Improving Memory, Comprehension, and Learning for Better Grades

These learning methods rely on basic brain mechanisms and learning principles.

^{=> For personal help and feedback, complete Dr. Stevens' free, online questionnaire which includes a major section assessing factors related to academic success and career success:  Click here to go to the Success and Happiness Attributes Questionnaire (SHAQ) webpage.}

Improve Comprehension and Memory for Better Grades

Tom G. Stevens PhD

What problems do you think might be interfering with your making top grades?
 

POSSIBLE PROBLEM  and  related COMMENTS

Intelligence (IQ) Are you smart enough? Even students with below average IQs have excelled in college if they do well on the other factors. Students who use poor learning methods often think that they are "slow" or have a learning disability.

Learning and study skills These learning to learn skills are crucial and the main subject of this self-help manual.

Specific background knowledge If you did not excel in previous courses that this course depends upon, then that can seriously affect your grades.

General motivation and time management If you lack the general motivation to make good grades, learn, and do well in college, then that may affect your grades. Similarly, having clear career goals, high achievement motivation, good work habits and time-management skills can help you improve.

Specific interest in the subject matter Students who are not committed to a college major usually are not as motivated as those who are committed. Find a major you want and make a commitment to it. If the course doesn't seem relevant to your college major or other major interests, then you may see no reason to learn the material. If that is a problem, find ways the course may be of use or interest to you. (See below.)

Negative motivational factors (anxiety, etc) It could be that the course or your grades are so important to you that you get a high degree of anxiety about performing well. That anxiety or other pressures may lead to avoiding the subject or to lack of concentration on exams, etc. Read below, but you may also benefit from counseling. Low self-esteem or low confidence in a subject area (such as math) may negatively affect motivation and performance as well. Again, counseling may help. See below for ways of increasing confidence in a subject matter.

For a self-assessment on many factors related to academic success and other life areas, go to my companion web site, http://www.csulb.edu/~tstevens/success and take the Success and Happiness Attributes Questionnaire (SHAQ).

If you go to any learning assistance center, you will find many useful materials that can teach you better study skills. I am not trying to duplicate those materials. Many of the students I have helped have already tried some of those study skill approaches, but still had problems comprehending difficult material (especially math, science, and engineering), problems with "test anxiety," or problems motivating themselves.

One difference between my approach and that of most study skill approaches is that I believe it is important to know more about the underlying principles of learning and motivation than these other approaches teach. Once you learn these, then you can analyze your own study problems and design new approaches that may vary from class to class.

After learning the basic principles, I will describe one specific approach to reading texts for comprehension and reviewing them for examinations. If you become confused while reading this manual, stop and figure it out until you clear up your confusion. Stop periodically to review what you have read, and do the simple practice exercises as a way of consolidation and applying what you have learned up to that point.
 

BORING, ROTE MEMORY METHODS AREN'T EFFECTIVE

What happens when you are highly involved in a conversation with a friend? Do you remember what your friend told you? Or do you have to take notes and "memorize" what they said to remember? You may need to take notes to remember highly detailed information--like an address, but chances are you will remember the most important points your friend told you.

Think of what happens when you see a movie that you get engrossed in. Do you have to force yourself to concentrate or use boring rote memory techniques to remember what was in the movie? Of course not; you concentrate and learn naturally, because your brain likes to concentrate and learn.
 

A primary purpose of your brain is to learn. You remember these points automatically, because a primary function of your brain is to learn. Just as your heart keeps beating and your lungs keep breathing because these are their primary purposes, so learning is a primary function of the brain and the brain is only happy when it is learning. It is not necessary to "try" to learn--all you need to do is focus your attention on something and your brain will learn something automatically.

The conclusion of decades of research on memory is that pure repetition and boring "rote" memory methods are very inefficient ways to learn and remember. Instead, involvement, comprehension, and integration into current knowledge is much more effective.
 

YOU HAVE A BUILT-IN SPEEDOMETER TO TELL YOU HOW FAST YOU ARE LEARNING

Think of a class in which you often felt bored. How much were you learning when you were feeling bored? Think of a class in which you became very confused. How much were you learning when you were feeling confused? Think of a class in which you became fascinated with the material and understood it well. How much were you learning when you enjoyed the learning experience?

Our emotions are a good measure of our involvement, understanding, learning, and memory. Boredom and confusion are signs of a low rate of comprehension and learning. Involvement, interest, and enjoyment are signs of a high rate of comprehension and learning. From now on you will know how to tell if you are learning at the maximum possible rate by tuning in to your emotions. If you are not fascinated with what you are learning, then you are learning at a less than optimal rate. The good news is that you can quit using any memory method that is boring. But if these old rote methods don't work, what does?
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YOU ARE RESPONSIBLE FOR YOUR OWN EMOTIONS AND LEARNING RATE

Who is responsible for your interest level, your happiness, and your learning? Is it your professor, the author of the book you are reading, or you? Many of us are tempted to blame our lack of interest (and all emotions) on outside forces. We say that our professor or book is "boring" or "confusing." Yet, how is it that some students found the same professor or book interesting and learned the material well enough to make A's? If you want to enjoy the class and learn as efficiently as those students, then you must learn those students' secrets. What were the mental states of those students who were successful?

Which of the following methods do you use (or think you should use)?

1. Force yourself to concentrate or study by willpower and discipline.
2. Learn how to memorize material better.
3. Rely upon help from other people (faculty, students, tutors) who can help you learn or do assignments.
4. Keep reviewing the same material over and over again.
5. Read every word and try to remember every detail.
6. Rewrite the material over and over again.
7. Use flash cards or have someone ask you the same questions over and over again.

While students may use all of these methods to learn-every method listed above has serious flaws that can drastically reduce your rate of learning, comprehension, and memory. Research has consistently shown that pure repetition is a very poor way to learn. Instead, research has consistently shown that the more meaningful associations you form with a new concept, the better you will comprehend it and remember it.

The key to maximum learning is not coercing yourself into learning, but becoming genuinely interested and involved in the learning. The key is to learn how to enjoy learning. Because, if you enjoy learning, you will be learning and remembering the material automatically and much more efficiently. But you--not your teacher or your book--is responsible for generating involvement and interest. No one can make you interested in something but you. You can learn how to control your own interest. Learning to take responsibility for your own interest and learning is one of the first steps you can take to get control over your learning and memory.

You may be doubting that you can ever get yourself interested in that "boring" math, English, or history class you can't stand. You may not be able to get yourself to the fascination level in some classes--yet. However, you can at least increase your interest level. After all, you're going to have to spend several hours a week in class or studying for that class, wouldn't you rather be enjoying those hours than spending them bored or confused? In addition, you will learn the material better and make better grades. What have you got to lose by learning methods for increasing your enjoyment and comprehension of the material?
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YOU CAN CHANGE HOW YOU FEEL ABOUT A SUBJECT

Do you think that you were just born to be interested in math or not? Or perhaps you think that you were just born without any ability in math or some other subject area. Do you think that you can't change your own interest level in a subject? Let's take math as an example (or some subject you dislike). Answer the following questions:

1. How well do you like math?
2. When did you start liking/disliking it?
3. What do you think made you like/dislike it in the first place?
4. Did you every change from disliking math to liking it (or vice-versa)?
5. What do you think caused you to change how you felt about it?

