Physics Course Survival Strategies
By Donald E. Simanek
Students taking their first physics course often come with study habits that have, perhaps, served them adequately for good grades in other courses, but are inadequate and counterproductive in physics. Habits are hard to break, but once one realizes why certain habits don't work, one may be motivated to try a new way.
The special challenges
Introductory physics courses have a reputation among students of being more difficult than other introductory science courses. This may be because success in physics courses requires a different approach, attitude and perspective than other science courses. This requires some adjustment. Cramming, memorization of facts and blindly following rules and recipes are never sufficient for success in physics. Ideally no course should allow students to succeed by these methods, but it's not an ideal world.
Compared to other introductory science courses, physics uses mathematics more intensively, and has far more and stronger internal logical connections and unifying principles. Physics builds on a few fundamental principles, laws and theories that lead to and link together a wide range of physical phenomena. You have surely taken courses that were little more than a collection of facts and descriptions of processes and phenomena, with only vague hints of the underlying physical processes. In a physics course, the focus is on these processes and logical connections, and far less on mere facts and descriptions.
Focusing on the wrong things.
Three components of a physics course must be put into balance: textbook, lectures and homework problems. A fourth component, laboratory, will not be discussed in this document.
In most physics courses the textbook is the most important learning tool. We assume, of course, that your instructor has chosen one of the many very good textbooks available, perhaps one that has undergone extensive testing and critical review, and perhaps has been revised continually through several successful editions. The authors and publisher have taken great pains to organize the material for accuracy, logical structure, ease of reading, and pedagogical effectiveness. Yet many students ignore the textbook, and some don't read it, and some don't even buy it. I had a student once who came to me near the end of the first semester, asking whether I thought she could get a refund on her textbook. The reason was that she has just discovered that one whole "signature" of the book had blank pages, about at chapter two. It took her the entire semester to discover that fact, for she had never opened the book before. This is certainly something you should not do.
Other students read the textbook only as a last resort, hoping that the professor will discuss the material in class, making reading of the textbook unnecessary. There is never enough time in class for that. The professor must be selective, and cannot cover everything in the textbook as fully and completely as the material deserves. Nor should the instructor be expected to use valuable class time to repeat what's adequately treated in the textbook. The professor's function is to give additional insights, provide a broader perspective, show different ways to do things, look at concepts, and respond to some student questions (those questions that are worthy of class time).
The professor can accomplish this best if the student reads the text material before the lecture, and already has a fairly good idea what the chapter is all about, and has a reasonable understanding of it.
Then there are students I call "grazers". They skim the textbook, or read only the chapter summaries. If that is all they do, they miss much of the content, and miss the logical development. Sometimes they skim only for the "boxed" or highlighted equations, ignoring the material explaining where these equations come from (experiment, or theory), their uses and limitations, the special conditions that are required for an equation to be valid. Seldom is the "equation in a box" enough to ensure it is used correctly. The surrounding context is all-important. So students need to pay attention to the text outside those boxes.
Most instructors assign end-of-chapter problems. Usually these are assigned, and due, before the material is discussed in class. There's a good reason for this. It can motivate students to read the chapter before class, for they must, to learn the material necessary for doing the problems. This also can motivate students to ask questions about basic physics they are having trouble understanding.
Any motivational tool can also have unwanted side effects. Some students immediately go to the assigned problems, then leaf back through the chapter to find what seems to be the information needed to do the problems, looking at nothing else in the chapter. But think about it. A typical textbook these days may have 40 to 100 problems at the end of each chapter. A selection of a few of them cannot cover all the material that's important in the chapter. The few problems assigned are necessarily a sampling of what you should be able to do, and not always a representative sampling. If you read only the material necessary to do the problems you will be missing much that is equally important. And you will be missing out on the broader implications and the meanings of the underlying physical principles.
Most books these days have sample problems, fully worked, with explanatory comments. Indeed, they are models for the style and content you should use when you do your own homework. But you should never treat these as "recipes" for solving certain "types" of problems, following the recipe as a cook follows a recipe for baking a pie. By the way, textbooks 50 years ago usually had no such example problems. If your book doesn't have enough sample problems, your college library probably has other books that do.
