Content Panel Report:

Physics



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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Content Panel Report: Physics

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools This page intentionally left blank.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 1 Introduction The National Research Council’s Committee on Programs for Advanced Study of Mathematics and Science in American High Schools (parent committee) formed a physics panel to provide advice on the effectiveness of and potential improvements to programs for the advanced study of physics in American high schools. Appendix A presents the parent committee’s charge to the panel. The physics panel met twice (in May and July 2000) to address its charge from the parent committee. The panel was chaired by a member of the parent committee, who served as liaison to the committee and consolidated the panel’s findings and recommendations into this report. Panel members included experienced college and university physics professors noted for their work in physics education, as well as high school physics teachers (for biographical sketches, see Appendix B). To develop a framework for its recommendations, the panel began with a thorough discussion of recommended practices that it would expect to find in a good advanced high school physics program. Chapter 2 presents a summary of the panel’s review. Using the model that emerged from that discussion, the panel evaluated the two dominant advanced high school programs—Advanced Placement (AP) and International Baccalaureate (IB)—to determine the extent to which they encourage the use of those recommended practices in their physics courses. The results of this evaluation are presented in Chapter 3, along with the panel’s recommendations for improvements to both programs. Although the panel lacked sufficient time to consider all possible alternatives to the AP and IB programs, it did consider one alternative approach, presented in Chapter 2. The panel recognizes that each high school is a unique environment with its own strengths and limitations. Thus there is unlikely to be a single advanced program that could reasonably be implemented with complete uniformity across the nation. Instead, the panel suggests that high schools and school districts offering advanced physics instruction adopt a program that has the general characteristics described in

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Chapter 2 but is flexible enough to be implemented in a school’s or district’s specific context. Chapters 4, 5, and 6 examine three topics of importance to the panel’s review of advanced study programs in physics: Chapter 4 looks at the crucial role played by teaching and learning; Chapter 5 summarizes changing emphases in physics and their impact on advanced physics instruction; and Chapter 6 addresses the linkage between advanced high school physics programs and college physics programs. Each of these chapters includes the panel’s specific recommendations in the respective area. Finally, Chapter 7 summarizes the panel’s main findings and overall recommendations.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 2 Recommended Practices for Advanced Physics Instruction WHAT IS AN ADVANCED PHYSICS PROGRAM? The term “advanced” is taken here to mean study that is substantially beyond the level of the physics required for high school graduation under the National Science Education Standards (NSES) (National Research Council [NRC], 1996). Although the goal of an Advanced Placement (AP) physics course is to substitute for a physics course that would otherwise be taken in college, that is certainly not the only possible reason for undertaking or offering an advanced program of study in high school. In some cases, traditional high school–level courses are simply not sufficiently challenging to interest the brightest students. In many cases, students undertake advanced study to enhance their college applications. In still other cases, students may be interested in particular areas of physics that are not covered in available high school–level courses (as discussed later in this chapter). Certainly, the particular program adopted by each high school will depend a great deal on exactly what goals that program is intended to meet. PREREQUISITES FOR AN ADVANCED HIGH SCHOOL PROGRAM The panel recognizes that the level of preparation of students entering advanced physics programs varies widely from high school to high school. Nevertheless, we believe that there are two fundamental prerequisites most entering students should meet: Prior to enrolling in an advanced physics course in high school, students should have studied the physics that is suggested as a requirement for high school graduation in the NSES (NRC, 1996). This requirement can be satisfied with the first year of a 2-year physics program. This is the approach adopted by the International Baccalaureate (IB) program (as discussed in