Compare your results to the results of hundreds of students whom I have polled. In general people who like math started with encouragement from others and/or good enough instruction so that they began doing well at math and feeling good about their abilities. They describe the assignments as "challenging." Students who don't like math usually started behind other students (perhaps because their parents didn't give them a head start). They usually describe their early math assignments too confusing or too hard. Perhaps parents, teachers, or other students made negative remarks about their math abilities or forced them to do math. Soon they thought of themselves as not having much math ability and that set a process of self-fulling prophesies going the rest of their lives.

However, some people who once hated math now love math. One man made mostly D's in math in high school and thought of himself as being very "dumb in math." Then in college he took a math class with an instructor who taught him well. Once he began to find math challenging instead of overwhelming, he began enjoying the class and doing well. He developed enough interest in math to take the next math class. Today that person who was so "dumb in math" has a PhD in engineering and teaches at a major university! So, whenever you find yourself assuming that you are "dumb" in some subject matter, remember this true story (and there are many more like it). You can change how you feel about almost anything! Return to Index

THE HARMONIOUS FUNCTIONING MODEL OF LEARNING--the key to understandingyour motivation

The harmonious functioning model explains how we come to like or dislike anything-including academic subjects. We can think of three basic mental states-overstimulation, understimulation, and optimal stimulation.

Optimal stimulation (harmonious functioning). Think of a time when you are really fascinated with something. It could be anything-a stimulating conversation, a song, dancing, reading about something you are fascinated with, watching a movie, playing a sport, or watching a beautiful sunset. During that time your thoughts are focused, they are in harmony, and it feels great. You feel challenged and "in the zone." You are in the zone of harmonious functioning.

As a result of this optimal stimulation you will tend to (1) perform at your best, (2) learn and remember everything about the situation, and (3) enjoy the experience. The probable long-term effects of harmonious functioning are that you (1) will increase your enjoyment of the activity and (2) increase your self-confidence in your abilities in the activity. People who spend a higher proportion of their lives in harmonious functioning tend to have higher self-esteem and better mental and physical health. So spending more of your life in harmonious functioning not only will increase your learning, memory, and grades, it can have additional benefits.

This sounds too good to be true. How can it be that high interest, high learning, high performance, high confidence, high happiness, and high health all go together? The basic reason is that your brain loves to learn. What have brains evolved to do better than anything else? Process information and control our actions. Through evolution the brain has developed basic motives to process information and learn efficiently. It doesn't like overwhelming or boring input situations. It loves to be optimally stimulated and optimally challenged.

I once had a student in an introductory psychology class who put his head down on his desk most of every class. I never saw him take a note. It used to irritate me that he appeared to nap in my class. When I graded the first exam I expected that he would do poorly. However, he had almost a perfect paper-the highest grade in the class. When I asked him how he did this he said that when I lectured, he would focus intently on what I said and try to understand it and relate it to other ideas he had or to situations in his life. His goal was to understand it well enough to be able to relate to it and use it. He would continue to struggle with ideas outside of class. He said that once he understood the material, he didn't forget it. He had learned how to get himself into the zone of harmonious functioning to maximize comprehension, learning, and memory. I am not suggesting that most students not take notes, but otherwise try to emulate his approach.

Overstimulation. Think of a time when you are feeling overwhelmed with too much input-especially in a class. The input may be overwhelming in one of several ways. There could be too much new information, it could be too complex, it could be too different from your current expectations or beliefs, it could be in an area you have a poor background in, or it could be emotionally overwhelming. In all of these cases, what makes it overwhelming is not the input itself. A calculus problem may be overwhelming to a student who doesn't even understand algebra, but boring for a math professor. The degree of challenge is related to the match between the input and the person's ability to process the input.

What happens when the input is too challenging for your abilities? The results are usually that you will (1) feel overwhelmed and confused, (2) not comprehend, learn, or remember the content very well, and (3) not perform well at whatever you are doing. The long-term results tend to be (1) disliking the activity more and (2) lower self-confidence in the activity. In addition, people who spend too much of their lives feeling overwhelmed, confused, and anxious tend to develop lower self-esteem and lower mental and physical health.

Understimulation. When people feel bored in a class, it is usually either (1) because the class was so new or difficult that they felt overwhelmed and tuned-out, (2) because they never engaged in the class in the first place, or (3) because the class was so easy that they never felt challenged enough. The last case is not such a problem, because the students obviously don't need to learn a lot, and if they want a high grade, they should be able to obtain it (since it is so easy). It is the first two cases that cause low learning, low grades, and dislike of the subject.

From now on, when you are feeling bored in a class, ask yourself which of these three causes is making you bored. If you are thinking thoughts like, "I don't like this class," "this stuff bores me," "I won't need this stuff," or "I'll never get this stuff," then you are probably overchallenged by the material and just rationalizing to yourself so that you won't have to put out the mental energy it takes to engage yourself in the material and learn it.

Another way students often tune-out is by blaming their problems of lack of interest on the professor or the textbook. If you find yourself blaming that "poor instructor" or "poor text" for your troubles, then you are turning yourself off. Even if the instructor or text is not up to par, consider the following:

Other students in the class are making A's and probably finding it interesting enough to tune-in and learn.

During the years that you are in college you will probably have several instructors or texts that really are below average. Will you choose to just tune-out, not learn much, and make poor grades? Or will you choose to try to stimulate your own interest, work hard, and make good grades? It's your choice. Using the ideas in this article, you can increase your interest and learning.

If you are bored and have disengaged in a class because it really is too easy for you, you may still be at risk of learning less than you need and making poor grades. Some students make their worst grades in their easiest classes! If this describes your situation, then it is still important that you find a way of arousing your interest and making it more challenging for yourself. Try raising your goals or try finding subtopics that catch your interest and putting extra thought or work into becoming more expert at them-perhaps for extra credit. Try helping other students or discussing finer points with the instructor. Imagine ways that you might need class-related material in your professional or personal life later. Invent a business or other scenario and challenging situations that force you to think in greater depth. Try creating your own overall theory or mental model of the subject matter. Compare it to the ones used in the class. How is yours better or worse?

To get an overview of these three mental states, study the harmonious functioning model figure below.

Practice: (1) Try to think of a class where you often felt very interested. What made you so interested? Consider this question in some detail. How well did you learn and remember material compared to classes in which you felt confused or bored? What were the effects of how well you liked the subject matter on your confidence in the subject matter?. Were there broader effects on your self-esteem or life?

(2) Think of a class where you often felt overwhelmed and confused. How well did you understand the material? What was your reaction? Did you avoid coping with it or tune out? Did you actively engage and finally master it?

(3) Think of a class where you often felt bored. Was it because it was difficult or unfamiliar and you tuned-out? Or was it truly because it was so easy that you were bored? Did you find some way to overcome your boredom and get engaged in the class? What worked?

Have you ever wondered if you have "test anxiety"? What is test anxiety? We all feel anxiety whenever we are uncertain about the outcome of something important to us. If you care about your grades and how well you do on tests, you will surely experience some "test anxiety." That is normal. A moderate amount might even help you get into the zone and perform better. Test anxiety is only a problem when it reaches a level that it interferes with performance.