Usually the sample problems are inserted to illustrate material of the previous section of the chapter. You should never read the sample problem's solution without first trying to solve it by yourself. After all, it depends on the material you have just read, and if you understood that material, you may not need to see the sample solution. After you've done it yourself, then, and only then, compare your solution with the book's solution.
Books often have end-of-chapter summaries. Don't even read these until you have studied and mastered the chapter. Write your own summary, in your own words. Then compare it with the textbook summary, to test how well you have discerned what is important in the chapter.
Plug-and-chug and memorizing.
A common student approach to assigned problems is deplored and discouraged by most physics teachers. The student reads the problem, then looks for a boxed equation that seems to apply, "plugs" given values into the equation and does the math to "chug out an answer". The student may get the "right" answer without the brain being fully engaged, and therefore learn very little from the process. Teachers call this the "plug and chug" method, and strongly discourage students from doing it.
|It is better to know a few things, and know them very well, than to know a little about everything but not much about anything.|
Some students try to memorize all the patterns of sample problems, hoping that similar problems (but with different values) will be on the exams. Then it is just "plug-and-chug" again to grind out an answer. Teachers know that such methods result in very little learning of physics concepts, and many or us try very hard to structure exams so that such tactics will fail, thus convincing students that they should not waste their time on this superficial strategy.
It's partly a matter of focusing on the right thing. Students often think that the only important thing is getting the "right" answer. Professors, of course, like "right" answers (they make paper-grading easier), but they want students to focus on the process of using basic principles of physics to correctly analyze some physical situation intelligently, to squeeze from it all the insight one can possibly reveal. Physics teachers want students to learn the basic principles so that they can apply them effectively to a problem, even if that problem is unlike any problem they have seen before.
Memorization is discouraged. If you find yourself having to memorize basic equations and principles, you are in real trouble. Of course, some things, like fundamental constants, aren't likely to stick in your mind, and must be looked up in tables when needed. Such a table is usually provided for that kind of information needed on exams.
The order of the planets in the solar system has no logical basis, and is not likely to be remembered without memorization. But are such things important to your understanding planetary physics? Of course not. Niether are the names of the constellations of fundamental importance. Any exam testing for understanding will not include questions about such trivial facts.
But things you use repeatedly, and things that are used frequently in class and textbook, and are reinforced by practice, will naturally stick in your mind. Of course, if you don't pay attention when they are used, and don't use them yourself, they will not imprint on your mind. But in that case, you probably won't be familiar enough with them to use them correctly or effectively even if they were given to you.
Following recipes. You need to be able to follow a set of instructions correctly and intelligently. However, if you find yourself solving problems by following the pattern of an worked-example problem, you are indicating that you haven't yet grasped the basic principles. At this point you should redirect your attention from the problem to the principles. The problems on an exam are usually significantly different from the examples worked in class and in the textbook, yet they yield to the same strategies and principles.
Tutors. Schools these days often provide tutoring services, staffed by upper class or graduate majors in each discipline. These can be very helpful. But students too often pressure the tutors to "do the homework problems" for them. Instructors tell tutors not to do this for homework problems before their due date. But then students ask tutors to "Do a problem like this (assigned) one." Do you see the problem with this? It's the counter-productive "follow a recipe" habit again. Tutors should be asked basic questions that get at understanding of fundamental principles. Once the principles are understood properly, "doing the problems" seems almost a trivial afterthought.
Study guides. Most publishers these days sell study guides keyed to textbooks. They provide chapter summaries, hints, more sample problems, and perhaps solutions to selected end of chapter problems. Personally I think these are almost always a waste of paper. Oh, they are done well enough, but who has time to read all that stuff? If a student feels the need for them, then the student's grasp of the textbook material is weak. As one of my colleagues used to say, if that material in the study guide were really necessary for the course, it ought to have been in the textbook. Actually "studies have shown" that most of these study guides that are sold (at high prices) are not used, or are not useful, to the students who buy them. The textbook is usually quite sufficient for learning the essentials that you need to know for the course.
