There's a common difficulty that a lot of people have when studying physics—you practice a bunch of problems over and over again, and you get better at solving *those problems* or problems very similar to them, but those skills don't always transfer well to completely new types of problems; or you think you're understanding the material pretty well but then you feel utterly lost on the tests. I don't think there's really a one-size-fits-all solution to this, but I can offer a few general pieces of advice on "thinking like a physicist," or at least "thinking like a physics teacher":

• Study together! Talk about this stuff with others who are also studying it! Much of the best learning happens while talking about the subject—partly because other people with a different perspective might notice something you missed (and vice-versa), but mostly because the very act of putting your thoughts into words helps to organize them and forces you to explicitly pay attention to details you might not have considered. Also, this stuff *is* difficult to understand, and coming together to acknowledge that fact as a group can help build confidence and let you know you're not alone in the struggle. Science is a team activity!


• Look for connections: when you're working on a practice problem or studying a new idea or deriving a formula or whatever, you should be constantly asking yourself "How is this related to other ideas I've seen in this class? How does it follow from material I've seen in previous classes in this subject? How might it be applied in classes or research I'll see later? How is it similar to or different from material in other subjects entirely?" Finding those connections gives you a better understanding of that specific topic, strengthens your overall intuition of the subject, and often leads to insights that you might never have noticed by looking at the one topic in isolation.


• Investigate the practice problems more deeply: instead of just asking yourself "How do I find the answer to this problem?" try also asking yourself (or others!) "Why exactly was this problem assigned? What precisely am I supposed to be learning from it? Does it include 'stumbling blocks' that are supposed to challenge me in specific ways?"


• Try variations: once you've solved a problem one way, try approaching it from a completely different direction; maybe apply a different formula, or use a different coordinate system, or consider it from the perspective of a different branch of physics or mathematics altogether. Compare the answers (they should be the same) and the methods (they're different, but lead to the same answer—why is that?). Or try changing the problem itself—check what would happen if the numbers were different, or investigate how a result depends on a particular input variable, or consider what could be done if a certain variable's value were unknown but a different unknown had a known value. Whenever certain quantities are always positive, ask yourself what would "go wrong" (both mathematically and physically) if they were negative instead, or vice-versa.


• Draw graphs and diagrams for everything you possibly can: it's often easier to understand what's going on if you can visualize what's happening, and it can be a good way to organize the information as well. Even if it's something as simple as projectile motion, draw a couple of stick figures throwing a ball around or whatever and label every quantity that's important or might be important with a number or a variable.


• Seek out everyday applications: physics is, after all, the study of *gestures wildly at everything* all this stuff, so look for ways to apply it to your everyday life. If you're studying thermodynamics, observe water boiling on a stove or consider why a jacket helps you stay warm; if you're studying aerodynamics, watch birds taking off and landing; if you're studying kinematics, go bowling or play billiards; if you're studying magnetism, get some magnets and play with them. You don't necessarily even need to make and solve actual equations with actual numbers here—just get some hands-on experience and develop an intuition for the phenomenon, and start thinking conceptually about how your observations relate to the theory. Birds tend to fold their wings in a certain way when coming in for a landing; how does that manipulate the forces involved and why? How should a pot be shaped to allow the water to boil as quickly as possible? Why do certain moves in bowling work the way they do?


• Challenge yourself by making up absurd Fermi problems: whimsical questions for which you probably don't have enough information, but you could at least make up a list of what information you *would* need and an outline of how you would solve if you *did* have that information... and then make your best educated guess for that missing information. How much does the Great Pyramid weigh? If you had a stack of hundred-dollar bills as tall as the Salesforce Tower, could you buy enough bottled water to fill San Francisco Bay? What's the speed of the moon? How many piano tuners are there in Sacramento? You can find more good examples in John Allen Paulos's books "A Mathematician Reads the Newspaper" and "Innumeracy."


• Read about the history of physics and mathematics: either online, or seek out old textbooks or books about "the heroes of science" in a used bookstore. It's fascinating to learn about where these ideas came from in the first place and who figured them out, and you might find a lot of insight and inspiration in the way they addressed their problems.

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