I’ve been working and tweaking a Teaching Philosophy Statement. I would like to document what I have so far so I am posting it here. Feel free to read and comment on it. Make suggestions, if you have them.
My Teaching Philosophy
Many college classrooms have a reputation of being a dry and monotonous necessity in obtaining the necessary qualifications for a future career. It is my belief that this need not be the case and in fact, a dynamic and interactive classroom environment better prepares students for modern careers.
I love teaching mathematics and it is one of my true passions to help students begin to develop a mathematical mindset in which they can rigorously formulate assumptions and parameters to a model and then use that model to make decisions. In my near 8 years of teaching in the college classroom, I have utilized a mix of traditional and non-traditional classroom techniques to help students learn this mathematical mindset. It has clearly been demonstrated in research and in my own experience that self-discovery is an extremely effective method of learning mathematics but due to time constraints and other constraints often inherent to the particular area of study, it is generally not the only to be used. Of course, by traditional classroom techniques, I am referring to purely lecture style with some or little interaction between students and the lecturer. By non-traditional, I am referring to interactive approaches such as class participation in lecture, group work, projects, student presentation, etc.
My lecture style has always been one of constant interaction, involving students to motivate the next step. Early mathematics is often taught with the basic approach of explanation of method, followed by examples, then a series of mathematical drills through homework. Although I still employ a similar version of this technique, I prioritize the motivation for the techniques that we cover, explaining that there is reason why we do the things we do. Mathematics makes sense.
For higher level courses, there is much more room for discovery and motivating new directions as the students develop skills for proof and verification of claims. In those classes, it has always been a priority that I keep myself as informed as possible on the current abilities of each student. Drawing attention to gaps in knowledge or reasoning helps students to identify their weaknesses and build on their strengths.
All of the approaches I take in class attempt to minimize the intimidation that many students feel toward the subject of mathematics. I often find it necessary to interact with the students one on one during office hours or simply in the classroom; this helps alleviate many of their fears of the subject. While there should always be a clear separation between professor and student, it need not be one of intimidation. In the end, I believe mathematics to be infinitely fascinating as well as applicable, so I constantly try to draw connections between the world around us and the subject at hand.