Chapter 1: The Challenges of Teaching

It was career day at the local high school and we were talking to the students who had expressed an interest in physics research or physics teaching. The group was small. At first we described the daily life of a person engaged in pure research at one of the national laboratories. Interest was high and questions were directed along rather idealistic lines concerning how discoveries were made. When we turned to the subject of physics teaching, however, the students clearly thought that we were trying to sell them a bill of goods. Some students in the school belong to a club for future teachers. They had thought about being grade-school teachers or high school English or history or math teachers. None of them, apparently, had thought of himself in the role of a high school physics teacher, and no one had ever spoke to them about this possibility. They were tolerant, bemused by our pitch, but asked no questions.

How would you sell the job of being a high school physics teacher to your students? The traditional image is certainly not very appealing. Most of us studied high school physics under a man who taught the same subject in the same way year after year. In many schools he had to teach that way because the subject was strictly prescribed by state or college requirements. Like all other teachers, his professional contacts were limited to those between students and teacher-between teenagers and an adult. Among themselves teachers were mainly concerned with matters of administration. In most schools there was only one person who taught physics, and there was no one with whom he could have talked about physics or physics teaching even if he had wanted to. During the summer months, the physics teacher, like most others, had to leave his profession and find a temporary job in some shop or local industry. Maybe things were better for your high school physics teacher, but that's the way they were when we went to school.

Times have changed! Maybe not everywhere yet, but in many places high school physics teaching is now an honorable and rewarding profession. First of all salaries for all teachers are beginning to be respectable. There are summer institutes providing small stipends for additional study, and an increasing number of local and national curriculum workshops that need the help of experienced teachers. Even if the physics teacher is isolated within his own school, there are many ways to work with Science Teachers Associations, or to contribute to science teaching journals.

Instead of being forced to teach the same topics in the same sequence year after year, the physics teacher today has an almost bewildering array of course models from which to choose. There are Physical Science Study Committee, Harvard Project Physics, a new engineering syllabus, and several varieties of physical science for eleventh and twelfth graders. The existence of these new courses provides a real challenge. The good teacher must become familiar with all of them. He should also be familiar with the science curriculum developments for the lower grades. Many new junior high and elementary school science programs are being developed or are now available. The high school physics teacher should know about these courses because they ought to affect what he teaches in his physics class. Even more important is the obligation to be a leader in the coordination of science courses from kindergarten through college. The high school physics teacher can occupy a crucially strategic position in these efforts. More contacts to the colleges and curriculum development projects are available to the physics teacher than to any of the other science teachers. On the other hand, being part of a school system he should be a natural contact for scientists wishing to work with the schools. In the continual assessment of the K-12 science program which every good system should undertake, the physics teacher has an obligation to advise and suggest. He should know in detail what the various elementary and junior high courses provide and should be prepared to lead in the in-service training of non-specialist science teachers. The profession of high school physics teaching has changed in many places and can change everywhere. Besides the traditional personal satisfaction with successful teaching, there are widespread opportunities to engage in other aspects of the profession. It can be a rewarding career, but the increasing rewards have brought with them serious obligations. That is the way a profession ought to be.

Surely the title is an oxymoron, a contradiction in terms. Who would start out to make their fortune by becoming a physics teacher? Ah, you say, I know the purpose of this gambit. The editorial is going to turn into a paean to the joys of learning and teaching, even though one is mired in ennobling poverty.

Nonsense! I'm talking cold, hard cash. I'm talking about living it up, on the footstool if not the lap of luxury. I'm talking about advice to questing youth with their eye on the bottom line.

I know the folklore. Teachers are overworked and underpaid. Any of us could leave our ungrateful institutions and go to work in industry at twice the salary. The myth is most poignant when applied to school-teachers, as opposed to university professors, who, as everyone knows, earn two to three times as much, though still a pittance.

We got a letter a few weeks ago from a high school teacher who is resigning from the American Association of Physics Teachers because we raised our membership dues slightly. She says she earns one third to one quarter of a university professor's salary, and that we should have a more modest category of membership for high-school teachers.

I feel bad about that letter. It came as a shock because it doesn't at all reflect our local situation. Quite a few of my former students are teaching high-school physics here on Long Island or in the New Your metropolitan area. Those who have been out for twenty years or so are earning as much or more than I am. We're all doing all right compared with some of our colleagues or students who went into industry and are now looking for jobs. A typical starting salary on Long Island for a high-school teacher with a bachelor's and no experience is $32 000. With a masters and ten years” experience, the salary is around $57 000. All salaries are determined by a step matrix that gives credit for longevity year by year, and for graduate studies. Top salaries, without administrative responsibility, are above $80 000. The average salary for a public school teacher on Long Island is $63 000. Of course, you should see our living expenses! Real estate taxes are ferocious. They have to be to pay those salaries.

Are we in a particular Eden here, so close to The City? I made phone calls to friends far and near to enquire about their financial well-being. In most regions around the country the relative status of physics teachers in high school and college is about the same. In rural regions both are earning less than in big cities, but in both places the high-school teacher with masters and ten years earns about the same as a fresh Ph.D. in the local college, with about the same prospects for future increases. In some southern states, particularly in Texas, things appear to be different. In exchange for the tornadoes and warmer weather, our southern brothers and sisters (indeed a higher ration of sisters) who teach in high school are earning considerably less than their age cohorts who teach in college. The salaries in college are slightly less than those up north, although it appears that nationwide competition serves to normalize college salaries.

So here's my advice for youth just starting out. If you want to make your fortune, get your teacher's certificate along with your bachelor's degree. Start teaching immediately at a suburban high school in the northeast. Take additional summer and inservice courses to get a master's degree within five years. Then, at your leisure, take an extra course each year to continue your diagonal route across the salary matrix. Eight years later, notice that one of your classmates who went on to graduate school has just become an assistant professor at your local college at a salary that is about the same as yours. Pity that she had to scrape along on an assistantship for those eight years, and is now at least $100 000 behind you.

I still feel bad that we lost a member because of our dues, but I think the remedy is to increase salaries everywhere (except locally where I have to pay those higher taxes). To do so it might help if the nationwide situation were better known and publicized. I would like to hear from readers everywhere about their local salary scales, particularly the comparison of high-school and college salaries. Let me know, and I'll report back.

I am reminded of the biennial investigation of the state university by the legislature out in the Midwest. They got this here professor on the stand, and the legislator asked, “Now then professor, what sort of workload do you have?” The professor answered, “This semester it's nine hours.” “Well.” Said the legislator, “that is a long day, but then the pay is good, and it's easy work.”

Education has a new fad word-competency. It is closely akin to “mastery” which students are supposed to attain, but competency is an attribute that teachers must demonstrate. Ideally, teachers would demonstrate competency by having their students attain mastery. Of course, no one knows how to do that and it would probably be harmful if we did. Nevertheless, many states are busily planning to license teachers in terms of competency-based certification. (CBC known last year as PBC: performance-based certification.)

Strange as it may seem, I was one of the first to administer competency tests (CT). Years ago, through skillful political bargaining, I was elected captain of my sixth-grade baseball team. The chief function of the captain was to choose the pitcher. To be fair, I set up a CT. which in this case consisted of ten throws toward a strike zone chalked on the school wall. Every boy in the class tested his competency in this eminently rational way. The worst possible pitcher won. Even though during the test he pitched the largest number of balls into the strike zone, we all knew he was the worst choice, and he was. The early failure of CBP (competency-based pitching) made me cynical about all school tests as well as many other education programs.