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Chapter 3). If a 1-year advanced course is the first time that entering students encounter physics, the usual result is a packed schedule that allows too little time to develop the depth of understanding that is the fundamental goal of the program.1 Students should be fluent in mathematics through the precalculus level (see the discussion below). In particular, by the time they are ready to study advanced physics, students should be skilled in algebraic manipulation and have a firm grasp of basic trigonometry. Emphasis should also be placed on the use of proportions to solve problems, estimation skills, the use of international units, and scientific notation (powers of 10). Acquiring all necessary mathematical skills may well take several years of study before a student enters the advanced physics program. The panel encourages high school physics teachers to work closely with the mathematics departments of their schools to develop the necessary courses of instruction. Mathematics is the language used to describe the fundamental laws of physics. Just as it is very difficult to teach physics to students who barely understand English (or the language of instruction), it is equally difficult to teach physics to students who do not “speak mathematics.” At the level of advanced physics study in high school, speaking mathematics consists primarily of facile manipulation of algebraic equations and an intuitive grasp of the significance of those equations. For example, students should have no doubt that linear relationships lead to straight-line graphs and that the presence of curvature in a graph implies that the relationship cannot be linear. While knowledge of calculus is unquestionably helpful in the study of advanced physics, it is not absolutely essential. Ideas such as the derivative and integral can be introduced in physics classes by discussing the slope of tangent lines and the area under curves. However, the level of mathematical skill of students may well play a role in the selection of optional physics topics (as discussed later in this chapter). THE MOST IMPORTANT OBJECTIVES There was strong consensus within the panel that the most important objectives for advanced study in high school physics are not tied to particular topics in physics. The panel is far more concerned with promoting more general dispositions, abilities, and habits of mind. In particular, advanced study in physics should help students further develop the following: 1   The panel acknowledges that there are circumstances under which it is appropriate for students to take advanced physics as a first-year physics course. This may apply to exceptionally talented students or to students in schools where scheduling considerations leave no reasonable alternative. Nevertheless, most students would be well advised to begin their study of physics with a sound high school–level course.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Excitement, interest, and motivation for further study in physics Facility with mathematics as a means of communicating, examining, and refining ideas Scientific imagination and creativity Scientific habits of mind or the abilities and inclinations:2 To look for and examine assumptions hidden in the student’s own and others’ reasoning To seek precision and clarity in forming and communicating ideas, including the use of mathematics To design and conduct empirical investigations to answer scientific questions To identify and reconcile inconsistencies between the student’s understanding and observations To develop, implement, test, and revise models of physical phenomena To develop and learn to work within a framework of theoretical principles DESIGNING A CURRICULUM TO MEET THESE OBJECTIVES The Central Role of Newtonian Mechanics Although the objectives listed in the previous section can be met through a thorough study of many different areas of physics, some commonality among programs is clearly desirable, especially when advanced programs serve as substitutes for physics courses in college. Given the central role of Newtonian mechanics in physics, both historically and conceptually, the panel recommends that any advanced study of physics include Newtonian mechanics. Mechanics provides an ideal framework for achieving the objectives cited above. At the same time, familiarity with mechanics is universally expected of students entering college who have completed an advanced high school physics program. Maximizing the Commonality of Advanced Programs in Newtonian Mechanics Because the study of Newtonian mechanics serves as the foundation of any good program of advanced physics study, the panel recommends that 2   We note that the Theory of Knowledge course included in the IB program (see Chapter 3) deals with the habits of mind listed here. This is an advantage of the IB program; since it is a program rather than a course, one teacher need not do everything.