Self-Directed Learning: A Heretical Experiment in Teaching Physics

1. Introduction

Science is difficult enough without the added burden of being perceived as boring or irrelevant. It becomes relevant - and consequently interesting - when it addresses questions arising out of the learner's own curiosity. How does a teacher tap that curiosity and elicit each student's natural inclination to learn? I discuss here an educational framework that I believe accomplishes this; I call it "Self-Directed Learning".

What follows is an account of an experiment in the teaching of physics at the level of college and university. The underlying principles and methods of instruction are equally applicable, however, to the teaching of any science at any level. Nevertheless, as the most fundamental of the natural sciences, physics is widely perceived as a subject of exceptional difficulty. Whether warranted or not, this perception and the heightened anxiety it generates give urgency to the need of more humane and effective ways to teach physics, if not all sciences. I have applied the principles of self-directed learning for many years in the instruction of my own children, and I know that they work. What qualifies as a "heretical experiment" in the present context is the implementation at institutions of higher education where traditional modes of teaching are ordinarily strongly antipathetic to those recounted in this chapter.

The essential idea underlying the self-directed learning of science is in principle very simple, as I have written before : Science as it is taught should more closely resemble science as it is done by professional scientists. This requires recognizing what good science is and how it is practiced - two points over which even professional scientists may hold divergent opinions. But one must start somewhere, and I draw my own inspiration and hypothetical basis from some thirty years of personal experiences as a research physicist and chemist.

Since the above key assertion colors strongly the attitudes and activities herein described, it is worth asking at the outset why the teaching of science should embrace activities of a practicing scientist. Would the statement make sound educational sense if, as one reviewer asked when these ideas first entered the physics literature , "science" and "scientists" were replaced by other disciplines and other practitioners? Is there no art of appreciation of science distinct from the practice? "I can imagine," wrote the reviewer, "taking a good art appreciation course in which one looks at paintings and never paints, oneself."

Although the rationale for my assertion is addressed in one way or another throughout the entire chapter, in the main it follows from the belief that science is meaningful and its learning of lasting value only to those motivated by their own curiosity to study it. This observation is undoubtedly true (at least to me) for any subject; one could replace "science" by "art" in the preceding sentence. However, when it comes to motivation, introductory courses like art appreciation are often overflowing with eager students; physics by contrast is taken, often grudgingly, by large numbers of students who need it to satisfy the requirements of other programs that interest them far more. Were it not for these requirements, most students enrolled in physics, I suspect, would not be there.

Yet physics is intensely interesting as any practicing physicist knows. What makes it so? There is no unique answer but a reasonable reply would certainly recognize that the study of the natural world raises intriguing questions that arouse a researcher's curiosity, and that there is an intrinsic personal satisfaction in the quest to answer these questions. I doubt whether students who never study physics or who study it unwillingly are aware of this. Does it not seem plausible that students could be motivated by engaging in activities similar to those that have made scientists devoted to their work?

Furthermore, I am concerned with learning physics - and not just learning about physics. Certainly one can appreciate art without ever painting, oneself, and similarly one could study the history or philosophy of physics without ever solving an equation or making a measurement, oneself. But one does not learn physics this way. As is characteristic of any real science, physics is concerned with the ways in which information is sought and tested, knowledge extracted, conclusions drawn and verified. To learn science one must learn at some level, however rudimentary, to analyze, synthesize, and experiment - i.e. to perform activities routinely undertaken by practicing scientists.

A seminal element of the approach to teaching science advocated here is that the major activity of scientists is inquiry. However, it has been my overwhelming experience in examining programs of science instruction that inquiry does not play a significant part. The aspect of the "hard" sciences (physics, chemistry, astronomy, geology, biology, etc.) most emphasized is the network of supposedly solidly known and accepted facts and principles. It is this image of science as a "storehouse of knowledge" - rather than as a dynamic activity by means of which knowledge is acquired and tested - that characterizes nearly all science instruction I have observed in the United States and other technologically developed nations. Moreover, even in curricula which incorporate to some extent a component of student inquiry, the major objective of the investigations - as, for example, the required exercises to be performed in an instructional laboratory - is to reproduce predetermined items from this storehouse of knowledge. Authentic inquiry in science, however, is driven largely by the investigator's own curiosity.

The perception of science as a rigid and infallible source of information percolates the institutions within society and can have serious repercussions. Thus, for example, in his essay, Uneasy Bedfellows: Science and the Law, forensic scientist H. J. Walls eloquently describes the deleterious effects of misunderstanding the nature of science in the courtroom.

"One of the difficulties of communication between science and the law is that the law, or at least its practitioners, seem to have a wrong idea of what science is all about and how it advances. Lawyers appear...to think that science was a corpus of exact knowledge firmly established for all time and that its main business was the collection of facts. If they did think so, they could scarcely be more wrong on both counts."

One important societal consequence, as Walls points out next, of regarding science as a corpus of exact knowledge is that "...lawyers seem to imagine that all scientific measurements are made with absolute precision, whereas all scientists know that this is impossible. The scientist is quite happy to accept this, as long as he knows how large the error is liable to be, or what the mathematical probability is that the true value differs by less than some known amount from the measured one. The conscientious expert witness, however, who tries to put this fundamental idea across from the witness box is likely to provoke a pained rejoinder: 'Dr. So-and-So, you are here to give us the facts, not probabilities.'"

Walls' comments were written some twenty-five years ago, but there is every reason to believe from more recent accounts of the presentation of scientific evidence in the courtroom that little has changed. It is not the purpose of this paper to comment in depth on the misunderstanding and misuse of science in the courtroom. The principal point here, as illustrated by this one example, is simply that the public perception of science diffusing out of the academic communities is no mere academic matter, but has practical consequences that reach to the very foundations of a democratic society, such as its judicial system. Lawyers and judges presumably constitute one of the most educated sectors of a democratic society. If their understanding of the content and purpose of science is faulty, one can only imagine how much less satisfactory is the understanding of the general public.

Self-directed learning is a general approach to education that attempts to remove (or at least minimize) the element of coercion in instruction, and correspondingly give students wide latitude over what they choose to learn. It is based upon a framework in which (i) curiosity-driven inquiry is recognized as an essential ingredient of both science and science teaching; (ii) the principal role of the instructor is to provide students the incentive to learn by helping raise questions that they find personally meaningful; (iii) mistakes are considered a natural part of learning and are not to be penalized; (iv) the laboratory is seen as a place for minimally restrictive free exploration rather than rigid adherence to "cookbook" recipes; (v) research skills are developed through out-of-class projects that involve literature search, experiment, and analytical modeling of real-world phenomena; (vi) articulate communication, both written and oral, is regarded as seminal to science (as it is in the humanities) and encouraged; and (vii) performance is evaluated on the basis of a portfolio of accomplished work rather than on the outcome of formal testing.

2. The "Standard Model"

Although a number of innovative approaches to the teaching of physical science have been proposed over the years, most to my knowledge concerned how best to master the factual content of a particular science, rather than how that content came to be known and how the learner could use it. There is nothing necessarily improper to mastery of detail as part of an overall program of instruction, for clearly students, like scientists, must have a base of knowledge with which to operate. The difficulty arises when detail in and of itself is the aspect of science instruction most accentuated. This is the situation which occurs in almost all classroom instruction I have witnessed or learned about vicariously. Under these circumstances, despite variations among instructional methods and philosophies, the interactions between students and teacher largely share the following common characteristics:

1. The content of the classroom lectures largely repeats the information in an adopted textbook.
2. Assigned problems, which involve primarily formula substitutions, usually test one basic idea or principle at a time. Indeed, textbook problems at the end of each chapter are frequently arranged according to chapter sections.
3. Examinations of various kinds (quizzes, hour exams, laboratory tests, final exam) are frequent, and the final course grade is effectively a measure of cumulative performance on these tests.

So entrenched and universal is this mode of instruction, that I refer to it as the "standard model", an appellation familiar to all physicists. Within the standard model of science instruction, education consists principally of "teaching" - an activity that the skilled (the teacher) does "to" the presumably unskilled (the students) - and testing.

When I think of all the time spent by teachers in constructing and grading tests, and by students in preparing for and taking them, I can not help but believe that such time could be used more productively by all participants to understand better what science is all about. I have often posed the question, "Why is it necessary to test students?", to various scientists and educators. The replies were usually obvious: testing enables instructors to determine what a student has learned. But why should it be necessary for an instructor to know what a student has learned - if indeed that is even possible? This question elicits astonishment, yet the responses basically distill down to the following belief. Unless instructors ascertain what students have learned, they cannot evaluate students fairly - and without such evaluations it is not possible to determine which students should be permitted or denied access to various courses, programs, schools, etc. In brief, testing and evaluating serve to lubricate the administration of education.

