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Teaching Philosophy

An effective instructor is a navigator and coach, pointing students in the right direction and critiquing their practice. The instructor should paint a broad picture, highlight the interconnections between subjects and ideas, enabling students to assimilate a comprehensive image of the discipline. It is important that the student see the forest and not merely the trees.

Ultimately the learning is done by the student, and what the student gets out of a class is proportional to what the student puts in.

Various ideas helped me form my teaching philosophy; some of these are quoted below. The mathematician George Polya observes that as educators we have been granted a unique opportunity which we must use wisely:

“Thus, a teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of independent thinking.”

G. Polya, How to Solve It, Princeton University Press, 1957.

Richard Hamming notes that:

“Teachers should prepare the student for the student’s future, not for the teachers past.”

“I am, as it were, only a coach. I cannot run the mile for you; at best I can discuss styles and criticize yours. You know you must run the mile if the athletics course is to be of benefit to you…. Again, you will get out of this course only as much as you put in, and if you put in little effort beyond sitting in class or reading the book, then it is simply a waste of your time.”

Richard W. Hamming, The Art of Doing Science and Engineering:
Learning to Learn
, Gordon and Breach Science Publishers, 1997.

Charles Vest adds that:

“One may start out as an effective and even brilliant teacher, but without the kind of continual renewal that research and scholarship provide, one may not grow in wisdom and breadth, and over time may lose rather than gain in effectiveness as a teacher.”

“… the very best learning environment is one in which undergraduate and graduate education are blended with the conduct of research and scholarship. The issue should not be teaching versus research, it should be the proper interweaving of the two.”

“The object of education… is to prepare people to live full and responsible lives.”

Charles Vest, Learning in a Research University, (President Vest’s letter to the parents of MIT undergraduates) MIT Parents News, Spring 1994.

It is important to provide students with a broad view of the big picture and to enable them to transfer their knowledge in one area to another, and to apply what they learn in their mathematics classes to their other (e.g., science and engineering) classes.

You need both training and education:

Education is what, when, and why to do things, Training is how to do it.”

“Either one without the other is not of much use. You need to know both what to do and how to do it.”

Richard W. Hamming, The Art of Doing Science and Engineering:
Learning to Learn
, Gordon and Breach Science Publishers, 1997.

One must see education and training as a whole, and take a holistic approach. Richard Hamming refers to this as the system approach to education:

“While taking any one course, it was not a matter of passing it, pleasing the professor, or anything like that, it was learning it so at a later date, maybe two years later, I would still know the things which should be in the course.”

Richard W. Hamming, The Art of Doing Science and Engineering:
Learning to Learn
, Gordon and Breach Science Publishers, 1997.