HOW TO STUDY SCIENCE:
SOME SUGGESTIONS AND THE PSYCHOLOGICAL REASONS FOR THEM

SUMMARY:

1. Stir up your curiosity to know things before you read and study.
2. Organize your time in frequent short sessions.
3. As you begin to study, review what you studied in earlier sessions for 3 to 5 minutes.
4. For 10 to 15 minutes just read ahead of the place that you will seriously study to get the general idea of what's coming.
5. Do both reading and studying in the same session.
6. Do self-testing.
7. Do a lot of rereading in order to make new and strange ideas familiar to you.
8. Compare the new definitions and principles to your existing preconceptions. Notice if you have had any mistaken ideas and correct them.
9. As you read new information, think about how it fits into the categories and big problems that the scientific field uses.
10. When reading, choose a slow enough speed that you get the meanings of the words.
11. When reading, translate words and symbols into pictures, other words, feelings.
12. When you study new concepts, learn them 3 ways: the technical definition, the procedures to follow to identify an instance of the concept, and important examples.
13. When you cannot understand a section, find another source to read on the same topic.
14. When you study, practice discriminating between similar concepts.
15. When you study, practice generalizing new concepts and principles to new situations.
16. When you memorize, use prototype examples of concepts.
17. When you've learned to do a type of problem, make up an easy prototype problem and solution and learn it.
18. When you memorize, use both natural memorizing and a mnemonic method like the keyword method.
19. When you memorize many things, build up sets of memorized concepts one-by-one.
20. When you get stuck in studying hard topics or solving hard problems, MOVE and BREATHE.
21. When you get stuck, slow down, check your work, write more on paper, write neater, write in more organized ways.
22. When you get stuck on problems, give your mind the order to search your memory or your book for general principles that apply. Look away from the problem itself.
23. When you get stuck on problems, look for the specific features of the problem that give clues about what type of procedure to use.

Introduction:

You can do any job in different ways. But using different ways will affect your results: they will work quickly or slowly, be effective or ineffective, and lead to long-lasting results or quickly fading results. It's the same when you try to study science. You can use different methods of studying, practicing and memorizing, but they don't all cause rapid long-lasting learning. What methods work best? Some answers are known. By now psychologists have studied learning and memory long enough to know what works well. This article tells you some of what they say.

Stir Up Curiosity Before You Study

You can increase the amount you learn from a study session by arousing your curiosity to know and learn the material. Try to feel a desire to know the facts and theories that you will study. Do not read with your spirit dead and with just a passive sense of duty.

Why does curiosity increase the amount you learn? Psychologists have discovered that what people really want during the time they do something will influence what actually do. When you read and study, if you strongly want to know something, then your mind will actually be faster to notice ideas that satisfy your goal. If you feel curious about an upcoming topic and can think "I'd like to know about that", then you are likely to spot the relevant facts and theories and not miss them. Also your curiosity will lead you to associate the answers to questions in your mind and build the kind of mental links that cause good memory.
However, if you merely do your homework because it has to be done, you learn less. Your passive motives do not lead you to notice what is important because you have not asked yourself to look for it. Neither will you associate new information to other information because you haven't asked questions that the new stuff can link up with.

Curiosity is a positive, life-affirming motive. You will get pleasure when you learn knowledge that satisfies your desire to know.

If you understand that you can increase your learning by feeling curious, it is natural to wonder next how you can arouse your curiosity voluntarily. And how can you arouse it at times when you do not have any natural curiosity about a topic?

Here is how I stirred up curiosity once. A few weeks ago I was about to read a biology chapter on organic chemistry and noticed that I was making negative pictures to myself about those boring complex molecules. I was able to arouse my curiosity in two natural ways: First, I associated organic molecules to the fact that when younger I had stopped studying chemistry before I got to organic chemistry. I had heard that organic was hard, was the "real thing", and was the basis of medicine. So I thought, "Now I have a chance to find out in a short chapter what it's all about." Second, I knew that my daughter, who expects to study a lot of chemistry and biology, will study this. I could easily feel curious about getting a taste of knowing what she will know. Those two thoughts quickly got me wanting to know about organic chemistry and I read the material feeling curious and alert.