3. Basic Premises

The motivational basis of self-directed science learning differs radically from the standard model of instruction. For one thing, the purpose of education is to foster "learning" which - in contrast to "teaching" - is something a person does for him - or herself. Second, the purpose of testing - which does serve an important educational function - is for the exclusive benefit of the individual student and not of the teacher or of educational administration in general. It is a means by which students can assess, for their own knowledge and subsequent personal action, the extent of their mastery of course material. However, within the framework of self-directed learning, tests are not graded by the instructor, and, most importantly, the outcome of testing - either directly by examinations, quizzes, etc., or indirectly through out-of-class (i.e. homework) assignments - is not a basis upon which student performance is evaluated.

To avoid at this point any semantic confusion, I would like to stress that the designation "self-directed learning" does not imply that students are expected to learn science entirely on their own with no assistance from an instructor, or that the role of the instructor is in some sense a minor and possibly dispensable one. Quite the contrary, a skilled science instructor - and preferably one who has personally engaged in authentic scientific activities involving research and possibly publication or public presentation - is of vital importance.

In self-directed learning the instructor's principal role is to motivate the study of science in such a way that students do not find the process of learning discouraging and threatening. The justification of this role derives from the experience of many educators, particularly those involved in programs of non school-based instruction , that students who understand the significance of what is being taught and who see the personal need to learn it will master on their own, sooner or later, what they believe is important to know. For the remainder of this section I would like to elaborate on the italicized portion of this paragraph which constitutes, in essence, a sort of credo of self-directed learning.

The preceding assertion regarding a student's capacity to learn independently is not simply a paraphrase of Gibbons, that "The power of instruction is seldom of much efficacy except in those happy dispositions where it is almost superfluous." Quite the contrary, the underlying idea is that the power of instruction can be very effective, when it is utilized in an appropriate way. It is worth emphasizing that those happy dispositions of Gibbons are rare, and that most students are not able on their own to see the significance of what they are studying or inclined to undertake its mastery voluntarily. This is particularly true in the case of physics, and quite possibly in other sciences as well, where fewer and fewer students enroll for introductory or general survey courses to learn science, but rather to fulfill the requirements of other educational programs.

Under circumstances such as occur all too commonly in schools, where an instructor faces a captive audience who are unlikely to follow through with additional science courses of the same kind and who believe they will rarely, if ever, use the facts and principles of the present course in their future occupations, emphasis on memorization, drill, and problem solving for its own sake is educationally unproductive and difficult to justify. It is precisely then (as well as under the more congenial setting of having interested participants at the outset) that students need to be helped to understand the universal significance, personal relevance, and intellectual excitement of the scientific studies upon which they are embarking voluntarily or otherwise. Such motivation is not easily effected, and, without an adept instructor with both knowledge and enthusiasm, is unlikely to be achieved at all. Clearly, then, self-directed science learning does not minimize the contribution of teachers, but instead redefines their primary role.

There are two additional related points essential to the foundation of self-directed learning that are neither trivial, nor widely recognized, nor ordinarily implemented in educational practice. The first of these concerns the holistic nature of normal (i.e. out-of-school) learning, in contrast to the linear nature of teaching within the standard model. The second point, to be discussed at the end of this section, concerns broadly the issue of performance evaluation.

A heuristically apt metaphor for holistic learning is that provided by neural networks in which various network connections are simultaneously modified (the network 'learns') by repeated exposure to diverse stimuli and subsequent comparison of response with desired results. This is, in fact, not unlike the way a young (preschool) child learns. No one ordinarily instructs preschool children in the rudiments of their native language; a healthy child, motivated by the need and desire to communicate, simply "picks up" language by exposure to others who speak it (...one important reason, therefore, for parents to exercise good judgment in monitoring the influences to which their children are exposed). Unfortunately, once formal schooling begins, the holistic way of learning is discouraged, if not suppressed, and is supplanted by a linear mode of instruction.

Consider, for example, the skill of reading. One might imagine that normal children who can learn to speak can also, with suitable guidance and exposure to books, teach themselves to read. And yet at many primary schools within the United States reading is regarded as an ability which students acquire only through mastery of a progression of preliminary skills that only trained and certified instructors are capable of teaching. This partitioning of a holistically learnable activity, reading, into a formal sequence of artificially devised steps can be extreme. According to one 1977 newspaper report cited by educator John Holt

"It has been ten years in the making, but Chicago school officials now believe they have in place a complete sweeping program to teach children to read - a program that may be the pacesetter for the nation...For some years, a Board of Education reading expert...has been putting together a package of the reading skills children need to learn in elementary school. At one point, [the] list topped 500 elements. It has since been reduced to 273 over grades 1 through 8."

To such a linear and fragmented approach to education, I share Holt's reaction:

"This might be rather comic if it were not so horrifying. Five hundred skills! What in the world could they be? When I taught myself to read, I didn't learn 500 skills, or even 273; I looked at printed words, on signs, in books, wherever I might see them, and puzzled them out, because I wanted to know what they said. Each one I learned made it easier for me to figure out the next. I could read before l went to school...Most people who read, above all those who read well, were never taught 273 separate skills."

Indeed, that has been my own experience as well. When, some years ago, I was invited to be Chief Researcher at the Hitachi Advanced Research Laboratories in Tokyo, I realized that at the very least I would have to teach myself to read the Japanese language. There are two finite sets of syllabaries (Hiragana and Katakana) and a virtually open-ended set of Chinese characters (Kanji). If it were truly the case that 500 skills are required to read English, then the number of skills needed to read Japanese ought to be astronomical. This is, of course, not the case. Motivated by the strong desire not to remain illiterate, I, like Holt, puzzled out primers, journals, newspapers, traffic signs, shop windows - any source of printed words - until I could understand them. Motivation, rather than external instruction, was all that was needed.

The holism that characterizes the way in which both professional scientists and young children learn is the most natural way for college and university students to learn as well, if they have the opportunity. Holistic learning involves the integration of diverse threads of knowledge (synthesis) and the recognition of simplifying elements (modeling) in the development of tractable solutions to real-world problems. While it is true that the conceptual structure of a science like physics is to a large degree hierarchical - one could not, for example, understand Newton's laws of motion without first understanding the concept of acceleration, nor Maxwell's equations without first knowing what electric and magnetic fields are - this does not necessarily require that the teaching of science be partitioned into a linear sequence of nearly mutually exclusive units of information.

Consider university-level physics again. A course of study in general physics, which may last two to four semesters, ordinarily begins with mechanics, and then embraces in more or less the following order the topics of gravity, fluids, heat, electromagnetism, optics, and various aspects of 20th century physics including relativity and quantum physics. These different topics are treated separately in different parts of the textbook and in widely separated classroom presentations. For example, mechanics and electromagnetism often fall into different courses taught different semesters.

There is, of course, a certain sense to this organization; no sane instructor would begin a course with the most advanced material. However, most of the above topics are arranged not by complexity, but by the specific forces that apply. In the "real" world of science, however - as opposed to the academic environment of most classrooms - it is rare that a physicist would encounter an interesting physics problem so simple that it could be adequately described by a set of principles falling into only one of the units taught as an independent entity in introductory physics. In my own case, for example, a "typical" problem to be studied might involve the internal structure of an atom (quantum mechanics) subject to external static fields (electricity and magnetism) interacting with a laser beam (waves and optics) and exchanging energy with a heat reservoir (thermodynamics).

A successful scientist learns how to build appropriate models of real physical systems in order that the mathematical analyses be tractable and experimental tests lead to comprehensible results. It is generally the case that systems worth investigating involve many threads from the far-reaching fabric of physics. That is what in part makes an interesting science problem interesting. Conceivably, it is also what would make a course of instruction in science interesting. And yet, in the traditional presentation of physics, a student might well pass an entire semester listening to lectures and working homework and test problems involving electric and magnetic fields with hardly any connection to the mechanics course of the previous term or to the modern physics course to follow. One consequence of this strict partitioning of material is that students do not learn to make synthetic associations. Having analyzed, for example, the behavior of a small-amplitude pendulum in the mechanics part of Physics 101, the same students a semester later in Physics 102 might look upon the flow of electric charge in a circuit with inductance and capacitance as a totally foreign phenomenon. And yet the two different systems are both examples of harmonic oscillation.

