:: 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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