?

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