By contrast, one of the goals of a physics course following the principles of self-directed learning is to help students recognize the interconnectedness of the physical world. The task faced by the instructor is at least two-fold. First, to create - since textbooks are rarely of help in this regard - classroom problems, not of the substitution variety, that induce students to draw upon as much as possible of the previous physics they have encountered. Second, to formulate - or, better still, to help students formulate - independent out-of-class projects that engage each student in one of the principal activities of research scientists: realistic modeling of physical systems. Neither of these two tasks is simple. Indeed, to develop educationally meaningful problems and projects appropriate to an introductory course of study requires skill and commitment on the part of the instructor.

Although an important part of self-directed learning centers on building motivation through realistic and purposeful problem solving, students do not necessarily end up with an idiosyncratic or "spotty" introduction to physics where the beauty of the whole is obscured by the details of individual investigations. Quite the contrary. What is it about the whole of physics that physicists find aesthetically satisfying? Is it not in part the universal validity, internal consistency, and wide application of a few general principles - in effect, the recognition that there is reason in nature amenable to discovery and explanation or prediction and verification? Is the beauty of this whole more likely to be perceived through comprehensive, if not overwhelming, coverage of separate, sequentially presented topics, or through selected investigations each of which reveals the simultaneous and coherent interplay of different physical laws? I would choose the latter, having learned from years of teaching that coverage by itself and unrelated to students' own questions has a deadening effect which, far from exposing the beauty of physics, obscures it under a veneer of disconnected fact and mathematical formulas. Moreover, in implementing self-directed learning, an instructor is certainly at liberty to present unifying class lectures to complement the personal out-of-class investigations undertaken by students.

Lastly, a holistic approach to education does not imply, as some might fear, the daunting prospect that one must learn everything in order to learn anything. Clearly this is not possible. In self-directed learning, as with traditional teaching methods, classroom discussion focuses on a particular topic at hand. Nevertheless, by recurrent and varied encounters, facilitated by the instructor, with principles and phenomena beyond their present ability to understand fully, students can become familiar with the broader content of physics and see much of that content as logically interconnected instead of fragmented. The details of the logic will be sharpened progressively if continued interest leads to further study. I will give examples in the following section of how holistic learning can be fostered in the classroom. It is worth illustrating by a personal example, however, that this is a natural way in which scientists, themselves, learn.

As a physicist whose graduate studies centered on atomic and optical physics, I had occasion early in my career to be faced with a problem involving application of general relativity, an esoteric subject in which I was not explicitly "trained". With this problem as my incentive - and no longer in a position to take courses - I turned directly to the science literature to learn what I could about the system that interested me. What I first came to realize, however, was the existence of whole areas of mathematics and physics of which I was ignorant, but now needed to know. In pursuit of the answer to a problem in which I had a personal stake, I had to inform myself about the elements of non-Euclidian geometry, the manipulation of tensors, the theory of continuous mathematical groups, the approximate solution of nonlinear differential equations, and the principles of astrophysics - none of which I had studied in school.

I emerged from this problem - certainly no expert in any of these areas - but more knowledgeable than before. And, as the need again arose from time to time to investigate systems where general relativity was applicable, I immersed myself again in the arcana of the above topics, each time emerging with a broader and deeper knowledge and more confidence in my problem-solving abilities. I am still no expert, but I can understand the significance of general relativity, the conceptual connections among different domains of physics to which it allows access, and basic problems at the frontiers of astrophysics and cosmology to which real experts devote their attention. The research I have done in this self-taught subject has even received several distinctions from the Gravity Research Foundation.

The above (and other similar) experiences have impressed upon me three significant lessons: (i) I did not have to learn all of general relativity in order to learn to use some of it, (ii) I would not likely have learned any of it had not an express purpose motivated me, and (iii) what I did was not exceptional, but part of the normal way scientists teach themselves. No accomplished scientist I know would have sat through a series of courses to be taught step by step all the skills necessary to study some physical phenomenon of interest. (Long before such a course of study was completed, the original problem would undoubtedly have been solved by someone else.) These lessons apply not only to the way physicists "do" physics, but also to the way students can learn physics.

I conclude this section with the thorny question of assessing performance, or, more specifically, issues related to error, penalty, and student self-esteem - matters that are handled more humanely, in my opinion, in self-directed learning than by traditional modes of teaching. As a scientist and teacher, I am often reminded of the advice given by the Princesses Rhyme and Reason to young Milo in Norton Juster's delightful adventure story for children, The Phantom Tollbooth

"You must never feel badly [sic] about making mistakes," explained Reason quietly, "as long as you take the trouble to learn from them. For you often learn more by being wrong for the right reasons than you do by being right for the wrong reasons."

"But there's so much to learn," [Milo] said, with a thoughtful frown.

"Yes, that's true," admitted Rhyme; "but it's not just learning things that's important. It's learning what to do with what you learn and learning why you learn things at all that matters."

Most scientists, I surmise, would hold feelings similar to my own that, in the course of their research, errors are critical to advancement. Indeed, it is precisely when one corrects a mistaken idea or measurement that learning begins again.

If science is to be taught as it is practiced, then students must be allowed to commit errors and learn from them without the fear of punishment or failure. "Essentially, it seems, our brains learn best - and grow to learn more - ", said educator John Abbot, "when we exercise them in highly challenging, but low-threat environments." This is decidedly not the case in the standard model of instruction where students are tested and evaluated continually. Judgmental monitoring of this sort is one of the most pernicious ways of suppressing creativity and transforming what ought to be a pleasurable activity, namely learning, into a nightmarish experience.

Aside from the anguish that testing and the threat of failure may engender, the traditional methods of evaluation are often misguided and do not generally provide educationally useful information. Students frequently do poorly on exams who, under less stressful circumstances - such as in personal discussions with the instructor - show good understanding of course material. Conversely, many students receive high marks in a course for the wrong reasons (in the words of Princess Reason) by "plugging and chugging" their way through prepared material, yet (in the words of Princess Rhyme) having little idea what to do with it or why it was worth learning.

Effective learning is not an activity that can be adequately assessed over the short duration of an academic term, but is demonstrable only over the long run - perhaps years - by the ways in which a person meets the challenges of life including, among others, those of career, family, and society. This applies as well within the narrower domain of science. When I consider the many students who have worked on research projects with me over the past two decades, I do not find course grades, determined in the conventional manner, to be a reliable indicator of a student's potential abilities to use scientific facts, principles, and modes of reasoning in constructive and creative ways. And is this not, in fact, what science teachers are ultimately trying to achieve - to prepare students for meeting the challenges of the future?

Self-directed learning recognizes at the outset that errors are part of learning, that mistakes made while learning should not be penalized, that it is fruitless to try to measure - as one would a volume of liquid - the volume of material absorbed by a student in the course of an academic term, and that the judgment of students is best based on what they actually do (i.e. on their effort), rather than on what they supposedly learn.

4. Implementation

Self-directed learning is more an attitude, than a uniquely formulated program or procedure. Once the underlying framework and goals discussed in the previous sections are accepted, an instructor can undoubtedly find a variety of ways to achieve them. For illustrative purposes I will describe the principal features of an approach I followed in teaching the second half of a four-term sequence of introductory physics. The students had already completed the first two terms comprising basic mechanics and thermodynamics; these courses were taught by other instructors in strict conformity with the standard model. The final two terms, during which the ideas of self-directed learning were implemented, were nominally devoted to electricity and magnetism (Term 1) and optics and "modern" physics (Term 2). The course format, fixed long ago by the Physics Department in accordance with basic institutional requirements, consisted of three one-hour lecture sessions and one three-hour laboratory session per week. As at many other schools, the individual instructor had no control over this general format.

Although the following account uses examples drawn from the teaching of physics, any natural science can be taught within the same philosophical framework. The central issue here is the reshaping of instructors' attitudes toward teaching and students' attitudes toward learning.

It is worth stressing that what transpires during initial contact with students the first day of class is critical to the smooth and successful progression of the course throughout the rest of the semester. It is essential that students have an understanding of the new mode of instruction to be followed, the rationale for it (as just outlined), and what precisely is expected of them (to be elucidated later in this section). With no exception that I have ever encountered in many years of teaching, the students entering my courses have all been educated traditionally - i.e. in accordance with the standard model - for a span of some 12 or 13 years from the day they first entered primary school. Under this system the principal motivation is external, originating, at least among the more conscientious students, in securing high marks and teacher approval by doing well on tests and other graded exercises. Since only a few receive the highest grades, the system fosters competition among students, rather than an internally motivated drive to do well for the sole sake of personal intellectual advancement. The reader can well imagine, therefore, that it is not an easy mental adjustment for students to make initially when, in contrast to all they have experienced previously, their physics instructor now tells them at the start of term the following:

(i) This is a course based on self-directed learning. I will talk to you (in the morning lectures) about what I think is conceptually important, practically useful, historically interesting, philosophically challenging, or (to me) personally meaningful - but you are free to take away from this course as much or as little as you choose.

