MC: Kate, I would like to start off by thanking you for giving me the opportunity to interview you and share your responses with my students. To begin with, please tell us a little bit about where you are in your math education.

KS: Thanks! I’m excited about this opportunity.

If you read my résumé, you’d find out that I am currently a Ph.D. Candidate in mathematics at the University of South Carolina. I’ve been in graduate school here for four years, and in May 2007, I finished my Master’s degree. Before coming to South Carolina, I lived in California, where I graduated with a B.A. in Pure Mathematics in 2004 from the University of California: San Diego.

But this is a really unfulfilling answer to your question! Really, I am at the stage in my math education where I have just begun to get paid to do math. My full-time job is learning how to teach math effectively, learning how to write professional math research papers, and learning how to be a professional mathematician.

MC: I understand that you have won awards for teaching math. Tell us about those and what you think makes you an excellent math instructor.

KS: For the 2006-2007 academic year, I won the “Outstanding Graduate Teaching Assistant Award” from the University of South Carolina’s Department of Mathematics. In April of 2008, I was awarded the university-wide “Outstanding Graduate Teaching Assistant Award” by the USC Education Foundation. Each academic year the university gives only two teaching awards for graduate students: one for teaching in humanities, social sciences, and education, and one in science, math, and related fields. Because there are only two awards and over 8000 graduate students, I was very excited to win!

I think there are probably two big ideas that influence the way that I teach. The first one I heard in May of 2004, while attending a lecture given by Professor Leonard Haff at the University of California in San Diego. Professor Haff said, “Mathematics should never be abstract and difficult. From Kindergarten to Ph.D. it doesn’t matter; there should always be a simple way to look at things.” His statement immediately became my goal as a math student, and later became my goal as a math educator: to translate the abstract, difficult, and detailed ideas found in a math textbook into smaller pieces that are easy to understand. It’s not always the concepts that makes math tough. The difficulty most students have is they can’t translate between the math jargon – the vocabulary, the notation, the phrasing – and their own experiences. My daily goal is to explain the strange-looking equations found in their textbook into normal language describing experiences they have all the time.

The second thing that influences my teaching is something I hear most often from math students. Nearly every student I have ever taught has told me, “I’d be great at math if I didn’t make so many stupid mistakes!” I don’t know why students believe that being good at math requires never making mistakes; if this were the case, there wouldn’t be any human mathematicians. Stupid mistakes happen. They happen to math majors, they happen to math teachers, and they happen to math professors. I tell my students that their goal as math students should not be, “Never make a stupid mistake.” This is unattainable and is very frustrating to attempt. In order to be successful at mathematics, you need to be able to catch your mistakes quickly. Most students would do far better in math classes if they learned to check their answers and ask themselves, “Does this answer make sense?” If not, you need to go back and check your work. That’s the beauty of mathematics: things are supposed to make sense.

MC: As you move closer to finishing your Ph.D., what career options are you currently considering and why?

KS: I’ve considered several different career options along the way. When I was in high school, I was very interested in astronomy, astrophysics, and engineering. At that time, my career goals were to become an aerospace engineer, get a job at NASA, and build neat orbital machines. I went to college for engineering, but in taking the introductory coursework, I realized I didn’t enjoy the laboratory aspects of the courses - I much preferred the more mathematical classes, like General Relativity and Quantum Theory. That’s when I decided to pursue mathematics.

As my college graduation date came closer, I started wondering about what I’d do now that school was over. Someone explained that if you attend graduate school in mathematics, most universities will pay you! I thought, “Wait, someone will pay me to take more math classes?!” This sounded like a good deal! Graduate assistantships are common in math. Generally they come in two types - either you’re a teaching assistant or you’re a research assistant (or sometimes you’re both). Going to graduate school gave me the opportunity to get paid to learn more math while gaining experience as a math educator. I had never taught a math class before. I didn’t know if I’d enjoy it or if I’d be any good at it.