I suggest you do this: First, look over the material so that you know what topics you will study. Next, think of what you really are curious to know. Thinking of the upcoming topics, ask yourself if they remind you of any things you are naturally curious to know about. If so, you're in luck. Finally, take those natural curiosities and think of ways that this upcoming science material can help satisfy your pre-existing desires to know. The science is the means; the pre-existing curiosity is the end. Say to yourself, "I wonder...."

Remember: if you get curious and interested about a subject, you will actually remember it better than if you read it like a drudge.

How to Organize Your Time: Use the "distributed study method".

If you distribute your study time on a topic over several short sessions, you will require less time to learn it than if you study the topic in one or two long sessions. With this method you study your science frequently and you use reasonably short sessions. You also study and review the same topics several times. By using several frequent sessions (a few minutes up to one hour long), you can learn more material and remember it longer than if you study in a few sessions 3 or 4 hours long that are separated a few days apart.

DON'T study your text just once or twice a week in long study sessions. You should avoid letting gaps of time more than 2 or 3 days separate your sessions.

Can you believe this claim about distributed study? I believe so because psychologists have experimented many times trying to find out what method works best. Repeatedly, they have found that the people who study in short frequent sessions learn information in less total time. And their gain in efficiency is a big one, not a little one.

Why do short frequent sessions work? First, they fight forgetting. After each study session, you start forgetting. The more time goes by after studying a topic, the more your memory fades. But if you review material, after a short gap of time like a few hours or a day, you still remember a lot of it. Your act of reviewing revives your memory and makes it much stronger. In contrast, people who don't study often and who leave big gaps between their study sessions forget a lot between sessions. So they have to relearn information that they have almost forgotten. That wastes time.

Second, short frequent sessions work well because your repeated studying of the same material clears up confusions. In the short gaps between study times, your conscious mind rests, but your unconscious mind works and makes interconnections among the ideas. But people who study in long sessions don't get that advantage.

Third, psychologists find that the factor that determines the strength of learning is the number of contacts you make with a topic. The more contacts, the more memory. One long contact with a topic is not as good as several shorter contacts that are separated.

For these reasons, I recommend that you study science by using short sessions several days a week.

WHAT TO DO DURING A STUDY SESSION:

1. Start by reviewing briefly.
    
   Start your study session by taking 3 to 5 minutes to review material that you have already studied. Look at your text or some recent class notes. If your text has chapter objectives, summaries, outlines, and vocabulary lists, review them. Also look at homework and any problems you did recently and remind yourself of the techniques you used. You don't need to reread every single word or problem, because when you look at some of the information, your brain will begin thinking of associations to other topics you studied before but haven't consciously reviewed today.
    
   DON'T start your day's work by jumping cold into a new chapter.
    
   What's the reason? You need to activate the memories that will be relevant to your study session. The brain builds memories by taking new information and associating it to familiar information that you have been currently thinking about. If you have not activated the old information by thinking about it recently, then you cannot expect the new information to link up with it. For example, if you start to read a new science chapter right after talking with a friend, your brain will try to associate the new science information to your friend and your talk. However, if you warm up your science memories by reviewing them for 3 to 5 minutes, then your brain will successfully link up the new science with the old science. That link up will improve your memory for both the new and old material. And your review can be short -- only 3 to 5 minutes.
    
2. Read ahead.
    
   During each study session include 10 to 15 minutes of reading ahead. I recommend that you set the goal to give yourself an overview, the big picture, of what the science book will be trying to teach you later. Try to just scan it, not read word for word, not study deeply. Choose material that you will normally get to in the next week or so. Scan it slowly enough to get the overall picture. But when you come to difficult material, don't force yourself to understand it. Just read on. Expect that your brain will start to work on it and will make it easier for you later when you seriously study it.
    
   DON'T study blind ahead into new material all the time.
    
   What's the reason? Perhaps you have heard the saying, "They can't see the woods for the trees." It describes people who are so fixated on details that they cannot see the larger pattern that the details add up to. When you read ahead in science, you will see the woods, see the larger patterns. And psychologists have proven that people who already know what the larger patterns are will learn the small details faster, understand them better, and remember them longer.
    