But surely we can tell the difference between a good teacher and a bad one! I used to be able to, but that was fifteen years ago when I first got into this business. Take that first in-service institute where I delivered solid and polished lectures about the subject matter in the new Physical Science Study Committee (PSSC) course. You can imagine, there was only one man out of the fifty high-school physics teachers who knew enough calculus to follow my derivations. He quit teaching the following year-couldn't control his students. At the other end of the ability spectrum was the character who always came late, sat in the front row, and asked questions. It took me quite a while to realize that he was asking questions that everyone else was too embarrassed to ask. In the years since I have often visited that teacher's classes and have also talked with men who used to be his students. I'm sure that he is a master teacher, but I'm not sure he would do very well on a written CT.

Note, however, that I do claim that this man is a good teacher. Apparently, teaching skill can be rated. The trouble is, this mans success depends on his style, which is very special, impossible to copy, and probably not effective with certain types of students. This man is flamboyant and always “center-stage.” Another local teacher who is also very successful is quiet, almost to the point of being shy. Which personality type should we certify for competence? What sort of test can we administer to judge effective personality? Let's face it: teaching is an art, and judgement of good teaching is also an art.

If this fad of competency tests were just another silliness propagated by theorists in the ivory towers, I could enjoy the joke as well as the next man. After all, the cult of efficiency ratings rose and fell in the 1920s leaving the schools untouched. In the normal quagmire of the school systems, competency-based certification would also sink without a trace. Unfortunately, there's a lot of money behind this move, because various legislatures are demanding new tokens of accountability. The New York State Education Department has mandated that within a few years all prospective teachers will be certified in terms of competency tests. Committees are forming, conferences are being held, and new words are being coined every day. It looks as though there will be a whole new industry to draw up these civil-service type standards.

My own suggestion is that the way to make a competency test for teaching any subject at any grade level is to chalk up a rectangle on the school wall and give each candidate ten free throws. It's a lousy way to select a pitcher, but there is absolutely no education research to say that it is not as effective as any other formal test for picking a good teacher.

Fall came early this year. I wasn't expecting it for several more months. When it became clear that summer was over and that school would really start, I began to prepare my annual outline of topics, facts, and skills I would teach during the year. The list is not quite the same as last year's because I want to try a different emphasis in mechanics, and there are some interesting developments in optics. Needless to say, the list is a summary of things I already knew or have just learned. You can't teach something you don't know.

The trouble is, there is a lot about physics that I don't know, and I discover new things all the time. Great vistas of ignorance keep opening up. In fact, I now know so many things that I don't know that it's not clear that there has been any overall gain. Let's face it: in the great competency-based exams of life, I have not achieved mastery.

This rationalization of my limited knowledge would make me feel worse if I didn't live in a large and powerful university physics department. At least once a week a journal or manuscript arrives with a fact that I hadn't heard of before or an argument that doesn't seem quite right. So I'm stupid, but at least can't I get expert advice just down the hall? How frustrating, but how satisfying, it is to discover that in many cases my colleagues are also baffled. Ignorance, it turns out, is endemic among physicists. It's also a lot of fun. The blackboards around here are covered with partial calculations and tentative sketches left over from bull sessions about things that we aren't sure of. If we already knew everything about the subject, we'd be bored stiff.

But shouldn't we let the students in on this? I was in a high-school classroom some years ago, and heard a student ask the teacher a very perceptive question. A look of puzzlement and the dismay swept over the teacher's face. How embarrassing! “I don't know,” he said. “I've never thought of that question before. How will we find out the answer?” It takes a master teacher to do that. Maybe we should all learn how to admit our ignorance. In fact, maybe the most important thing that we can teach about physics is that there's a lot about it that we don't know.

Let's list the categories of our ignorance. First of all, science is surrounded by questions that have been bypassed. Instead of asking why an object should keep moving, Galileo asked why it should stop. Instead of worrying whether light is a particle we now require that our equations predict successfully the results of experiments with light. Of course young students keep asking the old dead-end questions. Somehow we must let them discover the power of asking the right question, without squelching their annoying tendency to ask questions in a form for which we have no prepared answers. They must learn that physics doesn't tell why; it tells how. And then they ought to mistrust the philosophy enough so they can occasionally keep on asking “why.”

The most embarrassing category of ignorance consists of those facts or skills that are really part of our teaching repertoire but which we have forgotten or never learned. I just found out last month how to determine the radius of percussion of a baseball bat. No excuse. Somehow I had missed that in school and in all these years had never wondered about it before. I suspect that it might be reassuring to a student to find that his teacher doesn't know all the answers right offhand, even to simple things. Besides being reassuring, it would also be instructive if the student could then work with the teacher and watch his technique as he tries to find the answer.

There's another realm of lack of knowledge for most of us. If we specialize in subatomic particles, we probably aren't up-to-date in solid state physics. If we are skilled with the equipment and techniques of experimental physics, we may have trouble with manipulation of certain mathematical forms. If you think a professor of theoretical physics has no blind spots, invite him to teach anything to a high school class for a few weeks. Students ought to know that everyone has blind spots. If one appears in you make sure that the class knows its depths and boundaries. That doesn't mean that we should be proud of our ignorance, like the English teacher who says, “Oh, I just can't understand science.” On the contrary, let the students know that we can be fascinated by any topic that is of interest to some other human. We may not have studied that field so far; we may not have time now; but if the student is interested, how can he find out. The skill of the physics teacher should be not so much in knowing things, as in knowing how to find out.

Finally, there's one great truth we must make sure our students understand. Besides the facts that we don't personally know because we are forgetful, or stupid, or limited, we are surrounded by mysteries to which no one knows the answers. That's what physics is all about. What a dull field this would be if it consisted of a closed bunch of facts and techniques. No one knows the complete nature of the subatomic particles. No one knows (in spite of the August discovery) whether or not there is a magnetic monopole. No one knows whether the universe will expand forever. No one even knows what humans are doing in this universe. The science of this century hasn't explained everything; instead, it has raised the curtains on regions that we never knew we didn't know. The physical universe is much more mysterious than it was in 1900.

The only excuse for listing the things I know, and which I will teach this year, is that it's a short list. I don't even know how long the list would be of the things that I don't know. But that's the list that makes the teaching enterprise forever fresh and fascinating. This year I intend to make sure my students know the awful truth about how little I know, and the exciting truth about how little any of us knows.

I was in a holding pattern in our local hospital when a radiologist friend walked by and asked after my health. When I told him that I was scheduled for a thallium stress test, he said. “we don't use thallium anymore; it's technetium now.” Five minutes later as I was being wired up, I said to the attending physician, “I understand that it's technetium I'll be getting.” Oh, no,” she said. “It's thallium. We hardly ever use technetium.”

There's probably some simple explanation, and besides, it probably didn't make any difference in the results. Gamma rays are gamma rays. It did occur to me, however, as I was being slid into a large ring machine, that I didn't know how the machine worked. Evidently those gamma rays were going to produce an image of my heart. How? I'm supposed to know about gamma rays, but I don't know how their effects are scanned to form an image. I asked the nurse technician, who cheerily assured me that “it's like a camera.” But note! She knew how to make the machine work.