(ii) There will be no scheduled class exams, and the quizzes that will be given periodically will not be graded; they are for your personal guidance in keeping you informed of what I think you ought to know.

(iii) Homework problems will be assigned throughout the term and solutions will be subsequently provided and discussed - but they are exclusively to help you learn physics; they will not be graded, and you will not be penalized for working problems incorrectly.

(iv) Your grade for this course will be determined on the basis of your effort, rather than on the outcome of testing, as demonstrated by a portfolio of work to be prepared throughout the term and submitted by the last day of class.

Grading, according to either standard or nontraditional modes of instruction, always involves considerable subjectivity, and a full discussion of the matter is not possible here. Personally, I would have preferred to teach physics without assigning letter grades - or on a simple pass-fail basis - but this was not an available option. Suffice it to say that, since the fear of doing poorly is one of the principal reasons why in many cases student performance in physics actually is poor, I decided to alleviate that fear at the outset in the following way. Every student whose physics portfolio met the minimum criteria of acceptability was guaranteed a grade (B-) representative of "good" work. Since a course grade now depended more upon the individual conscious decision to work or not to work, rather than on the vicissitudes of testing, students had more control than before over their destiny in this course.

The physics portfolio, which was to be prepared in accordance with specified guidelines that I will discuss shortly, represents concretely what students have actually done in the course and serves as a more meaningful basis for evaluation than the inference from tests of how much or how well they may have learned. Each physics portfolio is to contain the following items:

1. A written account (original or recopied) of class activities, which includes, for example, lecture notes, solutions to in-class problems, interpretive discussions of physics demonstrations, summaries of class "workshop" sessions and student-led presentations.
2. The student's own written solutions to assigned or suggested homework problems
3. Class quizzes, reworked correctly if necessary
4. The laboratory notebook with originally submitted experimental reports and any subsequent revisions
5. The account of one (or more) independently researched projects during the course of the term

Although the portfolios are to be submitted and evaluated at the end of the course, it is essential that students understand they are to be preparing their portfolios throughout the term. Indeed, the very nature of the contents almost assures this - although instructors would be prudent to remind their classes periodically.

Within the general framework of (A) class work, (B) laboratory work, and (C) out-of-class work, I will comment on the above portfolio items to the extent they reflect the distinctive objectives and methods of self-directed learning.

5. Class Work

In courses taught traditionally, class notes serve the principal purpose of summarizing the information students think most likely to appear on examinations. Correspondingly, the notes, which are taken at the sole discretion of each student since the instructor rarely has interest in them, are usually consulted only shortly before a scheduled test. In many cases, they are discarded upon the termination of a course, since they contain little more than reworked examples and exercises from the textbook.

In self-directed learning students are not faced with tests, and a record of classroom activity serves a different purpose. First, it is clearly not possible for students to take personal class notes unless they show up for class. In this regard, the requirement of note taking is tantamount to a requirement of course attendance. Obligatory attendance, I believe, is a reasonable part of the required "honest effort" upon which a guaranteed grade is contingent. More importantly, however, the responsibility to present a legible set of notes in the portfolio has a beneficial influence on study habits. It necessitates that students review, and possibly recopy, their notes each night (or perhaps several times per week) if the procedure of note preparation is not to become too burdensome. Students who take notes attentively and review them regularly can become aware quickly of what they do not understand - and can seek assistance in a timely way. By contrast, when students take and consult notes for exams only, they frequently do not realize how little they understand until it is too late.

The purpose of keeping records, however, is not merely - or even mainly - to write down what the teacher puts on the blackboard. If students are required to attend class and take notes, then instructors are under a particular obligation to utilize class time effectively - in particular not to repeat what students can readily acquire from their books. I do not dispute that discussions of textbook concepts and applications, including worked numerical examples, as typically comprise the lectures of traditionally taught science courses, can contribute to productive use of time (presuming students know why they are doing these things). Nevertheless, there are other educational opportunities that, if not unique to self-directed learning, are certainly facilitated by it.

I have at times begun a class by posing a problem suggested to me by some recent report in a science periodical, physics conference, or even daily newspaper, and have the students break up into small groups to attack it. Or I have assigned different problems to separate groups, each group reporting on its progress in the class discussion that later ensued. At other times, in the course of my lecturing, one of the students might raise a particularly thought-provoking question. Rather than answer it myself and continue with prepared material, I would use that question as the focal point of a class discussion exploring the different aspects - physical, mathematical, philosophical - of the new issue. In self-directed learning, as in home schooling, a teacher can proceed flexibly without the frantic rush through a syllabus. The goal is not so much to cover a subject, as to "uncover" it.

In traditional modes of instruction, students frequently perceive new material as threatening - particularly if it lies outside the scope of the textbook - since they will often see it again on an examination. Thus, instead of eliciting intense curiosity and animated classroom discussion, the presentation of intellectually challenging and significant ideas evokes instead the apprehensive query, "Do we really need to know this?" An advantage of self-directed learning is that instructors can enrich course content without simultaneously arousing anxiety within their classes.

I would like to give one specific example of how, by exploiting the opportunities of self-directed learning, I have been able to make students aware of an issue of great import to physics and direct relevance to the thematic content (electricity and magnetism) of their course (Term 1). This seminal topic, which is ordinarily ignored in introductory physics, is the Aharonov-Bohm (or AB) effect (introduced in Chapter 10). The significance of this illustration lies not only in the physics, but also in how it promotes holistic learning by exposing students in a nonthreatening way to the essential principles, historical development, and philosophical underpinnings of a far-reaching contemporary controversy in science.

Following the researches of Faraday and Maxwell, it has become an integral part of the philosophical and mathematical foundations of physics to regard all interactions between matter as being mediated by fields of influence that are directly related to forces and propagate through space from one material particle to another. Each particle interacts locally with a field in its immediate vicinity. Thus, in regard to the presentation of classical electromagnetic phenomena, virtually all elementary general survey textbooks I know take electric and magnetic fields as the fundamental theoretical constructs. An introductory course of electricity and magnetism is concerned primarily with the characteristic motions of charged particles accelerated by specified electric and magnetic fields, and, reciprocally, the configurations of the electric and magnetic fields created by charged particles in different states of motion.

One can perhaps imagine the consternation among many in the physics community when, in 1959, Yakir Aharonov and David Bohm demonstrated theoretically that the state of motion of a charged particle can be altered by the presence of a static magnetic field through which the particle never passes and which therefore could exert no local classical force on it. The effect on the particle's motion, according to AB, derives instead from a local interaction with other fields (vector and scalar potentials) that had been introduced into electromagnetism by Maxwell to facilitate calculation and were considered by most 20th century physicists to be devoid of "reality" since they exerted no forces. Consider, for example, the following brief eyewitness account of the reaction of Niels Bohr - foremost among quantum exegetes - and his disciples upon first learning of the AB paper:

"Our tranquility was rudely disrupted when in the fall of 1959 a paper entitled 'Significance of Electromagnetic Potentials in Quantum Mechanics' came to our attention. The authors of this paper had the audacity to claim that in quantum mechanics, unlike classical physics, the potentials can directly affect the motion of charged particles, although they are 'merely' mathematical instruments introduced in the 19th century to simplify the calculation of electric and magnetic fields that are 'truly' the quantities that one observes.

Many physicists, including Bohr and his associate LŽon Rosenfeld, were profoundly taken aback by this suggestion. For a while Bohr was extremely skeptical; in the lunchroom Rosenfeld declared the Aharonov-Bohm proposal...to be not only an affront to the Copenhagen concept of a physical observable, but also 'contrary to the spirit of Galileo'."

Subsequent theoretical analyses and difficult experiments have confirmed the existence of the AB effect, and - after some thirty years of controversy - most physicists interested in the foundations of physics have reconciled themselves to this strange but calculable behavior of charged particles. Indeed, this behavior is not by any means an unimportant side curiosity, but absolutely essential to the internal consistency of quantum mechanics .

Although the AB effect reflects the quantum, rather than classical, behavior of charged particles - a subject that students had not at the time encountered - it still concerns only classical electric and magnetic fields. The quantum nature of electromagnetic fields (the concept of the photon) does not enter at all. Thus, the conceptual implications of the AB effect were of direct relevance to this introductory class. These implications are far-reaching. The AB effect forces physicists to accept that either (1) the electric and magnetic fields can have nonlocal influences on the state of motion of charged particles, or (2) the potentials, which exert no forces and can not be uniquely specified, are more fundamental than the electromagnetic fields.

