Teaching Statement, Spring 2003
During graduate school, I taught two solo courses in mathematics and assisted with seven other courses. I also taught five high school mathematics courses while completing my undergraduate degree in mathematics education. In 2002, I received the Outstanding Teaching Fellow Award for the mathematics department at BU, and my teaching evaluations have been consistently excellent.
Teaching Style and Techniques
Every student is capable developing his or her mathematical ability. To teach students effectively, however, I have to accept that their goals, backgrounds, and interests will be different from mine. In order to help students learn, I strive to determine where they are mathematically and where they want to go.
At the beginning of each course, I think about the students’ background and what they might need or want from the course. For example, in designing an abstract algebra course for fall of 2003 at Emmanuel College, I knew that most students in the course were majoring in mathematics education. According to The Mathematical Education of Teachers published by the Conference Board of Mathematical Science, “It appears that instead of (or perhaps in addition to) acquiring knowledge of advanced mathematics, what effective teachers need is mathematical knowledge that is organized for teaching – deep understanding of the subject they will teach; awareness of persistent conceptual barriers to learning.”
I have tried to follow this advice in my course, while at the same time preparing students who are considering graduate school in mathematics. Part of my approach has been teaching the algebra of integers and polynomials first. Integers are familiar objects from elementary school mathematics, and polynomials are the topic of study in high school algebra classes. In lectures and homework, I have emphasized the connection between abstract algebra and the more familiar high school algebra. I have also been working with the students to develop their ability to prove theorems, and to write proofs in a style appropriate for graduate coursework.
My lecture style communicates my enthusiasm about mathematics. The students that say they “hate math class” sometimes become my favorites, because I enjoy the challenge of helping them deepen their ability and interest in a subject that was previously unappealing and obscure.
I am also proud of my ability to give students the tools they need to solve a problem, and then to wait for them to solve it. Waiting can be difficult. You have to know when to ask a leading question, when to apply a gentle nudge in the right direction, and when to simply listen. I encourage students to ask and answer questions by communicating my respect for them. When a student answers a question, even if the answer is incorrect, I give them some positive feedback. When a student asks a question, I not only answer the question, but also point out a reason why the question was important or thoughtful.
Assessment Practices
The most common tools of assessment – homework, quizzes, exams, and projects – are not just methods of collecting information about student learning, but also serve as motivational tools. Without quizzes and homework many students would not spend the time necessary to learn the course material because of more immediate demands placed on them by other classes.
Assessment is also a way of giving feedback to the students so that they might correct problems. Students need the time and opportunity to correct their errors, since this is where some of the most productive learning takes place. Once feedback is given, motivation becomes a problem again – will the student see enough rewards for improving their performance that it is worth investing their time?
One of the ways that I have balanced motivation, feedback, and assessment is to allow students to turn in homework multiple times. For example, when I taught multivariable calculus in the summer of 2002 at Boston University, I had two different daily homework grades. For the first grade I would look at the entire assignment and judge whether or not the assignment was done. This assessment was designed to encourage them to do the work, not to judge their understanding.
For their second daily homework grade, I picked one or two problems and graded them rigorously. If a problem was not perfect I would return it to the student with comments. The student could redo the entire problem and hand it back to me within a few days for a second grading. If necessary, the problem could be handed in a third time. The students could not get credit for the problem until it was correct. This provided excellent feedback to the students and motivated them to correct their mistakes. As one student said in the course evaluation “The homework policy was outstanding and it…encouraged learning and rewarded persistence in problem solving.”
Interests and Future Plans
I am interested in communicating about mathematics to a wider audience than college students. I have given presentations to high school students about a variety of topics, and I would like to do more enrichment activities for high school and the general public. In the summer of 2003, while working as a science reporter for the St. Louis Post-Dispatch, I gave a PowerPoint presentation to writers and editors at the Post-Dispatch explaining some of the numbers and statistics that they use on a daily basis. The participants were enthusiastic, and I hope to do similar work in the future.
Interdisciplinary projects also interest me. I have done research on the influence that models of mathematical surfaces had on modern artists in the early 20th century, and I would like to explore more connections between mathematics and art. I would also like the chance to develop a meaningful course on mathematics in our culture, including topics from art, literature, and media.
The education of future mathematics teachers is important to me. My undergraduate degree is in math education, and I have worked with the “PROMYS for Teachers” program which is designed to enhance open-ended exploration in the mathematics classroom. In particular, I would like to develop instructional tools to better link material from abstract algebra to pedagogical issues in high-school and middle-school algebra.
Doing independent research can be of great benefit to undergraduate students. I have done some research with plane curves that would make a good undergraduate research project, and I have also assisted my advisor in supervising undergraduate research. In addition, I am interested in developing student projects in mathematical origami, puzzles, and relationships between mathematics and art.
I would like to develop my use of technology in the mathematics classroom. I have previously used Mathematica for classroom demonstrations, and I would like to design projects and homework problems that make use of Mathematica or Maple. I am also interested in developing mathematics courses that use web-based communication tools, such as WebCT.