Test anxiety is heightened by factors such as (1)the importance of the grade to you (including concerns with graduate school or job acceptance), (2) the difficulty or unpredictability of the test, (3) your abilities to cope with academic pressure situations, and (4) your confidence in your mastery of the test material. If one of the first three factors is a major issue that causes a repeated problem, then good psychological counseling should help. However, of all of the students who have been referred to me for "test anxiety," the overwhelming majority have had test anxiety because they know that they are confused about the material. Their anxiety is realistic because they know that they probably won't do well on the test because the know they don't understand the material well enough. So what is the solution to their "test anxiety"? Is it to take a medication for anxiety? No. It's to learn how to master the material. Then their "test anxiety"amazingly returns to normal levels.

OUR BRAIN AUTOMATICALLY CREATES TREES OF KNOWLEDGE

If the key to comprehension is clarifying confusion, how do we do that? However, before I can teach the methods for clarifying confusion, you must understand how your brain stores information. Let's start with a simple example I often use in my workshops. Do you know what a dog is? You may be thinking "Of course I do-what a dumb question." What I want you to do is to analyze your knowledge of what a dog is. First, I want you to notice that when I asked the question, you felt confident that you knew what a dog is. You felt confident because your brain knows that you know what a dog is. It is our goal that you eventually feel that confident about every important concept that will appear on your next test.

To do that we want you to have knowledge stored just like you have stored it about a dog. So let's examine your knowledge of what a dog is. First, what comes to mind when you think of the word "dog"? Most people see an image of a dog. If they own a dog, it is usually their dog that they imagine. What did you see? Examine your image more closely. Many people notice that their image includes sounds, smells, and emotions. Think of all the associations that you have with the concept "dog." You have had many real life experiences with dogs. You also know a lot about dogs and their behavior. That is why you get a confident feeling when asked if you know what a dog is. In order to get that same feeling with classroom concepts, you must form similar sets of associations.

The animal knowledge hierarchy. There is very strong research evidence that your brain stores information in some sort of "knowledge hierarchy" (or "knowledge tree"). Understanding that knowledge hierarchy can help you develop more effective learning strategies. The bottom of the hierarchy consists of more concrete/sensory-motor information and the top consists of very abstract, comprehensive information. Usually there are many more concrete concepts in the hierarchy than there are very abstract concepts.

As an example, let's return to your knowledge of dogs. Your knowledge of dogs probably started as a child when you saw your first real dogs or saw pictures of dogs. You may have petted a dog or been frightened when a dog barked at you. These sensory-motor events are a necessary part of all knowledge. They are the building blocks of more abstract knowledge. Have you noticed that when an instructor gives a good, concrete example to explain what a new concept means that you may suddenly understand it. Concrete (sensory-motor) instances are the roots of our knowledge trees.

When I ask students if they recognize the dog they first imagined, most say that they do. Lance said he pictured his dog "Godzilla," I asked what type of dog "Godzilla" is and he said a "great dane." Other students list "bull dog," "lab," and "terrier." So already we have constructed a small knowledge tree. At the lowest level we have real, live creatures such as "Godzilla." At the next level are the types (or classes) of dogs-great dane, bull, lab, etc. At the top level is the concept "dog."

Note that the lowest level (of Godzilla, Fido, etc.) is the only level of the knowledge tree that consists of real objects in the world. Every other level consists only of our ideas about these real objects. (Of course these real objects are only our images of these objects, but we won't get too philosophical here.) There is no such thing as a "dog": the word "dog" is an abstract word we use to arbitrarily group together all of those barking, four-legged creatures we find around the neighborhood.

What is the next level of the tree? It is the "canine family" which includes foxes, wolves, coyotes, etc. The tree goes on up. At a higher level is the category of "mammal." Included in types of mammals are the class to which whales and dolphins belong, the cat family, and primates-such as monkeys and humans. Above the mammal class is the class of "animal." We could keep going.
 

Differences in hierarchy levels. Let's look at some of the important differences between categories at the bottom and categories higher up. The lower (more concrete) categories are more sensory-motor related. You can get a clear mental image of them. Try to picture the particular dog "Godzilla" versus the general category of "dog." Can you get a detailed image of "dog" that adequately represents all dogs? No. The features of the different types of dogs are too different from one another. Your image could not simultaneously have a long and short nose, long and short hair, or a long and short tail. If it is hard to get an accurate picture of dogs, try to imagine what a mammal looks like. That category includes humans, dolphins, dogs, elephants, and mice.

What I am illustrating is why it is so difficult to understand very abstract concepts. When you were in elementary school, you learned more concrete concepts. Now your professors assume you know all that and focus on teaching very abstract concepts. Many of these concepts are remote from your daily concrete experience. That remoteness is why these concepts are so hard to understand and relate to. That remoteness is why many students complain that their classes seem "irrelevant" to life.

So why do we bother to invent such abstract categories in the first place? What use are they? Let's go back to our dog example again. When a young child who knows the word "dog" first sees a cat, he/she may call this strange creature a dog. All the adults laugh. Why did the child make that mistake? Since cats are furry and have four legs, the child may have called it a dog because it was more like a dog than any other category he/she had in his/her knowledge hierarchy. The parents may then explain to the child that there are differences in features between dogs and cats. One barks and the other meows, etc. How is this useful? Suppose that I ask you what a "zughit" is. What do you know about a "zughit"? Probably nothing. But suppose that I then tell you that a zughit is a type of dog. Then what do you know. You will assume that a zughit has all of the features that all dogs have-such as barking, four legs, hair, a tail, etc. Before I told you that, you didn't even know that a zughit wasn't some sort of rock. In other words, words and concepts contain lots of meaning that helps simplify our lives and communicate with other people.

Let's take another simple word-"atom." That word was invented centuries ago to explain that objects we see are composed of a smaller set of very small particles that determine their nature. Over the centuries that concept and the study of it and related ideas has transformed our world. Chemistry, physics, electronics, and the resultant inventions are based upon these ideas. Without them we might still be living in the middle ages. So, even though you don't normally experience atoms directly in your everyday lives, it's a good thing that scientists and others understand that concept. Certainly, if you wanted to become a physicist, you would need to know a lot about atoms. To become an expert in any field you would need to know the knowledge hierarchy in that field in great detail.

That's what college is all about. You are here to become more of an expert in several knowledge areas. That is what a "well-rounded" college education is all about. In your major, you will become even more of an expert. And if you go on to get a doctorate, you will become a real expert in an area that is only one small part of the university. Return to Index
 

HOW TO CLARIFY DIFFERENT TYPES OF CONFUSION-DOWN, UP, and ACROSS

As we have seen, becoming an expert means that you are learning about concepts that may be foreign to your previous daily existence. That's what makes them hard to learn. The lack of connection to your current "real life" may also cause you to feel unmotivated or uninterested in learning these new ideas.

What can you do to overcome this gap between your present knowledge and experience and the ideas being taught in class? There is no one simple answer. Instead, we will discuss a variety of strategies to increase your interest and comprehension. First, let's go back to the harmonious functioning model. Recall that being exposed to new input that you don't relate to typically causes confusion. Therefore, to gain comprehension, focus on clarifying confusion.

Also recall that when you really understand something well, you never forget it. Some of the details may fade with time if not used, but you will probably never forget the important points. You don't need repetition to remember-only good understanding.

