We can discuss technology, the Harvard project, the new and leaner calculus, "the student as customer," accountability, remediation, group learning, the Web, and whatever else is currently on the minds and tongues of the experts in education. At the end of the day, though, it still boils down to relationships between the teacher and the student. Some we connect with; others...well, it's another story. We who teach must know and continue to learn, be enthusiastic, and love mathematics. We must encourage, respect, and honor our students.
We should let them know when we are proud of them and take the time to let them know we believe in them. We must have standards and mercy. We must push and demand and hold out in front of them goals and aspirations and always try to leave them wanting "just a bit more, sir." Some days they will not like us, but hopefully some day they will appreciate us. We should help them see a larger world...teach them to differentiate well, not only functions, but also between the good and the better.
"Cabbages and Kings--A Philosophy of Teaching"
MAA FOCUS, March 2005