A REVIEW OF THE GOALS

As stated in the overview, the core goal of the Six Ideas project is to empower students to:

• Apply basic physical principles to realistic situations and solve realistic problems,
• Understand the nature of physical models and the art of model-building,
• Grasp the hierarchical nature of physics concepts,
• Perceive and resolve contradictions involving their preconceptions, and
• Appreciate the full scope of physics applications in the 21st century.

These goals are meant to address specific and well-documented problems with traditional introductory physics courses, which are discussed in detail at the bottom of this page. But for the moment, let's accept these goals. The question then becomes, how does one realistically achieve these goals given where students are and how much time is available? This project seeks to meet this challenge by applying three basic techniques:

• Supporting and encouraging active learning in all aspects of the course,
• Explicitly discussing the model-building process,
• Rethinking and reworking the presentation to make learning more efficient, and
• Taking advantage of computer technology to broaden students' experiences.

This section discusses each of these techniques in more detail. Why these techniques? What does each provide, and why is that important?

Active Learning

The robust and nearly unanimous conclusion of physics education research is that students simply do not effectively learn to think like physicists (successfully applying physics principles in realistic situations) by attending traditional lectures. They can only learn by practicing for themselves that kind of thinking in a context where they can get expert feedback on their thinking.

For example, Richard Hake (Am. J. Phys, 66, pp 64-74, 1998) showed that students' post-course gains on a test evaluating their abilities to apply very basic Newtonian principles to everyday situations was significantly better in courses involving what he called "interactive engagement," independent of the quality of the instructor, institution, or the students' background (for more details, see the Evidence of Success page). This is just one of many studies that have shown (over and over) how important student engagement is for effective learning.

In the face of this kind of evidence, why doesn't every introductory physics course involve active learning? Multiple issues impede such a change (see the discussion of the traditional course below), but two of the most obvious reasons are that many textbooks do not really support active learning, and many professors have little experience with it, and so need such support. These are issues that the Six Ideas project seeks to remedy.

But part of the problem is also how our Enlightenment-rooted culture models the learning process. Many in our culture think of physics as simply being a body of information, a set of propositional facts, that can be downloaded from the professor's mind and uploaded into students' minds. Since the human mind is intrinsically reasonable (in this picture), providing that mind with the appropriate information is all that is required to make one a physicist.

But this picture is incomplete at best. Physics is more realistically a practice, a way of knowing, an (actually unnatural) approach to viewing the world. Physics knowledge doesn't merely provide grist for the reasoning process; thinking like a physicist transforms the way that one reasons about the world. New ways of thinking require personal struggle and practice to master.

The metaphor that the author uses with his students (who almost universally enter sharing that cultural mindset) is the following: If you want to learn to play the piano, you know that you must practice, practice, practice. A piano teacher who claimed to teach simply by playing beautiful music him or herself and then saying to the student, "Now, you do that" would be rightfully scorned. A wise teacher gives his or her students thoughtfully chosen exercises, illustrates how to do them, has them practice the exercises, and then gives them expert and timely feedback on their performance. We know that this is what works with learning to play musical instruments or learning a sport. The point of this course is to provide the same kind of learning experience for students of physics. Just as you learn to play the piano by practicing playing, you learn to be a physicist by practicing doing physics.

Therefore, this project seeks to provide professors with the tools to make creating an active, student-centered course as easy as possible. Two-minute problems (and some carefully crafted Basic problems) provide the basis for many natural in-class activities. We have carefully designed the textbook so that it can provide the exposition that students need, so that lecturing is no longer necessary. The instructor's manual and the sample course materials posted on the instructor's site illustrate how one can construct an active classroom and provide ideas. The homework system described in the instructor's manual (and on the Homework page) involves students actively not only in doing the homework in the first place but also in assessing and polishing their work. Finally, the text itself has features that encourage students to read actively.

MODEL-BUILDING

The need for an emphasis on model-building emerged organically as we developed this course (indeed, it was entirely unexpected and took the author more than a decade to appreciate its importance). The construction of simplified tractable models is core to the process of doing physics (and indeed any kind of science). We use such models all the time in introductory physics: frictionless inclined planes, free-fall without drag, constant acceleration, ideal strings, uniform circular motion (and the list goes on and on). Yet physics courses rarely talk about the process of choosing and deploying these models (or even that they are models at all), even though this is the core problem that students have with learning physics.

