Jerry Gollub and Robin Spital's recommendations for improving the Advanced Placement physics program ( Physics Today, May 2002, page 48) are excellent, as far they go. But they omit the fact that AP physics makes sense only if it is preceded by a broad conceptual physics course. The College Board states that "the strongly recommended format for both [AP] Physics B and Physics C courses is a second-year course following the usual introductory physics course" that "better prepares [students] for more analytical approaches taken in AP courses."1 Unfortunately, most AP students have had no previous course that emphasizes concepts over calculations (see Physics Today, October 1999, page 68).
For at least three reasons, a broad and conceptual first course is an essential prerequisite to any more technical course. First, as the College Board and lots of physics education research have shown, a grounding in the concepts of physics is an essential prerequisite to a meaningful math-based treatment.
Second, for many practical reasons, math-based high-school courses must concentrate on Newtonian mechanics. So-called modern physics, our current view of the physical universe, is hardly mentioned. Many future biology, medicine, engineering, and other students, then, will never take a course that presents such central concepts as quantum uncertainty and the relativity of time.
And third, traditional math-based courses give no time to such societal topics as energy resources, global warming, pseudoscience, and scientific methodology. Yet it is fairly obvious that industrialized democracies cannot survive unless their citizens are literate in such topics. The American Association for the Advancement of Science puts this fairly strongly: "Without a scientifically literate population, the outlook for a better world is not promising."2
Students who skip a broad conceptual course to enter AP physics are harmed more than helped; they would opt for the broader course were the AP choice not available. Although AP physics is better than no physics at all, a conceptual course plus AP is far better still.
I applaud Physics Today for featuring an article on advanced physics education in American high schools. Jerry Gollub and Robin Spital offer good suggestions for what high-school physics students need. I am greatly disappointed, though, that so much attention was given to the Advanced Placement program. I took AP courses in Latin, Spanish, Calculus BC, and Physics (mechanics only), and I believe the AP program is more of an obstacle than an aid to providing quality advanced education. Students use AP exams only to boost their resumés. And from the reaction of faculty, I concluded that AP scores did tremendous things for the reputations of high schools. So much for knowledge for knowledge's sake.
The article did not mention the economics of the AP program. Currently, the cost for taking the AP examinations is $85 each. Why should a student or his or her parents have to pay such a hefty sum, especially when the high cost of college tuition is looming? How much of that fee goes toward paying graders of the exam and how much toward promoting the AP program and lobbying high-school administrators? Although students are informed of the many benefits of taking AP exams, very few are told that most universities and colleges offer placement tests for free. The most disparaging effect of the high cost is on students with lower socioeconomic status. As the authors stated, those students "do not fare as well on the examinations (on average)," which makes the exam an even larger waste of their money.
The loss to the student is not only monetary. This year, the AP examinations were administered during the first week in May, which gave AP students limited time to learn advanced, complex topics. Given the limited time and a very structured syllabus, laboratory experience falls by the wayside. The statistics I would like to see are the numbers of AP teachers who offer experimental work to their students. I would expect very few, because the pressure is mounting to achieve high test scores. The irony is that, as scientists and teachers of science, we preach to students that theory and experiment work hand-in-hand to advance our understanding of the universe.
I am also disappointed in the authors' suggestion that "formal calculus should not be required." Without calculus, physics reduces to a set of equations that the authors do not want students to memorize. Students should be given the elegant mathematical tools to broaden their understanding of physics.
I suggest we abandon the AP program altogether. The University of Chicago does not accept AP scores, and that stance has not hurt its reputation. Let's break the constraints of the standardized system and allow schools to develop their own advanced curriculum. Of course, local curriculum development on an as-needed basis will require qualified, confident, and experienced physics teachers. College professors are expected to develop their own courses; why not high-school teachers?
One of Jerry Gollub and Robin Spital's principal recommendations for improvements to the Advanced Placement physics program is to develop a high-school physics curriculum that is not based on introductory college courses. However, the authors neglect what I consider the most useful aspect of the AP program: the perceived authority of courses that replicate college-level work.