What do most college students do when they are reading and feel confused? Most barely notice their confusion and just keep reading. They may not notice each little incident of confusion, but by the end of the chapter they feel a lot of confusion. Is that what you do? Other students (usually the top students) stop reading and try to clear up their confusion. One engineering student came to me for help because he had received a "D" in his thermodynamics class. He was currently retaking that class and taking a new class that required thermodynamics as a prerequisite. His first test in the new class was to be a review of thermodynamics. He said, "I hated themo and was so confused about it that I know I'll flunk this review test." I taught him the methods of how to clarify confusion that you are about to learn. In addition, we made a deal. He agreed that when he read the review chapter, he would stop every time that he felt any confusion and try to clear it up. He could refer back to his old thermo textbook. When he returned after the test, he was elated. He had made an "A" on that exam. We were both surprised. He said that he had done exactly as we agreed. He said that one particular page took four hours to get through. But he said that once he had finished his review, "I felt like I learned more more about thermo in those few hours than I did the whole semester. . .and now that I understand what it's about, I think thermo's really interesting."

The methods I taught him are the same that follow. First, to clarify confusion, we need to know what type of confusion we are dealing with. Following are three types of confusion that reflect the three major dimensions in a knowledge hierarchy-down, up, and across. For each I suggest methods of how to clear up that type of confusion.
 

1. Clarifying DOWN (or lack of referents) confusion

Let's take the concept of dog. If a young child had never seen a dog or picture of a dog, and his/her dad were to start talking about dogs, the child would not understand what a dog was because it had no sensory-motor referents. Your brain cannot understand a concept unless it is tied to sensory-motor information in the knowledge hierarchy. Seeing one dog can dramatically help the child understand what a dog is. However, seeing a variety of dogs will help the child's brain automatically abstract the key features that dogs have in common-such as having four legs and barking.

To clear up referent or down confusion, you must get examples that are concrete enough. If your instructor or text doesn't give you clear examples, then it is up to you to create clear examples. Good examples are the key to "down" understanding of the concept. Generating good examples is a skill that you can acquire with practice.

The methods for generating examples will vary from field to field. If possible, try to generate examples that you can relate to your common experience and "common sense." In fields such as history, psychology, philosophy, and business where people are important elements of many ideas, try mental role-playing or putting yourself into imagined situations relevant to the concepts being taught. For example, put yourself into a certain period you are studying in history as if you were viewing a historical movie. What would daily life be like? What would your pleasures and worries be like? How would it compare to other periods in history-such as now? Learn to ask yourself the key questions that relate to important historical concepts. In subjects such as psychology, where you read about many experiments, try putting yourself in the place of a subject in the experiment and in the place of the experimenter.

Business professors have told me that their night-class students typically are much more interested in class than their day-class students, because so many of them are working in business while so many day-students have never been in business. If you are not involved in business, invent your own business and role-play relating new concepts you are learning to your own imagined business. Use this same principle in other fields as well from art and literature to psychology and health science.

In very abstract subjects such as higher mathematics, there are several basic strategies of generating concrete examples that help you understand the concepts. For lower math, letting numbers represent objects will do the trick. If you have five balls and subtract three, two are left. You can see what happens with our eyes. However, when it comes to higher math such as algebra, statistics, and especially calculus often the best way to get a concrete image of what is happening is to draw graphical representations of the equations involved. One of the secrets to becoming good at math is to be able to think graphically instead of just math symbols and equations. The visual part of the brain is capable of representing much more information at once than is the verbal part of the brain. As they say, "One picture is worth a thousand words." How many words would it take to describe all that you see in a three-second look around the room?

Practice: How to think graphically. Let's take one math example to demonstrate what I mean. Lets take the equation y=x². What does the graph of that equation look like? To find out do the following:

(1) separate the independent variable (x) from the dependent variable (y).
(2) Plug a variety of values into the independent variable (x). Such as 0, 1, 2, 3; -1, -2, -3.
(3) After each test of plugging in an x value (such as "0"), find the y value. x²=0²=0.
(4) Plot the (x,y) point (0,0) on an xy graphical space (see figure below.)
(5) Repeat with other values of x until the shape of the graph becomes clear. (It should be a parabola.)

Plugging in values for y=x² is just one way to increase understanding. Another way is to vary the right side of the equation in some systematic way to see what happens. We can work on understanding "power functions" better. Try plotting the equation y=x⁴. Do exactly as you did above. What does the graph look like. You will notice that it is also a parabola, but that it is narrower than the one for y=x². What do you think will happen to the shape of the equation, y=x¹⁰? (You are right if you think it will be the same except much narrower.) Notice how playing with these graphs already gives you an intuitive "feel" for understanding power functions that you may never have had before. It is just this type of "play" or experimenting with numbers, equations, and their relations to graphical representation that deepens your understanding of math, because you now have more concrete referents for these abstract concepts.

Application (how to) confusion. Another type of "down" confusion, is not knowing how to apply an abstract idea. In psychology, a student may learn abstract ideas about how to do "cognitive therapy," and think they understand it pretty well. However, when their first client comes in for help, they may be at a loss of how to apply the idea of cognitive therapy to the problem the client is having with her husband. After learning all of this "textbook" knowledge, you may find it challenging to apply this knowledge to real life situations after graduation. The inexperienced college grad may be embarrassed when some of the applications of these ideas turn out to be fiascos-even though they should have worked "in theory." So part of learning a concept is learning the practical "how to" applications of it in real world situations. Solving real world problems not only increases your understanding of the abstract concepts, it teaches you how to apply them to problems you will be facing in later life.

Therefore, as you are learning ideas and techniques in the classroom, keep generating images of real world problems that they might apply to. That will increase comprehension, memory, and later "practical knowledge."Return to Index

2. Clarifying UP (lack of perspective) confusion

The expression, "he can't see the forest for the trees" describes a person who sees only the detail and can't see the big picture. One of the most common problems I see is illustrated by a student I will call Carrie. Carrie came in to see me because she was spending huge amounts of time studying, but was not making good grades. She had had the same problem in high school. She thought that she must just be "dumber" than her best friend Marcie, who studied far less, but made better grades. When I asked Carrie how she studied, she told me that she read every word and took extensive notes from the text. When I looked at her textbook I saw masses of yellow on each page. She said that she could never tell what the most important ideas were, so she tried to memorize everything in the chapter. What a gruesome and overwhelming task A typical textbook chapter might have 10,000 to 20,000 words in it. How could anyone memorize all this information?

Instead of adopting a "learn it all" or "let's get lost in the forest" approach that focuses on learning every detail, it is much more productive (and interesting) to develop the chapter knowledge tree. The most important concepts in most knowledge hierarchies are the ones at the top-the more abstract ones. Most top students recognize this fact and adopt study strategies to match. Carrie's friend Marcie would just "skim" the chapters and make "A"s while Carrie spent countless hours trying to memorize them and made "C"s. Yet Marcie would learn the more abstract "big" ideas that the professor also thought was important, while Carrie hardly noticed those ideas because she was so lost in the detail. So, even though Marcie spent less time, she learned the few important ideas better than Carrie did. Marcie felt clarity about a few, big ideas, while Carrie felt overwhelmed and thoroughly confused by many small ideas.

