ONLINE PREFACE TO SIX IDEAS THAT SHAPED PHYSICS

1. INTRODUCTION

This online preface is meant to supplement and extend the short preface provided in the printed texts.

Six Ideas That Shaped Physics is a fundamentally new approach to the two- or three-semester calculus-based introductory physics course, created in response to a call in 1989 for innovative curricula from the Introductory University Physics Project (IUPP), which subsequently supported its development. The second edition represents the culmination of more than a decade of development, testing, and evaluation at Pomona College, by IUPP, and by many courageous early users. The course is presently used at more than 50 colleges and universities around the world.

Six Ideas That Shaped Physics is more than just another introductory physics book: the six volumes in combination with the instructor's manual and supporting computer programs offers a comprehensive set of tools for re-energizing the entire introductory physics course. These materials suggest (and provides support for) tested ideas for organizing classes, homework assignments and lab experiences in ways that help students more effectively learn. The text and teaching materials use notation, terminology, and arguments consciously designed to help students avoid well-known conceptual problems, provide exercises that focus on developing students' conceptual knowledge and problem-solving skills, and provide tools to help involve students in active learning both inside and outside the classroom. Indeed, one of the main motivations for developing the text was to provide materials that better support active learning.

The text and course are based on the premise that innovative approaches to the presentation of topics and active learning can support each other in helping students learn physics more effectively. I have completely rethought every aspect of the course with an eye to what we have learned during the past few decades about how students learn physics, and I have done nothing just because "that is the way it has always been done." My focus has instead always been on empowering students to think like physicists.

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2. PROBLEMS AND GOALS

The structure of a typical introductory physics course has remained essentially static for almost 40 years. This traditional course structure has number of problems that researchers have documented in recent years. Pressures from users wanting specific topics have caused introductory texts to grow to the point that there is so much material to "cover" that students do not have time to develop a solid understanding of any part, and instructors do not have time to use classroom techniques that would help students really learn. Even with all this material, the course (with its focus classical physics) does not usually show what physics is like today, and thus presents a skewed picture of the discipline to the 32 out of 33 students nationwide who never take another physics course.

In my opinion, though, the most important shortcoming of the traditional course structure is that it often fails help students develop good physical thinking skills. A number of studies since the 1980s have shown that even students who earn high grades in a typical introductory physics course often cannot

1. apply basic physical principles to realistic situations,
2. solve realistic problems,
3. perceive or resolve contradictions involving their preconceptions, or
4. organize the ideas of physics hierarchically.

What such students do effectively learn is to solve standard homework problems rapidly using random-search methods that do not require much physical reasoning. A very recent study (E. Kim, S. Pak, Am. J. Phys. 70, 7, p. 759) showed that even students who worked more than 1000 typical homework problems failed to resolve basic conceptual difficulties with newtonian mechanics. Other studies have shown that the high pace of the standard course drives students to adopt non-thinking behaviors even when they would prefer to develop a deeper conceptual understanding.

These problems exist not necessarily because the traditional course was initially poorly designed but at least partly because both the context for the introductory physics course and the type of students taking it are significantly different now then they were in the early 1960s when the course was designed. The course now serves a much larger number of students, with a broader range of skills, motivations, and needs. In the 1960s, it was important to select and rapidly educate a handful of students to contribute to the Cold War effort. Now it is important to empower a much more diverse group of students to reason carefully about physical problems in a much broader set of situations. The different situation and different desired outcomes call for a different approach to the course.

The primary goal of Six Ideas is to help students achieve a meaningful level of competence in each of the four thinking skills listed above. The text, homework problems, and course recommendations are designed so that students are goaded toward (and then rewarded for) behaviors that help them develop these skills. While (mostly for practical reasons) the course does span the most important fields of physics, the emphasis is not particularly on "covering" material or providing background vocabulary for further study, but rather on developing students's conceptual understanding and problem-solving, thinking, and modeling skills. Facts and formulas evaporate quickly (particularly for the vast majority that will take no more physics) but developing a student's ability to think like a physicist in a variety of contexts gives them something that they can use throughout their lives.