Study groups. Getting together with others in small study groups may be helpful. But not all benefit equally. Some are followers, some are leaders. Sometimes the leaders are the blind leading the blind. In my experience, small study groups of two or three are the most effective, if all participate and contribute fully. Just explaining something to someone else can help you organize and improve your own thinking and understanding, even if your understanding was a little shaky at first.
Time. You are probably taking several courses. You need to avoid spending so much time on one that you neglect the others. Most students spend too much time studying physics because they are not studying in the right way, or because they are studying in inefficient ways. The above warnings can help you restructure your efforts. Students often do not realize how much time they squander doing unproductive things. I find it interesting to read the time budgets students commonly made for themselves in previous centuries. One finds them handwritten on the inside covers of old textbooks, or on a handwritten sheet in the textbook. These would include a detailed breakdown of each hour of the day and each day of the week, allocating specific time slots to study math, physics, rhetoric, history, and even scheduling meals and recreation. In one case I read, the student allowed a whole hour after dinner "for doing whatever catches my fancy, taking a leisurely walk, talking with friends, playing a musical instrument, or just thinking about nothing in particular." Everyone should include such an hour. I am told by historians that the best students really did follow the schedules.
Exceptions to the rules.
While the above advice is good for most students, every so often exceptions are seen. I usually tell students that they should read the entire exam before doing any of the questions, and then first do the shortest and easiest ones and the ones they are very confident of. Yet once I had a student who never followed that advice. He did the questions in order, not even turning the page till he'd finished the first one. He wrote his answers and problem solutions with a fountain pen, seldom having to neatly line out an error. Finishing in about half the allotted time, he'd spend about five minutes checking his work, but never found anything in need of correction. Then he handed in the exam and left while all other students were still working. He'd always get 100% on every exam he took from me.
I tell students that doing homework problems is useful for testing one's understanding, so I generally give some credit for homework in the final grades, say 10 or 15% to encourage that. One student never handed in homework the entire semester, yet he scored about 98% on his exams, and therefore got an "A". I asked him afterwards why he didn't hand in homework, for he certainly was able to do it. His answer: "I budget my time. I spent all of the time learning the physics, and didn't have time left to do problems." Obviously he didn't need to do problems to learn the physics, and was so confident in his knowledge that he didn't even need to put it to the test before the exams. But he was demonstrating an important principle. If you study the material, learn it well, and understand it, you can then solve the prolems with ease. Trying to solve problems before you achieve understanding is the wrong way to learn physics.
Another student was just the opposite. I tell students they should "be able" to do any of the end-of chapter "homework" problems, even if they were not assigned. Most students don't follow my advice. But one student not only did all the problems at the end of chapter, but asked me for suggestions where he could find additional problems more challenging to hone his skills.
One student told me he never read the chapter first, but read the chapter summaries. Then, still without looking at the chapter text, he'd expand these summaries into text in his own words, with explanations, and full derivations where necessary. Then he would read the chapter to see how well he had done. It worked for him. It's no surprise he went on to be a college professor, and wrote several successful textbooks in his field.
Such students are rare.
Avoiding the pitfalls.
|You may not have to study more or, even study harder if you learn to study efficiently and effectively.|
Physics seeks to develop genuine understanding, and physics professors value that more than anything else; more even than "getting the right numeric answer". Don't get the wrong idea here. Correct answers are definitely important, but correct answers without broader understanding are not the objective of the course. If the student achieves genuine understanding of basic principles and laws, the process of grinding out answers becomes a relatively trivial footnote. But the ability to get right answers with ease is a good indication that understanding has been achieved. Understanding should come first. Successful working of problems strengthens that understanding.
|Ask yourself: Do you understand all you think you know about it?|
Here lies a trap. It's very easy for students to listen to lectures, read the textbook superficially, watch the professor work problems, read problem examples in textbooks, and say "That looks goodI get it." These may give only an "illusion of understanding". Students must continually put their understanding to the test.
Break unproductive and counter-productive habits of thinking.
Students come to a physics course with many habits that aren't helpful. Some of these arise from everyday modes of thinking about their experience with physics; some come from habits reinforced by high school physics courses. Here's a few examples:
- Using imprecise language. Careless language reflects and encourages careless thought. Strive to be complete and precise in your speaking, writing, and thinking.