I don't know how most things work. Our oil burner stopped today and I watched the serviceman take things apart, including things I hadn't even noticed before. He had never taken physics in school, but he knew where the filters were and what the flame should look like. In his column and book, How Things Work, Dick Crane has explained the innards of a lot of devices. Down in Virginia Louis Bloomfield has made a physics course out of explaining the operation of simple things. He described the course in the October 1997 issue of The Physics Teacher.

In most introductory physics texts there is an explanation of electric motors and a simple diagram showing the principle. Have you ever compared the diagram with a real motor? The ones in electric clocks don't look at all like the text version. The ones in kitchen devices or pump motors are much more sophisticated than the ones in the text diagrams. High powered electric generators are turbines that are a far cry from the pistons and cylinders of the textbook Carnot cycle. Indeed, their efficiency is not given by the standard Carnot formula. The apparatus used by Geiger and Marsden to measure the size of the nucleus was very different from the schematics that describe Rutherford's experiment.

If studying physics and teaching it all these years doesn't equip me to understand the technical world we live in, what's the use of it? I hope-we all believe-that the physics of the introductory course provides a foundation for understanding a wide range of technical applications. We may not know the detailed operation of the devices we use every day-the watch, the carburetor, the computer, the TV-but we have the tools to ask the right questions and to understand the first approximation.

As teachers, there are other mysteries we face. We can't be aware of the day-by-day psychological state of each of our students. We may not even notice if they're asleep, or if they're there at all. Even in one-on-one conversations with students, we have a hard time knowing what they are thinking while we are talking. Of course, we should try to get the students to talk while we listen, but even then it's hard to know what they are thinking, or what model is in their minds.

For high-school teachers, certification requires courses in adolescent psychology, learning theory, and methods of teaching. This preparation is analogous to studying the introductory course of physics. The foundation is supposed to make it easier to understand the applications. College teachers rarely take these courses. Their ability to understand the learning process and to teach descends upon them like grace as the doctoral hood falls on their shoulders. Whether in high school or college, the teacher is expected to be a dual specialist in the subject matter and in the application of the teaching process.

We all know that it is seldom that way. It is usually a straightforward process to explain technology in terms of basic physics. However, it is much more complicated to interpret the efficacy of teaching methods in terms of basic theories of learning. The many factors involved usually prohibit simple conclusions. Good teachers are like good specialists, they may not know why the system works, but they do know how to make it work.

What a wealth of resources we physics teachers now have available! In this issue we celebrate high-school physics texts. There are many to choose from and the quality is high. Compared with the pre-Physical Science Study Committee (PSSC) days our current texts are mostly free from factual mistakes and are generally written by people with a good understanding of modern physics. Thirty years ago this was not the case. I remember displaying the most popular physics text at that time as a horrible example of what had gone awry in science education.

The most advertised feature of the book was a four-color transparency overlay showing a steam shovel in a pit. Take off the top transparency and you could look in the cab. Take off the next and you see the gears. So much for modern physics! Years later when I chided the editor responsible for the book, he chuckled and said, “Wasn't it frightful? But it swept the nation.”

Thirty years ago, following the lead of PSSC, all publishers transformed their texts. It was one of the major accomplishments and by-products of the PSSC project. So now we have reasonably accurate texts to which authors have devoted years of writing and checking, on which publishers have gambled huge sums for production, and for which school boards and tax payers have sacrificed their money.

So who reads the textbooks? Not students, apparently. I seldom find an entering college student who knows the name or the author of his high school-physics text. In fact, the most common claim is that they did not have a text in high school, except maybe for homework problems. In one school I'm familiar with, their teachers boast that their students don't need the text on their shelves. They have their own program. In another school the teacher says that most of today's texts are too difficult for today's students. Now it is a truism that no one is satisfied with any particular text, even the author. What is more natural then, to supplement a text with your own material. In fact, if you accumulate enough of these sections, you have a start on another text and should be sounding out publishers. Usually, however, these home-produced texts have serious drawbacks. I have seen many, but have seldom seen a good one. The writing of most of us needs reviewing and editing. Amateur composition and reproduction is usually hard to read. But even if your writing is lucid, your physics sound, and your typography professional, what makes you think the students will read your opus? They appear not to read anything. At every level we hear the complaint that the text is either too difficult or not needed. At most, the student thumbs through the chapter to find the right formula in order to do the homework problem. In a junior-senior level college physics course we are using one of the classic texts. My students say that it is too terse and sparse for them to read. After exploring how they use physics texts I ran a remedial reading session for the whole class. First we scanned the chapter, and then we went back to the first section, questions and pencils in hand. Of course we must have paper and pencil while reading a physics text and of course you must have questions. At every step you must fight back, checking up on the author, following through on every statement that “it can be shown” or that “as we saw on page 132.” With publicly owned texts, the students should not write in the margins, but they should and can produce their own text notebooks of criticism and commentary.

Years ago the first edition of a popular text in introductory quantum mechanics had a number of typos and mistakes. According to legend, the author responded to people who wrote him about these by saying, “Thank you and congratulations. You're right and I was wrong. I'll be sure to keep that mistake in the next printing so that others can be similarly tested.” What a great idea! What we need are texts with a carefully planted mistake on every page, preferably in some formula needed for homework. If the kids don't find the mistake they get their homework wrong. The book might be called Phallacious Physics. That would really be educational. Everyone should grow up with a deep love for the printed word and a deeply ingrained skepticism about its truth. As for students not needing to read texts because we teach so well, maybe we're doing them a disservice. Maybe it's our obligation to teach our students how to read physics, which is a different skill from reading the Hardy Boys. Then it might not be necessary for college students to buy study guides on How to Read the Text, or the cartoon sequels on How to Read the Study Guide. In the meantime, authors are still confident and writing, publishers are still hopeful and printing, schools are still trusting and buying, and of the making of many books there will surely be no end.

The choice I faced was between writing this editorial or spending an afternoon on the ski slopes here at West Point. It was a clear choice between duty and pleasure. A short time later as I rode the T-bar to the top of the mountain, I promised myself that I would nevertheless think about physics and physics teaching all the way down. Why, for instance, can heavier people go faster than lighter people, and why can you go faster with longer skis? What is the angle of an inclined that looks from the top like a precipice, and what is the insolation in February on a northern-facing slope? What's the shape of the snowflakes coming out of the artificial snow machine?

These are all good thoughts for a physics teacher on a downhill run. Since speed actually does depend on weight, I conclude that some of the friction forces must not be proportional to mass. That's certainly true of air friction, which is important. In spite of our textbook examples, the surface friction of skis on snow depends on the surface area of the skis. Longer skis are faster. Evidently, a large surface area cuts into the snow less. As for the steepness of the hill, a 15° or ¼ radian slope means a one meter drop out of four. That would produce an acceleration of 2.5 m/s/s. In ten seconds, straight away, you would be going 25 m/s, or about 55 mph. Some of the trails are certainly steeper than that, but not ones I go on. In February, at our latitude of 42°, the sun rises to 40° above the horizon. On a northern slope of 15°, the angle between the sun's rays and the normal to the surface is 65°. The cosine of 65° is 0.4. Hence our snow should last a while longer if it doesn't rain and the temperature at night goes below −2 °C for the snow machines to work. I don't know what artificial flakes look like. You want to know how the machine works? Pretty well, I would say.

