I've always been fascinated by the concept of teaching. What a high privilege is given to a teacher: to help someone grow and mature, guide him in his learning, shed seeds of knowledge that may, who knows, change his life forever. How high is this task, and how great the responsibility.
I'm not one of those mentors who strive to become a personal role model for their students, my goal is of a different kind. I want each and every one of my students to take something with them upon leaving my class, something that will help them be better learners, better professionals and ultimately find their place in today's world. Knowledge is power, and whether or not they realize it, a few years from now today's students will be judged by what they've managed to learn and absorb along the way. I see my role as a teacher in helping them get the most out of these years. I strive to do my best in providing my students with guidance, support and conducive learner-centered environment that makes learning an enjoyable and rewarding experience.
Luckily enough modern teacher is not limited in his tools to the chalkboard, he has technology at his hand to aid him make learning process more effective. There's a saying, "mediocre teacher tells, good teacher explains, great teacher inspires". In my opinion, the most important and noble role the use of technology can play in educational process is to help inspire and motivate students. In the world of computers, PDAs and teleconferences, traditional methods of teaching mathematics, both instructional and organizational, cannot fully live up to students expectations. It would become more and more difficult to make students interested in a subject that has so little in common with the world they live in. If we want to gain their trust, we need to be able to talk to them on their own terms. Time calls for newer technologies, and if you think about it: who is better equipped to meet this call than mathematics? Numerical algorithms, various industrial applications and even abstract theories are an excellent source for computer enhanced presentations. Technological base allows to present well-known concepts in a different light, provides new tools and ideas, revealing hidden connections between practice and theory and allowing students explore things with their bare hands.
However, as with all discoveries, there is a danger of going too far. While playing with technology, we may forget to teach our students how to "read and write" in mathematics, and very soon they'll lose ability to understand the language of mathematical abstraction. So it's extremely important not to become "technology blind" and to maintain a healthy balance between tradition and modernization, no matter what goals we choose to pursue.
Another important role technology plays in education is that of a facilitator. Technological advances change our life and our habits, so it's natural that they change the way we communicate. Teacher-to-student communication is the corner stone of any educational process, so anything that has a chance of making it more productive deserves a try. There are multitudes of web-based tools and packages available nowadays, one only needs to have the courage to try them. In my experience, students respond well to innovation, be it a message board or online lecture notes, provided these tools serve their purpose. And if they don't, students themselves will identify the flaw. Most of them value teacher's efforts upon creating healthy working environment and are ready to provide feedback if they feel their opinion will be taken into account.
Overall, my philosophy on teaching with technology can be summarized as follows: good use of technology is a moderate use of technology. I always use caution when experimenting with new approaches and try to tailor them to my audience. I believe that if used wisely technology in mathematical education has a great potential, which not only can better serve students' aspirations, but can also foster curiosity and critical thinking.