All this is fairly 'heady' material, but contains the ingredients - surprise, paradox, controversy, action (experiment), resolution, deeper understanding - of an intellectual drama that can attract and sustain a student's interest in a physics course. It provided an occasion to review the basic philosophical premises of classical physics - matters relating to cause and effect, prediction, precision, and the local nature of laws expressed in the form of differential equations - as well as interesting biographical details of some of the principal contributors (e.g. Newton, Faraday, and Maxwell). Likewise, it permitted me to expose students in advance of the traditionally prescribed sequence of courses to the phenomenology and concepts of quantum physics and to the historic personages (e.g. Planck, Einstein, Schršdinger, Heisenberg) upon whose work this edifice was built. And - since the AB effect was an area which has occupied my own attention as a research physicist - I could convey to students personally the exhilaration of research and discovery.

In discussing a topic like the Aharonov-Bohm effect, one must of course take care to present it at a level that physics students can follow to a sufficient extent to reap some benefit from attentive listening. But I have seen that with self-directed learning this was both possible and advantageous. Students came to appreciate that

(i) the content of science is intricately interconnected, and a discovery in one area of it can have far-reaching major repercussions. (The AB effect led to a reformulation of classical electromagnetism and a reinterpretation of the roles of fields and potentials.)

(ii) science is a human activity where not only personal creativity but also articulateness and persuasiveness matter. (The AB effect was actually reported about ten years earlier by British physicists Ehrenberg and Siday ; their paper was narrowly directed to electron microscopists, and the full conceptual implications of its content were not widely appreciated.)

The basic message of the preceding example is not limited to physics teachers. Metaphorically speaking, every field of natural science has its AB effects - i.e. critical points of development beginning with universal disbelief and culminating in major reversals of contemporary thought. In the earth sciences, for example, the idea that continents "float" upon a plastically deformable planet was first ridiculed and rejected (in part because the idea originated with a meteorologist rather than with a geologist), but was ultimately sustained by a confluence of evidence from diverse fields of science, especially physics. This makes another gripping and instructive story interweaving the principles of physics and the vagaries of human nature.

In short, one of the most effective ways a teacher can utilize class time to help students learn is by the regular presentation of historically and conceptually significant material beyond the textbook that fosters a holistic and challenging learning experience within a nonthreatening environment.

6. Laboratory Work

From discussions with many science instructors, I would say that the laboratory in introductory science courses is ordinarily meant to serve three principal purposes: (1) to allow students to witness basic phenomena; (2) to introduce students to practically important apparatus and measurement techniques; (3) to give students a flavor of scientific research. Although it is possible to realize the first two objectives in a traditionally taught laboratory, I have grave misgivings concerning the extent to which any course taught in accordance with the standard model could approach the third objective which reflects the activity of inquiry and is, I believe, the most essential part of both science and science education. As I have written elsewhere

"...as usually constituted, [an instructional laboratory] does not in the slightest way represent what a scientist experiences when he is performing experimental research; for teachers to portray it as such, as is frequently done, is very misleading. A science instructor deceives himself who believes that any laboratory programme designed from the outset to yield clean, unambiguous data in a reasonably short time on previously well-studied phenomena with low probability of failure could in any serious way reflect what experimental science is like! I attest to this as one who has engaged in experimental work for over a quarter century."

Although practices vary, of course, among institutions, the divers modes of laboratory instruction that I have witnessed usually have the following attributes in common. First, to the extent that lectures and laboratories are coordinated, a particular experiment is usually meant to illustrate material that has already been discussed in some detail by the instructor. Second, the students are given information sheets detailing the experimental objectives, the apparatus to be used, the instructions to follow in executing the experiment, what physical quantities to measure or observe, what formulas to use for analysis, and ultimately what experimental or theoretical end result to deduce and compare with some known standard result. Third, students are expected to report on their exercise according to a formal prescription covering everything from the content of the introduction (title, objectives, schematic design of apparatus, etc.) to how and where to record data, calculations, results, interpretations, and conclusions. Finally, the students' notebooks are collected weekly and graded, often on the basis of the accuracy of their results.

While the foregoing mode of laboratory instruction might turn out functional technicians or engineering assistants, I do not believe it is accomplishing what ought to be one of the principal objectives of science education - namely, to interest students in science. It is worth noting again that many, perhaps most, of the students in an introductory physics course are not there by choice, but by force of circumstances. Assuredly the above ritualized procedure does not foster curiosity-based inquiry, for it scarcely permits students to exercise their curiosity. Worse still, it may be destructive of whatever creative instincts lie dormant in the students. The widespread emphasis, especially in physics courses, on detailed random-error analyses may also border on the ludicrous, given that apparatus available for instructional laboratories is generally far below that of research laboratories in quality, and poor results are more often attributable to systematic problems than to randomness.

In a laboratory organized around the principles of self-directed learning students are encouraged to observe, question, and experiment under conditions that provide adequate time for inquiry and that do not penalize them for the conclusions they reach, even if these conclusions are at variance with accepted results. In short, the purpose of a scientific experiment is to satisfy the curiosity of the experimenter; it is not another type of academic test upon which students' grades are based.

Irrespective of the exact format of laboratory organization, the essential ingredient to an educationally productive laboratory experience is that, to the extent possible, experiments not be of the cookbook variety. The laboratory exercises should be so designed that students can employ their own ingenuity in executing them and must at times go beyond the information provided in class - e.g. to use the resources of the library or computer center - to analyze and interpret them. It is important to emphasize - since state-of-the-art apparatus is ordinarily out of the financial reach of many colleges and universities, not to mention secondary and primary schools - that such apparatus is not required, or even necessarily desired, for a successful learning experience. Indeed, I have often found that experiments flawlessly performed and analyzed by expensive equipment for which the students' role consists largely of pushing the start button and subsequently collecting the computer printouts have little, if any, educational significance. As any research scientist knows, the learning experience in experimental work comes from solving the problems attendant to assembling the apparatus and making and interpreting the observations. Thus, the apparatus for experiments which are meant to interest and educate students should not be "black boxes", but rather open to inspection and capable of comprehension. In this regard it is worth noting that in Japan, where for decades students have traditionally excelled in the sciences, interest in science has been declining, according to the Japanese Science and Technology Agency, in part as a result of the black-box nature of consumer electronic products. "Gone are the days when youngsters acquired a taste for science from their investigations of the innards of clocks and wirelesses", since it is no longer possible to tell from the external appearance of a device how it works.

I would like to give one example of the implementation of a laboratory based on self-directed learning in which students examined the nature and effects of light polarization. Historically, the investigation of light polarization by French "opticians" such as Arago, Biot, Malus, and especially Fresnel contributed seminally to the wave theory of light and the demise of the corpuscular theory associated with Newton. Although many instructors neglect the historical evolution of scientific concepts in their struggle to cover in their lectures the technical material of the textbook, it is noteworthy that the laboratory, and not just the lecture hall, can provide an appropriate forum for discussing issues of historical significance. Also, given the times in which they were performed, historically significant experiments generally employed relatively simple, intellectually accessible apparatus (as opposed to black boxes) of the kind suitable for educational purposes today.

At different work stations over a period of two weeks students had the apparatus and materials they needed to investigate the effects of linear polarizers, to measure the intensity of light of different polarizations specularly reflected from a smooth surface, and to examine the properties of birefringent media. At the start of the first session topics like Malus' law, the Fresnel relations, and light interference had not been discussed in lecture, and so most students (who do not read ahead in the text) did not know the explanations for what they were "supposed" to find. Indeed, they were not required to find anything, but rather to experiment, observe, and at some future time (three weeks later) to account for what they saw and measured.

In the course of the experiments students encountered a number of enigmatic results. For example, if a polarizer acts to filter out light, why does inserting a third polarizer between two orthogonal polarizers lead to greater light output? If the polarization of a light source is a measure of the "degree of order" of the light waves, why does reflection of unpolarized (and therefore totally disordered) light at Brewster's angle lead to a 100% polarized reflected beam? Does this not somehow violate the Second Law of thermodynamics that natural processes always occur in the direction of increasing disorder? Why does placing certain transparent colorless materials (like cellophane) between two neutrally colored polarizers give rise to a profusion of bright colors? Does the thin cellophane layer refract the light like a prism? (Subsequent experimentation readily showed that this was not the case.)