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools the set of topics addressed be standardized as much as possible across the nation. While the exact details of such a nationwide mechanics syllabus can be agreed upon at a future time, the panel makes the following two recommendations: The syllabus should include the study of rotational dynamics. It is important for students to learn to apply the laws of mechanics to extended bodies, not just point particles. Not only is the physics content important, but the study of rotational dynamics also presents substantial intellectual challenges that help prepare students for the challenges of their future higher education. There should be no distinction made between the study of mechanics with and without calculus. Whether or not the mathematical background of the students includes calculus, the concepts necessary for physics [e.g., (lim/Δt → 0) of (Δx/Δt)] can and should be introduced. The primary goal of the study of Newtonian mechanics is to develop conceptual understanding, rather than the ability to perform complex mathematical manipulations. For example, it is not necessary for advanced high school students to learn how to calculate the moment of inertia of a cylinder about some given axis, but it is important for them to understand rotational kinetic energy and angular momentum. The Role of Calculus in the New Common Mechanics Unit The panel stresses that the new mechanics unit recommended above is by no means a noncalculus introduction to mechanics. Indeed, the concepts of calculus are absolutely essential to the physics subject matter. Specifically, the panel emphasizes the following points: Teachers with qualified students are encouraged to use formal calculus. Such students are eager to apply their mathematical prowess and should be encouraged to do so. It is likely that such students would continue their calculus-based study of physics in a second-semester course such as AP Physics C Electricity and Magnetism.3 3   AP Physics C Mechanics and AP Physics C Electricity and Magnetism are one-semester calculus-based courses, each leading to its own separate AP examination. AP Physics B is a two-semester noncalculus course leading to a single comprehensive AP Physics B examination. For a detailed discussion of the AP Physics program, see Chapter 3.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools The final examination for the new unit would not require students to use formal calculus. In all other respects, however, the new examination should be at about the same level as the current exam for AP Physics C Mechanics. This recommendation is in harmony with the current trend on that examination: less reliance on technical mathematics and increasing emphasis on conceptual physics (see Chapter 3). The final examination for the new unit would test students’ knowledge of the concepts of both differential and integral calculus required to develop the physics. For example, students would be required to know that instantaneous velocity can be obtained as the slope of the graph of displacement versus time and that the work done by a force that varies as a function of position can be obtained from the area under the force curve. Comparison of the New Mechanics Unit with Current AP Mechanics Students who today would study AP Physics Mechanics C would find the new unit to be very much in line with their expectations for that course. There would be less emphasis on formal mathematics and more on conceptual understanding, but the general level of the treatment of the physics would be the same as that of current AP Physics C Mechanics. All the important physics currently found in AP Physics C Mechanics would still be covered and tested on the final examination. Students who today would study AP Physics B would find the new mechanics unit to be a more comprehensive and in-depth treatment of the subject than that found in current Physics B courses, primarily because of the inclusion of rotational dynamics. Therefore, the primary effect for AP Physics students of the creation of a common mechanics unit as recommended by the panel would be to raise the standards in mechanics for Physics B to the level of Physics C. Coverage of Other Areas of Physics The breadth of material included in introductory college courses almost always requires rapid, superficial treatment. Unfortunately, the emphasis on breadth to the exclusion of depth is also growing at the secondary level, as more states are adopting encompassing frameworks and standards for science instruction. The panel believes, however, that for students to appreciate physics as a field of inquiry, it is more important for them to develop depth of understanding in the areas they study than to study any particular areas. The amount of additional material beyond Newtonian mechanics that can be covered in a particular course depends on its length. For a 1-year