3. Both read and study.
    
   It is a good idea for you both to read and to study in the same session. First, read the current material normally. Second, study it, making an attempt to understand it and memorize it. If you also have science problems to do, then you should also study sample problems and do problems on the material you studied. Try to do some problems on the same day that you study the principles. (It is, of course, okay to start problems one day, leave them unfinished, and then the next day to review the text and to finish the problems. That is very desirable. It fits the principle of distributing your studying over several sessions.)
    
   DON'T start to do homework problems in a session where you have not studied the material. DON'T read and study and go away without trying to do some problems.
    
   What's the reason? If you have forgotten the overall patterns of ideas that organize the details, you will see specific details as meaningless. It is harder to slowly study the details of complicated material. So if you can arrange your study time to both read for understanding and study for memory in the same session, you will improve your memory. When you have to study the details on a day or so later than when you read for understanding, then you will speed your learning if you prepare for studying by doing a gentle fast review. It will revive your understanding of the big picture. Concerning science problems: you can't succeed in doing them unless you can mentally associate new science principles with the actual problem-solving methods. The way to associate two things is to link them together in your mind. Any bad study method that interferes with you linking principles and methods and problems will hurt your learning. So you should both study a topic and do the problems during the same session.
    
4. Test yourself.
    
   During a study session you should test yourself and observe the feedback. This is one of the most powerful techniques of studying available. Whenever you learn something, try to test yourself to see if you know it. Try to do it, notice the results, compare them to what's right and wrong, plan a correction, and try again. One method of self-testing is to do problems. Another method is to study a principle and look away and check whether you can say it. Another method is to watch the logic that your science book uses when it explains something and to check whether you understand every single reason.
    
   DON'T read material and be uncertain whether you understand it.
   DON'T make a careless blind stab at problems and omit checking how right your work is.
    
   What's the reason? The major way humans can learn a mental skill in science is to practice the skill and to get feedback that says they did it right or wrong. When people test themselves and notice feedback, they notice what's right and resolve to repeat it. When they get something wrong, they notice it, sense a mismatch between what the result should be and what the result is, and their brains automatically get alert. Our brains are wired to learn by noticing changes, differences, discrepancies. Therefore, test yourself and make corrections.
    
5. Read new strange material several times.
    
   You should read and reread science material that seems unfamiliar and new to you. Your repeated readings will help it make sense to you. The first time you see and think about new material will often leave you confused. The second time you read it will cause you to notice some patterns in it and make some strange things make sense. The third time you read it will often seem friendly and familiar.
    
   Be sure that you let some time pass between your readings. Why? While the time passes, your unconscious mind is building associations.
    
   Don't plunge into studying and memorizing material that seems foreign, strange, and senseless to you. If you do try to memorize ideas that seem senseless, it will take you longer than if you reread it over a period of a few days until it falls into place.
    
6. As you read and think, compare new facts and principles to what you thought you already knew. Correct your false ideas.
    
   While you read new scientific findings, you should compare them to what you believe already about the field. Sometimes you will have mistaken ideas, and you need to notice them and correct them. If you deliberately notice how the scientists have different ideas than you do, you will be able to drop your old false ideas off. But if you read carelessly, you may let a few hours or days go by and let your mind revert to its familiar wrong ideas. Then you'll make mistakes on problems and tests.
    
   This problem of students having misconceptions is common in science courses. For example, often when students study the physics' concept of momentum, they can't learn it because their everyday ideas interfere with learning the truth. The same thing happens when they study dozens of other concepts.
    
   The cure: Notice how the new idea compares to what you thought. Correct it.
    
7. As you read, think how the new information links to the categories and big problems that scientists work on.
    
   If you take any particular fact and link it to a general idea that it is part of, your mind will remember it better. For example, if you read about a specific acid and then think how it is similar to and how different from the general family of acids it belongs to, your memory improves. You have made a link. Easily. Just a few seconds to think as you pause while reading will do it.
    
   This trick of linking facts to general problems and categories is what makes some science writers write well. Many don't. The good ones will constantly tell you the significance of information. The poor ones just tell you the information, and it sits there in a dull lump. The method used by the good writers to make information significant is one you can use on almost any science book. If you use it, it will improve your understanding and your memory.
    