Model-building is hard precisely because it is an art, not an algorithm. What simplifications are reasonable? Which are not? How can one approach a complicated realistic situation and analyze it using models at hand? The main reason students need to learn physics actively is that one can only learn the art of answering such questions through practice and feedback.

Again, our culture's Enlightenment picture of physics as a collection of facts stands in the way. This vision prompts students to think of physics as being a rock-solid presentation of physical Truth. Many imagine that there is only one right and true answer in any given situation, and that the trick to seeing that answer is simply knowing a sufficient number of facts.

This pre-20th-century vision therefore actively blocks students' understanding of the true nature of physics (and indeed science in general) as a collection of larger and smaller models that only imperfectly and incompletely represent the physical world. It also impedes their appreciation of the learning task that faces them, which is to understand the models (including their limitations) and deploy them artfully, rather than simply to learn a set of concepts and formulas.

The Six Ideas project therefore assumes that an introductory physics course needs to teach the art of model building explicitly and continually. This starts in chapter C1 (the first chapter of the first volume), which discusses nature of science and provides both the big picture of the models that define physics as well as a thoroughly analyzed example of the model-building process. Units C and N also provide a metacognitive analysis of examples of expert problem-solving presented in the book, so that students can better understand the thinking process lying behind the example. Examples and problem solutions also consistently discuss issues of simplification and approximation and illustrate habits of self-criticism that students can emulate. All this helps students fruitfully focus their attention on the skills that will help them be more effective.

PRESENTATION

While many educational-research studies underline the importance of active learning, very few have investigated whether the order and/or manner in which the ideas are presented can make a substantial difference. A core assumption of this project is that a thoughtful reworking of how core ideas are presented can also make an important difference in students' learning.

The author first learned this principle in the context of teaching special relativity. Many classical treatments of special relativity provide an overly mathematical (and abstract) development of the Lorentz transformation equations from poorly defined ideas like "moving clocks run slow" and "moving objects are contracted," ideas that also lead students straight into misconceptions and paradoxes. In relativistic dynamics, the concept of a speed-dependent mass also leads to profound misconceptions and impedes students continuing with relativity.

In the early 1960s, John Archibald Wheeler and Edwin Taylor (in their textbook Spacetime Physics, Freeman, 1963) developed an entirely different approach to the subject based on the logically precise concepts of events, spacetime coordinates, proper time, and spacetime interval and which took advantage of spacetime diagrams (which provide a wonderful tool for visualization). The author found (by experience both as a student and a teacher) that this approach was far more effective than the classical approach in helping students reason about relativity clearly and correctly, avoiding paradoxes and misconceptions. Unit R owes a huge debt to Wheeler and Taylor.

If a new approach is so effective for relativity, might it be for other topics as well? One of the most enjoyable parts of the Six Ideas development process was to imagine, craft, and test significantly different approaches to core topics, approaches that do end runs around (or entirely sidestep) well-documented misconceptions and stumbling blocks. Every aspect of the presentation has been carefully considered, and nothing has been done because "that is the way it is always done." You will find the textbook full of innovations targeted at making it easier for students to think about the topics, avoid misconceptions, and/or develop a more sophisticated understanding of a topic than is typically possible in an introductory course.

SOFTWARE

Advances in computer software make certain things accessible to introductory students that have been inaccessible in the past. The Six Ideas project includes a variety of supporting web-based apps that enable new kinds of instruction. Broadly, the provided apps fall into three categories:

• Apps that simulate a physical situation or illustrate a physical model (e.g. Drude)
• Apps that provide quick access to data (e.g. NucInfo)
• Apps that automate certain kinds of calculations (e.g. Newton, StatMech, SchroSolver)

Some of these apps (particularly those in the last category) have been integrated into the text presentation because they augment students' abilities in such important ways. Others are optional and can be used or not as the instructor sees fit.

The Six Ideas project, however, does not require students to learn computer programming in any language. Requiring students to write software can provide huge benefits in principle, but also huge costs. We considered this early on but eventually rejected it, because it requires too much overhead and because even simple computer languages are not friendly enough for students to focus on the physics instead of the computer language.

