Teaching Philosophy
Mathematics is a discipline that has attracted brilliant minds since ancient times. Its importance in science and technology cannot be overemphasized, and it is not surprising that it has been taught for more than 2000 years.
I received my undergraduate education in Greece and the presentation of the subject was influenced by the work of ancient Greek mathematicians. There was strong emphasis on classical geometry and rigor. At the university level, because of the specialization approach predominant throughout Europe, I had to take only mathematics courses. In a liberal arts system, as in the United States, the approach to how and why mathematics is taught is understandably different. Reasons for teaching mathematics at the undergraduate level should include its historical significance as well as its applicability and usefulness.
One of the strengths of the mathematics discipline is its ability to cultivate a certain way of thinking. Mathematics develops critical, non-dogmatic thinking, because everything has to be proven based on a specified set of axioms. It demands the use of logic and teaches techniques of argumentation, which are useful in everyday life. These traits are particularly applicable and needed in a society where information is abundant. Thus, there is need for critical examination of accuracy and compatibility of news, and for careful selection and sorting of information. At the same time, mathematics is by no means a dry and technical subject. It encourages innovative thinking and cultivates problem-solving skills. It builds new and reinforces existing intuition about structures that exist in nature as well as abstract mental constructions. It offers a different perspective about our world and, at the same time, a deeper understanding of it.
It is my view that these special attributes, unique to mathematics among other subjects, should be incorporated into undergraduate instruction. The material is to be used as a means of training the students’ minds in addition to disseminating knowledge.
During my first year in Vanderbilt University, I had the
opportunity to work with some excellent teachers, in a mentoring program for
new instructors. I was assigned to an instructor, my mentor, and I had to
attend his lectures, discuss teaching techniques with him, hold office hours
for the students in the class, and practice lecturing four times per semester.
For the next three and a half years, I was assigned my own class and had the
chance to apply my teaching ideas, receiving a great response from my students.
My approach is to encourage them to explore and “invent” the material for each
meeting by presenting the students with situations that call for a new tool or
lead to the forming of a conjecture. Then, I reinforce their intuition and
provide hints for the discovery of the ideas of the proofs. The result is often
maximized when the students work in groups. This way, the students acquire
useful experiences of discovery and of critical evaluation if it.
The development of the framework for such explorations is a
very interesting task and provides a better understanding of the learning
process. I was privileged to be selected as a mentor for new teaching assistants.
I have the opportunity to discuss my philosophy with my mentored students and
teach them my approach on instruction of undergraduates in a liberal arts
system.
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