TEACHING STATEMENT YANG LIU

Teaching greatly interests me. It is a great pleasure to see students grasp new mathematical concepts and apply their mathematical knowledge to solve problems. The experience of working as a teaching assistant and the graduate level mathematics coursework at the University of Georgia have well prepared me to teach undergraduate mathematics courses at various levels. Teaching undergraduate mathematics and statistics courses at Marlboro College and the College of William & Mary has also been a great experience. In my teaching, I like to give interesting examples to motivate students and sometimes show geometric intuitions to them because I have a background in geometry. In this way, I am able to help my students acquire a deeper understanding of mathematics and to develop their abilities in applying mathematical knowledge skillfully. My experience in giving talks on various mathematical topics has also helped me develop the ability to teach new mathematical concepts and theorems to students in a clear and concise way. Furthermore, I have also learned to present deep or general mathematical theorems by introducing simple or basic mathematical facts first. For example, in the talk on the Rauch comparison theorem and its applications, I began with the comparison of two trigonometric functions in calculus, and then introduced the comparison of the solutions to two ordinary differential equations, and finally the general Rauch comparison theorem, in which way one can clearly see how the theory was developed, and the geometric pictures I provided can help one obtain a concrete sense in general theories. I have been as a tutor for individual students, a teaching assistant, and an instructor. My primary responsibilities include helping students with solving math problems, teaching student new pieces of mathematics, teaching students how to apply new pieces of mathematics, and advising students on final projects, further courses to take and further research to do. These valuable experiences have developed and enhanced my teaching skills and techniques. Mathematics is mainly the study of quantity, structure, space, and change, as well as the relations among them. Accordingly, it is my belief that solving mathematical problems and working on examples can be an effective and efficient way for students to understand and apply new mathematical concepts. My philosophy is simply learning math by doing, because I think that students can construct their own knowledge through doing. My students have greatly benefited from doing the mathematical problems, some of which are written by me, and from the examples, that I provided for them in my classes. I also strive to promote students’ interest in the study of math in several ways: (a) to let them realize that mathematics is useful for science and many other areas, and can even be applied to real life, and (b) to encourage the students’ initiative and creativity. In my lecture classes, I present the course materials in an efficient way and make them interesting to the students. For instance, I used practical problems that can be solved by using differential calculus and integral calculus to stimulate the students’ interest in calculus. I like to ask directed questions and intriguing questions to get all students actively engaged in class. For example, when teaching optimization in calculus, I asked the following 1

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question first, how much area is the largest rectangular base of a house that can be built on a semicircular land with radius 30 feet? Students guessed different answers. Then I taught them to find a function that expresses the area and to find the maximum of the function by using derivative. Also, I encourage my students to have discussions on class materials. In group tutorial, I usually ask students to present different materials and projects on which they work so that they can share what they have learned and done. Also, I provide one-to-one help to individual students in doing class exercises, since students in the class could be in various levels. I have also taught a statistics workshop. I led the students to study advanced materials in statistics and inspire them to do some research projects. I got students engaged in the workshop by asking the students thought-provoking questions and encourage them to discuss topics with each other, making the workshop interactive. In addition, I have given advice to some senior undergraduate students who are writing their thesis in mathematics or related. These have been very valuable experiences for me to engage students in mathematical research. Technology has also been very useful in my teaching. For example, the WeBWorK system has been used in many math courses and statistics courses. I have included as much computer technology as possible in my teaching. This has made my teaching more efficient. For example, with the assignment function of WeBWorK, I was able to identify the homework problems on which students needed the most help. Then, I could spent my office hours most efficiently with students who had individual questions. I have also used the online system, Moodle, where I post my lecture notes and through which I can easily have after-class interactions with the students, MyMath Lab and WebAssign, where I assign homework and evaluate students’ progress in their course study. I have also coded some of my own homework questions in WebAssign. It gives the students faster and more useful feedback. These technology tools have made my teaching more efficient and effective. It might be a challenge to meet the variety of needs in a class made up of students with differing interests. I came up with covering diverse topics in some of my courses. For example, in my Differential Equations class, there are students majoring in engineering, students majoring in physics, and student majoring in math, so I cover topics on theories, topics on numerical methods, and topics on applications in that class. I believe I have been successful at reaching my goal in teaching because I have received many positive comments on my evaluations. I would like to conclude with some representative narrative comments from the student evaluations of my teaching as an indicator of my teaching effectiveness. These include: “He was always very organized, and we made excellent progress through the material.” “Very helpful in answering questions in a clear manner. He wanted everyone to understand the material and be successful. ”“He does a great job as a math professor, and address clearly on the topic.”“I have learned a lot in a short amount of time.” “He really helped me with stuff that I couldn’t understand. He explained everything in depth and at a good pace. I liked him a lot.”“He taught this class very well. He kept the class engaged and still enriched my knowledge of math.”“I have learned a lot in a short amount of time.” “He has a thorough knowledge of his subject and a clear teaching method.”“He is a very good teacher. I love this class.”“He was extremely helpful and fair, approchable, and showed great enthusiasm for the subject. I would definitely take a class with him again.” and so forth. Current address: Department of Mathematics, College of William & Mary, P.O. Box 8795, Williamsburg, VA 23187-8795 E-mail address: [email protected]