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools program, the panel believes strongly that students should study at most one other major area of physics.4 In a 2-year program, the number of topics can be increased as long as the essential goal of depth of understanding is attained. Additional Areas That Match Instructors’ Talents and Resources The panel believes that advanced physics programs should be able to choose from among various options the extra topics that best meet their needs. We offer the following possible optional topics for illustration only; a detailed list of options and a syllabus for each need to be carefully developed: Electricity and magnetism/circuits Models of light and sound (geometrical optics, mechanical waves, physical optics) Complex systems (thermal and statistical physics, computer-assisted conceptualization, chaos) Atomic, nuclear, and particle physics Again, we are not proposing here the specific makeup of these other options; we are proposing that they be developed. In each case, physics teachers and students would be motivated to pursue greater depth of coverage in a limited area. We note that the ability to develop such options gives advanced high school instruction the flexibility needed to address emerging areas of physics, as discussed below. Second Semester Options In this section, we provide additional detail on some optional curricula that could be used in the second semester of an advanced physics program. In describing these options, we assume that students have already completed the new common mechanics unit discussed above. Our goal is not to specify these curricula completely; that is a task for other organizations, such as the College Board and the International Baccalaureate Organisation (IBO). Rather, the brief summaries below are intended to give the reader a better understanding of the overall content and goals of these example courses. 4   The panel is aware that many current AP Physics C programs spend the entire academic year on mechanics. We have no objection to this practice, which may well provide the extra time necessary for those students to achieve the depth of understanding that is the central objective of advanced physics study.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools AP Physics C Electricity and Magnetism. This existing semester course is already familiar to many readers; it is the usual follow-up for students who take the current AP Physics C Mechanics course during the first semester. The content of the course is specified in the 2000/2001 edition of the Advanced Placement Course Description: Physics, published by the College Board (1999a) and known as the Acorn Book. (See Chapter 3 for a detailed discussion of the AP Physics program.) The course is highly mathematical and covers Maxwell’s equations in integral form. There are numerous applications of calculus, as well as an introduction to direct-current circuits. Capacitance and inductance are introduced, and the time dependence of currents and voltages in simple circuits is studied. The panel recommends decreased emphasis on the technical mathematical details and more emphasis on conceptual understanding. However, there is nothing to prevent this curriculum from being used as a second-semester option in its present form. Biomedical Physics. The IBO has already defined a syllabus for the study of this topic in the IB Diploma Programme Guide: Physics (IBO, 2001). (See Chapter 3 for a detailed discuss of the IB physics program.) This noncalculus course covers the following major topics: Fluid statics, fluid flow, and the physics of the cardiovascular system Rotational statics, with application to the muscular-skeletal system Hearing—normal function, defects, and correction Radiation—types, sources, properties, and detection Medical imaging Biological effects, hazards, dosimetry, and diagnostic uses of radioactive sources The course is currently designed to be covered in 30 hours, or approximately half a semester. Therefore, if the course were used as a semester option, several of these very interesting topics could be covered in greater depth, consistent with the fundamental goal of achieving deep conceptual understanding. Special and General Relativity. This is another area for which the IBO has already created a detailed syllabus for a noncalculus course. The major topics covered by that syllabus include the following: Frames of reference and Galilean relativity Postulates and fundamental concepts of special relativity Historical context and experimental support for special relativity Postulates and fundamental concepts of general relativity Experimental support for general relativity (IBO, 2001)

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools References Chabay, R.W., & Sherwood, B.A. (1999). Electric and magnetic interactions. New York: Wiley. Chabay, R. W., & Sherwood, B.A. (2002). Matter and interactions, volume 2: Electric and Magnetic Interactions. New York: Wiley. Champagne, A. B., Gunstone, R. F., & Klopfer, L. E. (1985). Instructional consequences of students’ knowledge about physical phenomena. In L.H.T. West and A.L. Pines (Eds.), Cognitive structure and conceptual change. New York: Academic Press. Clement, J. (1982). Student preconceptions in introductory mechanics. American Journal of Physics, 50(1), 66–71. Coleman, L. A., Holcomb, D.F., & Rigden, J.S. (1998). The introductory university physics project 1987–1995: What has it accomplished? American Journal of Physics, 66, 124–137. College Entrance Examination Board. (1994a). 1993 AP physics B: Free-response scoring guide with multiple-choice section. New York: Author. College Entrance Examination Board. (1994b). 