A cadet rides up the T-bar with me and learns that I teach physics. He's in another section. “Doing all right,” he says, “but there's an awful lot of formulas to learn.” He asks me why we define magnetic field lines to be perpendicular to the velocity of the electric test charge. Why not just plot the forces on a charge at various points and say that those are the field line directions? It's a good question for a T-bar and I try to answer at the top with a diagram in the snow. He's polite, as all cadets are polite, and thanks me as we wish each other a good run. But all the way down I wonder if maybe we should start the subject of magnetic fields with permanent magnets. That's the way we used to do it. Then we plotted the fields with the north pole isolated at one end of a magnetized knitting needle. Some lessons later, after the field patterns from pole to pole were established and familiar, we learn what happens when we put currents in those fields. The logic was not so clear as in our present system, but maybe the pedagogy was better.

The next time up I ride with another cadet, one of my own students. I ask him how he likes studying electricity. It turns out that the subject isn't what he expected-Gauss’ law and all that. He wanted to learn how to wire things. In high school he had learned about charges and the right-hand rule and even about cyclotrons. But he had never really wired anything. It was like last fall in mechanics where he had learned about cross products and torques. But he had never rigged a pulley. I tell him to forget it. He's going to be an officer. He can tell other people to wire the circuits and rig the pulleys. Up at the top we wish each other a good run, but I feel guilty all the way down.

OK, coach. Here's the new team of hopefuls, trying out for the physics varsity. You've got to let them know what they're in for, instill some discipline, and develop a fighting spirit. Of course you'll do this by making sure the sport looks easy and attractive. They'll have a lot of fun here. Tell them how they can team up with their pals to work together. Eases the work for everyone, and they can spend the time talking over the plays or things to do on weekends. Not much homework practice involved. No reason to scare off the team members. Everyone can play and succeed under the new rules. We'll temper the academic winds to the shorn lambs, poor kids.

Who are we kidding? Can you imagine a football coach proposing such a program? Physics is a tough sport. It requires at least as much dedication as soccer or basketball. It requires at least as much practice as the five-finger exercises for piano. There's no golden road to education. There never was and there never will be.

Remember the old story of the professor who opened the school year by saying, “Ladies and gentlemen, I want each of you to shake hands with the person on your left. Now shake hands with the person on your right. Only one of you will finish the course.” There may be something to that.

Perhaps there's no need to be so draconian. But fear is an honest goad for student progress. Of course, you should entice your students with the mysteries of physics and invite them to enjoy the beauties of our world view. But make them work to get there. Nothing so clarifies the academic mind and makes students hungry for learning as the imminence of an exam.

This may be an unpopular doctrine. I may feel a little better tomorrow if the Sun comes out or if a student asks a good question. Today, however, I am reminded that we have lots of meetings and projects designed to make physics more palatable and to make us more knowledgeable about our students and their problems. Maybe the emphasis should be shifted. Maybe our students should worry about understanding us. If we have good physics to teach and know how to present it, let the kids get down to work. In college the traditional formula calls for two hours of work outside of class for every hour spent in class. There should be a different but similar formula for high-school students.

It is our responsibility as teachers to choose appropriate explanations, to make the example interesting and relevant, and to design lessons at the right level for efficient learning. It's the student's responsibility to spend efficient time and effort on the assignments and to ask good questions. When I play the pipe, I expect the students to dance. And when I mourn, they'd better weep.

Consider now the physics learner. We usually meet this person in a course for which we prescribe a sequential series of lessons. We choose a text, organize lab exercises, assign homework problems and administer frequent tests. The heart of our service is the lecture. There we tell the Learner what is important in the text, thus providing clues about the topics to be examined in the test. Since the Learner is unfamiliar with the subject, there is no need to base instruction on what the Learner already knows or wishes to know. This state of affairs is illustrated by a picture of the head into which knowledge is being poured. Unfortunately, it is all leaking out the bottom.

The situation isn't really that bad. Throughout school days students are immersed in a system where the facts are poured in. Most of these facts are forgotten, which is just as well, but as the students age, more and more facts get used and assembled in the fingertips. The high school senior is clearly more capable, at least physically, than the seventh grader. Schooling does seem to help most students, even when it gives the illusion of squelching enthusiasm for learning.

Suppose we didn't know about our standard and partially successful system of education. How would we organize our effort? Why not first ask about the learner, and figure out all the things we know about how people learn things? Consider your own experiences, or those of students you have known.

People learn many things by rote. In some cultures, memorization by repetition of a few classical texts is the only formal education. This kind of instruction has a bad reputation in Western culture, but when the memorized information is important it is a very effective method. Clearly there is a great practical usefulness in being able to recite the alphabet or to know the multiplication table. There is no better way to learn these than by rote repetition, preferable in childhood. Even in adulthood, musicians learn to sing or play by repetition. Somehow the fingers or throat learn during the first run through so that the second time is easier. Physics teachers gain experience in solving simple physics problems by solving them over and over again, year after year. With enough practice, the method looks like the logic of an expert.

Some people learn best by studying by themselves, reading texts and solving problems. Others do better in social settings, teaming up with one or two others and explaining things to each other. The problem in organizing a learning environment is to cater to the needs of each and to the pace of each. Many attempts have been made to provide individualized instruction, either by paper workbooks or by computer programs. Some students like these systems, but there have been no outstanding successes, at least none that have survived and propagated. Some people should study alone, some do better in small groups.

The common experience is that cyclic learning is useful. If at an early age you literally handle phenomena illustrating Newton's laws of dynamics, and the in high school describe them algebraically, and in college run through the explanation in freshman year and again in junior year, then you are in good position to understand the laws when you first start to teach them in graduate school. The trouble is that only a few people specializing in physics will study the subject over and over again. We give most students a course in one or two semesters, and at the end lament about how little they understand.

In our rush some years ago to beat the Russians or the Japanese, many schools succumbed to the temptation to shove advanced materials into lower grades. Thus we have college freshman who have taken “calculus” but who can't do algebra or trig. We all know the silliness of teaching elementary-school children about atoms or genes. The Piagetian fad in education has faded, but you still can't teach a six-month old child to walk, and you can't teach most elementary school children to reason by analogy. In tempering the wind to the shorn learner, we must be aware of age limitations on concept development.

Even students who have achieved the formal operational stage of Piagetian development like to see concrete examples. Physics instructions without demonstrations is like dinner without food. To be sure, there are a few students who can understand and use information that has been introduced with only symbols and math derivations. But most learners need to see phenomena, preferable under their control. Better yet, they should feel it in their muscles. The bigger the muscles the longer the memory.

What drives a Learner to study something? There has to be a need to know. Perhaps they need to pass a test. That's a valid purpose and a useful goad. Hovering over every exam is an applied need to know. It is called fear. A student's future can be changed completely by an exam grade. If a premed fails the Medical College Admissions Test (MCATs), there goes the country club membership. The main virtue of a formal course of study is the provision of exams at regular intervals. Of course, simply cramming for an exam usually leads only to short term memory. On the other hand, reviews produce new views. A good teacher exploits reviews and exams for teaching rather than for grading.

A more effective goad for the Learner is simple curiosity. To satisfy that, people would not normally take a course. Instead they would use acquired skills of library search or online computer references. The trouble with disorganized searching for understanding is that a lot of information must be approached sequentially. In college this problem is recognized by establishing prerequisites.

A good teacher can supply the seeds for curiosity and a need to know. That's the purpose of the lecture. Facts can be obtained from the text. In a lecture the teacher can wax enthusiastic about a derivation, marvel over a demonstration, view a false explanation with scorn. A good teacher inspires; there is no better word for it.

