Teaching

As a teacher of mathematics, I expect my students to enjoy the beauty of the subject. To achieve this, I keep a philosophy that contains only one keyword: interaction.

Interactions between me and students

It was in the first semester at Duke University that I realized the importance of interaction with students when I was a TA for a calculus course Math122L. A main part of my job was to supervise group work. I assign the students into groups and let them work on problems. It appears to me that some students are too shy and do not come to me even if they have questions. Only when I check their progress, they are willing to ask questions. After realizing this phenomenon, I consistently reach out and offer them help as a wise friend to them. They seem to appreciate my help so much that one student brought a photo of our selfie to the final exam and put it on the desk as a fortune. Later, I served as a TA for the same course and a linear algebra course Math216D. I care about students’ needs, which brings success to my students: the average score in my section of Math216D was 81.88 while the score was 69.69 among all sections.

My understanding of interaction was enhanced when I became the instructor of record for a calculus course Math112L at Duke, where I teach calculus II three times per week. There are seven students in my class. During each week, there are usually two 50-minute lectures and one 75-minute meeting with group work and a short quiz. I soon realized that students need interactions with me in different ways. So, I began to discover these ways. One example was that when we learned sequence and series, I asked students to speak out examples of convergent/divergent sequence/series. I expected that we give two examples for each case, so there were eight cases to be given. They engaged actively and soon provided seven examples and I gave the last example.

In my lecture, I often pause and ask if students have questions. Even if I am teaching new materials or illustrate examples, I will look at their faces if I am not writing on the board. I believe that students’ faces provide immediate feedback to my lecture. For example, when I taught about comparison test, I gave an exercise and asked students to give a series that we compare with. This process involved trial and error and some students had no face expression. In fact, their first try fails. After I explained why it failed, another student immediately shout out a correct series that we can compare with. I saw that all students were satisfied of the second try. Outside the classroom, I make myself available to students so that I can individually address the questions students may have. In these ways, I make connections with students, which inspires them to overcome difficulties in mathematics. For me, every minute involves interaction and I believe that interactions make great presentations.

Interactions among students

I encourage students to make interactions with each other. During group work, I encourage students to talk with each other and write down their progress. In a class of small size, I prefer them to write on the board. It turns out that this way works perfectly as students speak out what they learn. Aside from that, group work is not only restricted to work within groups. Students from one group can see the solutions of other groups, which in turn helps all the groups in class. For example, when I lead a group work section, I assigned a hard problem on the system of linear differential equations. Only one group had the correct idea. I asked them to explain the idea to the whole class, which gave them the chance to practice the skill of communicating mathematics.

Interactions in other situations

I constantly seek the feedback of my courses from faculty members, other instructors, students in my class, and other students. Faculty members and instructors gave me confidence in teaching as well as small issues that I may improve on. I always welcome emails of comments from students and sometimes write a short survey after a quiz. For example, I did a survey on the majors that students were interested in so that I would provide more applications of calculus on specific majors. To further improve my teaching, I participated in the Certificate in College Teaching program (CCT) at Duke, where I learned how to teach effectively. As a part of the CCT, I participated in the Teaching Triangles program, in which three student instructors from different disciplines observe courses of each other and discuss observations. I found it helpful in the Teaching Triangles in the sense that all three people realize potential improvements we may make. For me, the idea of writing answeres on the board was, in fact, a suggestion from my partners.

Interaction as a goal

I believe that interaction is not only a part of teaching; it is the most important part. In the future, I hope to have a better interaction and this will make me a better teacher of mathematics. Students might face the challenge of studying mathematics for various reasons. For example, they may not be confident in their mathematical abilities or may lose interest in mathematics. To deal with the difficulties, I constantly encourage my students that they can do well in mathematics. This is a hard topic for me because I need to discover various ways to make my students confident. I believe that I will make better interactions to help students overcome these challenges and become a better teacher.