Instead, our guiding principles, particularly with apps in the final category, have been

• Keep the app's task as focused and simple as possible.
• Design user interfaces that as obvious and foolproof as possible.
• Ensure that what the app is doing is as transparent as possible.

In particular, for apps that automate certain kinds of calculations, we require (when possible at all) that each student practices the algorithm by hand before seeing the app, and then verifies that the app simply automates what he or she could do by hand given sufficient time. We consider this an extremely important principle that ensures that the student does not see the app as a black box, but rather as an extension of his or her abilities.

Applications such as WolframAlpha also make certain kinds of symbolic calculations accessible that were not before. The 4th edition of unit T takes advantage of this capability to explore certain ideas that require evaluating some fairly nasty integrals.

LEVEL

The Six Ideas course is targeted at good students who are at least concurrently taking calculus. While the course does many things to make ideas easier and more accessible, the goal is not to "dumb down" the presentation but rather to lift students up to new levels of, understanding, sophistication and achievement.

The level of mathematics required is roughly similar to that required by standard calculus-based courses. Indeed, calculus is deliberately avoided in unit C and developed slowly in unit N precisely so that students taking a first calculus course have a chance to develop those math skills in their math class before needing them in their physics class. While units N, Q, and T use differential calculus and some basic integral calculus, students are never asked to calculate integrals by hand that involve more than simple powers or basic trig functions and are only rarely asked (mostly in units E and T) to look up more complicated integrals. Unit Q also asks students to multiply row and column vectors, but does not require any linear algebra. Unit E is the most mathematically intensive unit by far, and involves calculating some partial derivatives, line integrals, and flux integrals (concepts all taught from scratch), looking up a few integrals, and facing some scary-looking notation, but the main problem is simply the unavoidable level of abstraction.

However, the sophistication of thinking that this course expects is fairly high, and we do not apologize for that. The entire point of this course is to make sophisticated thinking about physics as widely accessible as possible.

One feature of the 4th edition is that adjustments to the level are now easier than ever. The chapters that involve the most difficult ideas in a given unit are typically now optional. The use of complex numbers in unit Q is now optional. Exploration of distributions in Unit T is now optional. By carefully choosing the chapters and problems to assign and the chapters and problems to omit, professors have more ability than ever before to choose the course level.

Even with the relatively more rigid 2nd edition, professors from a huge range of institutions (from elite private colleges to public universities to community colleges and even to a few high schools) have adopted Six Ideas and made it work successfully at their institutions. This will only be easier with the 4th edition.

WHY THESE GOALS?

We mentioned above that the "standard" introductory university physics course has well-known problems. Identifying and addressing these problems were precisely the focus of the 1987-1996 Introductory University Physics Project (IUPP) that provided the impetus and initial support for Six Ideas That Shaped Physics.

What do we mean here by the "standard" introductory course? This is the kind of calculus-based introductory physics course that is still taught in the majority of institutions nationwide. It is a lecture-based course usually taught in large sections (60 or more students). The seminal textbook by Halliday and Resnick (Physics, Wiley, 1960) provided the template for the course sequence and choice of topics, but many other introductory texts (including texts by Serway, Tipler, Young and Freedman, and Knight) now follow a virtually identical outline. This course design effectively ends with late 19th-century physics (though some current texts now have grafted on a smattering of early 20th-century physics).

This course arose in the context of the Sputnik era and the Cold War. Earlier engineering-focused physics textbooks were rapidly displaced in favor of a new curriculum that designers hoped would raise the kind of brilliant physicists needed to keep America's edge in the Cold War. This new physics course was more sophisticated, theoretical, mathematical, encyclopedic, and challenging than what had offered before. It was also offered in a cultural context where relatively few students went to college at all (much less took college physics), and because interest in physics (as a prestigious profession) was very high, physics departments were content to fail many students, because ensuring quality was of foremost concern, and only a few of the best and brightest were needed to be the era's rocket scientists. This is partly the origin of the cultural meme that physics is the most difficult of the sciences: it became difficult partly because it could afford to!