Methods of learning the big ideas in a chapter. There are a variety of ways that you can focus on the main ideas of a chapter. (1) Preview/overview of chapter. Before your read a chapter, skim through it focusing on the overall chapter title and how it relates to the main subheadings within the chapter. Just go down one or two levels and read a few topic sentences or summaries of sections to get an idea. Also, read the chapter summary.

(2) Review/overview of chapter. Have you ever read a chapter in a book and then asked yourself the question, "What was this chapter about?" Were you surprised to find that you couldn't answer that question about a chapter you just spent two hours reading? You aren't developing Alzheimer's disease. Instead not knowing what a chapter "is about" is a result of not focusing on the bigger, higher level ideas in the chapter.

After reading a chapter, summarize the big ideas of the chapter. One method I recommend is to draw a "map" of the knowledge hierarchy in the chapter. Draw a circle near the top of a page to represent the main concept or idea in the chapter. Below that circle make circles to represent each major subtopic (or section) within the chapter. Connect them to the main idea with lines. Repeat this process within each major subtopic in the chapter. Don't go down more than about three levels in most chapters-or you'll get lost in the details again.

(3) Create your own theory or model. A great way of learning the big, important ideas is to create your own theory. Theories are wonderful ways to create knowledge hierarchies. A good theory is a knowledge hierarchy that ties together general/abstract ideas with more specific ones-eventually connecting to observable data or events. You may be thinking that you are no expert; how can you create your own theory. One way to start is to borrow theories that you read about in your text. Comparing them and thinking about which one(s) make the most sense will not only help you create your own theory, but it will help you comprehend, remember, and apply those theories in a very interesting way. One of my own personal goals is to create my own grand theory of everything about the psychology of people. I find that almost every article I read can be compared to my grand theory in one way or another. It's fun and helps me integrate all of my knowledge about people.

An example of a small theoretical model is the harmonious functioning model. It is partly described here and at length in my book. Sometimes a diagram is a very useful way of condensing a lot of related information. Your visual cortex is especially good at representing and storing complex relationships.

(4) Create a role for yourself that integrates a body of knowledge. I mentioned above how pretending that you own your own business is a good idea for a business major. Role-playing gives you a good way to understand how to apply abstract ideas to practical, real-life situations in order to understand those ideas better. Role-playing can also help you integrate higher level concepts across broad subject areas. If your pretend to own your own company, you can integrate ideas from management, marketing, finance, and computer courses by thinking of your business in ways that cut across these different areas as a good CEO would.

(5)Use a memory-device to link unrelated terms or ideas together. What are the colors in the rainbow? Red, Orange, Yellow, Green, Blue, Indigo, Violet. How could you memorize them in that order if you had to for an exam? A simple method is to make an acronym. In my high school chemistry class I learned the acronym "Roy G. Biv" to stand for the initial letters of those colors. I have never forgotten them. Another trick is to make up a sentence or story that ties together the initial words (or key words) in a series you need to memorize. Normally, the best methods (by far) to permanently learn a group of ideas is to find meaningful relationships between them. However, sometimes that is difficult to do (as in the colors of the rainbow). If you cannot find real meaningful relationships, it is often best to invent relationships that serve as substitutes for meaningful relationships. I do not focus on these methods, because they are a very poor substitute for learning real, meaningful relationships between concepts or ideas. Use them sparingly.
 
 
 
 

What is the big picture of the course? Reviewing for a comprehensive final exam? Put yourself in the role of the course instructor for a minute. Suppose you were asked what are the 10 to 20 most important ideas in the course you want all your students to leave with? Would they be dates or details? Not likely. They would be big, broader ideas that affect many topics or events. The final exam should reflect this emphasis on knowing these 10 to 20 big ideas well.

In the same way that you "mapped" the overview of a chapter, map the overview of the entire course. First, draw a big circle that represents the topic of the course. For example, I teach a course entitled, "Self-Management." The course title is what the entire course is about. Every tiny idea in the course somehow relates to the bigger idea of self-management. If I were mapping the overview of the course, it might look something like the following:
 

One method of generating this course overview is to start with the textbook title. It becomes the first tier topic. Then go to the table of contents. Group the chapters by units or by categories (you invent) that group similar chapters together. Those chapter group categories become the second tier. The chapter titles become the third tier. The major sections within the chapters become the fourth tier. Or, if you have already mapped the chapters during the semester, all you need to do is complete the broader overview. If the course does not closely follow the outline of the textbook, then use the syllabus (or even your own scheme) to find the second-tier categories. You may have to use more than one book or class notes to develop the overall course map.

"Why" confusion-the opposite of "how to" confusion. The more abstract, higher-level concepts and principles are usually the ones that we describe as "deeper" or "underlying." They are usually used as explanations of lower-order phenomena. When we ask the question, "why?," we normally are looking for a principle or concept higher up in the knowledge hierarchy as an explanation of a lower-order event. Knowing a few principles can explain many lower order events. That is one reason that abstract principles are so useful.

If you are confused about the "why's" or don't know the right reason or explanation, then you are suffering from "up confusion" and need to study the connections between the question and the more abstract or higher level ideas that relate to it. Ask yourself, "What principle, law, model, or formula applies to this situation?"

If you are trying to solve math or science problems (or almost any applied problem), and don't know how to proceed, you are probably suffering from "up confusion" since the key to solving most problems is to figure out what principles or formulas apply to that problem. If you often feel lost when approaching math (or other) problems, then you are probably not learning the principles well enough.

In summary, when you don't know "what something is about," "why," "what principle or formula to apply," "the big picture," etc. then you are suffering from "up confusion;" you have not learned the bigger, more abstract ideas higher in the knowledge tree. Or, you may not have learned how they relate to the problem situation (lower in the tree). Focus on learning the underlying principles or other ideas well, so that you are confident that you know what they mean, how they relate to each other, and how they relate to the ideas lower in the knowledge tree.

Practice: Map the overview of a course. Map a textbook overview map as described above. Observe what happens to your "up confusion" ("what is this course is about."). Your up confusion should diminish as you clarify the overall structure of the main course topics and ideas.
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3. How to clarify ACROSS (lack of discrimination) confusion

The last major type of confusion we will discuss is the kind that occurs because we don't understand the differences between similar concepts or ideas (at about the same level in the knowledge tree). Recall the example of a young child who has a dog and has never seen a cat. The first time it sees a cat, the child calls it a "dog." The child may at first be very confused due to parallel or "across" confusion. After all a cat is about the same size as a dog, also has four legs, and has lots of fur. The key question is, "What are the differences?"

Before we explore that question, it is also important to note that one of the main reasons that across confusion occurs at all is because the two have so many similarities. The child is not likely to confuse a snake with a dog. Note that if we look up the knowledge tree to the first place where "dog" and "cat" fall under the same category, it is at the level of "mammal." That means that dogs and cats must share the main features that all mammals have in common. Dogs and cats will all have a total of four arms/legs, hair, five toes, a four-chamber heart, etc. To clear up "across" confusion, first list the main similarities between the concepts/ideas, then list the differences. For more abstract concepts, you may want to list an example of each type of difference.

One visual way to clarify ACROSS CONFUSION is the following:

You may have heard ads of speed-reading approaches that promise to double your reading speed and increase your comprehension at the same time. Is this magic? No. That outcome is possible only with easier material-such as novels. This type of approach works because you basically learn how to skim the material for the main ideas and form an overview of the material. Skimming increases speed and can help your comprehension, because you are focusing on the more general and (usually) more important ideas.

