Mathematics & Computer Science

1997-98 FINALIST Chancellor's Distinguished Teaching Award

Philosophy of Teaching

My job as a teacher is to provide the framework that allows my students to grow and to improve their skills, knowledge, and understanding of mathematics. This framework includes a variety of assignments, an inclusive classroom atmosphere, and respect for each student. For students to willingly engage in assigned activities, they must see their assignments and classroom activities as worthwhile and valuable. At the same time, I must see the assignments as containing appropriate and sufficient mathematical content. I work to establish a classroom atmosphere of acceptance and tolerance. In my classroom, students have to be willing to make and support conjectures. They must listen to others and judge the mathematical validity of their comments. Students must be free to make mistakes, to correct mistakes, and to try things that they are not sure they can do. I work diligently to establish a classroom where students are willing to take risks. Students who are afraid of me, the class, or the material are not likely to make much progress in their studies. I always learn my students' names and use them in class, even though I am not very good at remembering names. I also learn where my students grew up, their majors, their hobbies and interests, and other details that make them individuals. They reward me by being individuals who willingly participate in class. To help my students become independent learners and to prepare them for class participation, I assign some homework in a way that is unusual for mathematics classes. I ask my students to read ahead and to work problems ahead of the class period in which the sections are to be discussed. While this may sound perfectly natural to someone in English or history, it is very unusual in mathematics. Many students balk at this method, protesting that they cannot solve problems that they have not seen demonstrated. However, most students persist in trying this method, and they find that they learn more and are more confident of their knowledge. Another part of my teaching that is somewhat unusual is the use of lab activities to emphasize major concepts. I use a series of activities which require students to collect some type of data and analyze it using the concepts under discussion in class. For example, to explore the concept of derivative, students use a motion detector and their graphing calculators to create graphs of position and velocity functions. Walking to produce different types of curves is a concrete method for approaching an abstract concept. The concrete nature of the activity demonstrates the relevance of abstract mathematics to simple, real situations. The active participation of students promotes ownership of the exploration of derivatives. The physical nature of the activity encourages students to use different types of thinking to complement their logical reasoning.

Examination of the position and velocity graphs aids students in making the mathematical connections between a function and its derivative function. After collecting and analyzing data, students write formal lab reports that allow them to communicate their understanding in writing. In their reports, students move from the concrete example of the lab back to the abstract concepts of the course. And of course, there are periodic exams where students show what they have learned thus far in the class. A typical day in most of my classes begins with small group discussion on the homework that they have prepared or on the current lab. After a short time of intense group discussion, I ask students to recap the major points of the section. Collectively, we decide which parts need further clarification and explanation. Using prepared examples, activities, and extensions, we explore these parts. Sometimes, a student question will suggest a different avenue of exploration, and if it is reasonably connected, we will explore that question as a class. If not, I will invite the student to explore it with me later. The problems that students have prepared for each class are used as examples and springboards for further investigation. I end the class with a brief preview of the next topic or with a summary of previous work. Taken together, these methods and activities require students to work independently, to work collaboratively, to communicate mathematics orally and in writing, and to demonstrate mathematical competence in a variety of ways. Because different people have different strengths, it is my belief that students need multiple ways of showing what they know. I also believe that students need different levels of support for their work. The opportunity to connect with many students on an individual basis was one factor in my choice of Western as my academic home. Consequently, I have an open-door policy for students. I have established office hours, but I am just as likely to have students in my office at other times. I let my students know that I am available for help when they need it, and they take me at my word. Teaching is not just something that I do. Being a teacher is who I am. It is an integral part of my identity. Working with students in class and out gives me great satisfaction. My approach to teaching can be summed up by four principles: I like my students; I want them to succeed; I believe that they are capable; and I push them to give their best effort.