My Favorite Math Memories

School starts tomorrow, and I am really excited to have my own classes for the year again.  One of the assignments I give my students on the first or second day is to write a math autobiography, including their best, worst, and earliest memories of math.  I wrote about my earliest math memories here.  I thought I would share some of my best memories today.

I recall several moments working with students after I started teaching; I think about these often, but they are more about teaching than about doing math, so I'll save those for another post.  The other good memories that stick in my brain are two episodes from college math classes.  I'll write about the one that occurred later here, and save the other story for another post, I think.

Abstract Algebra was a three-course sequence, of which the first two courses were required of all math and math-ed majors.  The third course was an elective.  This is the course that studied groups, rings, and fields, and included lots of strategies for proving that a particular set of numbers could be classified as a group, ring, or field.  (I wrote about a discussion with my younger son around the topic of groups here.)  Since it was a required course, the first class started with about 30 students, which was about as big a math class as there was at DePaul at the time.  My favorite college professor, Jeff Bergen, was teaching it.  He had a great sense of humor, was very patient about answering questions, and explained complicated ideas well.  Nevertheless, the class was difficult, and by the midterm, only about 24 students remained in the class.

The second course began with 18 students, and was again taught by Dr. Bergen.  He had taught most of us in Calculus and Differential Equations in prior years, and we all knew each other to some extent.  The class was interesting and fun, but still difficult, and only 12 of us remained by the midterm.  I can't recall a set of math classes I have worked harder in, but I asked lots of questions, spent many hours on homework, and did well overall.  Knowing Dr. Bergen would teach the third course, I signed up for it, even though it wasn't required.  Only two other students signed up, and I thought the class would be cancelled.  It wasn't.  The three of us met in Bergen's office, and furiously took notes while one of us or Bergen solved problems on the board.  Talk about pressure!  No place to hide, no other students to answer the hard questions, and it was great!  But still beastly difficult.  By the midterm, only one of us (not me!) had a decent grade, and I had to think long and hard about whether or not I would drop the class.  I spent at least one sleepless night walking around campus trying to weigh my options, and thinking about the different strategies I would have to use for studying if I was going to stay in the class and have any hope of passing with a reasonable grade.  (At that point, I would have been happy with a C, folks.)  I talked to Dr. Bergen about my worry, and he suggested a couple more strategies.  I stayed in the class, along with the one guy who was passing, changed how I was studying, used more office hours to get more questions answered, and had a great time.  I did pass the class, and I will never forget the satisfaction I felt in completing all three courses, working through the difficulties I faced, and coming out with a better understanding of not only the math, but also of my own learning capabilities.  That was probably the lowest math grade I've ever received, and yet that is the one I am the most proud of.

High Expectations

The Fields Medal, viewed as the highest award given to mathematicians, was recently awarded to Maryam Mirzakhani, a mathematician of Iranian descent currently working at Stanford University, and studying the topology of abstract surfaces.  There is an article about Dr. Mirzakhani here.

What struck me when I read the article was that Dr. Mirzakhani did not set out to be a mathematician, but thought early on that she wanted to be a writer.  During her first year in middle school in Iran, Dr. Mirzakhani did poorly in her math class, her belief in her ability stunted by a teacher who "didn't think she was particularly talented".  The article goes on to say, "The following year, Mirzakhani had a more encouraging teacher, however, and her performance improved enormously."

I continue to be amazed at the power teachers have in demonstrating their belief (or lack thereof) in their students.  And I often wonder if I am consistently sending those positive belief messages to each of my students.  

Sometimes I know I have been successful.  I remember Laura who would tell me "I can't do this" whenever we started something new.  At the beginning of the year, I would respond "Of course not, we just started learning it.  But you'll get better at it; I'll help you."  As the year went on, I responded, "You can't do it, yet, but you will."  At one point in the second semester, Laura looked up from the problem she had barely started and again said, "I can't do this."  She looked at me, sighed, and said "Yet," then went back to work on the problem and solved it correctly.

Other times, I don't know if I am as successful, so I am always on the lookout for ways to make sure I am sending the messages, "This is important; you can do it; and I won't give up on you."  Recently, I came across Richard Curwin's article, Believing in Students: The Power to Make a Difference and was reminded about some of the things I can do to communicate positive expectations for my students.

It is my hope and my intention to demonstrate to my students my belief in their ability to succeed, through my words, my grading policies, how I build relationships with them, and through every one of the hundreds of decisions I make in a class period.  Each of my students needs to leave my class feeling like I cared and believed in them.

And not just because one of them could be a future Fields Medal winner.  

Because each one of them deserves it.