The proof of learning is usually taken to be the results of those course exams. They allow the Learner to demonstrate skill in problem-solving and familiarity with many specialized terms. There are now attempts to judge students in terms of projects they have tackled. This so-called authentic testing is meant to determine if the student can integrate what has been learned and create something novel or useful with it. Like most educational fads this idea has a valid kernel, but it has proved devilishly hard to implement the idea in practice. We all have known students, or colleagues, who appear brilliant on exams, but as the years go by they never really accomplish much. And there is the inverse, the student who does only medium well on the multiple-choice exams, but somehow links disparate ideas into a new and useful discovery.

So how do people learn? By rote, and by logic. Singly or in groups. In lectures or in lab. Immediately or after many cycles. Within their conceptual range. Because they have a need to know. Because they are inspired by a good teacher and their curiosity is raised. And when they have learned enough, they may or may not be able to use it by creating something new.

If everyone learned the same way and at the same pace there would be no difficulty in teaching. However, because learning takes place in so many ways, our profession is more of an art than a science. If we try to impose any particular system of education we will harm some of our students and frustrate ourselves. Physicists have a reputation for freewheeling attacks on problems and a healthy disregard for rigid rules. Because of the many differences in our students, we should avoid the shibboleths of fads and use many different teaching methods to provide a wide variety of learning experiences.

Apparently there is folklore that the distribution of grades in any class and in any subject fits a predetermined “curve.” Presumably, the curve is “normal,” which presumably means Gaussian. Then, as every schoolchild knows-but I never learned-the distribution can be divided so that a certain fraction get A's, another get B's, etc. The students at the high point of the curve, and a generous portion on either side, get C.

If that's the system, I ought to know whether or not I “grade on a curve.” Well, I do and I don't. I can, indeed, subdivide a Gaussian but would consider it was undignified to do so for such a purpose. Besides, whether normal or not, my students are seldom Gaussian. In the most recent exam, they were almost square. One year I had a camel distribution.

The students don't care about these statistical quibbles. They want to know if I am going to use a curve, as opposed to “the other way.” They have me there, too. As far as I can gather, the other way is, you know, like it used to be in school. Apparently students think that there is some system that yields absolute grades as opposed to relative grades. In New York this myth is perpetuated by the statewide Regents exams, where a grade of 65 is passing. These exams, of course, were not brought down from Mt. Sinai with the other tablets. Instead, they are laboriously hammered out each year by the mortals in the state capitol. If the exam makers are cunning enough in using their experience and the results of previous exams, they can devise a new one that will not trap too many youngsters below that absolute 65. If they miss, which they do occasionally, and if the howls of the citizenry are loud enough, the absolute grade is adjusted upward with a compensation formula. Any absolute grading system is based on a curve of past experience and informed expectations. If you want to you can prepare an exam on an absolute grade basis that will flunk everyone in your class or yield them all A's.

About once a month we receive a manuscript that describes yet another elaborate scheme for determining grades. Some of these are so complicated that the student must follow a flow chart to find out whether performance of an extra project is worth the extra credit. To be sure, it's a fact of life that grades can be goads or incentives for learning. I get uneasy, however, when the system gets too mechanical. Rewards for special projects can turn into merit badges. Is there extra credit for coloring graphs? Furthermore, grade hunger can eat up mechanical grading systems, but that doesn't necessarily lead to digestion of the subject matter. If you have a 1, 2, 3 step system for earning an A, with bonus points for extra work, many B students will be industrious enough to earn an A. But as for knowing physics, they will still be B students.

Keller plans of individualized instruction are supposed to produce large numbers of A students by providing opportunities to take tests repeatedly until mastery is obtained. If only it could work that way! In the true Keller method, used mainly in psychology courses, mastery is demonstrated by obtaining a score of 85% (or 72% or 92%-even mastery can be relative) on a multiple- choice exam. With such a system you could get a bright chimp to demonstrate mastery after a few tries.

The one feature of the Keller plan I like is the idea of frequent exams. We should all give exams frequently to let the students know what we consider important. We should grade those exams promptly, and then go over the results thoroughly. Giving an exam only for grading purposes and not also as a teaching tool is a mark of professional inefficiency. There should be an opportunity for salvation for a student who has done poorly on and exam. The penalty should not be a special project; it should be the learning of the material missed.

Absolute standards are an illusion of youth. There is no escape from making subjective judgements in grading. No matter what the mechanical system that we use for determining grades-and the simpler the system the better-we should insistent that the resulting number is just a first approximation to the actual grade. At that point, as professionals made to make judgements, we have to gather all we know about each student and wrestle with our experience and prejudices to say: “This is an A student; this one did poorly and should be shocked into action by a C; this one is borderline between B and C, but is trying hard and would be crushed by anything lower than B.

But, you say, such objective judgements may be unfair, and biased, and warped by personal antagonisms or sweet smiles! O.K. Let's use instead, the strength-test-system that our local phys. Ed. Teachers tried one year. On an absolutely absolute basis of grading, my son got 82½ in gym. If he had done three extra laps a day, he could have been an A student.

In the classic Greek plays it was customary to bring a god in at the end to wind up the story and explain what finally happened to the characters. Since the god arrived suspended by a crane, this method of plot resolution is known as deus ex machina. We have a similar problem and a similar solution in education. The whole enterprise is so complicated, and so mixed up with past events, and present problems, and future needs that there seems to be no salvation. Our freshman are not prepared for the calculus based physics course, which should therefore be modified in some way. Or perhaps the fault lies in the high schools that did not adequately prepare the students. In turn, the high schools fault the earlier grades, whose teachers blame society and parents. Faced with these unsolvable problems, professional educators have turned time after time to novel administrative methods or mechanisms. Failing to find any health in the characters or plot, they (we) have sought salvation out of the machinery.

(In case you are consulting your Latin dictionary, salus in the Church Latin means salvation in the spiritual sense as well as health in the more original and literal sense. It turns out that the Romans had no concept of spiritual salvation, and hence no need for such a word. See John 4:22.)

The primary administrative problem in education is, and always has been, how to get the student to work harder with less expenditure of teacher time. At least, the teacher wants to minimize the time; the administration wants to minimize the expenditure. One of the earliest forms of salvation for this purpose was the Lancasterian system of the early nineteenth century. The paid teacher trained a cadre of older monitors (unpaid) who in turn taught the younger students. Graded school started at about the same time, eventually winning out over the monitorial system. One teacher could instruct forty or more students of the same age more efficiently.

In the 1920s, with the assembly line so successful in industry, efficiency experts turned their attention to the schools. Time studies showed disgraceful inefficiencies in instruction, with the teachers often repeating lessons and the students failing to remember simple conclusions. In response, progressive educators pointed out that many students did not see the relevance of learning to their own lives, so new books and activities were created to bring the school closer to everyday life. Of course, reaction set in immediately. Many parents complained that although the children were learning to garden and hammer, they were not learning to spell. Back to basics. This seesaw of school practice and expectations has been going on ever since there have been schools. Each ten years a previous fad has been discovered and renamed. In a curious contradiction, the school system, although accused of not teaching well, has nevertheless been forced to take on the responsibility of teaching health, sex, driving, and other life-saving topics.

You may remember that a few years ago the solution to our problems was to provide the tools for Mastery Learning. This was best done with Individualized Instruction. For efficiency, however, you may want to try Interactive Lecturing. Failing that, resort to Group Learning. The current model calls for four in each group, one to read the instructions, one to press the buttons, one to take the data, and one to ask the teacher for help.

