Hardwidge, Mark

An instructor should be like a trail guide.  They should point out things that the student might not easily notice on their own, explain the big picture that people might miss as they travel through the details, and point out the tricky parts where people could go wrong easily.  The student should not be a passive learner, however, as this is ineffective and inefficient.  They student should work to learn and understand as much as they can from other sources, so the time with the instructor can be as effective as possible.

I believe in having high standards that the students can achieve, and I believe that a deeper understanding of material is essential, because this allows the ability to see how things fit together, and allows reconstruction of any small things that might have been forgotten.  

In mathematics, I believe that mastery of skills is necessary to move forward, because more difficult problems become effectively impossible, or would take far too long, if the basic skills aren't mastered.  In physics and physical science, I believe that a solid understanding of "how the world works" is just as important as the mathematics behind it.