In the 1980s, the newly developed field of physics education research began to document that students in standard courses often struggled to apply even simple physics concepts in realistic situations, partly because instruction failed to address or dislodge misconceptions that students had developed over years of living in a physical world. The Force Concept Inventory (FCI) text was developed in 1983 partly to explore this issue. This short multiple-choice test asked students to apply basic Newtonian principles to everyday situations. The ideas and applications were so simple that professors looking at the test would generally confidently predict that students taking their classes would ace the test. But few students showed significant improvement on this test or many others. Indeed, in some cases, researchers documented that instruction actually decreased student performance by introducing new misconceptions.

Researchers also documented that students failed to see many of the connections between ideas in physics and understand the logical and hierarchical organization of physic concepts. Though an improvement on the earlier generation of textbooks, the encyclopedic nature of textbooks gave most students the impression that physics was "just one darned thing after another" with the same organization as beads on a string. Even more disturbing was the evidence that those students who tried seriously to understand the concepts and their relationships were typically eventually reduced by the course structure and pace to settling for mindlessly copying examples and plugging numbers into formulas, because their efforts to understand took too much time and were not at all rewarded (in discouraged) by the grading systems.

These discoveries coincided with a significant shift in the clientele and purpose of such courses. The Cold War ended. Many more students were going to college, and (partly because of the successes of Cold War science) more and more jobs (including engineering, technology, and medical jobs) involved increasing levels of physics (specifically 20th-century physics). This meant that the goals for the introductory physics course shifted from selecting the best and the brightest for further training to providing an increasingly broad range of students with a solid and up-to-date understanding of physics that was crucial for their success. The course design from the 1960s was therefore becoming increasingly mismatched with the students attempting to learn from it. Of course, the most gifted students would get what they needed from almost any course design, but most other students are not being served well by the course.

These documented problems were the impetus for the IUPP project, and a number of other efforts to change the course arose at about this time (Workshop Physics is one of the best examples). However, though Knight's Physics (Pearson, 4/e 2016) grew up in this environment and sought to make some reforms to the traditional plan, of currently available textbooks, only Six Ideas That Shaped Physics and Matter and Interactions (Sherwood and Chabay, Wiley, 4/e, 2015) substantially deviate from the Halliday-and-Resnick template. Why do people in the second decade of the 21st century still stick with a demonstrably ineffective course design created for an entirely different cultural context more than 50 years ago, particularly when it seemed so easy for radical change to occur in the early 1960s? (In this century, the problem is even worse than it was in the 1980s, as the clientele also increasingly involves women and students of color, who have a hard time connecting this old course design to their current lives.)

Participants in the IUPP project (including this author) were initially astonished by how much any kind of change was resisted, in spite of strong evidence that change was required and beneficial. But this conservatism is not as irrational as it might seem. Public universities in particular grew enormously between 1960 and the 1980s. Classrooms and laboratories built during this era of expansion were designed (quite reasonably) around the then-prevalent model. The introductory physics course is increasingly interconnected to a wide variety of course offerings in other departments. Teaching introductory physics to thousands of students also requires a complex social organization of professors, TAs, graders, and support staff. As public tax support for higher education wanes, these people are under considerable pressure to do more and more with less and less. All of these things make significant change extremely difficult, because it requires time, commitment from (and cooperation with) a large number of people, and resources. The situation was significantly different in the 1960s, where the structures involved were much simpler and smaller, where support for higher education was very high, and there was a significant perceived national interest associated with making the change. (One might quite reasonably argue that the national interest associated with changing the course is just as urgent now as then, if not more so, but it is certainly not perceived as being urgent.)

Therefore, the Six Ideas project, particularly with this 3rd edition, strives not only to address the demonstrated problems with the traditional course design, but also seeks to make change as easy as possible. The 3rd edition textbook provides more flexibility to adopters to adjust the course sequence and level to fit their needs. The move to web-based software decreases complexities associated with using the software in class and requiring it for homework. Lesson plans and activity worksheets on the instructor's website make it easier than ever to create a student-centered classroom. The web-based system for displaying homework solutions makes the recommended student-corrected homework system more practical than ever, and a team is also currently working very hard to provide a computer-graded system for those who need it. Real reform always takes time and effort, but is now easier and more practical than ever!