1993 AP physics C: Free-response scoring guide with multiple-choice section. New York: Author. College Entrance Examination Board. (1994c). College and university guide to the advanced placement program. New York: Author. College Entrance Examination Board. (1999a). Advanced placement course description, physics, 2000, 2001. New York: Author. College Entrance Examination Board. (1999b). Released exams: 1998 AP physics B and physics C. New York: Author. College Entrance Examination Board. (2001). Advanced placement course description, physics, 2002, 2003. New York: Author. diSessa, A.A. (2000). Changing minds: Computers, learning, and literacy. Cambridge, MA: MIT Press. Edge, R.D. (1987). String and sticky tape experiments. College Park, MD: American Association of Physics Teachers. Eisenkraft, A. (1999). Active physics. Armonk, NY: It’s About Time. Eylon, B.S., & Reif, F. (1984). Effects of knowledge organization on task performance. Cognition and Instruction, 1, 5-44.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Hake, R.R. (1998). Interactive-engagement vs. traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66 (1), 64–74. Halliday, D., Resnick, R., & Walker, J. (2000). Fundamentals of physics: Volume 1. New York: Wiley. Halloun, I. (1996). Schematic modeling for meaningful learning of physics. Journal of Research in Science Teaching, 33 (9), 1019–1041. Halloun, I. (1998). Views about science and physics achievement. The VASS Story. In E.F. Redish, and J.S. Rigden (Eds.), Proceedings of the international conference on undergraduate physics education (1996). Washington DC: American Institute of Physics. Hammer, D. (1995). Epistemological considerations in teaching introductory physics. Science Education, 79(4), 393–413. Hammer, D. (1997). Discovery learning and discovery teaching. Cognition and Instruction, 15(4), 485–529. Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory. The Physics Teacher , 30(3), 141–158. Hewitt, P.G. (1999). Conceptual physics. Menlo Park, CA: Scott Foresman Addison-Wesley. Hewson, P.W. (1985). Epistemological commitments in the learning of science: Examples from dynamics. European Journal of Science Education, 7(2), 163–172. Hoy, R.R. (1993). A ‘model minority’ speaks out on cultural shyness. Science, 262, 1117–1118. International Baccalaureate Organisation. (1996). International baccalaureate: Physics. Geneva, Switzerland: Author. International Baccalaureate Organisation. (1999a). International baccalaureate: Physics, higher level, examination papers 1-3. Geneva, Switzerland: Author. International Baccalaureate Organisation. (1999b). Subject reports—May 1999. Geneva, Switzerland: Author. International Baccalaureate Organisation. (2001). IB diploma programme guide: Physics, 2001. Geneva, Switzerland: Author. Knight, R.D. (1997). Physics: A contemporary perspective. Reading, MA: Addison-Wesley. Kolodny, A. (1991). Colleges must recognize students’ cognitive styles and cultural backgrounds. Chronicle of Higher Education, 37(21), A44. Laws, P. (1989). Workshop physics: Replacing lectures with real experience. In E.F. Redish and J.S. Riley (Eds.), Computers in physics instruction: Proceedings. Reading, MA: Addison-Wesley. Laws, P.W. (1991). Calculus-based physics without lectures. Physics Today, 44(12), 24–31. Laws, P.W. (1997). Workshop physics activity guide. New York: Wiley. Laws, P.W. (1999). New approaches to science and mathematics teaching at liberal arts colleges. Daedalus, 128(1), 217–240. Lichten, W. (2000). Whither advanced placement? Education Policy Analysis Archives, 8(29), 1–19.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools MacIsaac, D. (2000). Communities of on-line physics educators. The Physics Teacher, 38(April), 210–213. Mazur, E. (1997). Peer instruction, A user’s manual. Upper Saddle River, NJ: Prentice Hall. McDermott, L.C. (1991). What we teach and what is learned—Closing the gap. American Journal of Physics, 59(4), 301–315. McDermott, L.C., & Redish, E.F. (1999). Resource letter PER-1: Physics education research. American Journal of Physics, 67, 755–767. McDermott, L.C., & Shaffer, P.S. (2002). Tutorials on introductory physics. Upper Saddle River, NJ: Prentice Hall. McDermott, L.C., Shaffer, P.S., & Somers, M.D. (1994). Research as a guide for teaching introductory mechanics: An illustration in the context of the Atwood’s machine. American Journal of Physics, 62(1), 46–60. Minstrell, J. (1989). Teaching science for understanding. In L.B. Resnick, and L.E. Klopfer (Eds.), Toward the thinking curriculum: Current cognitive research (pp. 129–149). Alexandria, VA: American Society for Curriculum Development. Minstrell, J. (2000). Student thinking and related assessment: Creating a facet-based learning environment. In N.S. Raju, J.W. Pellegrino, M.W. Bertenthal, K.J. Mitchell, and L.R. Jones (Eds.), Grading the nation’s report card: Research from the evaluation of NAEP (pp. 44–73). Washington DC: National Academy Press. Moore, T.A. (1998). Six ideas that shaped physics. Boston: WCB/McGraw-Hill. Morrison, P., Morrison, P., & Pine, J. (1996). ZAP! Electrical circuits and fields. Sudbury, MA: Jones & Bartlett. National Center for Education