-Teaching physics: is there only one way?

For the last year I have been the TA for a pre-med physics course. My job was basically to prepare the homework questions, hold a few hours of problem sessions a week and have reviews every time they had a test coming up (the nicest part was that I didn't have to grade anything, the professor decided to do the grading himself). I had always taught labs for engineering students and the experience of TAing for a lecture has been very different than that for labs. For one, in the labs we are always given a manual (written by professors in the department) with the experiments, procedures and goals all stated in it. As a TA I never had any chance of doing things the way I wanted or thought would be better.

This time, it was very different. I was given 1)the syllabus, with all the dates and topics/chapters the professor would cover in the lecture and 2) a copy of the textbook they would be using. The rest was up to me: what to do during problem sessions and how to review for the exams. It ended up with me first giving a mini-lecture of the most important concepts in the chapter and proposing a few problems to solve. The rest was for students to ask questions about their homework problems.

At the end of the semester I asked the students to give me their feedback on my performance (I do not get official evaluations as a lecture TA, but I would as a lab TA). I was surprise because this time almost all of the students that filled out the feedback form said that my teaching style and analogies was what actually helped them get through the course. Apparently (I say apparently because I have never seen the professor give a lecture), the professor did a horrible job in the classroom being way too technical in this teaching of physics. I told a few fellow grad students and they wanted to know that this teaching style and analogies was all about. So I decided to give them an example:

One of the last chapters covered in this class was on Quantum Mechanics, mostly on potential wells and hydrogen-like type of problems. When I was trying to describe that in these "constrained" systems the particle can only take discrete values of energies I noticed that while everybody shook their heads in a yes motion, most of them didn't understand what that meant (I found this out by asking them a question and very few got it right). So I made the analogy to a stair, I said: Unless you can fly, the only values of potential energy that you can have while both feet are at the same level are those given by mgh, where h depends on the number of steps you have gone up or down. Then, I realized that I could use this same idea to explain why lower energy levels are always first filled, I said: Now, imagine that the atom (for example) is actually a concert hall, and in the nucleus you have the stage. You are an electron that wants to go see the show, would you like to sit in the front or in the back? Everyone said front. If you imagine a concert hall with the layout of the room we were in, the front seats had the lower energy, and therefore electrons would take always the front seats, to be closer to their idol (Ok, I actually said American Idol and they all laughed). The professor later gave a quiz related to level-filling and I checked to see how "my" students did. Most of them were in the higher-grade group.

When I was done telling my fellow grad students my analogy, they all disagreed with my "style". They asked: is this how you always do it? I replied, well, it's definitely not always the same analogy :), and it definitely depends on the audience, but yes, for not physics and engineering majors this is how I do it most of the time. Some got mad at me, and said that I was hurting physics instead of helping. They reasoning is that while I might've told them how things were, I didn't teach them why things were that way. Plus, my analogy was incomplete. They couldn't tell me how it was incomplete and I conceded that yes, in a quantum well, the energy levels depend on the mass of the particle and in my stair example they didn't, but that was beyond my point. All I was going for was that there are discrete energy levels.

I asked them how they would teach the same idea, and two of them said that the only way to do it was through the mathematics, another said he didn't know how to except by repeating what was in the book.

I don't care what they think, in my opinion doing mathematics doesn't explain either why things are the way they are, it only tells you how they are. I am not even sure physics can explain why things are a certain way. But what worries me the most is that many non-majors students will (and many already do) encounter people that think physics can only be thought one way: the way a Physics PhD learned them. Plus, the final grades in this class (not assigned by me, so you can't claim I was biased) were much higher in average for the people that attended my office hours than for those who didn't.

For those of you who teach physics for non-majors, and think/know you do a good job, do you follow the book, rely heavily on mathematics or use alternative methods to teach? If you use the last option, can you provide me with some examples?