HOW TO LEARN

(Physics and Perhaps Anything Else)

Donald N. Langenberg, Professor of Physics

University of Maryland, College Park

Introduction

These notes are intended to help students understand better how to learn physics (and perhaps anything else). That is not a simple matter. Although almost everybody thinks they know how to learn things, or to teach things, only recently have learning researchers begun to understand what really goes on in a person’s brain when he/she learns something. It is astounding that one of the few characteristics that – to some degree – distinguishes humans from other animals is so poorly understood, scientifically, and so fraught with mythology and ideology. Nevertheless, that is the case.

What follows is not the perspective of an expert, but that of a student deeply engaged in learning about learning. Some of it is probably wrong. Nevertheless, it is hoped that it will be helpful to other students confronted by the challenge to learn something about a subject commonly thought to be difficult and abstract, something beyond the intellectual reach of most mere mortals.

A First Step

Attitude is all important! So, the attitude of any student embarking on a physics course ought to be based on a profoundly true observation by Ernest Rutherford, a famous physicist:

“All of physics is either impossible or trivial. It is impossible until you

understand it, and then it becomes trivial.”

Cute, but powerful. It means that the task of every physics student, aided by his/her mentors, is to negotiate successfully the transition from impossible to trivial.

What Goes on When One Learns?

Whenever one uses an instrument or a machine to do something important, it is always helpful to have at least a rudimentary understanding of how it works. That is especially important in the case of using one’s brain to learn.

There is something called “The Learning Cycle¹.” This describes the stages in learning in terms of a cyclical process illustrated by the following diagram:

Active Testing

Abstract Hypotheses Concrete Experience

Reflective Observation

As with many cyclical processes, this one can proceed in either direction, but it is perhaps best thought of as proceeding clockwise, beginning with “Concrete Experience.” One can imagine this as any kind of direct detection of events or stimuli originating in a source external to the brain, e.g., observation of the consequences of falling down a flight of stairs, or listening to a professor’s lecture. The next step in the cycle is consideration and integration of what has been detected, i.e., “making sense of it.” Next comes the development of an abstract hypothesis, i.e., “deciding what the experience means” by developing a mental construct (picture) that connects what has been detected to what is already known and understood. And finally comes deciding on appropriate action, “active testing,” to respond to what has been detected. This might mean deciding to hold on to a banister so as to avoid falling down stairs again, or designing and expressing an appropriate answer to a test question based on a professor’s lecture subject.

This might appear to be just a convenient and rather arbitrary way to picture the learning process.

But, as James Zull has noted in his book, The Art of Changing the Brain,² this Learning Cycle literally maps directly onto the functional structure of the human brain. That is, its elements correspond directly to the principal functions of different parts of the human brain, as illustrated by this diagram:

Since it is now well established that learning actually causes physical and chemical changes in the brain, e.g., by guiding the ongoing development of interconnections between neurons, it follows that taking a physics course (or any other university course) will “mess with your brain.” It is the task of the student and his/her mentors (professors and graduate teaching assistants) to do everything possible to ensure that the outcome is large and positive.

Who’s Responsible for Learning?

The owner of the brain, primarily! That is, the student! Only the student is in direct touch with and in control of the operation of his/her own brain, and thus the student is best equipped to monitor and direct the learning process. The student’s mentors can certainly help. Indeed, they are obligated to understand the learning process sufficiently well to optimize what they do (teaching) so as to maximize the outcomes of the learning process. But the ultimate responsibility for learning rests with the student. Because the Learning Cycle described above is a dynamic process in which each of the four elements is crucially important, it is essential that each of them be addressed in a balanced and effective manner. For example, it is a serious mistake for either the student or the professor to presume that the student is merely a passive receiver of knowledge from the professor, seen as a form of “concrete experience.” There’s a lot more to effective learning than simply receiving knowledge.

So What’s the Best Strategy for Learning Physics (and Perhaps Anything Else)?

Go with the flow! That is, follow the natural course of the learning process dictated by the structure of your brain, and represented by the Learning Cycle. Here are some specifics.

Concrete Experience

The initial step of the learning process involves detecting and receiving information about the subject at hand. This can happen in a variety of ways.

Probably the most widely used and most important way is direct observation via one or more of the physical senses. Beginning at birth, every individual acquires information about the physical world in which he/she lives using vision, hearing, feel, smell, and taste. From those observations, the individual constructs a mental picture of how and why the physical world functions as it does. Thus, every individual knows a lot about physics whether or not he/she has ever had any formal training in the academic subject called “physics.” It is a mistake to presume that someone who’s never taken a physics course is a “blank slate” when it comes to understanding and explaining physical phenomena.

The physical conceptions acquired in this universal manner may be called “native intuition.” There are two common problems with native intuition. The first is that people often observe phenomena without really noticing and taking into account significant aspects of them. The intuitions constructed from such observations may therefore be inconsistent with what actually happens. The second problem is that native intuitions are often specific to particular phenomena. Thus, intuitions about different phenomena that have underlying relationships or commonalities may be inconsistent with one another.