Statistics. (1998). Pursuing excellence: A study of U.S. twelfth-grade mathematics and science achievement in international context (NCES 98049). Washington, DC: US Department of Education. National Council of Teachers of Mathematics. (2002). Principles and standards for school mathematics. Reston, VA: Author. National Research Council. (1996). National science education standards. National Committee on Science Education Standards and Assessment. Coordinating Council for Education. Washington, DC: National Academy Press. National Research Council. (1997a). Improving teacher preparation and credentialing consistent with the national science education standards: Report of a symposium. Center for Science, Mathematics, and Engineering Education. Washington, DC: National Academy Press. National Research Council. (1997b). Science teaching reconsidered. Committee on Undergraduate Science Education. Division on Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. National Research Council. (2000). How people learn: Brain, mind, experience, and school: Expanded edition . Committee on Developments in the Science of Learning. J.D. Bransford, A.L. Brown, and R.R. Cocking (Eds.). Committee on Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. Neuschatz, M., & McFarling, M. (1999). Maintaining momentum: High school physics for a new millennium. College Park, MD: American Institute of Physics.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Redish, E.F., Steinberg, R.N., & Saul, J.M. (1998). The distribution and change of student expectations in introductory physics. In E.F. Redish, and J.S. Rigden (Eds.), Proceedings of the international conference on undergraduate physics education (1996). Washington DC: American Institute of Physics. Reif, F., & Larkin J.H. (1991). Cognition in scientific and everyday domains: Comparison and learning implications. Journal of Research in Science Teaching, 28, 733–760. Roelofs, L.D. (1997). Preparing physics majors for secondary level teaching: The education concentration in the Haverford College physics program. American Journal of Physics, 65, 1057–1059. Roth, W.M., & Lucas, K.B. (1997). From “truth” to “invented reality”: A discourse analysis of high school physics students’ talk about scientific knowledge. Journal of Research in Science Teaching, 34(2), 145–179. Serway, R.A., & Beichner, R.J. (2000). Physics for scientists and engineers. Philadelphia: Saunders College. Shaffer, P.S., & McDermott, L.C. (1992). Research as a guide for curriculum development—An example from introductory electricity. Part II: Design of instructional strategies. American Journal of Physics, 60(11), 1003–1013. Sherin, B., diSessa, A. & Hammer, D. (1993). Dynaturtle revisited: Learning physics through collaborative design of a computer model. Interactive Learning Environments, 3(2), 91–118. Sokoloff, D.R., Laws, P.W., & Thornton, R.K. (1994). Real time physics: Active learning laboratories, mechanics. Medford, MA: Tufts University. Sokoloff, D.R., Laws, P.W., & Thornton, R.K. (1997). Real time physics: Active learning laboratories, electric circuits. Eugene, OR: Department of Physics, University of Oregon. Taylor, E.F., & Wheeler, J.A. (2001). Spacetime physics: Introduction to special relativity, 2nd edition. New York: W.H. Freeman. Thornton, R. &, Sokoloff, D.R. (1990). Learning motion concepts using real-time micro-computer-based laboratory tools. Amercian Journal of Physics, 58(9), 858–66. Thornton, R.K., & Sokoloff, D.R. (1998). Assessing student learning of Newton’s laws: The force and motion conceptual evaluation and the evaluation of active learning laboratory and lecture curricula. American Journal of Physics, 66(4), 338–352. van Zee, E.H., & Minstrell, J.A. (1997). Reflective discourse: Developing shared understandings in a physics classroom. International Journal of Science Education, 19, 209–228. Wells, M., Hestenes, D, & Swackhamer, G. (1995). A modeling method for high-school physics instruction. American Journal of Physics, 63(7), 606–619. White, B.Y., & Frederiksen, J. R. (1998). Inquiry, modeling, and metacognition: Making science accessible to all students. Cognition and Instruction, 16(1), 3–118. Wilensky, U., & Resnick., M. (1999). Thinking in levels: A dynamic systems perspective to making sense of the world. Journal of Science Education and Technology, 8(1), 3–19. Wosilait, K., Heron, P.R.L., Shaffer, P.S., & McDermott, L.C. (1999). Addressing student difficulties in applying a wave model to the interference, and diffraction of light. American Journal of Physics, 67(7), S5–S15.