An important secondary goal of Six Ideas is to introduce students to contemporary physics and contemporary thinking about physics. It is increasingly absurd that many 21st-century introductory courses include little if any 20th-century physics. Such a course does not serve the 32 out of 33 students whose entire view of physics is shaped by that course; how will such students make thoughtful decisions about the applications of physics in their 21st-century lives when their horizons only extend through the 19th century? How will they ever become excited about what physics can offer in the future?

These goals are fully consistent with the stated principles of the IUPP:

1. Less is more.
2. Present more contemporary physics.
3. Use a story line.

(For more detail about these principles, see the Overview.) In my opinion, the point of these principles is to support the goal of developing a reasonable level of competence in physical reasoning skills that are appropriate for 21st-century applications. The point of the first principle is to oppose the pressure to keep "covering" more and more in the introductory course: the first principle recommends that we instead reduce the pace of the course enough so that there is time for the kinds of activities that really develop student understanding. The second principle is in tension with the first (to put it mildly), but the point is that even well-developed 18th and/or 19th century physical reasoning skills do not prepare students to deal effectively with 21st-century applications. The point of a "story line" is partly to help motivate students but also (in my opinion) to help students understand that the ideas of physics are logically and heirarchically organized (something that research suggests distinguishes expert from novice problem-solvers).

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3. THE ORGANIZATION OF THE COURSE

In Six Ideas That Shaped Physics. I have addressed the story line issue by dividing the course up into six units, each of which examines in depth a physical idea that has changed the course of physics during the past three centuries. This organization (in combination with boxed equations and the "menus" and overviews at the beginning of each chapter) helps students see the heirarchical organization of ideas in physics. Note that each of the six ideas is stated concisely as part of the unit's title, so that every time a student opens the book, he or she is reminded of the idea.

The list below describes each unit's letter name, its length (1 d corresponds to "one class day," which I am defining to be one 50-minute class session), the idea, and the corresponding area of physics. This list also specifies the recommended order of units and how they would fit into a typical two-semester class structure.

Table 1: The Two-Semester Plan

First Semester (37 class days, not counting test days):

Second Semester (33 to 40 class days, not counting test days):

Note that covering all the chapters in the book requires a spring semester that is longer than fall semester. This is the case at Pomona and many other institutions, but one can adjust the length of the second semester to as few as 33 days by omitting parts of unit Q.
 

The non-standard order of presentation has evolved in response to our observations in early trials.
 

1. Conservation laws are presented first not only because they really are more fundamental than the particular theories of mechanics considered later but also because we have consistently observed that student understand them better and can use them more flexibly than they can Newton's laws. It makes sense to have students start by studying very powervul and broadly applicable laws that they can also understand: this builds their confidence while developing thinking skills needed for understanding newtonian mechanics. This also delays the need for calculus.
    
2. Special relativity, which fits naturally into the first semester's focus on mechanics and conservation laws, also ends that semester with something both contemporary and compelling (student evaluations consistently rate this section very highly).
    
3. We found in previous trials that ending the second semester with the intellectually demanding material in unit Q was not wise: ending the course with Unit T (which is less demanding) and thus more practical during the end-of-year rush.

The suggested order also offers a variety of options for adapting the course to other calendars. For example, one can teach these units in three 10-week quarters of two units each as follows:

Table 2: The Three-Quarter Plan:

Note that the shortest units (R and T) are naturally paired with longest units (E and Q respectively) when the units are divided this way.

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4. MANAGING THE PACE

Superficially, the course might seem to involve quite a bit more material than a standard introductory physics course, since substantial amounts of time are devoted to relativity and quantum physics. However, I have made substantial cuts in the material presented in the all sections of the course compared to a typical textbook. I made these cuts in two different ways.

First, I have omitted entire topics, such as fluid mechanics, most of rotational mechanics, almost everything about sound, many electrical engineering topics, geometric optics, polarization, and so on. These cuts will no doubt be intolerable to some, but something has to go, and these particular topics did not fit as well as others into this particular course framework.