Those who are not directly involved with high-school politics tend to underestimate the pressure teachers receive from students and parents. Many students have earned top marks in all their classes, including math and science, through middle school and early high school simply by, in Gollub and Spital's words, "rote memorization of facts or equations, or following narrowly prescribed instructions." Many physics students become shocked and angry at the beginning of the school year when that approach does not lead to success in physics. Only the rare, ideal student decides for himself that such disillusionment necessitates a reevaluation of his approach rather than a complaint about the teacher's unfairness and unrealistic expectations. High-school physics teachers who face such complaints are often placed at a further disadvantage because most administrators have no understanding of the content or goals of the physics course. The path of least resistance is thus to water down the course so that the "rote" learners can earn an A.
Students and parents do not usually see the cause-and-effect relationship as "learn a lot, develop intellectual prowess, earn admission to college." Instead, they understand "get As, get into college." It is the grade, not the course content, that motivates most students. Students often develop an adversarial relationship with a physics teacher because they perceive that the teacher is "making" them work too hard. In their mind, the less depth of material, the more likely an A becomes. The teacher is perceived as bad for requiring any depth of thought.
With the AP curriculum replicating a college course, though, the tables are turned. A teacher of an AP course can answer those "you're too tough" complaints in a language the students understand: "If you want to get Advanced Placement and do well in college, you must trust me and learn the skills I ask you to learn."
Using college admission as a motivation tool is a temporary thing, to be used in that difficult first month of the school year. I find that, by December, such artificial motivation is unnecessary. Once students finally adapt themselves to the study habits and thought processes required for success in physics, the course can drive itself. High-school students are eager and willing to learn physics for its own sake, once they recognize the intellectual beauty of the subject. For teacher and students to get to December, though, the perceived authority of a non-negotiable college-level course is a practical necessity.
I was surprised that, in the article on advanced physics in high schools, the expression circular momentum and rotation appears in the table on page 51 in item E under "Newtonian mechanics." The correct term is angular momentum, which is related to the general motion of a particle. Angular momentum is not necessarily circular and is certainly not a rotation. Even a particle with rectilinear motion has angular momentum relative to any point not on its path. Although the rotation of a body also has angular momentum, that is the aggregate of the angular momentum of each of the particles composing the body. I hope that those interested in improving physics education in high schools get their physics straight.
The article "Advanced Physics in the High Schools," although it raises some interesting truths, has also created apparent paradoxes. Those of us who have taught both of the Advanced Placement Physics courses in high school can testify that the AP Physics B course is the more difficult of the two to teach. Here we arrive at the first paradox. The AP Physics C course covers only two of the five big areas of introductory physics--mechanics and electromagnetism. The B course also includes thermodynamics and fluids, waves and optics, and modern physics. A score of 5 on the B exam is much more praiseworthy than a 5 on the C exam. Yet the broader, more comprehensive exam gets less respect from universities and colleges.
The National Research Council implies that the AP Physics B course is too broad to be stimulating. However, many AP physics teachers have observed that the B course produces more physics majors than the narrower C course. Many of my former students who went on to declare physics as a major said that physics offered more variety than other sciences. The NRC says that "stimulating interest . . should be a key goal," yet it wishes to abolish the course that has motivated more potential physics majors than any other high-school course I offer.
The second paradox concerns the time spent on topics. If done correctly, both AP physics courses should be second-year courses for all but the top 5% of high-school students. For most of my students, getting a 5 on either exam was a result of 360 classroom hours. According to the NRC, teachers do not have enough time to completely develop conceptual understanding, inquiry-based learning, and problem-solving skills for the material on the AP Physics B exam. Colleges and universities across the nation, however, have a similar curriculum, use the same books, yet claim to be able to accomplish these learning objectives in 90 hours over two semesters. Why does the NRC question the group that spends 180 or 360 classroom hours on the material instead of the group that spends only 90 contact hours?
The third paradox has to do with a statement from the article. On the one hand, the authors say that, as teachers, they "have found that students at all levels like intellectual challenges that are within their reach." And on the other hand, the NRC wants to disband both AP physics courses in favor of one course focused around "a single version of Newtonian mechanics." How can the more limited course challenge a diverse group of high-school students "at all levels"?
A small amount of the article "address"es the only real problem with the AP Physics C course: waiting on the students to get to integral calculus. At that point, the AP Physics C course becomes an asset. Instead of mathematics being used to understand physics, the reverse usually occurs. As the science teacher in a team, I can show how summations lead to integrals without losing continuity in either AP course, Physics C, or Calculus. The NRC acknowledges that problem solving is important and emphasizes collaborative learning. Yet it recommends isolating physics from the rest of the nonscience high-school curriculum. In my opinion, this last is the saddest contradiction of all.