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Appendix A Charge to the Content Panels from the Parent Committee Charge to the Parent Committee and Content Panels: The charge to the committee is to consider the effectiveness of, and potential improvements to, programs for advanced study of mathematics and science in American high schools. In response to the charge, the committee will consider the two most widely recognized programs for advanced study: the Advanced Placement (AP) and the International Baccalaureate (IB) programs. In addition, the committee will identify and examine other appropriate curricular and instructional alternatives to IB and AP. Emphasis will be placed on the mathematics, physics, chemistry, and biology programs of study. Charge to Content Panels: The content panels are asked to evaluate the AP and IB curricular, instructional, and assessment materials for their specific disciplines. Below is a list of questions that the content panels will use to examine the curriculum, laboratory experiences, and student assessments for their specific subject areas. The content panels will use these questions to issue a report to the committee about the effectiveness of the AP and IB programs for educating able high school students in their respective disciplines. In answering these questions, the content panels should keep in mind the committee’s charge and study questions. The panels should focus on the following specific issues in advising the committee: I. CURRICULAR AND CONCEPTUAL FRAMEWORKS FOR LEARNING Research on cognition suggests that learning and understanding are facilitated when students: (1) have a strong foundation of background knowledge, (2) are taught and understand facts and ideas in the context of a conceptual framework, and (3) learn how to organize information to facili-

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools tate retrieval and application in new contexts (see, e.g., National Research Council [NRC], 2000). To what degree do the AP and IB programs incorporate current knowledge about cognition and learning in mathematics and science in their curricula, instructions, and assessments? To what degree is the factual base of information that is provided by the AP and IB curricula and related laboratory experiences adequate for advanced high school study in your discipline? Based on your evaluation of the materials that you received, to what extent do the AP and IB curricula and assessments balance breadth of coverage with in-depth study of important topics in the subject area? In your opinion, is this balance an appropriate one for advanced high school learners? Are there key concepts (big ideas) of your discipline around which factual information and ideas should be organized to promote conceptual understanding in advanced study courses (e.g., Newton’s laws in physics)? To what degree are the AP and IB curricula and related laboratory experiences organized around these identified key concepts? To what degree do the AP and IB curricula and related laboratory experiences provide opportunities for students to apply their knowledge to a range of problems and in a variety of contexts? To what extent do the AP and IB curricula and related laboratory experiences encourage students and teachers to make connections among the various disciplines in science and mathematics? II. THE ROLE OF ASSESSMENT Research and experience indicate that assessments of student learning play a key role in determining what and how teachers teach and what and how students learn. Based on your evaluation of the IB and AP final assessments and accompanying scoring guides and rubrics, evaluate to what degree these assessments measure or emphasize: students’ mastery of content knowledge; students’ understanding and application of concepts; and students’ ability to apply what they have learned to other courses and in other situations. To what degree do the AP and IB final assessments assess student mastery of your disciplinary subject at a level that is consistent with expectations for similar courses that are taught at the college level?

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools III. TEACHING Research and experience indicate that learning is facilitated when teachers use a variety of techniques that are purposefully selected to achieve particular learning goals. How effectively do the AP and IB curricula and assessments encourage teachers to use a variety of teaching techniques (e.g., lecture, discussion, laboratory experience and independent investigation)? What preparation is needed to effectively teach advanced mathematics and science courses such as AP and IB? IV. EMPHASES The NRC’s National Science Education Standards and the National Council of Teachers of Mathematics’ Standards 2000 propose that the emphases of science and mathematics education should change in particular ways (see supplemental materials). To what degree do the AP and IB programs reflect the recommendations in these documents? V. PREPARATION FOR FURTHER STUDY Advanced study at the high school level is often viewed as preparation for continued study at the college level or as a substitute for introductory-level college courses. To what extent do the AP and IB curricula, assessments, and related laboratory experiences in your discipline serve as adequate and appropriate bases for success in college courses beyond the introductory level? To what degree do the AP and IB programs in your discipline reflect changes in knowledge or approaches that are emerging (or have recently occurred) in your discipline? How might coordination between secondary schools and institutions of higher education be enhanced to optimize student learning and continued interest in the discipline?