However, that speed-reading approach will not work with new, difficult content such as calculus or philosophy. Instead, to comprehend difficult material you must read only at a rate that allows you to comprehend the material well (clear up all confusion). You may think that the methods I have been talking about are very time-consuming. It is true that you will spend much more time working on understanding difficult material. However, that extra time invested will pay off by stopping use of your current time-wasting methods. Many students I talk with spend huge amounts of time using boring, ineffective "rote" memory methods such a flash cards, re-copying notes, and listening to tape recordings of lectures. Also, many students spend hours seeking help from peers and professors instead of figuring the material out themselves. And after all of that effort, many still do not understand the basic principles in the course.

With these methods you will spend your time focused on the central job of learning-clarifying confusion and creating extensive knowledge trees in your brain. As you apply the methods in this manual, you will also sharpen you "learning to learn" skills and become a more expert, motivated, and independent learner. There are many possible ways to apply the above principles. Following is a step-by-step outline of my own preferred method. These are the same basic steps that I have taught to hundreds of college students. They are the same basic steps I used when I had over forty textbooks to review for my doctoral preliminary examinations (a test that lasted four days). When I finished, I had mastered a huge amount of information.

STEPS TO READING A CHAPTER

Step 1: Chapter's context--See how the chapter fits into the broader context. As described above, see how the chapter fits into the overall outline of the course and text. How is it related to the previous chapter and the one that follows?

Step 2: Chapter preview. Focus on the chapter title and introductory paragraph and read the summary at the end of the chapter. What is this chapter about? What are the main parts/sections of the chapter? Quickly focus on each one and ask yourself how it relates to the overall chapter topic or theme. You may want to quickly look at subheadings and/or topic sentences to get a clearer understanding of what the major sections are about. Learn how to do this step in about five minutes.

Step 3: Read UP, DOWN, and ACROSS. As you read, keep asking yourself questions like the following and STOP when you are confused. When confused, ask what type of confusion it is and how you can clear it up. Sometimes you will need to find earlier references to the concept; other times you will need to figure it out yourself (or as a last resort, get help).

UP questions like, "What is this about?" "How does it relate to the bigger, broader topics or ideas?""Why?""What are the relevant theories or principles?"

DOWN questions like,"What does this mean?" "How do I apply it to practical situations or problems?" "What is a good example?"

ACROSS questions like, "How is this similar and different to X?" "What are other members of this same type or category?"
 

Mark the chapter hierarchically (using a blue or black pen) using a system similar to the one illustrated below.
 

IMPORTANCE OF THE INFORMATION

Insert the following symbols in the margin near the idea, etc. to get your attention.

**= Most important KEY idea, judged by its comprehensiveness, utility, text or instructor emphasis, or interest to you. (Normally, use less than 1 per 2-5 pages)

*= Next most important KEY idea (1 per 1-3 pages?)

"check" "check"= Next most important idea (1 per 1-3 pages?)

"check":= Take note, but not exceptionally important (1or more per page?).
 

KEY WORDS

Draw a box around the most important terms. Circle less important key words or key phrases.
 

CONNECT key words with circled or underlined words or phrases

Draw lines between key words and key associated terms or ideas. Connect them even though they may be separated by several sentences or paragraphs. Connecting with lines helps you quickly associate a few key ideas from the page together and makes a mini-map of the page (see example below).
 

UNDERLINE main points within important paragraphs

Underline the main words and phrases-rarely entire sentences and never entire paragraphs.
 

BRACKET paragraphs of lower importance worthy of some notice

Put a bracket in the margin-possibly with a note in the margin or key word underlined. Examples: If a paragraph gives an example of an earlier term, write => EX or for Evidence of an idea write => EV beside the paragraph.

Note how much less cluttered brackets are than marking entire paragraphs.

NOTES or NUMBERS in the margins

Write additional notes for clarification, etc. Since you will be stopping when you are confused or want to use other methods to increase comprehension, you need to write down the results of your playing with ideas and figuring it all out. Write in the margins, put "sticky pads" on the pages, or keep longer theories, explanations, invented examples,"across" comparisons or other material in your notebook. However, mark in your text, the notebook page number and mark on your notebook page, the number of the textbook page it refers to.

Numbers in the margin. You may also want to add numbers in the margin when there are several points or steps that relate to some broader idea. These numbers may span several pages and help you see how material across several pages are related. Use "sticky notes" if you don't have space in the margins.
 

Flooding refers to the therapeutic operation of eliciting intense anxiety in a person through prolonged exposure to threatening situations. The therapist who uses this technique seeks to induce and sustain high levels of anxiety in the client until the anxiety reaction dissipates. Basically, the client is prevented from avoiding anxious thoughts or behaviors in his or her customary, well-learned ways. The usual explanation for the effectiveness of the technique is that the anxiety "extinguishes" as the client is force to dwell on upsetting thoughts or images over time.

EX An example of flooding came from. . .

EV A number of studies have shown that flooding . . .
 

Step 5: Apply what you learn. Apply the textbook knowledge to real-life or imagined situations (for fun, practice, and profit). Discuss what you have learned with others. Try to put it into simple "common sense" language to explain it to non-expert friends or family. This can help you understand and integrate the knowledge for practical, fast recall-a valuable asset for examinations and life.
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ADDITIONAL TIPS

In addition to (1) focusing on staying in the zone of harmonious functioning and (2) clearing up the three basic types of confusion (DOWN, UP, and ACROSS) by using the methods discussed previously, remember the following:

Study for optimal amounts of time. Once your mind feels like it is "full" of a particular topic, stop and take a break. Then review/overview and map. Next, if you feel clear-headed again, you may proceed. Otherwise, change to a wholly different course or topic-or take a longer break by doing something other than studying.

As you read, form as many associations of the new information with what you already know in as many areas of your knowledge and experience as you have time for.

Create imagined scenarios and roles for using the new knowledge. Play with it in a variety of ways-be creative
 

Practice: Do not omit this practice.

(1) Read the above passage on "Flooding" focusing on your feelings of mastery and confusion. When you feel confusion, try to figure out exactly what word, phrase, or idea you are confused about. What is the dominant type of overall confusion. Most likely it is down confusion. Create an example in which you apply the technique to some fear or anxiety.

(2)When you have cleared up most of your confusion and think you understand it clearly, then answer the following question. (This is the kind of question I really might put on an exam.) If a person came to you who was afraid of heights and you were to use the flooding technique to help them, exactly what would you do?

(3) Compare your answer to the one in the footnote at the bottom of the page.⁽²⁾
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Step 1: Preliminary overview and planning. Get an overview of your chapter "maps" so that you can have a good idea what is being covered by the exam and how it all fits together. Ask yourself how this part of the course relates to the course as a whole. If you see examples of "across confusion" between the different chapters, clear it up now.

Develop your study plan. What, besides the chapters do you need to review? Even if the instructor has given you a list of study topics or questions, start with the following review so that you can understand the material. Then outline possible essay questions or make other preperation that is specific to the questions or topics the instructor has given you.
 