My second approach was to simplify and streamline the presentation of topics we do discuss. A typical chapter in a standard textbook is crammed with a variety of interesting but tangential issues, applications, and other miscellaneous "factons." The core idea of each Six Ideas unit provides an excellent filter for reducing the facton number density: virtually everything that is not essential for developing that core idea has been eliminated. This greatly reduces the "conceptual noise" that students encounter, which helps them focus on learning the really important ideas.

Because of the conversational writing style and open page layout adopted for the text, the total page count of the Six Ideas texts is actually pretty similar to a standard text (about 1400 total pages), but if you compare typical chapters discussing the same general material, you will find that the density of concepts in the Six Ideas text is much lower, leading to what I hope will be a more gentle perceived pace.

Even so, this text is not a "dumbed-down" version of a standard text. Instead of making the text dumber, I have tried to challenge (and hopefully enable) students to become smarter. The pace described in tables 1 and 2 (one text chapter per 50-minute class session) really represents a maximum possible pace: in my opinion, one should never plan to go any faster than this. Indeed, this pace is pretty grueling even for well-prepared students, and you may well find that a lower pace is more appropriate for your particular institution. If so, there are several possible options.

One would be to go through all the units, but in three semesters. The calendar would look pretty much as in table 2, but with semesters in place of quarters. This would free up about one class session in three for further review and discussion of the material.

The alternative is to cut material. While the first four units essentially provide a core curriculum that is difficult to change substantially, omitting either Unit Q or Unit T (or both) can create a gentler pace without loss of continuity (since Unit C includes some basic thermal physics, a version of the course omitting unit T still spans much of what is in a standard introductory course). I have also designed unit Q so that several of its major sections can be omitted if necessary. In a pinch, unit R might also be omitted, but a previous discussion of relativity is useful for both units E and some sections of unit Q.

Many of these volumes can also stand alone in an appropriate context. Units C and N are tightly interwoven, but with some care and in the appropriate context, these could be used separately from the others unit. Unit R only requires a basic knowledge of mechanics. In addition to a typical background in mechanics, units E and Q require only a few very basic results from relativity, and Unit T requires only a very basic understanding of energy quantization. Other orders are also possible: while the first four units form a core curriculum that works best in the designed order, units Q and T might be exchanged, placed between volumes of the core sequence, or one or the other can be omitted. See the instructor's manual and the individual prefaces in the printed volumes for more suggestions about possible cuts.

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5. FEATURES OF THE TEXT

Many studies have suggested that lectures are neither the most efficient nor most effective way to present expository material. One of my most important goals was to develop a text that could essentially replace the lecture as the primary source of information, freeing up class time for activities that help students practice using those ideas. I also wanted to create a text that not only presents the topics but goads students to develop model-building and problem-solving skills, helps them organize ideas hierarchically, encourages them to think qualitatively as well as quantitatively, and supports active learning both inside and outside of class.

A number of features of the text are specifically aimed at making it easier for students to use as their primary source of information:

• An expansive and conversational writing style make the text engaging and easy to understand.
• One chapter corresponds to one class session. This breaks up the material into more bite-sized chunks and also helps instructors appropriately pace the course.
• A map and overview at the beginning of the chapter helps students see how the chapter fits into the general flow of the unit, helps them anticipate the line of argument within a chapter, and helps them review the chapter's material later.
• Boldface terms coupled with a glossary at the end of each unit help students recognize and review technical terms.
• "User-friendly" notation and terminology help students avoid misunderstanding due to misleading or careless use of symbols or technical terms.
• Sidebar comments help readers find information in the text quickly.

If the text is to serve as the primary source of information, students need to read the text with their minds fully engaged. Several features of the text are designed to support students in becoming "active readers," a habit that is valuable not only for this course but for learning effectively from written material in general.