   How can you know what categories and problems to link ideas to? You will partly be able to figure it out as you study the subject. For example, in biology you will notice that you should link biological structures to the functions they perform. You will think in terms of evolution and of "levels" from the molecular up to big ecosystems. In physics and chemistry, too, there are clusters of overarching ideas.

There are also some more general categories that you can use to link ideas to. Look at the list below which comes from the broad concerns of scientists.
 
* If they see something, they wonder about its causes. (Explanation.)
* If they see something, they wonder about its effects. (Prediction.)
* If they see something, they wonder what its traits are. (Description.)
* If they see something, they wonder what its parts are. (Analysis.)
* If they see something, they wonder what larger wholes it fits into. (Synthesis.)

Good writers, as they write, will focus your attention on big intellectual questions that revolve around the causes, effects, traits, parts, and larger wholes of natural happenings. You will read information and naturally classify it as an answer to one of these questions. You will find yourself understanding the significance of the information because you have classified it--with the author's help.

Now if the author does not help you, you can help yourself if you know how to spot causes and effects and wholes and parts. So here is the recommendation: train yourself to classify what you read into these categories.

Unfortunately, there is a difficulty with what I said. Besides these categories, there are others. When you take physics, there will be somewhat different categories and concerns than when you take biology. And geology differs from chemistry. In fact, each science has some unique concerns. For example, biologists are interested in living things. They are always trying to explain how organisms take in food and excrete, how they grow, how they reproduce, how they move, how they adapt to environments, how their structures (parts) get shaped to perform their functions efficiently. Yes, you will still study causes and effects. But you will learn so much more biology when you focus on these additional specific categories. Similarly with physics and chemistry and geology.

I strongly recommend that you try to figure out the unique categories and the unique intellectual problems that each science tries to explain. How can you find out? Ask your teacher. Check your book's table of contents for the major topics. Read between the lines. Look for repeated topics and questions.

Then once you've got these categories, try to read each new chunk of a chapter and classify the information. When you warm up your mind for a study session, tell yourself to notice these categories. This is another example of the fact that people who see the big picture can learn the details better and faster. When you can think in terms of the secret inner core of concepts that professional scientists use, you will automatically understand the subject better. Look for these big ideas. I promise you: they are there.

HOW TO READ SCIENCE BOOKS

This section of advice applies to the times that you read and study your science book. It is designed to increase your understanding and to prevent mistakes.

1. Read slowly and understand.

Choose a speed of reading that is slow enough for your brain to get the meaning of all the words, symbols, phrases and sentences. This advice comes from a cognitive psychologist. You need to have "adaptive control of your reading rate." You need to adjust your reading speed to how hard the material is. Read fast for easy familiar material. Read slowly for hard, dense new material.

DON'T read fast and merely "get the general idea".

What's the reason? I have to explain a little bit of psychology. When you make your eyes look at print on a page, then information goes to your brain to process. Your brain notices whether the words are familiar or unfamiliar, and it looks up the meaning of the words and phrases. The first signal your brain sends to your consciousness tells you whether you recognize the words as familiar. That signal comes about 200 milli-seconds, or about one-fifth of a second, after your eye sees words. A little later your brain looks up the meaning of the words and sends you a signal containing the meaning of the words. That second signal comes about 400 milli-seconds, or about two-fifths of a second, after seeing words.

So when you read fast, you often miss the second signal with the meaning and catch only the first signal that tells you that these are familiar words. Sometimes, if you're careless, you will be fooled into thinking you understand what you are reading. And at the time when you should be noticing the second signal of meaning, you have read so fast that you are by then reading new words and phrases and therefore are not noticing the meaning of the earlier ones. That situation gives you the false belief that you're understanding a passage when you're not.

Science equations and principles that include short symbols and formulas can cause even good students to stumble, because such symbols look like short sentences. But they are about 10 times as full of meaning as an ordinary sentence! Although fast readers think they've got it, they have gone too fast to think of the meanings.

Your brain's speed of looking up the meanings of the words varies at different times of the day. Your speed also varies with how familiar or difficult the material is. You need to use your own good sense as to how fast to read. So choose a natural pace for your reading speed. Don't ever let a sense of hurry trick you into reading too fast to get meanings.