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Appendix B Biographical Sketches of Physics Content Panel Members S. James Gates, Jr., the John S. Toll Professor of Physics, is the director of the Center for String and Particle Theory at the University of Maryland at College Park. His research focus is in mathematical and theoretical physics. Dr. Gates served on the National Research Council (NRC) Joint Strike Technical Review Panel and the Task Group I-Combat Power committee. He has taught university-level mathematics and physics for 30 years and has lectured on general education issues, consulted with the Educational Testing Service, worked on a municipal high school curriculum, and chaired the Howard University physics department. The Washington Academy of Science recognized him as its 1999 College Science Teacher of the Year. Dr. Gates received two B.S. degrees and a Ph.D. from the Massachusetts Institute of Technology. David Hammer is an associate professor with joint appointments in Physics and Curriculum & Instruction at the University of Maryland, College Park. He conducts research in physics education, focusing on students’ beliefs about knowledge and learning as well as on teachers’ interpretations of the strengths and weaknesses in student thinking. Dr. Hammer earned his Ph.D. in Science and Mathematics Education and his MA in Physics from the University of California at Berkeley. Robert C. Hilborn is the Amanda and Lisa Cross Professor of Physics at Amherst College, where he teaches introductory and advanced-level physics. Dr. Hilborn’s current research focuses on testing the symmetrization postulate for identical particle systems in quantum mechanics, a study of the effects of dynamic Stark shifts on laser-excited atoms, and control schemes for chaotic systems. Dr. Hilborn is involved in physics education and has served as president of the American Association of Physics Teachers. In this position, he interacted with high school physics teachers and also has worked

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools with high school teachers while at Amherst. He is chair of the newly established National Task Force on Undergraduate Physics. Dr. Hilborn earned his Ph.D. from Harvard University. Eric Mazur is at Harvard University where he is a Harvard College professor, Gordon McKay Professor of Applied Physics, and professor of physics. Dr. Mazur’s research in optical physics includes contributions in light scattering, spectroscopy, and electronic and structural events in solids. Dr. Mazur also conducts research in improving science education, becoming well known for his “peer instruction” method for teaching large lecture classes. Dr. Mazur will complete his term on the Advanced Placement test development committee this spring. At the NRC, Dr. Mazur has served on the Working Group on Science Assessment Standards. Mazur received his Ph.D. in experimental physics from the University of Leiden in the Netherlands. Penny Moore taught physics 60-percent time at Piedmont High School in Piedmont, California for twenty-five years and worked concurrently at the University of California, Berkeley. During this time she designed, obtained funding for, and directed three large national science education programs: The Science for Science Teachers and PRIME Science programs, both funded initially by the National Science Foundation, and The Journey Inside with Intel Corporation. In August 2000, she left a fulltime position in the physics department at Berkeley to work as director of Science and Math Education in the College of Mathematical and Physical Sciences at The Ohio State University in Columbus. At the NRC, Ms..Moore served on the Working Group on Science Assessment Standards and was a leader in assembling Science Teaching Reconsidered. Robert A. Morse is a physics teacher at St. Albans School in Washington, DC, where he has taught physics and AP physics for 20 years. Dr. Morse has been recognized for his teaching with the Presidential Award for Excellence in Science Teaching, the Tandy Technology Scholar Award, the American Association for Physics Teachers (AAPT) Award for Excellence in Pre-College Teaching, and was named the American Physical Society Distinguished Physics Teacher for the District of Columbia for the APS Centennial. Dr. Morse has been active in the AAPT, where he has developed and presented workshops on teaching physics. At the NRC, he served as a panelist for the How People Learn Conference. He received his Ph.D. in Science Education from the University of Maryland at College Park, his M.Ed. from Boston University, and a BA in Physics from Cornell University.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Robin Spital (committee liaison and chair) is a teacher of Honors and Advanced Placement Physics at The Bolles School in Jacksonville, Florida. His career began at Illinois State University in Normal, where he was assistant professor of physics. He subsequently worked in the private sector as principal development engineer for the AAI Corporation in Hunt Valley, Maryland, and as principal scientist for Pfizer Medical Systems. Dr. Spital received his Ph.D. in theoretical high-energy physics from Cornell University.

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