• Wide outside margins provide space for writing questions, notes, missing steps, and so on.
• Exercises embedded in the text prompt students to reflect on what they have read, fill in missing algebra, and so on. Answers to these exercises appear at the end of each chapter. Many of these exercises also serve essentially as "active-learning examples," so that instead of simply reading an example with glazed eyes, a student can practice working the problem first, and then get immediate feedback by comparing their work with the provided answers.

One of the things we discovered early in the IUPP evaluation process is that homework problems and exams must support the goals of the course (for a fuller discussion of this issue, see Homework below). The text therefore has a number of features that support students in developing useful problem-solving skills and rewards them for thinking conceptually about physical situations.

• Physics Skills sections in certain chapters provide explicit instruction in techniques and thinking styles that help students more effectively approach the material.
• Problem-solving frameworks (particularly in the first two units) are used to guide students in learning expert-like approaches to solving problems.
• Specially-designed homework problems push students to think more conceptually and less mechanically about solving problems and helps them practice applying concepts to realistic situations.

Finally, the text provides the following features that support active learning inside and outside the classroom:

• Two-minute problems provide a straightforward and tested way to actively involve students during class and get feedback on how they are doing.
• "Rich Context" homework problems provide an opportunity for group problem solving inside and outside of class.

These features are discussed more fully in the Support for Active Learning section below.

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6. HOMEWORK

As mentioned earlier, early IUPP tests made it clear that if a course is to be successful in teaching students to think conceptually about physical situations, the work on which they are evaluated must require and reward this behavior. Since students are pretty clever about finding shortcuts to avoid the hard work of conceptual reasoning, homework problems must be carefully designed to make such shortcuts unproductive.

With this in mind, the homework problems at the end of each chapter are organized into four types. Basic problems are closest to the type of problems usually found in physics texts. These problems are primarily for practicing the application of a single formula or concept in a straightforward manner and/or are closely analogous to examples in the text. While it is sometimes important to practice these basic skills, these problems generally do not require deep thinking, and therefore should be assigned only sparingly. Synthetic problems generally involve more realistic situations, require students to apply several concepts and/or formulas at once, involve creating or applying models, and/ or require more sophisticated reasoning. Since these are precisely the kinds of problems that challenge students to think conceptually and flexibly about what they have learned, most of the problems assigned for homework should be from this category. Rich Context problems are synthetic problems generally cast in a narrative framework where either too much or too little information is given and/or a non-numerical question is posed (that nonetheless requires numerical work to answer). These problems are generally more difficult than synthetic problems; they are meant primarily for group problem-solving sessions (see Active Learning below). Such problems should be assigned deliberately, but sparingly (I usually assign one such problem a week). Advanced problems usually explore subtle theoretical issues or mathematical derivations beyond the nominal level of the class: they are designed to challenge the very best students and/or remind instructors about how to handle subtle issues.

Precisely because they require conceptual thinking (which is necessary if the course is to achieve its goals), synthetic and rich context problems are often more difficult than the average homework problem in a typical physics textbook. Because of this, we found in early trials that grading such problems in the same way that one would grade simpler problems can make students very uncomfortable. These problems are more successful in achieving their goals if they are evaluated mostly on the basis of effort. This rewards students for making a reasonable attempt, but does not punish them unduly if they do not completely succeed. Students must feel free to take risks if they are to develop the desired kinds of difficult thinking skills. This issue is discussed in much more depth in the "Evaluation" chapter of the instructor's manual.

Students expecting a more traditional approach may also feel that there are too few examples in the text. In fact, there are many examples in the text (particularly if one includes the in-text exercises). The problem is not lack of examples, it is that the synthetic and rich context problems are deliberately designed so that one cannot solve them simply by tweaking an example in the text. Real life rarely serves up problems that map easily to textbook examples, so it is important to help students learn how to face such problems. If students complain about a lack of examples, the problem may be that they do not understand this issue (or that the homework evaluation system does not help them feel free to take risks).

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7. SUPPORT FOR ACTIVE LEARNING

One of my important goals in writing the Six Ideas text was to make it as easy as possible for instructors to make active learning an integral part of the course structure. Two textbook features help support this goal.