2. Think of pictures, sounds, feelings.

When you read a science book, translate the words and symbols into pictures, feelings, other words, and sounds. Translate them into what is familiar to you.

DON'T let your thinking stay just on the level of symbols, words, and rules. A common mistake is for students to work on science as if it were only meaningless symbols that they manipulate according to rules.

How do you do it? As you read slowly, give your mind the order to give you pictures of as many symbols and words as possible. Try to see images; even crude ones will help. Your brain can do it. Just ask it.

You can also think in terms of weight and forces and speed. When you read about little things, move your hand and fingers a tiny bit; when you read about big things, move them a lot. Think to yourself that this force is powerful, that object is moving fast or that object is light. And think in terms of physical feelings, as your hands or legs or body would feel. It makes a difference, because it activates the parts of your body that control movement and your brain understands your body movements very deeply. In chemistry you can sometimes work with chemicals and use taste and smell to help remember them.

To summarize, you should translate mere words into meaningful concepts that you can imagine yourself seeing, hearing, touching, tasting, or smelling.

3. When you study new concepts, learn them 3 ways.

When you try to understand and remember new technical concepts, try these three ways (all of them):

* Learn the technical definition.
* Learn the step-by-step procedures.
* Learn the key examples.

This is a bit hard to understand, so think about this example. Consider acceleration. It means to a physicist an object's rate of change of velocity with time. There are formulas that scientists use to calculate acceleration. (1) You would learn the technical definition. (2) You would study the steps you go through to figure out the acceleration of an object. (3) And you would study some key examples like objects thrown up in the air and dropping. You would learn this acceleration at the start, at the top, in the middle, etc. And you would study other examples like a person whirling an object on a string in a circle and like a pendulum. By knowing how to figure the acceleration quickly for key examples, you will save enormous amounts of time on new problems.

Research on learning proves that students who study new concepts in these three ways learn faster and remember longer. So watch your teacher, and if your teacher leaves out one of these 3 ways of understanding, ask for it.

4. Read other sources.

If you read some science material several times and cannot understand it, try to find the information in a different source. It is quite possible that your book's writer did a poor job of explaining the puzzling part. If you find a different writer who wrote better on that topic, you might understand it right away. This technique of studying science by using different books is often used by expert students. They find that they learn much faster and deeper by studying several different writers' explanations of the same topic. And has it occurred to you why your teachers are so knowing? They often prepare for their lectures by researching several books, too.

You can also take advantage of supplementary materials that most teachers can supply you with: posters, videotapes, audiotapes, handouts, etc. Ask other students or your teacher for an additional explanation.

HOW TO DISCRIMINATE AND GENERALIZE AND PROTECT YOUR MEMORY

There is more to studying than understanding and memorizing.
Set two more goals: to discriminate and to generalize.
To discriminate between two things is to see their differences.
To generalize from one thing to another means to see how the principle in the first thing can be applied to the next.

1. How to discriminate:

When you study a science text and it teaches you a series of concepts and methods to use, you will notice that a lot of them seem similar. Whenever you notice similar concepts that you might confuse, train yourself to discriminate between them. How do you do it? You should pick out the two places in the book or your class notes where the two new concepts are described and first look at one and then look at the other. Don't read the book passively; look directly from one similar topic to the other, letting your eyes skip over any material in between the similar topics. Deliberately notice the ways they are similar and different. Practice and test yourself until you've got them distinguished. Then you should mark them and should plan to review them in your next study period to prevent forgetting. It is important to do this because some writers don't do it for you.

2. How to generalize:

When you first learn a principle or method, you will study the textbook's examples. But later when you take a test or need the knowledge in real life, you will see unfamiliar examples and will need to remember and use the principles on new unfamiliar examples. Therefore, add the study method of imagining new examples of concepts and principles. Imagine things as bigger or smaller, in different shapes, in different colors. Imagine how a principle applies to different organisms, different environments. Imagine seeing a just-learned technique concealed in a problem that looks different. Think of how a new fact can be connected with others. When you later do the homework problems, continue to think about generalizing and notice the kinds of problems that the textbook writers give you that use that principle. All of these things will help you generalize. They will protect you from seeing a new situation and not recognizing how a principle applies to it.