- Using colloquial rather than technical meanings of words such as distance, position, acceleration, work, energy, force, cause, proof, hypothesis, etc. Learn the technical meanings precisely and use them carefully.
- Confusing mass and weight.
- Treating friction as a force, and other misconceptions about friction.
- Thinking that centrifugal force "pushes you against the car door when the car goes around a curve."
- Thinking that centrifugal force is another kind of force, to add to contact forces, gravitational forces, etc. It is actually just the net radial component of those other forces that act on a body.
- Thinking that "action equals reaction" means something physically profound. It is an empty slogan of no use in physics.
- Confusing force with work. They are different. Force is a vector, work is a scalar, for example.
- Confusing work with power. Power is the time rate of doing work.
- Falling back on using ordinary algebra when vector algebra is required.
- Using imprecise thinking about problems and failing to expose logical connections between ideas.
- Being satisfied with slogans, analogies, and particular examples rather than seeking deeper and broader understanding.
So how can a student achieve understanding?
- Question everything, including (especially) things that seem obvious. Ask yourself questions, and then try to find the answers to those questions.
- Never accept a "slogan" or crude analogy as a substitute for understanding.
- Insist on knowing where those boxed or highlighted equations come from. Experiment? Theory?
- Look for the logical/mathematical connections between equations, laws, theories and experiments.
- When results are developed through a chain of logic or mathematics, do not be satisfied until you know the reason for every step of that chain.
- Do the algebra first. Problems often have given numeric values. Do not substitute these values until you have worked the problem algebraically. The algebraic solution gives you more insight than mere numbers.
- Never be satisfied with obtaining a correct answer. Ask yourself what that answer tells you. Question whether it is reasonable by considering your experience, and even by doing some independent checks.
- Consider whether an answer can be obtained by another independent method. Do it. Do the results agree?
- After doing a problem or example, ask yourself what would be different if the given conditions of the problem were changed.
- Come to class with a good grasp of the material before the professor discusses it.
- Do about twice as many problems (for practice) than are assigned. Assigned problems are necessarily only a small sampling of what you should be able to do.
- "Reading" is not the same as "studying". Studying involves continual engagement of the brain, questioning, analyzing, looking for logical connections, relating the material to previous study, and to previous experience. It requires continually asking questions such as "Why?", "How?", "What are the assumptions?", "What are the limitations?", "How can this be tested?", "What experiments support this, and how do they support it?".
- Take class notes in abbreviated form, so the process of note taking does not interfere with active and critical listening. Don't attempt to write out full sentences, or every mathematical step of a derivation. You can fill those in later when you revise your notes.
- Expand and rewrite your notes as soon after class as possible. A typical lecture will expand to several pages.
- Every so often, at the completion of each topic or chapter, write your own summary of what was learned, including the essential and important parts. These summaries will serve you well as study aids when you prepare for exams.
- Well-organized notes, assignments and summaries are indicators of organized thinking. In fact, educational research has shown that the process of writing notes and summaries in organized fashion actually improves your thinking, and helps you become a more organized thinker. The hand-eye-brain coordination of writing down ideas reinforces those ideas greatly.
These are techniques used by successful students.
So how can a student know when understanding has been achieved?
- If you can do an end-of-chapter problem in about ten minutes after reading the chapter, but without looking up anything in the textbook and without too many false starts.
- If your notes and summaries are good enough and clear enough that they are sufficient to prepare for the exam, again without looking at the textbook.
- If you can quickly spot and correct errors, blunders or deficiencies in your own work, in the class lectures, and even in the textbook.
- If you can prepare for an exam in a couple of hours of review and feel confident that you are ready for anything that might be on the exam. (And after this brief review, get a good night's sleep before the exam.)
- If you are familiar enough with the material (from actual thinking about it) that the important and necessary things stick in your mind without conscious effort to memorize or cram.
© 1999, 2004 by Donald E. Simanek. Permission is granted for non-commercial non-profit uses. Einstein picture © 2001 by John Holden.
Other resources with advice on how to study effectively.
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