Teaching Statement

I teach because I enjoy sharing the beauty of mathematics and the thrill of its discovery. My goals as a teacher are to have my students develop the skills and confidence they need to do mathematics as well as to convey an appreciation and enthusiasm for mathematics as a subject. Because of my dedication to teaching, I am very involved with my classes and students. I am interested in the mathematical performance of my students as well as their overall academic careers, and in my classes I put forth great effort to take into account the various needs of each student.

To meet these goals I teach my classes with interactive lectures interspersed with group work and activities. When I teach I develop a well-organized lecture containing ideas and questions intended to elicit a dynamic interaction between the students and myself. I encourage students to ask questions and participate in class. I also try to make use of many different examples to explain a concept or exhibit ideas, while at the same time showing how these examples relate to each other and the overall picture of what we are studying. Furthermore, I bring technology into the classroom when it can be used to illustrate a concept or demonstrate a useful application, and in my Calculus classes I have used calculators as well as had weekly MAPLE labs.

I realize that there are many different styles of learning, and in order to reach all of my students I make use of a variety of techniques in the classroom. I am also enthusiastic about improving my teaching and trying new methods in my classes. I believe teaching is a skill that one must continue to develop throughout a lifetime, and as a result I am open to new ideas and consistently strive to make my teaching more effective. To this end, I talk with my colleagues about classroom strategies, I respond to feedback that I receive, and I look for practical new techniques that I can implement in my courses. I have also participated in various programs, such as an intensive 10-week Teaching of Mathematics Seminar at Dartmouth College and the MAA's Project NExT, in an effort to learn about different teaching methods and gain exposure to new ideas.

I believe that a good teacher not only teaches facts, but also leads students to think in new ways, challenges them to be original, and generates enthusiasm. Students need encouragement as they proceed in their mathematical undertakings, and they need to learn to explore the ideas that they have and to pursue their own avenues of inquiry. They also need to learn the importance and necessity of hard work and perseverance, and to realize that even for the best mathematicians some ideas come only after considerable effort.

In order to convey these values to my students I put a great deal of effort into preparing dynamic lectures, I carefully select interesting and challenging homework problems, and I interact with students both inside and outside of the classroom. I let students know that I am available outside of class to answer their questions and discuss mathematics, and I tell them that I am interested in hearing their ideas and thoughts about the material. I give my students detailed feedback regarding their work, compliment them on things they have done well, and provide suggestions for ways in which their work may be improved.

I have learned that an important part of being an instructor is advising students, both in an official and an unofficial capacity. I am always happy to provide guidance or assistance to my students in any way that I can. In the classes that I have taught I have had students ask me to write letters of recommendation, I have been asked for advice on which courses they should take, and I have also had students come to me for assistance when they were having academic problems. I make it clear to my students that I care about them and that they can come to me when they have questions or problems.

I am also an advocate of using the history of mathematics in the classroom. In my classes I will frequently make references to the historical events that precipitated the results being discussed. Stories of the wrong turns taken by mathematics in the past, tales of the struggles to develop rigorous treatments of certain subjects, and anecdotes about the lives of mathematicians help students to understand that mathematics is not a static set of facts handed down from antiquity, but rather a living body of human knowledge that is continually undergoing development. In this way the history of mathematics helps students to see that mathematics is first and foremost a human activity.

An example of my use of history in the classroom occurred when I was teaching an introductory Calculus class. During one class period we were reviewing some basic trigonometry and facts about circles. One of the topics was a rather mundane formula relating the angle measurement of a sector and the length of the arc it subtends to the radius of the circle. When I presented this formula to the class I told them the famous story of Eratosthenes, the ancient Greek who measured the shadows made by two poles in the ground placed 500 miles apart and used this to calculate the radius of the earth. I then gave them Eratosthenes' data and had the class rediscover his method of determining the earth's radius. After we went through the calculations in class, we compared our result with the actual radius of the earth and marveled at how close our answer was. After class a student came up to me and told me how much he enjoyed that exercise. He said that it really made the formula come alive and showed him how powerful mathematics can be. I believe that the use of mathematical history can often serve this purpose. It gives students a context in which to view mathematics while at the same time creating an awareness of the role of mathematics in the development of human understanding.

Finally, I find that continued involvement in my own research contributes to making me a better teacher. It renews my enthusiasm for mathematics and keeps me mentally active. In addition, doing research helps me to identify with my students and to be aware of the difficulties one encounters when attempting to understand new ideas. It also keeps me connected with current mathematics. In my classes I try to impress on my students that mathematics is not an unchanging collection of facts, but rather a vibrant and exciting human endeavor that is still developing and in which research is being actively pursued. Through involvement in my own research I am able to better exemplify this. I often relate the material that we are studying in class to current areas of research, and I will sometimes tell my class about open problems that are connected to what we are discussing. In this way my research makes me a more effective teacher.

I enjoy teaching and I am dedicated to improving and refining my skills as an instructor. As a result, the student evaluations for my classes have been very positive. In these evaluations students have commented that I am patient, I create a comfortable atmosphere in the classroom, and that I am available outside of class and eager to help them. I believe that teaching is a vital and exciting part of being a mathematician, and I am seeking a position in a department that shares these values and supports those who strive to be effective teachers.




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