In college I took a Physics II course. I had been looking forward to that class since early High School. It was basically an introduction to circuits. I was eager to learn about resisters and capacitors and voltage and how circuits were built and designed. I thought I'd gain some knowledge that I'd be able to use in everyday life.
You wont be surprised to hear that I didn't gain any of that kind of knowledge. Sadly, I doubt I retained any knowledge from that course whatsoever. In truth, I barely made it through! Of course, it was one of those classes where a 60% test score can set the curve...
Anyway, there was one lesson in that class that I will never forget. The professor started class and turned to the board and said,
"This is a capacitor."
Then he wrote "C=Q/V" on the black board.
Yep, those 3 letters and 2 symbols are definitely a capacitor...
Now, maybe its just me, but when someone says "This is a capacitor," I sort of expect to glance up and see him holding one, or displaying a picture of one. I don't expect to see an equation. We never talked about what a capacitor DID, or why you might NEED one. In fact, it wasn't until I had a phone conversation with my dad that I learned a capacitor "stored charge". And I'm not even going to get into the fact that C=Q/V describes capacitance, which is a measurable quantity, and not a capacitor which is a physical device...
So what lesson did I learn from this? Different people learn and think in different ways. I'm a practical applied type of learner. That is, I need to understand and not just memorize. Thus giving me an equation or showing me a graph just isn't quite enough. I need to see steps and logic and explanation. In other words, I have to start from something I know and build up.
Other people certainly aren't this way. I've known lots of people who could simply see an equation and understand. I've known other people who could see an equation and then spit back and pass the class, but maybe not understand.
Fortunately for me, my learning style works great for computer science. Unfortunately for me, it's not how Math is taught. And only rarely how Physics is taught.
I've always believed that calculus and physics should be taught hand in hand. After all, the majority of calculus was developed trying to solve problems in physics. Add in a dash of History and you've got a thoroughly engrossing class in my opinion. But anyone who's been through college knows that isn't how its done most places.
Instead physics is taught with algebra, because the kids don't know calculus, even if they've taken it. And that means you have to memorize and spit back more equations for more circumstances. If it was calculus the number of equations would drop and the amount of logic to handle different circumstance would rise. Great for me! But again, not how its typically done.
Given all this, I guess I can't really blame my Physics II teacher. He was just teaching the way he thinks. Turns out a lot of people think and learn that way just fine. Even the Wikipedia article on Capacitance is written in much the same way. Of course, Wikipedia makes a distinction between a Capacitor and Capacitance and does a great job of describing Capacitors in English...
Still, I've never been convinced that people who were able to learn the equation and solve the "word problems" and ace the tests really understood any of it. Some of them did. But most of them? I find it hard to believe.
I have to end this by pointing out that there are certain topics to which my style of thinking and learning just doesn't help. Things like Quantum physics, for example. Where no matter how you look at it, you can't reduce it to common sense. In these circumstances you have to settle for memorizing the "way things are". Chemistry is like this. And yes, lots of Physics is like this too. But I still claim that after you've internalized the "way things are", you can start to reason logically about it.