As a result of these two problems, native intuitions are sometimes right and sometimes wrong.

An important challenge in the learning and teaching of physics for both student and teacher is to distinguish good intuitions from bad intuitions and to reinforce the former and rectify the latter. This can be a difficult task because, as learning research has shown, erroneous native intuitions are often much more firmly imbedded in the mind than the “book learning” one hopes will correct them.

Direct observation need not be, indeed should not be, always a passive act. It often can and should be active. The object or phenomenon being observed can be manipulated in ways that enrich the observation and make it more effective as a stimulus to learning. That is, the observer can experiment with what is being observed. Active experimentation lies at the heart of the learning process, especially in the sciences. Sometimes it is simple and easy. We all tinker with things to see what happens. We push this button or try that argument and observe the response. Often, however, we need the aid of tools or instruments to make a desired observation.

There are many things in our universe that are not directly observable using the unaided human senses. The extraordinary evolution of physics and the other sciences has been made possible by the development of instruments that greatly extend those senses and permit scientists to “see” (i.e., detect and observe) previously invisible things. Famous historical examples include the use of optical lenses to construct microscopes and telescopes that revealed the existence of bacteria and the moons of Jupiter and Saturn.

There are of course less direct ways to initiate a learning cycle through concrete experience. We read books and articles. We listen to lectures and presentations. We look at pictures and charts and graphs. All these activities are common practice in learning and teaching because they are more efficient than direct experiential learning. A lecture or a book can provide a uniform concrete experience to many learners at once, or over long periods of time. But there is ample research-based evidence that they are not necessarily the most effective initiators of a learning cycle, nor are they sufficient. They are not adapted to the circumstances of the individual learner, and they tend to be conducive to passivity on the part of the learner. Therefore, good teaching should use a comprehensive and balanced array of tools and methods, all aimed at optimizing the learning environment for each learner involved to the maximum extent possible. And it goes without saying that both student and teacher must engage in continuous testing of learning outcomes in order to monitor and assess the overall effectiveness of the learning process. We must always remember that it is a learning process for both student and teacher.

What then does all this suggest for advice to the student learner acquiring concrete experience?

• Pay close attention to the subject or phenomenon at hand. Both observe and notice as much as you can.
• Be curious. Wonder and ask “Why?” and “How?” and “How big?”
• Experiment. When you can, tinker, probe, prod, and fiddle. Often, the best way to learn what works is by learning all the different ways things don’t work.

• Don’t be a loner. It has been said that “Physics is a social science.” Involve fellow learners in your observations. Each of you has his/her own brain to manage, of course, but they’re all different and you can learn a lot from engaging your brain with theirs.

Reflective Observation

Once you’ve received a batch of new information from your concrete experience via the sensory and postsensory lobe of your brain, the action shifts from the back of your head to the part between your ears, the temporal integrative cortex. Its task is to sift through the new information and to begin figuring out what it might mean. That requires that the new information be compared and contrasted with knowledge and information previously stored in the brain. The new information may be consistent with and thus simply confirm pre-existing information. It may supplement and complement pre-existing information, in which case it needs to be functionally linked with that information. Or, it may be inconsistent with pre-existing information. That should raise a red flag as a question that needs to be addressed and resolved.

Here’s where all the available ingredients come together that are needed to decide whether and how to adjust intuition. That task may simply amount to reinforcing native intuition, or it may become a forward step on the path leading to the creation of a robust physical intuition that is solidly based on the fundamental principles of physics and differs from the learner’s original native intuition in important ways. The latter surely is one of the most important learning goals of any course in physics. It might be remarked that the hallmark of success in attaining that goal is the embrace by the learner of that new robust physical intuition as native intuition. When and if that happens in some sector of physics, the learner has successfully negotiated Rutherford’s transition from the impossible to the trivial in that sector.

Here’s advice for the student learner engaged in reflective observation:

• Ask yourself whether the new information you’ve gained from concrete experience is consistent with everything your intuition currently tells you. Ask “Does this make sense?” As you do this, remember that one of the fundamental bedrock premises of physics is that there exist a very few fundamental physical principles (laws) that ultimately describe how everything in the universe works, and always have since the Big Bang. (Like everything else in physics, that premise remains subject to skepticism and further testing, but so far it’s held up pretty well.) That means that the argument that a particular phenomenon is somehow exempt from the physical laws you may understand so far is not available to you. What are available are the “foothold ideas” you hopefully have learned in physics so far.
• Be sure to check for scale or magnitude. Relative size always matters in physics, and in a universe where the magnitudes of simple characteristics of well-known objects may differ by thirty or fifty orders of magnitude (factors of ten), one should always check for scale. If you suspect something may be too big, too far, or too fast, you’d better check how big, how far, or how fast, right away.