Why discriminate and generalize? First, it will help you on tests. Most teachers build a major part of their tests around similar concepts that students confuse: that is discrimination. And they use new examples to ask questions about concepts and principles: that's generalization. So if you learn discriminations and generalizations while you study, you will prepare yourself to handle test questions. Second, you can save study time needed for memorizing if you discriminate and generalize. Anything you do that helps you link concepts to one another increases your memory. Third, it will help you in real life because of all the new examples you will encounter.

HOW TO LEARN NEW CONCEPTS, WORDS, SCIENTIFIC SYMBOLS, AND FORMULAS

1. Read first for understanding.
You should first read a chapter or a section through so that you read the new words in their natural context. Don't worry about memory at this point. Your objective at first is to build your overall general understanding of the subject. Later when you start studying the chapter, then you should memorize the words.

When you are ready to memorize things, you will find that some concepts are easy and others are hard. Sometimes you can think about words and symbols and definitions and examples for a half minute or so and know immediately that you will remember them. If so, don't use any fancy methods. Just memorize them simply. If you cannot remember easily by looking and reciting and self-testing, then you should consider using mnemonic techniques. Especially useful for students learning new concepts is the "keyword method". It's a little too complex to describe here. If you are interested in this good memory technique, get Study Tip #2 at the LCC Testing Office. Another useful mnemonic is the "link", and Study Tip #3 describes it.

The last step is to test your memory. The way to test yourself is to look away from the book, ask yourself a question, recite the answer, look back to compare your answer with the real thing, plan a correction and try again. When you have it right two or three times, move on.

(Here is an example of a question that states the definition and asks for the concept: "What is the name of chemicals that have an amino group and a carboxyl group?" Answer: "Amino acids." Here is an example of a question that states the concept and asks for the definition: "What is a polypeptide?" Answer: "A chain of amino acids longer than two amino acid units.")

2. Memorize prototype examples.
When you want to memorize a concept, make yourself a prototype example, a typical example of the concept. For example, a prototype of a bird is a robin, a prototype of furniture is a table, a prototype of a mammal is a cow. In each case the prototype fits the definition. It is a normal example, not an unusual example. You use a prototype to make a visual image or a story image to add to the associations you are making to the concept. When you need to recall the idea later, you can ask yourself to recall the prototype example first. Then you inspect the example and its features and it helps you recall its definition.

3. Memorize prototype problems.
Suppose you are learning to solve a certain kind of problem and you have finally learned how to do it, and it requires a fairly complicated procedure. You will recall it later better when you make and memorize an easy "prototype problem and solution." A prototype is a general example. It stands for lots of examples, even though it isn't exactly similar to any one of them. For example, one math teacher taught students how to remember to do percentages by having them memorize, "10% of 50 = 5". It's an easy percentage problem, and if any part were missing, students could use simple algebra to solve it. Then when they worked on complicated percentage problems that had big numbers (like this: "37 is what percent of 152?"), they went back to their example, figured out how to do it, and then copied that method on more complex problems (X% of 152 = 37.)

DON'T just study examples and learn the principle but carelessly let yourself forget all the simple examples.

What's the reason? People can usually remember a specific example better than the abstract rules. They can remember and copy easy worked-out problems better than general procedures. There's something simple about a specific worked-out problem that people's brains can grasp easily. It increases memory. It rescues you from seeing complicated problems and losing your way.

4. Memorize facts in sets. Build them up one by one.
When you need to learn many new concepts and facts and principles, you will face the problem of overload--too much to learn at once. Confusion. You can cope with overload by using the method of building a set of new terms one-by-one.

Here is how to learn by the method of one-by-one addition of new concepts to a set. First, pick one item. Learn it. It doesn't matter whether you use a mnemonic or the link or repetition and self-testing. Just get to the point where you have learned it. I don't mean sloppy learning, but the ability to accurately state the definition or fact or principle or what-have-you.

After learning the first, leave it and pick a second concept and learn it. Really learn it. Then return to the first and test yourself and go to the second and test yourself. Keep working until you can accurately remember both together.

Then leave them and take a third concept. Learn the third alone. Then test yourself on the first and second concepts and now the third again. Work until you've mastered all three. Then add a fourth using the same procedure, then a fifth, then a sixth and so on.