Eventually the students came to understand by their own experimental work and out-of-class research the reasons behind the phenomena. By the time the sessions devoted to light were completed, the class had progressed in several ways. First, they learned something about the behavior of light (e.g. interference) - not by the traditional mode of sitting through lectures, but in the course of pursuing answers to questions (Where did the colors come from?) that personally intrigued them. Second, they became more skilled in analysis (disengaging the various processes that contribute to an observed phenomenon) and synthesis (developing a model for interpreting an observed phenomenon by combining various processes). Third, and perhaps most important, they came to appreciate that the laboratory, itself, can serve to introduce new ideas. This is an important point illustrative of one of the principal objectives of self-directed learning: one can teach oneself by observing.

While no claim is made that a laboratory employing the principles of self-directed learning replicates all the experiences of authentic scientific research, I do believe that it approaches this ideal much more closely than laboratories taught in the traditional format as previously described. For one thing, freed from the burden of test-based evaluations, students could approach experimental work with a more positive attitude and a greater willingness to explore and just "try things out". When grades are at stake, every false step in conducting an experiment is regarded as wasted time rather than as a useful learning experience. (Thomas Edison, having failed repeatedly to make a durable lamp filament, is alleged to have replied that he had not wasted his time at all, but simply learned of ten thousand ways not to make an electric lamp.) Secondly, the students, themselves, raised many questions for investigation directly from their observations, and, with their curiosities aroused, set about to answer them. To be sure, they were helped by the ensuing lectures and by conversations with the instructor, and were therefore able to continue the experiments with greater understanding of the phenomena they were investigating. Nevertheless, in stark contrast to the sense of futility that people often experience when perfunctorily executing some mandatory procedure in an attempt to answer questions they never posed themselves, self-directed learning permits students a greater sense of personal control over their laboratory work.

7. Out-of-Class Work

In traditional methods of instruction, the principal focus is on classroom lectures. So entrenched is this standard model of education, that many teachers can not believe or admit that students are capable of learning independently outside the classroom. At one institution where I have taught, for example, the faculty voted to eliminate a week of respite from classes in the apparent belief that little good can come to either students or teachers from having "free time". Yet the leisure to observe and to think is precisely what is necessary for learning. In this regard the reflection of educator Jerome Bruner is pointedly relevant

"The will to learn is an intrinsic motive, one that finds both its source and its reward in its own exercise. The will to learn becomes a "problem" only under specialized circumstances like those of a school, where a curriculum is set, students confined, and a path fixed. The problem exists not so much in learning itself, but in the fact that what the school imposes often fails to enlist the natural energies that sustain spontaneous learning - curiosity, a desire for competence, [and] aspiration to emulate a model..."

Bruner was concerned with the formative years of schooling, but his words are no less applicable to education at the level of college and university as well. And they are especially pertinent to the teaching of science.

What makes science a critically important and fascinating subject in the first place is that it is drawn from, and relates directly to, the "real" world. In physics, particularly, the basic principles are of universal applicability, as valid within the remotest galaxy as they are on Earth. The manifold implications of an abstraction like "universality" are not easily communicated to students, or grasped by them, within the confines of a classroom (even including instructional laboratory). To appreciate the notion that "science is everywhere" - that natural phenomena can be readily observed and their underlying causes understood - requires that one actually go outside the classroom and examine the world with an open and curious mind. A simple walk through the woods or along the seashore can provide to the receptive mind more of a science education than would come from hours spent listening to lectures. This is not simply empty rhetoric. I have, myself, encountered nearly the entire phenomenological content of a standard course in optics - polarization, refraction, reflection, interference, diffraction, scattering (Rayleigh; Mie) and dispersion - by puttering in my kitchen , observing submerged objects near the seashore, and gazing at the sky . Teachers and administrators who would "improve" education by lengthening class time and diminishing opportunities for outside contacts and leisurely contemplation do their students no genuine service.

Those who would teach science in accordance with the principles of self-directed learning - although they are constrained to operate under the same specialized circumstances (to use the words of Bruner) as all other teachers - must nevertheless find educationally meaningful ways for students to learn from their own experiences and research outside the classroom. One way I have tried to do this in physics is through "self-directed projects". As explained to students the first day of class, a self-directed project is an independent investigation of questions pertaining to the subject matter of the course (which, in the spirit of a holistic approach to science, can be broadly construed). Depending on the particular topic to be investigated, the research may entail any or all of the following: analytical calculation, numerical analysis, computer simulation, library research, or simple experiment. What is of importance is not that the students arrive at some predetermined right answer - there may, in fact, be no single solution - but rather that an effort be made to obtain results and to support them in a coherently written, grammatically acceptable report.

The projects are an integral - indeed most essential - part of the course. They represent, more closely perhaps than any other course-related activity, the elements of curiosity-driven inquiry which lie at the heart of science. Students are permitted - in fact, encouraged - to select their own topics for investigation. Although some do, others, particularly those not initially interested in physics, prefer to select from among twenty or more suggestions provided by the instructor. In compiling my proposals, I look for projects that (i) introduce students to contemporary scientific developments as reported, for example, in high-quality general science periodicals like Nature, New Scientist, Science, Scientific American, and American Scientist, (ii) engage students in simple, out-of-class experiments or observations, and (iii) give students practice in constructing and testing theoretical models of physical systems.

The development of predictive models constitutes a key part of scientific research and education. In terms reminiscent of Hesse's Das Glasperlenspiel, physicist David Hestenes has colorfully characterized modeling the real world as "The great game of science":

"The object of the game is to construct valid models of real objects and processes. Such models comprise the core of scientific knowledge. To understand science is to know how scientific models are constructed and validated. ... It has aptly been said that the purpose of a scientific experiment is to ask a question of Nature. This being so, the answer is a validated model, not merely a mound of data."

Faced with diverse phenomena, multiple possible mechanisms, and the complexities of real apparatus, a practicing scientist must produce an analytically or numerically tractable explanation amenable to testing. The more detailed the model, the better may be its predictions, but also the more arduous it may be to obtain analytical or numerical results. Thus, model building requires making judicious compromises.

In the traditional linear mode of instruction students rarely have occasion to develop the skills of the "game". Homework problems provide all the data needed to solve a problem usually by substitution into readily available formulas. Laboratory exercises are designed to elucidate a narrowly specified process or principle with an analytical procedure (in effect, the model) already provided. Yet, as Nobel laureate and accomplished expositor of the nature of science, Peter Medawar, has written, science is the "art of the soluble". Self-directed projects help students practice that art. (I find it interesting that scientists should discuss their work in terms of games and art, whereas students so often see it as anything but recreation.)

For the projects to serve their purpose, students should work on them throughout the semester, and not as a last-minute obligation to be satisfied just before the course portfolio is due. Nevertheless, as one measure of the vital role self-directed projects assume, the course syllabus specifically allows for two weeks - at points approximately one third and two thirds through the term - to be devoted to research and writing without scheduled classroom lectures or laboratories. In addition, the final week of term includes the oral presentation of selected projects by those students who volunteer to do so.

In the remainder of this section I will give several examples of self-directed projects that students pursued. As before, it is not the intrinsic physics that is the focus of interest in this account, but the way in which physics is (a) introduced through commonplace activities, (b) associated with contemporary discoveries or (c) made relevant to contemporary issues of concern. Attention should also be directed to the way in which individual topics usually (d) comprise diverse phenomena and concepts (rather than fall into specifically identifiable units of a textbook), (e) call for the development of simple, tractable theoretical models, and (f) foster learning in a holistic (rather than linear) way.

Topic 1:Lightning Investigate the subject of natural lightning. What is lightning? How is it generated? What accounts for the zig-zag shape of lightning bolts? What is ball lightning? How does a lightning rod work? How would you design a lightning protection system for (a) a single-family dwelling, and (b) the campus Engineering and Computer Science Building?

Comments: For all its familiarity, lightning is a subject that is still fascinating and in some ways mystifying. In the course of library research, students were challenged to understand fundamental ideas drawn not only from electricity and magnetism, but also from chemistry, thermal physics, and atomic physics. There are also significant aspects of lightning which remained controversial even after years of investigation. Even to so outwardly primitive a device as the lightning rod have been attributed various mechanisms of operation. The study of a topic like this one provides a needed counterweight to the overwhelming impression of scientific certainty conveyed by introductory textbooks.

In addition to simply reading about lightning, students were asked to make practical use of their findings by designing lightning protection systems for two structures very different in size and content. In the case of the computer science building, for example, not only must one protect against direct lightning strikes, but consider as well the effects of strong fields on the functioning of sensitive electronic apparatus. Although the research for this project was presumed to be largely theoretical in nature (I did not want a self-styled Benjamin Franklin standing in the middle of a sports field flying a kite in a thunderstorm!), students could, if they wished, construct a table-top model and test it with a small van de Graaff generator as a lightning source.

