Teaching Philosophy

Professor de Pillis’ experience at HMC has highlighted the interplay between research and teaching. Professor de Pillis subscribes to the belief that we are better teachers when we are active researchers (how else can we direct student research projects?), and we are better researchers when we are strong teachers (understanding and transmitting ideas clearly is essential to developing new ideas). This philosophy cannot be practiced in a sterile environment. Professor de Pillis believes that at HMC there are the fertile elements of high quality students, small classes, involved faculty, and rapport with industry: all ingredients which are essential to the practice and growth of this research and teaching philosophy.

In her teaching, Professor de Pillis aims to:

• Go beyond the textbook. Many textbooks, due to intrinsic space limitations, cannot present a motivational chain of ideas before presenting results. In the classroom, this gap can be filled. Students profit by learning underlying principles. The motivation and mathematical results then become clear and purposeful.
• Present context. Too often mathematics is presented as a stand-alone, isolated discipline. Since the times when Fourier presented the problems of heat transfer (which led to the mathematical Fourier series) there has always been a reciprocal symbiotic relationship between applications and theoretical classroom mathematics. Professor de Pillis’s intent is to make this relationship clear.
• Teach the art of communication. As words are a road-map of ideas, clear expression implies clarity of understanding. Mathematics is not just writing down numbers and equations, The ability to communicate with clarity is an important aim. Once a student communicates well, this skill will not be limited to the mathematics classroom. The rewards will be seen as the student engages in other disciplines as well.
• Customize. In the intellectual storehouse, one size does not fit all. In each mathematics class, the instructor should aim to discover what is particularly motivating to the unique audience of students, and then, within reasonable bounds, tailor the course content to the students’ specific needs. Accordingly, this is why Professor de Pillis discusses course content with students, as well as with faculty both within and outside of mathematics.
• Teach student responsibility. Active student participation in the classroom is paramount. Students should not be passive receptacles. Subscribing to the principle that the best way to learn is to teach, Professor de Pillis encourages students to give presentations in the classroom.This often results in an increase not only in student understanding, but in student self-confidence.
• Relate teaching to research. An active research program complements teaching, and teaching complements research. Teaching without a knowledge of important on-going research can become stale. Research that is never taught can be rendered artificially irrelevant. Professor de Pillis incorporates current research into classroom presentations, with the result that both teacher and student profit enormously.