The two-minute exercises at the end of each chapter (which are similar in many ways to what Eric Mazur calls ConcepTests) make it straightforward to devote at least part of each class session to active learning. These mostly conceptual questions do not generally require much (if any) calculation, but locating the correct answer does require careful thinking, a solid understanding of the material, and (often) an ability to apply concepts to realistic situations. Many explicitly test for typical student misconceptions, providing an opportunity to expose and correct these well-known stumbling blocks.

I often begin a class session by asking students to work in groups of two or three to find answers for a list of roughly three two-minute problems from the chapter that was assigned reading for that class session. After students have worked on these problems for some time, I ask them to show me their answers for each question in turn. The students hold up the back of the book facing me and point to the letter that they think is the correct answer. This gives me instant feedback on how well the students are doing, and provides me with both grist for further discussion and a sense where the students need the most help. On the other hand, students cannot see each others' answers easily, making them less likely to fear embarrassment (and I work very hard to be supportive).

It might seem that the letters are too small to use in a large classroom, but I did test a draft of the back cover in a classroom that seats several hundred students and found that I could pretty easily see the letters. The current design also avoids some problems with previous designs that made it difficult for students to actually hold the book without seeming to register multiple answers.

Once everyone gets the hang of the process, it is easy to adapt other activities to this format. When I do a demonstration, I often make it more active by posing questions about what will happen, and asking students to respond using the letters. This helps everyone think more deeply about what the demonstration really shows and gets students more invested in the outcome (and more impressed when the demonstration shows something unexpected).

The rich context homework problems are especially designed for collaborative active-learning experiences outside of class. Work by Heller and Hollenbaugh [Am. J. Phys. 60(7), 1992] has shown that students solving standard problems rarely collaborate even when "working together", but that a well-written rich-context problem by its very open-ended nature calls forth a discussion of physical concepts, requiring students to work together to create useful models. I typically assign one such problem per week, which students can work in groups during a modified "recitation" section. At Pomona, these "collaborative learning sessions" are monitored by an undergraduate physics major who knows the problem's solution but whose instructions are to help people only when they are stuck, and then only by asking questions.

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8. COMPUTER PROGRAMS

Computer programs are deployed in a few crucial places in the Six Ideas course to support a particular line of argument in the text and to allow students to explore more realistic applications than would otherwise be possible. For example, unit N uses the program Newton to illustrate the process of predicting trajectories and make it possible for students to apply Newton's second law to realistic situations (including projectile motion with drag and planetary motion). Unit Q refers to the program Interference, which simulates two-slit interference and single-slit diffraction experiements involving countable particles. This program helps students visualize the statistical nature of quantum mechanics and the collapse of the wavefunction. This unit also uses SchroSolver to solve the one-dimensional Schrodinger equation for a variety of potential energy functions and illustrate the basic logic of energy quantization. Unit T uses the programs StatMech and Equilib to illustrate important issues in statistical mechanics, and the program MBoltz and EBoltz to make tractable some otherwise nasty calculations.

All of these programs (as well as some other supporting programs not mentioned in the text) are available for download from this web site. These programs may be freely copied and distributed without cost. Most are available in Macintosh, Windows, and Linux versions.

Experience has shown that such programs are most successful as teaching tools if:

1. The program is extremely easy to use.
2. The program clearly automates a process that a student could (in principle) perform himself or herself.
3. Students (at some time) are required to operate the program themselves (rather than only having it demonstrated).

The first reason is why I have elected to write a handful simple, bite-sized programs instead of using broadly-aimed commercial programs like Excel or Interactive Physics. A simple program whose operation is completely transparent helps students focus on the physics involved, rather than getting sidetracked by figuring out the program.

The programs Newton and StatMech most clearly illustrate the second principle. In both of these cases, students learn to do exactly what the program does before ever seeing the program. This makes it obvious that the program is simply a transparent calculational tool, not a black box. An instructor can help make the second principle work in the other cases by helping students understand exactly what the computer is doing, working some examples by hand whenever possible.