Gollub and Spital reply: We appreciate the thoughtful letters our article has stimulated. The Physics Panel Report of the NRC study explicitly recommends an introductory course prior to AP, and we agree with Art Hobson on the importance of teaching concepts in depth, not only before AP, but also as part of it. Students often do not have time for two physics courses in their program. Currently, the problem is much more serious in physics than in chemistry, which typically comes earlier. What will happen if "physics first" catches on? Some schools are now teaching conceptual physics in the ninth grade, followed by an optional AP course in the junior or senior year. That approach seems promising.
Michael Wood sees the AP program as fundamentally wrong. We point out many problems, but our assessment is that the AP program makes positive contributions to serious science study in many schools. The NRC report includes specific recommendations for improving the AP curriculum and exams. Requiring the exams might well be problematic because of the cost. Some states, by subsidizing exam costs, make the exams more widely and equitably available.
Still, we are not advocating AP as the only or best option for advanced study in physics or the other sciences. The full NRC report has an extensive discussion of the International Baccalaureate program, and other approaches are treated briefly. Also, implementation of the present AP program varies widely from school to school. The AP "syllabus" that Wood mentions is actually little more than an outline. Many AP teachers do in fact design their own courses.
The panel recommended that "formal calculus should not be required" for the new standardized mechanics. Woods perhaps misinterpreted that recommendation to imply that no calculus should be used in the entire program. That was not the intention. It is certainly not true that dropping the calculus requirement would reduce mechanics to memorized equations. An excellent understanding of elementary mechanics can be achieved by students who have a solid grasp of algebra and the concepts of limiting slopes and areas.
Many experienced high-school teachers have found that complex calculations monopolize students' attention at the expense of central organizing ideas like conservation of energy. We also need to be concerned about equitable access to advanced study. In many schools, calculus comes late, and not all students take it. Our advice, if implemented, would somewhat raise the mathematical level for those currently taking AP Physics B, and would maintain the accessibility of advanced mechanics study to a wide variety of students. We stress that the panel makes this recommendation for mechanics only and expects that formal calculus will continue to play a central role in the advanced study of electricity and magnetism.
Greg Jacobs properly emphasizes the pressure that teachers receive from students and parents. The NRC committee and panels included many teachers, so we are, of course, aware of this pressure. However, even if the courses are redesigned with less emphasis on the precise replication of college courses, they will continue to be important for documenting students' ability to handle challenging college-level material, and will therefore continue to favorably affect admissions. Although that positive impact can continue to be used for motivation, we think that the best way to motivate students is to increase their success in learning rather than to try to convince them that the distasteful medicine of AP physics will be beneficial.
Marcelo Alonso detected a typographical error, for which we apologize. The College Board publication refers to "circular motion," not "circular momentum."
We strongly disagree with many of Robert Mullins's assertions. The NRC panel did not criticize the AP Physics B course as being "too broad to be stimulating," but rather too broad to allow learning in depth. However, if the B course is taught in two years, as some schools are doing, it is quite a reasonable curriculum. We agree that the problem of breadth versus depth also exists in college courses, and the NRC report points out that colleges also need to be more realistic. Oddly enough, the complete AP Physics-B program is more compressed than many college courses, in which instructors often choose to omit topics.
The NRC panel certainly did not recommend "isolating physics from the rest of the nonscience high-school curriculum." In fact, the report recommends increasing attention to interdisciplinary opportunities.
Although mechanics provides abundant intellectual challenge, the Physics Panel agrees with Mullins that the study of other topics should also be available to advanced physics students. Ordinarily, the common mechanics unit we propose would be covered in one semester; that would leave the second semester free for topics like electricity and magnetism or modern physics. Although students are excited by exposure to the forefront of physics, we should not underestimate the satisfaction they can derive from mastering mechanics: It is close to their everyday experience, and even mechanics contains challenging surprises--chaos, for example. Too many students are lost at an early stage. Because few students place out of a full year of physics at present, an agreed standard for mechanics could at least allow a larger number of students to omit the first semester of college physics.