Salvation also comes with machinery. The all-time classic was and is the chalkboard, first popularized 150 years ago by Joseph Henry. Does there exist a classroom today without at least one chalkboard? If there is a chalkboard, then the rest of the plot is determined as if by fate. In front of the chalkboard there is a teacher standing. In front of the teacher are students siting. But to save the teacher time along came the radio. Way back in the “20 s it was realized that the radio would allow lectures to be heard by thousands. Next, it was predicted that salvation would come from the motion picture machine. Lecture demonstrations could now be seen by millions. TV was just a plot refinement, but a potent one. Such a short-lived fad! The interactive computer has now arrived and just in time to save our educational system and turn it into way stations on the information highways of the future. The light at the end of the tunnel is blinding.

I prefer plots where the actions stem from the nature of the characters, their strengths and weaknesses. Life isn't like that of course. In real life, the gods do come swinging down, saving some and dooming others. However, I don't think they make any difference in the long run. If we were starting all over again in public education, and I knew nothing of the past, I would be fascinated by some of the administrative mechanisms that have been proposed or are now waiting in the wings. But in these latter days I am skeptical of easy solutions. Here is a touchstone with which you can test proposed educational panaceas. If the method causes the student to work harder, and if the method increases student-teacher contact, then it may be worth trying. Otherwise, laugh the apparition off stage and get on with the play.

As I remember the story, there was a king who had a new young wife. For reasons I won't go into here (after all, this is a fable for children) the king thought that his wife could spin straw into gold. One night he put her in a room with a spinning wheel and a pile of straw and told her to get to work. As you know, most young queens cannot ordinarily spin straw into gold, and neither could this one. So she cried. Now here's the good part. Out of nowhere there appeared a strange little fellow who offered to do the trick in return for a small favor. Just a necklace this time. The next morning the king was delighted and all was well. A week later, the same deal, and again the following week. Each time the elf raised the ante, and the final time he asked for the queens first born child. Since she didn't have any children she happily agreed. But then she got pregnant, presumably by the king, and the elf came back to demand payment. The queen cried harder than ever so the good little elf said, “One more chance! You can keep the child if in three days you can guess my name.” The queen called in the secret service, found out that his name was Rumpelstiltskin, saved the child, and banished the elf.

There are several morals to this story, including the need for elves to get their contracts in writing. What concerns me more is that I've seen an awful lot of straw during the past year with a lot of people solemnly assuring me that they are going to spin it into gold.

Illuminated by a thousand points of light, the United States is going to get the best science- and math-education system in the world. Not overnight, of course, but in nine more years. We will be able to do this with falling state budgets because now we realize the misconceptions (or alternative conceptions) that blind our students and can lead them toward self-enlightenment by employing the constructivist theory of teaching, which is the latest thing. And just in time because next year there will be a new latest thing in education. (You will excuse my use of the jargon here since it so nicely matches the profundity of the ideas.)

At the elementary-school level, the nation has poured twenty-two million dollars into the triad projects from the National Science Foundation (NSF). The three legs of each of these curriculum projects were supposed to consist of the developer, commercial distributor, and local school system. With cooperation like that, the product would obviously have the ingenuity of the developer, the real world practicality of the school, and the commercial backing of the distributor. Most of them didn't turn out this way, but who will ever know? The NSF Education Directorate rarely has external reviews about the results of its giveaways and certainly never makes them public. Still. The inverse miracle did occur, with much fine gold being spun into straw.

At the junior- and senior-high level, the spinning is being done by many disparate groups under the rubric of SS&C (Scope, Sequence, and Coordination). The straw here is piled high and deep.

The spinning wheels are being provided by NSF and the Department of Education at the behest of the National Science Teachers Association. With SS&C, all science topics will be taught at each grade level from 7 to 12. Somehow, interesting curricula that satisfy this requirement will be produced for this project. Indeed, committees are already at work, and you know how well committees write. Somehow, 60 000 junior-high science teachers will be trained to teach all science topics. This will be accomplished with workshops. Somehow, these new curricula will be hands-on, arranged for heterogeneous grouping, and relevant to all students (taking into account each ones developmental level). Mind you, this is not just one curriculum, or one method.

Rather, the project is to be multicentered, with each school faculty developing its own system in a way that will enhance the particular local strengths in an atmosphere of teamwork and collegiality. Such happy faculty teams are already at work in Houston, North Carolina, Puerto Rico, Iowa, and particularly, as you can imagine, California where the original “100 schools” project has now expanded to 214. Lest you fear that these efforts may be uncoordinated, rejoice to learn that a common assessment system is being planned that will make use of interactive video. Furthermore, if all goes well, the teachers can all talk to each other, and solve each other's problems, by email. (If you think that I'm making this up, read Currents, the SC&C newsletter.)

With all these wheels spinning, I say, “Pile on the straw!” We'll turn it into gold overnight, or at least by 2000, or perhaps by 2061. And if you believe all that, you must also believe in little old elves, named Rumpelstiltskin.

In various communiques about proposed school science curricula, we read that physics taught at the seventh- and eighth-grade level should be conceptual, followed by a quantitative treatment of the same material in the senior high. There seems to be a general agreement that conceptual physics means qualitative and easy, and that quantitative means abstract, mathematical, and therefore, hard. Even at the college level we hear arguments that students should first study the concepts and then later tackle the grungy mathematical details.

I don't understand this concept. Here at the TPT office we continually get manuscripts from people who have just discovered that students have misconceptions, politely called alternative conceptions, about the way the world works. The problem appears to be endemic with old college students and young grade-school children and with every age in between. Researchers keep discovering what good teachers have always known, that our physics concepts are not intuitively obvious, and are not transmitted to our students simply by telling them. Consider that the concept of energy in our modern terms was unknown to Newton, who was not at all that stupid. Unfortunately, in spite of all the research in probing student misconceptions, we have received precious little advice about how to warp student notions into our adult paradigms.

Conceptual physics isn't easy. The elementary concepts are profound. For instance, the nature of mass is still a mystery. Consider the complexities of energy and mass raised by Ralph Baierlein in the March 1991 issue of TPT or by Arnold Arons in the October 1989 issue. Can we fall back on the oft-heard excuse that the introductory students need only be taught a first approximation to the “Truth?” Beware the moral of Mark Zemansky's quatrain in the September 1970 issue of TPT.

• Teaching thermal physics

• Is as easy as a song

• You think you make it simpler

• When you make it

• Slightly wrong!

But isn't it good strategy to teach with a cyclic curriculum? Shouldn't we run through the concepts first in a qualitative way, with lots of show and tell? Then, when the children have reached the age of reason, we can give them the full mathematical treatment. According to Eddie Boyes in his article in this issue on American and English physics education, the cycle system that they have been using in England creates problems of its own. He points out that during the earlier treatment, with teachers who are not physics specialists, “…there will have been plenty of time for students to be “turned off” by physics because they see it as being too difficult, and they will have developed misconceptions, difficulties, and prejudices against the subject.”