Build a set of 10 or 15 related items. Start a new set if you switch topics or if a set of somewhat unrelated items gets too big to work with.

I really recommend this method because it makes your learning controllable, it conquers the problem of too many new facts interfering with each other, and it makes it easier to discriminate among similar concepts. You can expect to get big gains in memory power right away. And after you practice this method, the gains get even better.

WHAT TO DO WHEN SCIENCE PROBLEMS ARE DIFFICULT

1. When you've been working on a problem and are getting stuck, the advice is simple. Move. Breathe.
I mean, move your body, breathe deeply in and out, and move your thoughts. For example, wiggle, look out the window. Think of circusses and warm spring days. Think of anything else. Then look back at the material and try again.

DON'T stare fixedly at a problem that blocks you.

What's the reason? If you stare at a problem, you keep thinking the same thoughts that got you stuck. When you are stuck, your conscious mind does not know what to do. Therefore, you need to help your conscious mind by letting in other thoughts that are presently in your deep memory. So you need to detach your conscious mind temporarily from thinking again about the problem in the exact same way that got you stuck. That's why you move, breathe, and think about something else.

2. When stuck on a problem, you can also use the technique of transferring all the steps out of your brain and onto paper.

* Slow down.
* Check your work.
* Write down more on paper.
* Write neater.
* Write in more organized ways with numbers neatly in rows.

One of our math instructors told me, "I'm like most students when I start a problem: I work fast to see if I can get it. But when I can't get it right, I act differently. I treat being stuck as a signal to slow down and organize everything."

DON'T keep working fast when you are stuck.

What's the reason? When a person's mind works fast, the person cannot easily see little mistakes and catch wrong assumptions. It's hard to check your work when you do a lot of it in your head. The purpose of this advice that you slow down and be neater is to give you the information that will let you catch errors and do the problem's steps correctly.

3. When you have gotten stuck by looking at a problem and trying to think of the principles it reminds you of, do this:

Give your mind the order to search your memory for more of the relevant scientific principles and methods that you have available to use on a certain problem. If you have your book nearby, you should physically flip the pages looking for your available resources. For example, I once spent two hours agonizing over a simple problem using logarithms merely because I was trying to use two of the major principles and forgetting there was a third one. If, however, I had ordered my mind to think of all the principles that I know about logarithms, I would have remembered the third one and solved the problem quickly.

DON'T just stare at a problem. Don't just accept the methods that your mind gives you that instant.

What's the reason? Very often people see a problem and passively let the features of the problem remind them of a principles or method to use. If by accident they don't think of the right methods, they are stuck. If, however, they have a way to mentally review all the relevant principles that they have available, they can get unstuck. Such a mental check of principles frees your brain from being caught by strong connections between a certain problem's facts and principles.

4. Try to find the specific features of a problem that signal you which techniques you can use to solve it.

Some experts on teaching math have stated that many students who know how to use techniques do not recognize when to use the techniques. Students need to be able to see the distinguishing features of different kinds of problems and to use them to make themselves think of the techniques that work.

Here's another way to do it: When you are in the middle of doing problems that give you easy clues to help you think of the technique to use, add this mental step: Say to yourself, "Because this problem has these characteristics (and list them), that tells me to use this principle (and say it)." If you do this several times, you will make easier for yourself several days later to see a disguised version of the problem, scan its characteristics, and think of right techniques.

I have in mind that on problem after problem, after you have successfully figured out how to solve it, you will take 5 extra seconds to notice the problems' specific features and notice the techniques that they signalled you to choose. That act of noticing helps you next time you do a similar problem.

Warning to the Reader

If you just read through this article once and put it away, you will inevitably forget most of it. You can't use forgotten techniques to improve your studying.

So don't you think it would be a good idea to save this article? Why not put it near your science books and notes? Next time you study a science book, haul out the article and look at it. Then deliberately choose 2 or 3 methods to use. After you get comfortable with doing them, then choose a few more and do them, too. Eventually, you will have experience with them all.

Finally, remember that you do not have to use all of these suggestions. I know that you may find something wrong with any one of them. So hang on to your good judgment and use only the suggestions that work to improve your studying.