Step 2: Review the chapters (and class notes). Use a different color writing pen to review the text (eg. green). Use the following substeps to review chapters and/or class notes:

(1) Overview. For each chapter, look at the chapter title, then ask yourself what this chapter was about and what were the major subtopics within the chapter. Recall all you can about the big ideas in the chapter. Then check your answer against the chapter map or flip through the chapter to see what major sections you forgot. Mark them on your chapter map in green. Mark in green anything that you do not know well enough for checking during the next review.

(2)Major topics and sections. Now, find the first major section in the chapter. Look at the heading or topic sentence and ask yourself what this section is about and what its major ideas and subtopics) are. What else do I know about this topic? Mark any you don't recall. Then skim through the section and look for your penned boxes, circles, 's, and 's. Quickly examine the key terms, ideas, etc. and check your emotions. Do you feel confusion or mastery? If you feel confusion, STOP and learn the material NOW using the techniques described above. Otherwise, keep moving.

Step 3: Repeat step 2 at least one more time. Except this time as you review focus only on the green (second color) markings. This time, if you didn't recall the material well enough, make needed new marks ('s, and 's ) using a third color pen-such as red.

Step 4: Final text/notes review. The last time through, you don't need to make any more marks, by this time you should be flying through just double-checking the red marks to see if you recall them. If you don't recall them, study them this last time. (If you really require another look at them, put a sticky pad on the page that you can see when you close the book. And come back to it one more time.) Normally, I suggest going through this final review the same day as the exam, perhaps within a few hours of the exam. (All else being equal, memory is usually better for information studied closer to the exam.)

Step 5: Right before the exam. (1) Go over your overview maps if you need to and cover any last minute parts you still feel uncertain about. (2) Ideally, I suggest that you take a relaxation break of at least 15-30 minutes before the exam to clear your mind. Try thinking of relaxing scenes, etc. Don't enter the exam room too early if other students' anxiety tends to raise yours.

Length of time to review. Perhaps you are wondering how much time this process will take. I believe that generlly it is faster than almost any other method that is nearly as effective. Naturally, the difficulty of the material and the number of words per page will make a big difference in pages per hour that you can review. However, let me give you a very rough estimate. The first time you read the material (and mark in black or blue), you may cover 5-30 pages an hour for most textbooks. The second time you cover the material (first review time-focus on black/blue ink, mark with green ink), you will probably cover 30-70 pages per hour (unless you were left with a lot of confusion from your first time through). The second review time (focus on green, mark with red) through, you will probably cover 50-150 pages per hour. The third review time (focus on red, no marks) through, you will probably cover 100-300 pages per hour. For example, to review for a 200 page exam at 50 pages/hour, is 4 hours first time through; at 100 pages/hour, is 2 hours the second time through; and at 200 pages/hour, is 1 hour the last time through. The total time is 7 hours to review thoroughly and feel a sense of mastery.

Pacing of study. Recall the harmonious functioning model. Your brain will tell you when you've had enough. If your brain starts to feel "too full," you either need to clear up the immediate up, down, or across confusion or you need to take a break. Often, if you are understanding what you are reviewing, stopping and looking at the big picture on your map may help you get a sense of clarity and perspective again. Try doing this just before you take a break or at the beginning of your next study session.
 

SPECIAL STUDY SITUATIONS

The above method is designed for almost any type of course that relies on textbook and/or class notes to preserve the information required for the examination. However, depending on the type of course or instructor, you may want to vary the method to suite your own personal needs. Following are some common modifications to the above methods.

Instructor provided questions or topics. Suppose the instructor gives you a list or topics or questions to study for the exam. Do you focus on writing or outlining answers to these questions and omit the type of study recommended here? I can only tell you that with rare exceptions, I always used the above review method first. Then I would look at the list of topics or questions to see if I could answer them. Normally I would not write the answers to the questions (to save time) unless they were long essay type questions. In the case of long essay questions, I would make a brief outline.

Problem-solving course examinations. If the exam is primarily a problem-solving exam (often the case in math, science, and engineering courses), then consider your homework problems to be similar to class notes. After reviewing a particular chapter, then review the accompanying class notes and homework problems and see if you understand them (again mark in green and red inks).Return to Index

In addition to the general methods above, there are many additional learning methods that can help you become a more effective learner and effectively increase your practical "IQ."
 

TIPS FOR STUDYING INTENSIVE "READING" SUBJECTS--Such as history, social science, and humanities courses

These courses generally assign many more pages to read than physical science or math courses. Usually the exam questions have few if any quantitative problems on them, although there may be verbal problems of applying principles or methods to problem situations (as in the Flooding example above). Following are some tips for studying material that students often complain about.

Historical courses. A tip for organizing your study for historical type courses is to make a time line that covers the entire period of the course. On the overall course time line, label the major historical periods covered and their dates. For each exam focus on the part of the line relevant to that exam and do the following:

(1) Make sub-lines. For most history courses, it is a good idea to break the period into sub-lines. Each sub-line will repreent one aspect of history (such as political, religion, arts, science, social, personal life, business/economic, etc.).

(2) Mark important events, people, trends, movements, etc. on the sub-lines. Record the most important of these and their dates on the sub-lines.

(3) Review up, down, across. Once you have made this overview map of the historical period, then play with it to note the many interesting correlations between events. For example, note how the beginning of the Renaissance period brought about many changes in all of the sub-lines almost at once. What were the major themes and ideas of the Renaissance? Why and how did they have such a large effect in so many life areas? It is these questions that are the most important ones, not which date something happened on. By the way if you study the dates as you study the ideas, you will begin to remember the dates. Certainly you will know the dates well enough to know that a date you know to be during the Medieval period could not possibly be the right answer for the birth of a person who lived in the Renaissance period.
 

Research and Experiments. Many social science, health science, education courses summarize a great deal of research. They may briefly describe hundreds of studies in a 400 page textbook. How can you possibly remember them all? Or, if you have to get interested in them to recall them, how can you even get interested in them? Try this suggestion. First, focus on learning the overall theory, principle, or hypothesis the research is testing. What is the theory or idea? Why is it important? How can you think of it as important to you? How does it relate to up, down, or across to other ideas in the course-or ideas you are interested in?

For important studies, try role-playing. Imagine that you are the experimenter and you are trying to test this hypothesis. How would you do it? Why did the researcher choose this method? Was it a good method? And/or try imagining that you are a subject in this research? How would you have felt and reacted in this situation? Would you have responded as the majority did? What flaws might be in the research? I often write a "+,""-," or "?" in the margin to indicate if the study is supportive the main hypothesis or not.

As a summary of important experiments, write down the number of groups, the independent variables, the dependent variables, and the results. Were they supportive of the hypotheses or not? You can do this in the margin of the text or on a sticky pad placed on the text page.
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TIPS FOR STUDYING QUANTITATIVE PROBLEM-SOLVING SUBJECTS--Such as math and physical sciences

Quantitative problem-solving courses tend to have exams that largely consist of problems to solve or projects to create. The fact that the exams consist of problems tends to mislead many students. See if you are one of them.
 

Problem-solving by analogy and help-seeking versus by deduction. Do you skim through the chapter, focus only on the examples, then go to the end and spend all your time trying to solve the problems so that you can turn them in on time? When you see a problem, you try to find an analogous example in the book and try to make it fit the problem. If you can't, you try to work backwards form the answer in the back of the text, call a friend, talk to the professor, or give up. Later, on the exam, you do well on the problems that are analogous to the ones you solved, but are baffled by the "hard" ones the instructor threw in.

