In my first year of graduate school (2008), i TA'd for an introductory electromagnetism class that turned out to be very difficult. Except for the difficulty, i liked a lot of things about the way the course was structured. This letter, then, is advice from a younger me to students dealing with professors like the one i am trying to be.
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Dear Section 2,
A number of you have asked me for study strategies and tips for the final exam. So far i've given only half-answers and promises to think about it. Unfortunately, the number of people i've blown off is slowly approaching the section size. So rather than track you all down with an answer, i'm going to do this all at once. I'm sure there is at least one person who has asked me about a specific situation
that isn't addressed by this e-mail. Whoever you are, i'm sorry, i've forgotten. Ask me again and i'll try to give you a straight answer.
Most of you seem to be having three basic problems:
First, in some instances you just can't get your head around a concept, even in theory. For many, this is your first experience studying phenomena of which you can't immediately form a mental picture, so you are much more scared than you need to be.
Second, you may understand a concept in theory, but don't know when to use it. This issue is characterized by staring blankly at problems while a thousand unusable or unrelated tidbits of information swim through your head.
Third, once you've figured out what concept to use, you discover that you don't really understand it well enough to implement it properly. On exams this tends to manifest itself as a half-credit solution in which you picked random areas, charges, currents, etc. and plugged them into your equation wherever they would fit (or not in some cases).
Finally, as a corollary, several students have complained that they do homework with a group, but on their own they can never reproduce the work. Or they could eventually flail their way to a mostly correct solution, but in an exam there isn't time. These are all problems that are common but somewhat unique to physics. Again, since you have relatively little experience with physics, you are probably more upset than the situation warrants. So calm down, take a deep breath...and let's talk about study strategies.
To start, it might be good to re-read the notes i sent out before the midterm. They contain some tips for right before and during the final that i won't reiterate here. If you need a copy, let me know.
The first problem can only be dealt with by another person. Assuming you've read the lecture notes and the book as they relate to a particular concept, reading them over and over again is unlikely to impart any sudden epiphany. Ask a friend to explain it to you. If that doesn't work, take your friend with you and ask a TA or the professor to explain. I'm always available by e-mail, but basic conceptual questions are much better addressed in person. (Note that you can still use e-mail to make an in-person appointment.) On the flip side, if someone asks you to explain a concept, please make every effort to do so. You might just discover that you don't know it as well as you thought you did. When explaining an equation, if you need math, you don't really understand it. By taking time to just review the theory of the class to each other, you insure yourselves against that sudden feeling of cluelessness when you open the exam.
There is still the question of which concepts in the course are fundamental. If there's a demand for it, i can put together a list, but the part of me that feels responsible doesn't want to risk leaving something off and the physicist in me says it's obvious. Please let me know if this is grossly incorrect. (Update: Nobody asked for this, partly because it was covered in the exam review. If its ever unclear which concepts in my courses are fundamental, please let me know!)
Problem two is basically an inability to DO physics, despite understanding it. The antidote, then, is obviously to do more physics. However it is possible to struggle through many problems without really getting at the underlying skill that makes them look easy in a physicists hands. I've stressed that you can learn faster by working in groups, but there is a danger that part of the group does problems while another part watches. Therefore it is best to work in smaller groups and stay engaged in your group. I've found 2-4 to be about right at this level. That is NOT to say that you can't have more people than that working together. I strongly suggest you make a party of it. Order food, find a place with lots of whiteboard space and invite everyone you know in the class to a physics party. That means someone has to step up and organize it, but you all have to learn the material anyway and this is so much faster and more fun. Some of the best times i had as an undergrad were with some subset of the two dozen people who were just as buried in physics as i was. (Yes, i'm a nerd, but that doesn't make me wrong.) Freshmen: you might even get an RA to organize something for everyone in your dorm.
Several of you have told me that you do practice problems, but they always seem to take forever and/or you're never sure you've got them right. Remember that problems are always written to test one or more of the fundamental concepts. Figure out what those concepts are and you're well on your way to solving the problem. Not by coincidence, the grading rubric usually starts with a couple points just for writing down the relevant concept, often directly from the equation sheet. So in studying and on the exam, start by writing down the concept you are going to use! This will give you something to break into manageable pieces and calm the flutter of other facts running through your head. Once you have a concept, break it down. If it's Gauss' Law, find an appropriate Gaussian surface, calculate it's area and count/calculate the charge it encloses. If you want to integrate the force on a wire from a magnetic field, draw dL and B at some point on your diagram and use the right hand rule to locate the dF vector. At this point, i always wave my hands at the board and say "Do math." From there, you will usually see an obvious, mostly mathematical, path to a solution. If your math skills are a little rusty, group study can be a good time to brush them up.
The third problem is less frightening but more insidious than the first two. It certainly claims the most points. When you understand an equation well enough to see that it applies to your problem, but don't really know what it means or where it came from, you produce a solution that graders politely refer to as 'creative'. This is one of the best reasons to check that you can explain the fundamentals of the course to a fellow student without breaking out any math. This is the reason, when studying, to break each equation into parts and make sure you know what each part is and what it means. This is why every problem should start with a concept, not just an equation. For example: If you know that the voltage around a moving loop is vlB but don't know why or when, you have no idea what length to use and have restricted your knowledge of moving wires to linearly translating loops entering magnetic fields (although you probably don't know that). V=vlB is an equation, Faraday's Law is a concept. The moving wire problem should start with Faraday's Law. The cure to Problem 3 is a combination of the cures to the first two problems. Working problems from their fundamentals will bring out those things that you don't quite understand fully. At that point, it's important not to be afraid of asking about a concept that you thought you had down. In a group, that means asking why the group did what it did. Alone, that means finding a friend or asking a TA. (When you e-mail a TA, remember to tell us what problem you are working on and what you've already done.) Some of you have asked about good problems to study. Obviously old midterm and practice midterms are good. It helps that you have the solution key. But you've seen them before, so they may not build your confidence about fresh problems. Problems from <textbook> are also good, but you don't necessarily have the solutions and they tend to be easier than exam problems. I assume <Head TA> will post practice finals on <course management website>. Those are probably the best material.
I think that covers most of the issues i promised to address. Again, let me know if i've left out something you asked me. Actually, feel free to bring any problems i haven't covered, but hopefully this gets most of them.
Ben