Maybe the misconception is in the definition of “quantitative.” Quantitative is not the same as mathematical. In fact, most mathematicians are not particularly good at dealing with things quantitatively. Quantitative means knowing (and measuring) the sizes of things, not just in terms of numbers but in terms of other, familiar things. Quantitative also involves the way one quantity changes size when some other quantity changes. Relative size and functional dependence. That's what quantitative science involves. In those terms, elementary-school students and their teachers can and should learn quantitatively. By doing so they bypass the Piagetian obstacles of the slow development of concepts. Children can measure and compare quantitatively long before they can understand the simplifying and sophisticated concepts that we have developed. Children can get an operational feel for mass by measuring masses. But don't ask them to fill in the blanks to define mass. In junior high they can measure energy as it transfers from one form to another. But don't ask for a definition of energy on a multiple-choice test. The practice of working quantitatively leaves students with the power to do things. They can manipulate phenomena and when the time comes can construct mature concepts based on personal familiarity with the variables involved. Young people who have only memorized the words of a concept without any experience in handling the magnitudes involved are left powerless.

Of course, there is a shifting boundary between quantitative and mathematical. A functional relationship that seems concrete to one person may appear abstract to someone else. Classicists usually complain that physicists put Descartes before Horace. There is this unjustified fear that quantitative means mathematical. Back in the late 1930s, Einstein spent a summer on the North Fork of Long Island, New York. There he made friends and played violin duets with a local shop keeper. One day Einstein offered to explain relativity to his friend who protested that he wouldn't understand because he had no math. Einstein answered, “I can explain it to you without math,” whereupon he started writing down equations. “No, no,” said the shopkeeper. “I really don't understand math.” “But this isn't math,” said Einstein. “This is just algebra.”

So there is a conceptual misunderstanding. From my point of view, after many years of teaching and writing for students of every age group, the simple concepts of physics are tough and subtle. The development and understanding of these concepts requires maturity and years of experience in handling phenomena quantitatively. On the other hand, learning quantitative physics is child's play. And it should be.

A one-sided conversation is a common experience. I suppose I'm as guilty as the next party in turning a conversation into a monologue. It's an occasional hazard. Kid asks a question; I give an answer. At length. After all, that's why the students sit in rows facing the teacher.

And when I ask a question of the students, I want an answer right away. Perhaps I wait a second or two. Several decades ago, Mary Budd Rowe measured the intervals between teacher questions and the next words spoken by the teacher. The average time was a little over one second. It was embarrassing. Very few students can leap into a conversation with only a second or two of preparation. It turns out that if you wait at least three seconds, the student will frequently have something worth saying. Here's an interesting project for some social scientist or Ed major. Measure the ratio of class time during which students talk to the time the teacher talks. In a straight lecture the ratio is about zero (excepting for the whispering going on in the back row). What is it in your classroom, or recitation section, or lab?

Of course, there's the danger that if you listen to the student, it will take up time and you will hear nonsense anyway. There's a legend of a professor in Germany a hundred years ago who gave very formal lectures. One day a student raised his hand in class. When the bewildered professor paused, the student asked a question. After pacing a while, the professor responded, “if you persist in asking these questions, we will never finish the work of the course.” I know how he felt. When I was fresh out of grad school I ran a Physical Science Study Committee (PSSC) workshop for teachers on Long Island. One teacher would frequently interrupt my lucid lectures to ask a question. Those questions were so stupid that I often didn't know the answers. It took me a while to realize that this man (who was a great teacher) was asking questions that everyone else was too confused or too timid to ask. In the March 1997 issue there's a note about the physics of falling coffee filters. The story has a moral that's more important than the equations for terminal speed. The authors gave an open-ended lab assignment with no cookbook instructions to a group of bright freshmen. It was a disaster but a revelation. When you listen to students you discover that they don't perceive things the way you do. You then have to face the problem of finishing the course or trying to bring students up to t (0). The decision may be that the standard minimum material must be covered, letting the students fall where they may. Or you may undertake rescue measures. But if you don't listen you won't even know there's a problem.

Of course we listen to students every time we give an exam. However, if the exam is multiple choice or even routine homework type problems, we may not be hearing much. These exams are easy to grade but hard to interpret. I once took over a sick colleague's course and administered one of his multiple-choice exams. It was his custom to allow the students to justify their choices if they wished to, in hope of getting partial credit. There were more cases of students choosing correct answers for wrong reasons than the other way around. Now I never give an exam where there is not the opportunity for the student to explain or describe something in English sentences. These are as easy to grade as standard problems, and far more revealing.

The next time you get cornered by somebody talking nonstop, use the time profitably by considering how it is when the tables are turned and you are conversing with students. Whenever you are tempted to deliver a full lecture in answer to a simple question, keep in mind the immortal words of Ring Lardner in his story The Young Immigrants. “Are you lost, daddy?” I asked tenderly. “Shut up,” he explained.

The last week before school opened I received three desperate calls from local high schools, all looking for physics teachers for this fall. These were good jobs being offered. Straight physics teaching in suburban schools. In New York City they have been short of trained physics teachers for several years. There has been a steady loss of such teachers. Meanwhile, the number of high-school students wanting to study physics, at least in New York State, seems to be going up.

How many high-school physics teachers are there in the United States? The numbers are hard to pin down. The National Science Teachers Association lists about 18 000 who have indicated they have taught physics or can teach physics. It appears from test mailings, however, that most of these are not primarily trained in physics and do not really consider themselves “physics teachers.”

We figure that about 4000 copies of our magazine each month go to high school teachers or high school libraries. Our highest estimate is 5000 trained high school physics teachers, teaching physics as their prime assignment. The number could be as low as 3000. We are an endangered species.

Why aren't we trained more? The jobs are waiting, and the jobs are some of the best in teaching. The physics teacher usually deals with the brightest kids in school, and faces fewer discipline and motivation problems than any other field. Salaries are no longer disgraceful and in some places are even respectable. Opportunities continue to exist for in-service professional learning and accomplishment, both locally and through national organizations. Apparently college students don't believe high school physics teaching is a good career. Around here, most undergraduate physics majors think that teaching jobs are unavailable. Indeed, the schools are saturated with history, gym, and elementary school teachers, but not with physics teachers. Available or not, high school physics teaching jobs don't sound attractive to most of our undergraduates. Apparently the students attracted to physics were encouraged to think only of a research career. Practically no one comes to us from high school with the ambition to go back to teach physics there.

There's another reason we physics teachers are having trouble propagating ourselves. In the colleges we've pretty much given up trying. Throughout the northeast, at least, departments that used to have teacher training programs have lost interest in them. Usually, only one or two people in each department took an interest in teacher preparation or had any familiarity with schools. Because of age, or frustration, or tenure problems, many of these specialists have now turned to university assignments with greater respectability. Students aren't knocking on our doors for teacher training, and we aren't out there beating the bushes.

Sometimes it seems as if there are not even a few thousand high school physics teachers out there. The majority of manuscripts that we receive come from college teachers, though we bend over backwards to publish something from the high schools. Nevertheless, when we conducted a reader survey by mail last spring, the percentage response of high school teachers was far better than from our college subscribers. Apparently the physics teachers in the schools do care about the profession, and surely the ones in college ought to.

There's work for both groups if we're going to replenish our numbers. The high school physics teacher should be a prime recruiter for future teachers as well as future researchers. Personalities of these two types are usually quite different. Plant the notion that high school physics teaching is a career to be considered. Help a likely candidate to find the right college with a good training program-if there are any left in your part of the country. The colleges that still have such programs should advertise. Indeed, let me know the details of good programs and we'll publish them in the magazine-free.

As for whether or not physics teaching is a good career, let your students read the articles in our series that started last month—The Real World of Physics Teaching. We'll have descriptions of wildly different situations, in both high school and college. Our profession has both delights and special problems. Let's tell it like it is to both ourselves and our students. Maybe more will join the ranks. If they don't, the few of us left may want to learn to teach Latin as a hedge against obsolescence.