Topic 2: Mystery Top There is a physics toy called the Top Secretš. A small top spins seemingly forever on a plastic pedestal with small convex nub at the center. Examine the device and explain how it works.

Comments: A remarkable creation of the inventor Roger Andrews (first constructed when he was only fifteen years of age), the Top Secretš generated utter amazement when demonstrated to my classes. Once spun on its plastic base, the top executes a complex orbital motion about the central nub. If left undisturbed, the top can spin for hours, apparently defying the laws of thermodynamics by drawing energy from a hidden source to compensate for frictional losses. Even after the specific nature of the top and the hidden source of energy are revealed, the detailed mechanism of its operation is by no means trivial. In fact, the toy remains undeniably intriguing even when it is fully understood. Without divulging here the secret of the top, I would nevertheless say that it provided one of the strongest incentives I have ever found for students to come to grips with conceptual and practical implications of Faraday's law of induction. To explain the device is, in effect, to construct a model of its operation. The model, in this case, is not necessarily a mathematical one, but instead calls for a coherent explanation of how specific electronic and mechanical components, functioning in accordance with basic physical laws, give rise to an apparent perpetual motion.

It has been my experience in general that science toys and demonstrations can be used with great effectiveness to motivate students at any level to want to understand material that would otherwise be boring if encountered primarily in the form of classroom lectures and cookbook laboratory exercises. I collect such devices, have integrated them at times into my research program with undergraduates , and use them for teaching purposes whenever possible . Toys bring the abstract principles of science into the domain of a student's personal experience, not by shallow emphasis (as instructors are wont to do) upon their manifold implications for technology and society - but simply by raising in each observer's mind the burning question: "How does that work?" A student personally driven to answer that question is well on the way to learning science.

Topic 3: Conduction In his acclaimed textbook on electricity and magnetism Nobel laureate Edward Purcell states:

"In metals Ohm's law is obeyed exceedingly accurately up to current densities far higher than any that can be long maintained. No deviation has ever been clearly demonstrated experimentally. According to one theoretical prediction, departures on the order of 1 percent might be expected at...more than a million times the current density typical of wires in ordinary circuits."

Is this really the case? Look into the subject of mesoscopic rings - i.e. normal metal rings of about one micron in diameter with wire thickness of about 0.05 micron.

Ohm's law, of course, is not really a law in the same sense as the universally applicable laws of conservation of electrical charge and conservation of mass-energy. Nevertheless, as indicated by Purcell's remark, it is a relation thought to apply with great accuracy to ordinary (i.e. not superconducting) metals. In pursuing the questions raised by this project, students learn about the remarkable electrical properties of normal metal rings that, though small (a human blood cell may be about 10 microns in diameter), nevertheless contain billions of atoms, and so would not usually be regarded as a system of quantum mechanical size. A low current passes through a ring - not a current one million times greater than ordinarily encountered - and yet Ohm's law does not hold. In the textbook and classroom, the electrical conductivity of metals is commonly explained by means of the classical electron model in which electrons are treated as small, hard billiard balls of charge. The mesoscopic ring project helps make students aware that the wave-like behavior of electrons can fundamentally alter the electrical responses of a seemingly classical object.

A project of this nature, which clashes with textbook assertions, suggests to students that they should be willing to question what they read and believe - even in an outstanding textbook like Purcell's. This is not a trivial point. If science is a self-correcting process of inquiry, then a course that leaves students with the impression that scientific knowledge is fixed and certain, is communicating the wrong message.

Topic 4: Health Implications of E&M Fields Can low-level non-ionizing electromagnetic fields affect human health? Look into the hazards allegedly presented by electromagnetic fields in everyday living. For example, is it dangerous to live near a power line or power transformer? Is it dangerous to sit in front of a computer terminal? What evidence supports and refutes these claims? What frequencies and fields (electric or magnetic or both) are under suspicion? What mechanisms are proposed for the alleged hazards?

Comments:

This topic (and a similar one concerned with the potential dangers of radon in the home) provided pointed reminders of the relevance of physics to problems of everyday living. Indeed, the personal concerns of some students in regard to health issues were strong incentives for their studying physics (and biology) to a far greater degree through self-directed projects than they would otherwise have been inclined to do through assigned reading and classroom lectures alone. For example, to the extent that it bore on the questions that interested them, these students devoured outside sources of information (such as special reports by government, industry, and science academies) addressing topics in basic physics such as the power and frequency of electromagnetic fields, sources of electromagnetic fields, factors determining the strength of these fields, methods of measurement, and observations of these fields in the state where the students resided. Much of the same material, presented in the textbook for "academic" purposes, had previously been of little interest.

One salutary educational outcome of this project is that students understand better the fact that different scientists employing the same universal principles can nevertheless arrive at different results. This is not a trivial point, for too often the pat way in which academic problems - those encountered in class, homework and tests - are neatly and definitively resolved reinforce the caricature of scientific method that students carry with them out of school into society at large. According to this caricature, the steadfast accumulation of sufficient data accompanied by the ritualized exercise of logic inexorably leads to the correct scientific conclusions. Real-world problems are rarely so simple. Most are like those of this project: controversial issues about which many contradictory things have been written. It is not definitive answers that science provides in these cases, but rather the tools with which to make informed decisions in the face of uncertainty and risk.

The preceding are four representative samples of self-directed projects that I, the instructor, suggested. Space does not permit discussion of others, among which were studies of optical activity, optical and electron interferometry, image recognition and enhancement by spatial filtering, holography, the Einstein-Podolsky-Rosen paradox, highly excited (Rydberg) atoms, lasers, nonlinear optical phenomena, and pulsars. In succeeding years an increasing number of students proposed their own projects concerning, for example, the physics of how a nerve cell fires, application of piezoelectric devices in the design of downhill skis, the optics of the "glory" (a diffractive phenomenon), the origin of the auroras, magnetic resonance imaging, and the development of photovoltaic devices to harness solar energy.

Apart from their purely scientific benefits, the self-directed projects help develop language skills especially among science and engineering students whose regimen of technical courses provided few, if any, occasions to speak or write. Upon completion of their research, students were expected to prepare a written report for their course portfolios. The essays must be grammatically acceptable and, ideally, display a certain measure of eloquence and personal style. During the last week of term, those who desired to do so gave an oral presentation of one of their projects.

The importance of developing both writing and speaking skills can hardly be overestimated, yet these activities are rarely promoted in traditionally taught science courses that emphasize the technical (as opposed to cultural) aspects of science and the mechanical details of problem solving. Students who concentrate in science, engineering, or medicine frequently never have to write again in school (beyond the preparation of lab reports) after they fulfill some core English requirement. Professionally active scientists and engineers, however, are engaged in writing throughout their careers, as for example, in preparation of research papers, internal progress reports, and proposals for research funding. They also frequently speak at conferences and schools, and before civic groups and government committees. Communication, together with research, lies at the heart of science.

8. Assessing the Unassessable

There is, I believe, an important core of truth to B. F. Skinner's paradoxical remark that "Education is what survives when what has been learned has been forgotten." True learning is a long-term affair - ideally, life-long. Unless one intends to become a physicist, for example, the details of calculating the moment of inertia of a rolling cylinder or the oscillation frequency of a particular circuit are likely to be of little future importance and soon forgotten. If this is the only kind of information a student takes away from a physics course, then, for all practical purposes that course has been a waste of time. By contrast, the legacy of a science course that opens students' minds to the fact that nature is both marvelous and comprehensible, and instills in students the desire and confidence to seek understanding on their own, is of lasting value. That is the goal of self-directed learning. However, it is not a simple matter to evaluate an experimental teaching method that measures its success not in the "here and now" but in the capacity of students to cope with challenges of the future.

Although surveys of student opinion solicited at the end of term run the risk of providing hastily formulated judgments, it was nevertheless gratifying to find that the overwhelming majority of students who participated in this educational experiment expressed their satisfaction with the way the class was taught. In their anonymous replies, many pointedly remarked on the sense of freedom they felt for the first time in more than a dozen years of schooling in being able to learn without the fear of tests. Others commented favorably on the opportunities to explore interesting subjects outside the classroom. Still others appreciated classroom discussions of contemporary issues not treated in the textbook. Most were thankful for opportunities to improve their writing and speaking under conditions that did not subject them to embarrassing criticism. There were also one or two students each term who would have preferred the traditional regimen of graded tests and graded homework as a stimulus to "work harder". A teacher can not, of course, please everyone. The need of some students for an externally imposed motivation is all too comprehensible, for the educational legacy of a dozen years can not be entirely undone in one or two terms.

