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The whole art of teaching is only the art of awakening the natural curiosity of young minds for
the purpose of satisfying it afterwards.
I enjoy teaching. There is nothing like the experience of presenting mathematical ideas and
concepts to interested students, those who desire to know, to understand, to visualize. I have
never taught a course in which I didn't have at least one student come up after a class to ask a
what if question (i.e., one that goes beyond what is expected to fulfill a search for knowledge and
understanding just to satisfy a personal curiosity). Although days may pass in which no such
interest is shown, based on experience I expect that my enthusiasm for the content at hand will
generate this kind of response.
Teaching Methods and Strategies:
When teaching, one needs to keep in mind the abilities of the students, the level of the course and
the current topics under discussion. It is important to relate a current mathematical idea to an
idea with which the students will be familiar. For example, I like to relate the concept of
independence of path from Calculus III to that of the Fundamental Theorem of Calculus from
Calculus I or relate multiplication of polynomials in algebra to multiplication to numbers of two or
more digits from grade school.
Another consideration is to make the students feel comfortable within the classroom setting.
Students should be challenged but not intimidated. In one upper level course, I required each
student to present a proof to the entire class. But I didn't prepare the students for the pressures of
talking in front of their peers and their instructor, and presenting a proof. I now realize the
amount of pressure on them was just too great to expect success. Now I have each student begin
by presenting a simple problem, then building up to proofs after they have become more self
assured and thus empowering them to succeed.
Teaching at different levels; developmental, general studies, support and upper level courses; has
been a personal challenge for me. At the developmental end of the spectrum, it is essential to
keep a watchful eye on the students from the very start of the semester while working toward the
goal that each of them will understand that learning is their responsibility. Upper level students
have developed the responsibilities, but their curiosities need to be continually stimulated.
Assignments and Expectations:
It is very important that students are focused throughout the course. Clearly stated objectives and
expectations are given at the beginning of the semester. This includes type and frequency of
assignments, homework expectations and attendance policy. Assignments range from routine
mechanics to probing exercises designed for cognitive development. This semester, in differential
equations, students were required to read several essays related to the topics covered, while in
calculus, assignments were given to increase the students quantitative reasoning abilities.
Evaluation of Student Performance:
There must be an evaluation of each student. This will help to determine the progress of the
student and any need for a reassessment of current teaching methods. Evaluation comes primarily
through exams, homework assignments and periodic quizzes. Results from special projects,
assignments or readings are a good measure of a student's motivation.
Use of Technology in Teaching:
Not too long ago, a teacher of mathematics would use only a piece of chalk and a blackboard.
Today, the use of computers has extended to the classroom. Computer generated graphics help
the students to visualize mathematical concepts. Many of the routine calculations which
previously required much time now takes only moments. This allows the students to observe
more cases of a particular concept. I am somewhat familiar with Derive and have used a little (yet
powerful) program called Mathematical Plotting Program. I feel that technology should be on
tap, not on top. I have used computers in the past, and will continue to do so. However,
computers should enhance, not replace, much of the traditional classroom lecture.
The Teacher Outside the Classroom:
One thing that enhances learning is to have one-to-one contact with the students whenever
possible. Many students, especially those in large classes, are uncomfortable asking questions
with others present. Each student needs to feel at ease with his/her instructor. I need to make the
student feel that he/she is welcome and not an intruder. After all, I don't stop being a teacher just
because the class time has ended. I am truly interested in the complete development of the
student. Not just for my class or for the semester or even for the time they're in school, but I
hope to keep in contact with them long after graduation.
Teaching Strengths and Characteristics:
If you ask many of my students about my teaching, some comments may be: "he's able to clearly
explain the concepts", "he always has time for questions" or "he understands the difficulties we
have with some new ideas". However, I would say my strength is the desire to improve. As
stated above, not every method I have tried was successful. It is important to adjust so as to
optimize teaching performance.