Most math and engineering students who come to me because they are making poor grades use these "learn by analogy and help-seeking" methods. Let me contrast that to the method used by an engineering student who had a 3.8/4.0 grade average. He spent almost all his time focusing on the chapter text material so that he could thoroughly understand the theory, principles, and methods described. If he was confused, he would stop and use paper and pencil to draw diagrams or do whatever it took to understand the material. When he came to the problems, he spent far less time than most of his peers. He saw the problem as an exam preview. If he could figure out how to solve it out of his head, he would move on to the next problem. If he couldn't figure out how to solve it, he would try to figure out what he was confused about. Was it some principle he misunderstood? Perhaps he needed to go back and review a section of the chapter-not just study an example in the chapter. He would not just try to get a "right answer" by analogy, working backwards, or getting help until he had struggled with it much longer. His method is similar to the one I recommend.

One engineering student told me that he thought he was just "too dumb" to do well in engineering courses. I asked him why he thought he was "dumb." He said that though he tried his best, he could never solve the really hard problems so he knew he couldn't be as smart as the students who would solve the hard problems on the board in front of the class. After switching from the "analogy and help-seeking" method to the method I described here, he started solving the most difficult problems. He told me how thrilled he was to be among the "chosen few" whom the instructor called to solve those problems. It changed not only his study methods, but his image of his intelligence and himself.

Representing the problem with concrete images. Mathematics is an extremely abstract discipline. Numbers can represent almost anything, and by the time you get to algebra, calculus, statistics, and other forms of higher mathematics, the mathematical symbols, equations, and the like can become very confusing. Recall, that down confusion is often the most common type when learning new concepts or ideas. That is especially true in math. You cannot learn math well without ultimately connecting the terms to concrete representations. For example, when you teach a child to count, you show the child objects and have the child count the real objects. Only through this method does the child eventually understand that the word "three" can represent three of any type of object.

Remember the "a picture is worth a thousand words" cliche? Your visual cortex can represent much more concrete and complex relationships than can your verbal cortex. Yet mathematical symbols are all verbal. The trick is learning to translate the verbal math symbols into visual ones-such as graphical representations. I once saw an article in the LA Times quoting one of the worlds great mathematicians as saying the key to his success was simple. He translated all the verbal symbols into graphical ones, manipulated the visual ones in his head until he found a visual solution, then he translated the solution back into verbal symbols such as x and y. For an example, return to the practice exercise on y=x² in the section on "down" confusion.

Let's take an example of making concrete examples from a statistics course. To understand one of the basic ideas about what inferential statistics is about, start with a real population that you can imagine, such as all the people in the United States. Imagine what you think the real population distribution for intelligence would be if you actually gave IQ tests to everyone in the US. If you plotted the IQ on the "X" axis and the number of people with that IQ score on the "Y" axis, then it would look like the familiar "bell curve" with the mid-point at IQ=100. Very few people would have IQ's over 140 and very few under 60.

Now, imagine that you travel around the country and pick 30 people randomly and test their "IQ." Plot the points of that one random sample. What would it look like? Probably more of the scores would be in the mid-range (around 100). Why is that? Is it possible to draw a random sample with 8 of 10 having IQ scores of over 140? Not likely, but possible. The population distribution (IQ's of everyone in the US) and the sample distribution (IQ's of the 30) are two crucial distributions you will study in statistics. The mathematics of inferential statistics is largely about how accurately you can find "true" population values from sample values that represent our best mathematical guesses at the population values.

We could continue with this process to show how every statistical test eventually connects to points and pictures on a graph and represent real qualities we can at least imagine in the world. Once you lose sight of those connections, you will become throughly confused. The more statistical concepts you learn on top of that more basic confusion, the more confused you will get. Therefore, when you are taking a statistics course, go back and plot graphs, play with them, and relate the dots and curves to tangible qualities like IQ scores that you can understand.
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"ROTE MEMORIZATION" TASK TIPS

Students often assume that certain types of material "require" rote memorization techniques. It is true that certain learning tasks do not lend themselves to using the above methods as readily as others do. The more meaningful the material, the better these methods work. However, the rote methods still do not work well-even for non-meaningful material. Usually the best strategy is to create meaning. Following are some examples.

Names, words, and languages. Have you ever taken a foreign language and tried to use "flash cards" to memorize words? You put the English word on one side and the Foreign one on the other. Then to study, you look at one side and try to remember the other. If all you do is try to think of the other word, then that is a pure "rote" memory method. This is a a terribly boring and ineffective way to learn a foreign language. Let's compare this method to the way people learn languages in the real world. Have you ever been to another country and not known the language? One of the first things you learn is the words for "man" and "woman." Or, if you don't, you risk a great deal of embarrassment. The best way to learn a language is to associate the foreign word with the images or real objects, events, and relations they represent. When learning the words that describe furniture, think of the image of a piece of furniture as you think of the word. Don't focus on associating it with the English word, associate with the image of the furniture. Likewise, use imagery to learn all new words.

Anatomy. According to many students I meet, anatomy is a foreign language. Similarly, many try to use flash cards to study anatomy. The alternative to rote memory is to think about the anatomical term in many different ways. Associate the word with how it is related to other parts, how it functions, your own body part, diseases that may afflict it, or anything else that seems relevant.
 

A set of "unconnected" words or facts. Invent a story, theme, word or other meaningful idea that will tie them all together

Invent a picture that will tie them all together-again, a picture is worth a thousand words. Recall the example of using the acronym, "Roy G. Biv," to recall the colors of the rainbow.
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I have given you a lot of information in this self-help manual. You may be feeling somewhat overwhelmed with it all at this point. The methods described here may seem very different than the ones you are using now. Or, you may find them quite similar except for a few new ideas. In any case, use the method in this manual to learn the material in this manual.

If you mind is "full" now, go back and get a brief top-level overview and/or map the material in this handout. Within one day, go back and review the entire thing focusing on areas where you are confused or more interested in. As you do this ask yourself, exactly what will you do differently in your studying. Then try it. As you study your courses check back with this handout to see if you are applying the methods correctly.

If you are still having problems, try to find someone who learns using methods like these and ask them to help you. People who make top grades (time efficiently) are good candidates for help.

Finally, if you have continued problems with poor motivation, stress, missed deadlines, lack of career direction, or other problems that are affecting your learning or grades, get help at your local college counseling center or visit my web site below for self-help manuals on some of those topics.

For a self-assessment on many factors related to academic success and other life areas, go to my companion web site, http://www.csulb.edu/~tstevens/success and take the Success and Happiness Attributes Questionnaire (SHAQ).

2. One correct answer is to take the person with a fear for heights to the 30^th floor of a tall building and have him/her look out a window until his/her anxiety dissipates (returns to a normal level). The person may feel a great deal of anxiety at first, but even if it takes several hours, it will eventually diminish. [Note: Flooding is different from systematic desensitization (SD). In SD you would take the person to the first floor. When comfortable, take him/her to the next floor, etc. until he/she can be comfortable on the 30^th floor. The person would never feel much anxiety, but it is slower.]

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