At Pomona, we often deal with the third issue by having the students do active-learning exercises involving the programs during class. While the department happens to have a laptop for every group of three students in the class, one could accomplish the same goal by meeting in a computer classroom on certain class days. If this is completely impossible (as in a very large class), one can still assign homework problems that require students to use the programs. The text provides a number of such problems in crucial places.

Experience has also shown that unit T in particular makes much more sense to students who have had some exposure to StatMech, and the same thing will be true of the second edition of unit N and Newton, in my opinion. I strongly recommend that instructors build these programs (at least) into the syllabus, and that students make an effort to use and learn from these programs.

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9. THE INSTRUCTOR'S MANUAL

Early trials of Six Ideas showed that whether a course succeeds or fails depends very much on the details of how the course is structured. This text is designed to more easily support a productive course structure, but careful work on the course design is still essential. For example, as discussed above, a "traditional" approach to assigning and grading homework can lead students to be frustrated (rather than challenged) by the richer-than-average homework problems in this text. Course structures can also either encourage or discourage students from getting the most out of class by preparing ahead of time. Exams can support or undermine the goals of the course. The instructor's manual explores these issues in much more depth and offers detailed guidance (based on our experience) about how to design a course that gets the most out of what these books have to offer. In specific, the instructor's manual provides

• Specific advice about using the active-learning features of the text.
• General advice about alternatives to lectures (even for large classes).
• Ideas about how to get students to read the material before coming to class.
• Ideas about how to design homework assignments. As previously discussed, Six Ideas courses have been most effective when homework assignments are evaluated in such a way as to most strongly reward students' effort. This enables them to tackle difficult, mind-stretching problems without becoming discouraged or angry about their grades. The instructor's manual explores the issues involved and describes several approaches to assigning and grading homework that rewards student effort strongly while also rewarding quality of work, trains them in good problem-solving style, and helps teach them to be self-critical about their work.
• A discussion of the importance of good course design. A course's structure can make the course or break it (particularly in terms of its effectiveness for teaching physics) quite independent of the text or the instructor. The instructor's manual raises twenty questions that every instructor should ask him or herself about how a course is designed.
• A complete and detailed description of one possible course design (based on the course offered at Pomona College) and an analysis of that design based on the twenty questions previously mentioned.
• A discussion of possibilities for an accompanying lab program.

The instructor's manual is available online in PDF format. I strongly urge all instructors to read this manual carefully before offering a course based on Six Ideas,

Certified instructors can also receive passwords needed to gain online access to

• Short answers to all problems in a form that instructors may choose to make available to students. Making homework problem answers available ahead of time helps students solve difficult problems correctly and provides opportunities for further study that they greatly appreciate. Doing this also emphasizes that a satisfactory solution to the problem is not the same as simply providing the answer: students must do more.
• Complete solutions to all problems. These carefully-typeset solutions are more completely worked-out than solutions in a typical instructor's manual, and can be used as examples of excellent problem-solving style.
• Example tests and quizzes.

Such instructors can also define a list of problem solutions that their students can view (with a start and stop date for each solution). For more details, see the instructor's page.

If you are an instructor using the text, you can alternatively request a hard copy of the Instructor's Manual (including answers and solutions) using this McGraw-Hill site or by contacting your local sales representative. However, the online materials will be more up-to-date and are available immediately.

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10. DOES THE COURSE WORK?

While it is difficult to evaluate exactly how well a course succeeds, by one measure at least, properly-designed Six Ideas courses seem to be very effective in teaching newtonian mechanics. The Evidence of Success page describes the most up-to-date data on how Six Ideas students score on the Force Concept Inventory test compared to other institutions. It also discusses Pomona students' performance on the Brief Electricity and Magnetism Assessment test. The bottom line is that students in Six Ideas courses at Pomona College, Ohio State University, and DePauw University display gains on the FCI that are comparable to the best gains reported to date on this test, and that students at Pomona do significantly better on the BEMA than those taking traditional courses, even though students taking a Six Ideas course spend less time on mechanics and E&M than do traditional students.

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