In assessing the impact of this self-directed learning experiment, it is instructive to note that not one student in either course intended to become a physicist. All were engineering majors enrolled in physics exclusively for the purpose of fulfilling the requirements of an engineering degree. The engineering department had, in fact, dropped the requirement of my Term 2 course in the misguided belief that modern engineers do not need modern physics - and, in fact, barely encouraged its students to take the Term 1 course in the equally perverse view that only prospective electrical engineers needed a physics course in electromagnetism. In any event, the consequences to the physics department of this curricular revision in engineering were drastic. No longer mandatory, course enrollment had plummeted to such an extent that the physics department considered eliminating modern physics altogether from the college catalogue. This was the prevailing situation when I taught these courses for the first time according to the principles herein described. At the end of Term 1 - in marked contrast to the enrollment pattern of the previous years - 90% of the students either registered for the sequel, or, unable to do so because of course conflicts, planned to register the following academic year.

It should be said that the sudden and unusual "popularity" of introductory physics can not be attributable to an easy work load or generous grade distribution, for neither was the case. For most students the effort required to complete out-of-class projects and in general to prepare a satisfactory course portfolio was at least as great as that which they ordinarily expended in studying for exams. And yet, although no longer forced to do so, nearly all students concretely expressed their desire to continue the study of physics. Clearly these students must have believed they were learning something of value.

With respect to final evaluations, the majority of grades fell within the "average" and "good" categories as is typical of most university courses. What is especially significant, however, is that, of the students receiving the highest marks, all but one had previously done relatively poorly during the first two terms of introductory physics taught in the traditional way. Their low grades derived principally from lack of interest and poor test scores. On the other hand, the quality of their portfolios during the second two terms suggested that these students had the ability to use available resources to find information and comprehend it, to refine complex problems into tractable questions and solve them, and to communicate their findings cogently and articulately - in short to do creative work analogous to scientific research. Several, in fact, were subsequently awarded summer research fellowships to work with individual faculty members in science or engineering. Had the last two semesters been taught in the standard way as were the first two, it is likely the performance of these students would have been equally low and their interest in physics further diminished. Assuredly, they would not have received fellowships or perhaps even encouragement to continue in engineering. Seen directly in terms of lost opportunities for potentially talented and motivated students, the manner in which science courses are taught and individual ability measured is a matter of the highest consequence.

9. Progressions

In the years following this experiment in education, I continued using self-directed learning techniques in other courses with students whose career goals were not predominantly in engineering or the physical sciences, but in biology and medicine. In all cases, the outcomes were the same: students felt a deep appreciation, a sense of gratitude, for having an opportunity to explore physics in a sympathetic environment created principally to inspire, rather than to judge, them. I was not surprised to be told by many of my students - both personally and through the anonymous end-of-term questionnaires - that, though they had always disliked physics, this physics course was the highlight of their academic studies. Such remarks are not surprising if one believes, as I do, that physics is intrinsically a fascinating subject.

Despite the encouraging results with students, I can not say that I ever managed to convince colleagues at the same institution to adopt similar methods. The need to test, grade, and rank students was considered indispensable - although admittedly not because it helped students learn better - and the work involved in creating projects and reading portfolios was regarded as prohibitively time-consuming.

In the world beyond, however, dissemination of these ideas through journal articles and invited talks brought a large and favorable response. One 1995 article in American Journal of Physics, alone, elicited more personal letters - all supportive - than anything else I had ever written up to that time. There were requests to translate the paper into a variety of European and Asian languages, and invitations to visit and lecture, at both home and abroad. In Finland, for example, where I was a guest at the Helsinki University of Technology, one of my hosts had adapted the methods of self-directed learning to accommodate more than 350 students (ten times the number in my own classes) studying introductory electromagnetic field theory. Slowly, but progressively, I suspect attitudes can be changed.

"At college age," one teacher has remarked, "you can tell who is best at taking tests and going to school, but you can't tell who the best people are. That worries the hell out of me." Indeed, that disturbs me, too, but I believe that there are more appropriate ways than testing to identify the best people. To me, the outcome of this educational experiment in self-directed learning is both heartening and instructive. It confirms, along with all other experiences I have had, Einstein's inspiring advice: "Teaching should be such that what is offered is perceived as a valuable gift and not as a hard duty."

References

• M. P. Silverman, "Two Sides of Wonder: Philosophical Keys to the Motivation of Science Learning", Synthèse 80 (1989) 43-61
• M. P. Silverman, And Yet It Moves: Strange Systems and Subtle Questions in Physics, (Cambridge University Press, Cambridge, 1993) (provides an account of the author's experiences as a scientist and their bearing on his philosophy of education).
• M. P. Silverman, "Self-Directed Learning: A Heretical Experiment in Teaching Physics", Am. J. Phys. 63 (1995) 495-508
• R. H. Romer, "Reading the Equations and Confronting the Phenomena - The delights and Dilemmas of Physics Teaching", Am. J. Phys. 61 (1993) 128-142
• H. J. Walls, Scotland Yard Scientist, (Taplinger, New York, 1973) pp. 177-8, 180
• E. Gerjuoy, "Improving Courtroom Presentations of Scientific Evidence", Physics and Society 22, (October 1993) 6-9
• The interested reader might consult reports in Growing without Schooling, published by Holt Associates (Cambridge, Massachusetts 02140 USA)
• Cited in R. P. Feynman, R. B. Leighton, and M Sands, The Feynman Lectures on Physics, (Addison-Wesley, Reading Massachusetts, 1963) 5
• J. Holt, Teach Your Own: A Hopeful Path for Education, (Dell, New York, 1981) p. 17
• Norton Juster, The Phantom Tollbooth (Random House, New York, 1961) p. 233
• See M. P. Silverman, "Raising Questions: Philosophical Significance of Controversy in Science", Science & Education 1 (1992) 163-179 for a discussion of the role of controversy in the advancement and teaching of science.
• Y. Aharonov and D. Bohm, "Significance of Electromagnetic Potentials in the Quantum Theory", Phys. Rev. 115 (1959) 485-491
• E. Merzbacher, "The World Through the Master's Eyes", American Scientist 80, 484-485 (1992). This is a review of the book: A. Pais, Niels Bohr's Times, in Physics, Philosophy, and Polity (Oxford University Press, 1991).
• I discuss the Aharonov-Bohm effect and related quantum interference phenomena in the book: M. P. Silverman, More Than One Mystery: Explorations in Quantum Interference (Springer-Verlag, New York, 1995), as well as in Chapters 1 and 2 of Reference 3.
• T. T. Wu and C. N. Yang, "Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields", Phys. Rev. D 12 (1975) 3845-3857
• M. P. Silverman, "Science as a Human Endeavor", Am. J. Phys. 53 (1985) 715-719
• W. Ehrenberg and R. E. Siday, "The Refractive Index in Electron Optics and the Principles of Dynamics", Proc. Phys. Soc. (Lond.) B62 (1949) 8-21
• M. P. Silverman, "Two Sides of Wonder", Reference 2
• "Ready-made Entertainment is Killing Japanese Curiosity", New Scientist 140, No. 1903 (1993) 7
• J. S. Bruner, Toward a Theory of Instruction (Harvard University Press, Cambridge, 1966) 115
• M. P. Silverman, "Interference Colors with 'Hidden' Polarizers", Am. J. Phys. 49 (1981) 881-882
• M. P. Silverman, "How Deep Is the Ocean/How High Is the Sky? Some Thoughts on Imaging by Parallel Plates and Gravitationally Stratified Media", Eur. J. Phys. 11 (1990) 366-371
• D. Hestenes, "Modeling Games in the Newtonian World", Am. J. Phys. 60 (1992) 732-748
• P. B. Medawar, The Art of the Soluble (Methuen, London, 1967); quotation from p. 7
• The Top Secretš is manufactured by Andrews Manufacturing Company, Inc., Eugene, Oregon 97403 USA; U.S. Patent No. 3783550
• M. P. Silverman and G. M. Cushman, "Voice of the Dragon: The Rotating Corrugated Resonator", Eur. J. Phys. 10 (1989) 298-304
• M. P. Silverman, "The Vortex Tube: A Violation of the Second Law?", Eur. J. Phys. 3 (1982) 88-92
• Edward M. Purcell, Electricity and Magnetism (McGraw-Hill, New York, 1985) pp. 143-144
• J. Roger and P. McWilliams, Life 101 (Prelude Press, Los Angeles CA, 1991) p. 330
• M. P. Silverman, Reference 4
• J. Roger and P. McWilliams, op. cit. p. vi

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