If one of your own children is getting an award, then of course you have to attend the Awards Night. So I marched off last June to witness the annual ritual in the school auditorium. As I feared, the place was packed. Apparently, every student in town was slated to be rewarded for something. There were prizes in athletics and English and math and Latin and music and every other subject including physics. As the names were called and the students came forward, there developed a regular orgy of congratulations and hand shaking and general good feeling between the students and teachers. By the time we got to the music awards the auditorium was awash with tears and hugs and wild hyperbole. But nobody kissed the physics teacher.

Ask anybody, they'll tell you that physics teachers deal with a cold and logical subject. The abstractions of music can set your toes to tapping, but the abstractions of physics are tuneless. The good fellowship of a choir can bathe students and teachers in harmony, but the competition produced by a short answer quiz in physics leads only to discord. A smartly stepping band brings out the music boosters. A snappy physics demonstration may bring out only complaints from the custodian.

Actually, we all know that it needn't be this way. Physics can be exciting, and fun, and even thrilling, if not romantic. It's just that we have bad press. To overcome the legend we must use salesmanship, showmanship, and lots of public relations techniques. There's a great example of such methods in this month's article, “Physics Olympics,” by David Riban from Indiana University pf Pennsylvania.

Most science fairs are arranged as islands of individual competition. The projects are usually done in isolation and then are presented on their solitary tables. It's hard to develop an esprit de corps with each entry in grim competition with everyone else. Where would the cheerleaders perform?

The physics Olympiad creates an entirely different atmosphere for a science contest. Team effort and group projects become important, with school honor at stake. Whether or not anyone learns any physics, at least the reputation and atmosphere of the physics class will change. (As for the learning benefits, they are probably equivalent to the physical health benefits of varsity sports, but less painful.)

It's the group nature of activities that makes students feel comfortable and wanted. That's why most alumni remember their extracurricular projects more fondly than their scheduled classes. You don't have to mount an Olympiad to bring in the students, nor do the group projects have to be completely separated form classwork. A whole class might prepare an exhibit of physics phenomena for a younger group or a hall demonstration. A whole class might build a telescope, or try Galileo for heresy, or take over some of the technical aspects of the school's photography or public address system. If you have developed such group projects that are instructive and fun for both you and your students, send a note to The Physics Teacher and let the rest of us know.

We physics teachers realize that the study of physics contains its own intrinsic rewards. What could be more profoundly exciting than the study of the microstructure of matter, or the mysteries of cosmology? Back in the introductory classroom, however, the study of vectors and Newton's laws might benefit from a little razzmatazz. You may not want your students to kiss you goodbye at the end of the year, but there's no law of physics that says that every eye must be dry on that last day of class.

In spite of the injunction in Mathew 7:1, you and I are paid to judge. It is generally thought that our main job is to instruct. To the extent that we have received any training in our profession, besides the subject matter, the training has mostly been concerned with methods of making the subject matter understandable. Most of the pages of this journal are devoted to that end. Nevertheless, society demands more of us. In that awful day of judgement, we must grade our students.

Since final exam time will soon be upon us, it seems to be an appropriate season to ponder exam techniques. Actually, we should have started considering the subject last summer. The time to make up the final exam is before classes begin. Then throughout the year you can teach to the exam. Is that a scandalous suggestion? Let's be practical. Of course we think it necessary and appropriate to have goals for the year's work. These are spelled out in terms of a syllabus, either homemade or state mandated. The goals are matched to the text, or vice versa. Out of the text we select certain homework problems and laboratory exercises. Thus our goals are manifold and manifest. Or so we think.

What about the student goals? Whether in high school or college, students are very concerned, if not primarily concerned, about their final grade. They want to study and memorize whatever is going to be on the exam. One of the great selling points of any college fraternity is its library of past exams. In New York State you can buy review books of previous high-school Regents exams. These become the supplementary texts in high school classes at least during the last month of school. No matter what the state syllabus says in its carefully worded generalities, this year's final exam is next year's syllabus. Any good student knows that.

Well then, let's make up our exams before we start the course, and let's make sure the exams test whatever goals we are attempting. If we want our students to memorize the arcane vocabulary of our profession, including the Greek symbols, then the testing is easy. Multiple-choice test are ideal for the purpose. If you're going to work in physics, you have to know the language. No doubt that ability should be tested early and late. The same goes for other parts of the language that we use: Work has the same units as (a) force (b) momentum (c) energy (d) moment of inertia. Does it sound dull? French vocabulary drill is also dull. It has to be tested but if that's the main part of the exam and thus the main part of the course, the student will hate French and never get to use it.

If we want our students to be able to use physics, then the exam must test that ability. That's very hard to do with multiple choice questions. Recently a number of teachers got together with me to critique an exam in physics. This particular exam required us to read and analyze some paragraphs or diagrams before answering the multiple-choice questions. None of us could do well in the time allotted. But quite a few students had done very well. They knew how to take multiple choice exams. Most questions can be answered by inspection, or at least the choices can be narrowed. Then, if necessary, go to whatever reading or diagram is provided. That's the way most students do their homework. Instead of reading and analyzing the chapter, they turn immediately to the problems, thumbing back to the text for equations that have the required variables.

It may seem that it is impractical to test large numbers of students with anything but a machine-gradable exam. There are very real problems, of course, but consider these two exam questions. The first is from the New Your State Physics Regents exam of 1917: Describe with the aid of a labeled diagram the essential parts of an ammeter. Draw a labeled diagram showing how the instruments should be connected in a circuit to find the resistance of a given wire by the voltmeter and ammeter method. In the 1988 Regents there is a diagram showing a 110-V source in a series with three resistors. Voltmeters are shown across each resistor. One reads 20 V, another reads 20 V, and the problem is: What does the third one read? The choices are (a) 20 V (b) 70 V (c) 90 V (d) 110 V. Those two questions, 71 years apart, are testing for very different abilities and surely reflect very different courses and teaching.

In most cases the testing instrument doesn't make too much difference for grading purposes. For various reasons we are required to rank our students. Good students, as determined by our informal observations, usually do well on written exams of any type. Furthermore, most exams are reliable, because the good students do uniformly well and the poor students do uniformly poorly. But not always! Once I had a class where the star was very skilled at exam taking, but I was sure that he had less creativity and weaker insight than another student who rarely did well on formal exams. In the years since, the student who got all the scholarships has not accomplished much, while the slow but creative student has had a successful research career. The uniform, machine-gradable exam is particularly unreliable in judging the unusual cases.

Besides reliability in exams, we require, or assume, validity. Validity is not just the quality of being technically correct. A valid exam should test the skills and knowledge and ability that we have been trying to instill in our students. That's why we should make up our exams in advance. A sample of everything we teach should be tested in some form. If we expect our students to be able to wire a circuit, or to set up a lens system, then we should test for that skill. If we ourselves are fascinated by the accomplishments of our science and are still thrilled by the mysteries remaining, and if we have tried to communicate that to our students, surely at the end we should find out whether they got the message.

Tests can be a plan for ourselves as to what we teach. They can be a prod and a guide to our students about what they must learn. They can be instruments of judgement for ranking our students and predicting their future performance. Tests and their results can also be revealing to others about how we teach and what we teach. Thus we should bear in mind the flip side of Mathew 7:1. Inevitably, as we judge, which we are paid to do, we are also judged.