Teaching Philosophy
My teaching philosophy contains a three-fold approach that is centered around a single idea - communication. The first is to encourage dialogue in a classroom setting, second is to promote discussion outside of lecture, and third is to improve the mathematical communication of the student in written form.
In the classroom, I enthusiastically deliver my lectures, since I feel excitement flows from teacher to student. I encourage dialogue among my students, while maintaining a structured learning environment. I foster casual intellectual communication and provide opportunities for students to learn by discovery. I am self-reflective in my teaching, and I tailor my lessons and assessments to address the strengths and weaknesses of the individual classes. I construct comprehensive assessments that require computational, analytical, and qualitative skills as well as include writing components in order to allow each student to demonstrate his or her strengths. To address different learning styles, I enthusiastically present information in multiple ways including distributing handouts, incorporating Matlab and other interactive tools in my lessons, and introducing applications to complement the theories presented.
I encourage students to come to office hours or schedule meetings to address individual problems and issues that are difficult to hold in a classroom setting. I believe individual meetings provide a good opportunity to motivate students in their pursuit of mathematics. I also believe that communication can be enhanced outside of the classroom by using today's technology. While teaching Matrix Analysis in the Fall of 2005, I developed a class website in order to create an effective organized arena for posting homework, notes, and updates for the class. I also built a class blog. After every lecture, I wrote a brief synopsis of the class and would hold the blog open until the next class lecture for students to post questions and comments for the class. This allowed an open forum for the class to help itself with topics being presented, while allowing myself to proctor the strengths and weaknesses of the class. For my current Introduction to Engineering Computation course, I have incorporated discussion boards and a chat room for live discussion of course material. My next project will be to create 'wiki' pages for the main topics of the course. This idea, in addition to other projects I am considering, could help build class unity outside of the classroom and improve the mathematical writing skills of the students.
I recognize that there are inadequacies in the mathematical writing and proof skills of most undergraduates. Therefore, I would like to develop and/or teach a class similar to one I took as an undergraduate. This Foundations of Mathematics course emphasized careful and precise expression of mathematical ideas and introduced several common proof techniques. This was a unique class in that it nurtured professor - student communication and allowed for each to teach the other.
In conclusion, my main goal as a teacher is to improve dialogue in and outside of the classroom as well as through written form. I hope to be able to present mathematics in a clear, innovative, and enthusiastic manner, and I want my students to leave my class with an appreciation for the material and an ability to effectively communicate and utilize the subject matter that I taught them.