Abstract Hypotheses

After the learner has done a reasonable amount of reflective observation (which may take minutes or months), it’s time to hang the results on a scaffold of abstract hypotheses. Their home in the brain is in the frontal integrative cortex, the part you bang when you blunder headfirst into a closed door. There is almost certainly a scaffold there in everyone’s brain. For the naïve and untutored it may be the rather ramshackle structure that we earlier referred to as native intuition. For the professional scientist it will be a substantial intellectual mansion with a solid foundation of fundamental scientific principles and rooms richly furnished with detailed scientific knowledge.

For the typical student learner experiencing his/her first significant exposure to, say, physics, it will be something intermediate. The native intuition framework will still be there, but it will be buttressed with solid new foundations and pillars. They will be few in number because nature has provided us just a few that suffice for all purposes. They will include things like Newton’s laws of motion, the conservation laws of momentum and energy, and the universal law of gravity.

The function of the frontal integrative cortex is to use the materials from the temporal integrative cortex’s reflective observation to continue transforming the primitive native intuition structure into a soundly grounded intellectual structure that is consistent with known physical principles and that provides an adequate base for thinking about and understanding most physical phenomena. That can be thought of as analogous to renovating and/or rebuilding an existing real building. Both kinds of efforts demand careful attention to organization and to design and construction, in order to obtain the most functional structure possible using the new materials available.

Advice to the student learner engaged in building abstract hypotheses structures centers on the uses of language.

• A powerful test of whether one really understands a piece of physics is whether one can explain it to a non-physicist in simple understandable English (or other spoken language). Practice doing that with anyone who will listen. You most likely think in English, and this will help you get better at it.
• Remember that a few words commonly used in colloquial English are also used in physics, but with much more precise and narrowly defined meanings. They include words like “mass,” “force,” “energy,” “momentum,” “field,” and “potential.” Be careful not to confuse their physics meanings with their fuzzier colloquial meanings.
• Another language in which you should become fluent is pictorial representation – pictures, diagrams, graphs, and charts. These often are much more powerful ways to represent scientific information than spoken language. They can also be useful thinking tools. Most scientists think often in terms of pictures and analogies.
• The third language in which you need to acquire some fluency is mathematics. It is an enduring marvel that almost no kind of mathematics, no matter how abstract and esoteric, fails to find eventual application in describing some fundamental feature of the physical universe. Occasionally a physicist will literally invent a new form of mathematics in the course of pursuing a new research direction. Calculus is an historic example. Mathematics not only provides a means for expressing fundamental physical principles succinctly, accurately, and with quantitative precision, it also embodies tools with which novel physical ideas can be explored before the underlying ideas are well enough understood to be expressed in simple English. In terms of Rutherford’s transition, you can use math while the physics is still impossible, before it becomes trivial.
• It is important to understand and believe, however, that the mathematics necessary to understand much of the basic conceptual framework of physics is not very sophisticated. Basic algebra and a little trigonometry and geometry are usually sufficient. (You might find it interesting to test that assertion by reading Einstein’s famous 1905 paper presenting his theory of special relativity. It’s not the algebra of E = mc² that’s challenging, it’s the physics.)
• Unlike the equations that usually appear in algebra courses, the algebraic variables in physics equations represent things that can be measured in terms of standard measurement units like meters, seconds, and kilograms. Such equations represent not only relationships among the numerical values of the variables in them, but also among the units of the variables. This provides a useful tool for checking the validity of physics equations.

Active Testing

When the part of the brain just behind one’s forehead has finished fitting new information into its structure of abstract hypotheses, its time for some action. That’s where the top of one’s brain comes into play, the premotor and motor areas. There ideas are converted into instructions to relevant parts of the body to do a variety of things that can collectively be described as “active testing.” Those things can include guiding the hands in typing or writing a description of one’s new understanding, or directing the vocal apparatus in speaking to someone about it. They can include deciding what kind of answer to give on a physics exam.

A very important type of active testing is the design and conduct of actual experiments to test further the conceptual understanding developed during the learning cycle by generating more “concrete experience.” You will recognize that that closes the loop and completes the cycle. But it doesn’t end the cycle, for the Learning Cycle represents a continuous feedback loop, a process that should continue ad infinitum.

That is a crucially important idea. Learning shouldn’t end on arrival at some milestone like the end of a course or graduation. It should continue throughout one’s life (one might say post partum to post mortem). It will take different forms at different times, but it should always use the Learning Cycle. The better one understands that, the better a learner one can be.

Advice to the student learner at this point in the Learning Cycle thus boils down to two major points.

• Actively test what you learn in every way you can. Don’t wait for someone else to test you. Keep asking yourself “Why?” “What?” “How big is it?” “Is this reasonable?” “Does that make sense?”
• Keep learning! Use what you learn to guide the acquisition of new concrete experience, then continue following the Learning Cycle, around and around.

References

1. D. A. Kolb, Experiential Learning: Experience as the source of learning and development, Prentice Hall, Eaglewood Cliffs, NJ (1984).

2. James E. Zull, The Art of Changing the Brain, Stylus Publishing, Sterling, VA (2002).