:: Teaching Philosophy ::

"Tell me, and I'll forget. Show me, and I may remember.
Involve me, and I'll understand." ~ Native American Proverb

I began teaching in 1988 as an undergraduate teaching assistant in the mathematics department at Ohio State. Since most algebra and precalculus classes at Ohio State had enrollments of several hundred students, the recitation classes with graduate (and a few undergraduate) teaching assistants met twice a week. Since I had no formal teaching experience, I developed my teaching style by modeling professors I respected and admired. Those professors were prepared, innovative, engaging, motivating, patient, and challenging. I believed (and still do) that those qualities were prerequisites for being a good teacher. A great teacher was also noticeably approachable and welcomed, not just accepted, students' concerns. A great teacher involved his students in every aspect of the learning process, even if this meant having a line of students outside his door with questions on certain afternoons.

I have proudly aspired to be a great teacher according to those qualities I admired in others. From my first classroom experience twelve years ago to my first faculty address on new teaching methods as a full-time instructor at Virginia Wesleyan College, I have tried to pass along the beauty and excitement I see in math to my students and colleagues. I stress applying mathematical concepts to real-life situations, and I have spent hundreds of hours developing lectures and tests that not only teach concepts, but are fun, interesting, and generate student feedback and interaction. For example, on a calculus exam, I asked students to use differential equations and Newton's Law of Cooling to determine who killed Miss Scarlet, a calculus teacher who had been at home preparing a final exam when visited by several students from her class. In another example from a business calculus Maple lab this semester, students estimated the revenue Linus Van Pelt generated by selling pumpkins from his pumpkin patch given a marginal revenue function over a certain time interval.

As Ostebee and Zorn state in the introduction to their text Calculus: from Graphical, Numerical, and Symbolic Points of View, "Whether one views calculus as an introduction to pure mathematics or a foundation for applications (or both!), the conclusion is the same--concepts, not techniques, are truly fundamental to the course." The direction my teaching has taken in calculus courses is to stress the understanding of concepts. For example, what does P'(t) = kP(t) say about the growth of the population P at time t? The solution to this differential equation is important, but the meaning behind the equation is equally important. At Virginia Wesleyan College, I was awarded a Faculty Development Grant to prepare labs and workbooks that would further integrate the use of computer algebra systems into the mathematics curriculum. With the aid of graphing calculators and computer algebra systems in the classroom, instructors can explore problem situations that were previously mechanically arduous and overly time-consuming. It's hard for students to work with new ideas and difficult problems without crutches such as continuous repetition or step-by-step instructions. I encourage collaborative learning, in which students can draw upon their collective knowledge base, and expect students to take an active role in their education. I want students to think mathematically and do more than manipulate algebraic symbols.

Albert Einstein once stated that the proper formulation of a problem was even more essential than its solution. I stress seeing how pieces in a mathematical formulation fit together rather than just looking for "the answer." On more than one occasion, I have had a student bring his assignment up to me asking why he did not receive full credit for a correct answer. I explain to the student that clear explanations and a correct thought process are at least as important as a final value, especially when that value makes little sense without the correct interpretation of the problem.

In non-math major courses, I have been successful at creating a non-threatening environment where students are not afraid to ask questions. A Virginia Wesleyan student, who nominated me for a Distinguished Teaching Award in 1995, stated, "I feel as if I can ask any question and not feel ashamed or embarrassed about doing so. What makes her teaching style so effective is her energy, her assertiveness, and most of all, her enthusiasm." In these courses, students often arrive with poor attitudes toward the subject because of past undesirable mathematical experiences. I work hard with students to bypass these attitudes and fears so they can gain a new appreciation for the subject and its usefulness. Also, I want to show them that math doesn't have to be hard, and it can be interesting and applicable to their everyday lives.

For many students, especially freshmen, encouragement and direction is an essential ingredient necessary for their success in a math course or when pursuing a math major. As a "biology-turned-math major" wrote in a thank you note to me, "I also wanted to thank you for seeing my potential and urging me to pursue a degree in mathematics. You have always been there to restore my self-confidence when I've needed it most." I know what it feels like to struggle in a course and lose your confidence, so I believe it is important to have "pep talks" and cheer on students who are capable of succeeding with a little push. I instruct in a positive manner and return helpful and instructive comments back on assignments and tests. Since I am naturally excited about mathematics, I'm not bashful about sharing this excitement with students. In some instances, my enthusiasm for the material actually rubs off on them. One of the comments I receive most often from my student evaluations is, "She really likes math and tries to excite the students." As quoted by William Arthur Ward, "The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires."

When I left my visiting instructor position at Wittenberg University, the provost sent me a letter thanking me for my contributions to the education of the Wittenberg students. In that letter, she wrote, "Dr. Noyes (the acting chair) and other members of the Math and Computer Science faculty have evaluated your teaching as excellent, and they cite, in particular, your ability to lead insecure students to achieve their best in your classes. I would judge from the faculty's description of your work that you are not only one of those rare "natural" teachers, but also a mature professional who knows a great deal about how students learn. We appreciate your hard work - your investment of time, energy and enthusiasm in Wittenberg's educational program." What I had admired in my best teachers has become a large part of my teaching style as well.

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