Since starting graduate school, I learned that I do enjoy teaching math quite a bit! Occasionally, I have thought about pursuing a job with NASA, or working as an actuary, or as a statistician, or a ton of other options. Currently, the largest employer of Ph.D. mathematicians in the U.S. is the National Security Agency (NSA). I’m sure most of my fellow math graduate students have at least thought about working there. When school is really difficult, I still think about what I could do given my current education level in math. For me, what it comes down to is my enjoyment of working with students. I get excited to teach my classes, I enjoy seeing my students grow and learn, and I’m not sure I’d find the same fulfillment working from 8am-5pm in a cubicle in corporate America.

MC: Given your interest in math education, describe what you see as the good points and the bad points about the American math education system.

KS: The goal of mathematics education ought to be to create skilled problem solvers and good critical thinkers. I really dislike the trend toward standardized testing to measure mathematical aptitude. Almost never do any “real world” problems involve choosing the correct answer from a list of potential responses. Not only that, but really great problem solving often requires group discussions. In contemporary advanced mathematical journals, many (if not most) publications come from more than one author. Mathematics is not an individual sport; if done well, it requires a team effort. This needs to be reflected in the math curriculum found in our schools. The ability to work in a group, to communicate complex ideas effectively, and to understand perspectives different from your own is as important in mathematics as in any other subject, but this kind of learning is too often discouraged in most math classrooms.

I do not think we are teaching mathematics well, nor do I think we are teaching good mathematics. As a culture, we are so caught up with memorizing the rules and performing arduous and dull algorithmic processes we have lost sight of the role of creativity in mathematics. We want our students to know how to factor polynomials, how to use the Quadratic Formula, how to carry out long division, and a thousand other skills. While these things are important, they are not the most important things in mathematics. We have added so many drills and memorization tasks to the math curriculum there is no room for fun mathematics, like number theory and combinatorics and cryptography and probability and game theory and… There are plenty of fascinating mathematical ideas accessible to pre-college students but none are ever taught. This is like teaching grammar and spelling, but never reading the great poems or the great stories or the great books.

I am having trouble pinning down what I think we are doing well. This is not to say that things aren’t being done well. There are plenty of talented and dedicated math teachers across the U.S. who make a huge positive impact on future mathematicians. The problem is that my path to mathematics was very non-standard. I have not taken a typical public school math class since I was in the eighth grade, and my recollections of that experience leave little in the “well done” column. I learned early that if I wanted to know more math, math class was the wrong place to do it. I carved out my own path and tried never to let my school get in the way of my education.

MC: Please share with us an anecdote or two about how a heightened understanding of math has changed the way you tend to see the world.

KS: This is a hard question. It’s a bit like asking, “Tell me about how the color blue has affected the way you see the world.” I don’t know what it’s like not to see the color blue so I don’t know how seeing blue has changed my understanding of the world. It’s the same thing with mathematics. I’ve seen math around me most of my life and it’s tough for me to think about what it would be like if I didn’t see math everywhere! Part of this is because my father studied math in graduate school, and since I was a child he always talked to me about math ideas that no one was teaching at my schools.

I think the process of learning mathematics is akin to the process of learning a foreign language. In college, I studied French. After studying the French language for a long time, eventually I realized I wasn’t thinking in English and translating to French. I’d look at objects - like tables or chairs or flowers or motorcycles - and I’d think of their names in French automatically. It seemed natural for the French words to pop into mind first; no translation was necessary. In knowing math, it’s much the same way. I can’t help but see math concepts when I look around. For instance, when I look at an ATM, I think about the RSA cryptosystem; when I look at my cell phone, I think about graph theory; and when I listen to the radio, I think about wave functions. This seems as normal to me as seeing the sky and thinking “blue.”

This entry was posted on Wednesday, September 3rd, 2008 at 11:45 am and is filed under Education, Math Interviews, Mathematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.