I believe that teaching is a two-way street based on communication. As an educator, it is my duty to make sure that I communicate to each student in such a way that they understand the material I am presenting. I try to give definitions as straightforwardly as possible and then give a variety of examples to make sure each student can see how a concept is applied in different ways. For instance, when I am teaching how to solve a quadratic equation, I may start by showing how to algebraically solve the equation, and then I will show on a graph exactly what this solution represents. This way, students can get a physical understanding of what they are doing mathematically.
I make sure to use real-world applications whenever possible. When teaching Calculus, since many of these students are going to be using these concepts in their specific majors, I try to extensively put in examples where the mathematics is directly applied. If I have a small class size, I try to tailor the examples to my students’ areas of study, so they can better appreciate the reasons for learning the material besides learning it just for the class.
I often encounter students who learn in different fashions. Perhaps one student learns things from a visual perspective, while another learns from a direct proof of a concept. Again, this goes back to education being based on communication. I make sure to try to explain concepts to students based on their preferred method of learning. Realistically, as every student learns differently, this may not be possible in a single classroom sitting. I encourage students to come to office hours for a more detailed and tailored discussion of a topic.
As I said in the beginning, communication is two-ways. I emphasize to my students that without their input, I cannot help them to the best of my abilities. Therefore, I encourage participation in class so that I can see how the students are learning and what difficulties they may be having. I want students to think over a problem and then ask the core concept questions. That being said, it falls on me to motivate students into asking these important questions. To do this, I try to create an overarching project or theme to focus on for the semester. In this way, I create an anchor for the students to test the new concepts we learn on a template that they are familiar with and can explore. For example, in a Calculus 1 course, I would motivate our studies with the idea of modeling a roller coaster. This is a physical example that the students can certainly visualize and to which they can apply the new concepts we learn throughout the course.
My teaching experience covers a wide range of classes with a wide range of students. I have taught College Algebra and Precalculus in the AIM Program (Assisting students, Improving skills, Maximizing potential). This is a program that works to give at-risk first year college students extra attention and support. This has been my most rewarding teaching experience because I was able to develop a bond with the students and help them succeed in their first college courses. On the other hand, I have also taught higher-level courses such as Calculus III and Differential Equations, and I have been able to practice tailoring my teaching style to more specialized students. I have also had the privilege of being a course coordinator for Precalculus, where I taught nearly 300 students and managed 3 TAs. I have also taught several online Precalculus courses and online Calculus 3, which have given me the opportunity to gain experience in organizing and teaching through an online community.
I am also working with a colleague to design and develop an open-source, LaTeX based online homework system we call Xronos. It is based on the Ximera Project out of Ohio State University. We have worked to implement it here at UF for the Calculus I and II courses. It should roll out fully to the whole Calculus sequence in a year or so. We have a question bank that numbers in the hundreds of thousands and growing, and we are developing more help features as well such as interactive lecture notes and video walkthroughs. Since this project is open-source, it can be made and implemented at any institution. We are very proud of our work, and I would like to continue to improve this system in tandem with my teaching.
Throughout these experiences, I have constantly worked to better my teaching. The art of teaching is not something that is ever finished. My teaching is being constantly molded based on the goal of helping students learn. It is a privilege for me to have the opportunity to continue working to help students and one that I hope to continue my entire career.