I want to teach mathematics because of the important role mathematics and statistics play in our understanding of science and because math is the language in which virtually all media present information. Studying mathematics can be an enjoyable experience which enriches people’s understanding of the world around them. I have been fortunate to have family, friends, and teachers who have been excited about science and mathematics and who have shared their excitement with me. I try to pass on this enthusiasm and enjoyment for learning in my teaching by emphasizing connections between science and real situations to give motivation and perspective.
I began teaching and tutoring in high school in China where I participated in a student seminar on linear algebra, spent 4 hours a week doing walk-in tutoring, and graded for calculus and chemistry. These opportunities allowed me to interact with other students who enjoyed learning mathematics and gave me an appreciation of the value and rewards of teaching. My teaching opportunities continued throughout my graduate years at University of Science and Technology of China, where I graded for several math classes, led calculus discussion sections, prepared and graded for undergraduate physics labs, and worked in the Physics Tutorial Center. I also did personal tutoring for a variety of math, physics, and chemistry classes which afforded me the opportunity to interact with many students from different backgrounds. These experiences prepared me for the increased responsibilities of teaching as a lecturer and for instructing more advanced students. While at the Rutgers University, I have taught 3 different courses as a sole-contact instructor and 4 semesters leading discussion sections for advanced undergraduate courses. My responsibilities included writing syllabi, lesson plans, quizzes, and exams as well as grading and holding office hours.
On Lectures: When preparing lectures, I have always tried to draw from my previous teaching experiences and from the lectures that I found to be effective as a student. It is important that lectures are well thought out and cohesive, as the method of presentation affects the way students respond to the material. Well chosen, relevant examples give not only a good foundation for concepts but also provide motivation and context. For introductory classes, it is vital to maintain the students’ interest and keep them focused by tying the theory in with applications. For example, when teaching Introduction to Probability, I have found that students enjoy and understand more advanced concepts, like conditional probability, because they can attach the concept to simple situations like dealing cards or rolling dice. Introductory courses with good applications are particularly satisfying to teach because students who are not typically interested in mathematics ultimately enjoy the course after working with the different games used as examples. For a computationally intensive course, like linear algebra, it is essential to have prepared examples so that time is not wasted doing extraneous calculations that are not illustrative or illuminating.
While it is important to work out examples when introducing a concept, it is also important to leave time for the students to ask their own questions instead of simply solving equations on the board for the entire class period. This also encourages students to keep up with daily homework assignments. Weekly quizzes are another important tool for students to evaluate their understanding and for me to evaluate what material the students have mastered. Repeating the schedule of any upcoming quizzes, exams, and assignments at the beginning and end of each class also ensures that students are prepared and know what to expect in upcoming classes.
On Introductory Classes: When teaching an undergraduate mathematics class, the first obstacles are establishing effective communication and filling in gaps in understanding. A relaxed but serious rapport goes a long way toward students feeling comfortable and being willing to put in the work to succeed in a college course. I have found that the biggest mistake students, even gifted students, make in college is not fully utilizing individual and small group time such as office hours and discussion sections. I have also found that encouraging students to use these resources and to ask questions in class keeps students more engaged in lecture.
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