An Overview of Six Ideas



Six Ideas That Shaped Physics is a comprehensive plan expressing an innovative and student-centered approach to introductory college-level calculus-based physics. Its goals are to develop students' abilities to apply physical models to realistic situations through guided practice. Its six-unit structure makes it easy to adapt to two-semester, three-quarter, or three-semester courses. The textbook has many features deliberately designed to support student-centered active-learning experiences, and the online instructor's manual (under construction) distills the authors' decades of experience to guide professors in creating course structures that take full advantage of these features. (Much of the information in the instructor's manual also appears on this website, though it is organized differently.) In crucial places, web-based computer applications enable students to explore the implications of physical models in ways that would be otherwise impossible. Innovative homework grading structures described on this site and in the instructor's manual allow students to safely practice challenging new thinking skills in an effective way. We have tested and verified that the Six Ideas course structures and materials enable students to perform better on a number of measures of achievement and engagement than students in many comparable courses.



Six Ideas That Shaped Physics is designed 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 address specific well-documented problems with traditional introductory physics courses. The last goal is important because only about 1 out of 20 students in the U. S.  who take introductory calculus-based physics ever takes another physics course. The Six Ideas plan specifically addresses these goals through a variety of innovative design features, which are outlined in the sections below.




One way that Six Ideas course helps teach students about the hierarchical nature of physics is through the basic structure of the course. The Six Ideas textbook is organized into six units, each in a separate volume and each focused on a single physical concept at the top of the hierarchy. Each volume by its very nature, therefore, shows students how ideas lower in the hierarchy fit into the great idea that drives each unit. The six units (in their default order) are

  • Unit C: Conservation Laws Constrain Interactions (14 chapters)
  • Unit N: The Laws of Physics are Universal (12 chapters)
  • Unit R: The Laws of Physics are Frame-Independent (9 chapters)
  • Unit E:  Electric and Magnetic Fields are Unified (20 chapters)
  • Unit Q:  Particles Behave Like Waves (15 chapters)
  • Unit T:   Some Processes are Irreversible (11 chapters)

To make it easier to control the course's pace, the author has designed each chapter (by long experience) to correspond to one (perhaps ambitious but credible) 50-minute class session. One can therefore divide the entire course (in this default order) into two semesters that are 35 and 46 class sessions long, respectively, or three quarters that are 26, 29, and 26 class sessions long, respectively (though one can omit chapters to reduce the number of class sessions required). A three-semester course of more generous 70-minute class-sessions (or two 50-minute sessions and one review session per week) is also possible.

The default sequence was chosen partly so that each semester in a two-semester would end with topics that are engaging but not too challenging, so that Unit E could run with some ideas from unit R and Unit T with some ideas from unit Q. But many other organizations are possible, because the units are fairly independent (except C must be first): this is the main reason that the units are lettered as opposed to numbered. For example, one can also follow a more traditional ordering by exploring units C, N, and T in the first semester and units E, R and Q (or better R, E, and Q) in the second. At Pomona, we currently cover selected chapters in unit C followed by units R, Q, and T in the first semester, the rest of unit C and unit N, and then unit E alone in two second-semester half courses (learn more…). The point is that many sequences are possible.

One of the core goals in the 3rd and 4th editions was to also provide more flexibility within each unit. A number of chapters (even in units C and N) are now optional. This gives professors even more flexibility in defining the duration, pace and level of the course.




One of the main goals of the Six Ideas plan is to support active learning in the classroom. But one can only afford to do this if students get the basic exposition of the material outside of class, so that the time spent lecturing in class is minimized. The Six Ideas textbook is designed with this role in mind. The book is deliberately more conversational and less encyclopedic than most traditional introductory texts. Having one chapter correspond to one class session also presents the core material in logically coherent and digestible chunks, making each chapter more like a lecture. Each chapter also has a two-page overview at the beginning that helps students see the big picture before they get into the details and also provides a useful summary when reviewing.

In addition, the Six Ideas That Shaped Physics text has a number of features designed to support active learning as the students read:

  • Sidebar comments help guide students through the chapter and emphasize important points.
  • Wide margins provide space for writing notes and questions.
  • Two to four embedded exercises (with answers) help students test themselves as they read.
  • Boldface highlights technical terms when they are first introduced.
  • Formula boxes highlight important formulas and provide information that helps students interpret the symbols and understand each formula's range of applicability.

The last item in particular helps students understand that a physics formula is really a connected package of ideas that makes a physical statement in a specific context and that has certain limitations on its applicability.




The Six Ideas textbook also provides and identifies a variety of kinds of homework problems, providing instructors with multiple options for in-class or out-of-class activities serving different pedagogical needs.

  • Derivation (D) Problems help students practice extracting consequences of basic ideas and develop ownership of certain crucial arguments.
  • Modeling (M) Problems help students practice model building. These problems require students to collect and connect multiple ideas together and make appropriate assumptions and approximations in order to solve reasonably realistic problems.
  • Rich-Context (R) Problems are modeling problems that involve especially challenging realistic contexts that may require ignoring given information, estimating missing information, handling tricky assumptions, and/or answering qualitative questions with quantitative calculations. Physics education research has shown that solving such problems provide the best experiences for students working in groups, because such problems provide plenty of grist for meaningful student discussion.
  • Advanced (A) problems address mostly theoretical issues beyond the level of the text. These problems provide challenges for certain students and/or extra information for the instructor.




We found early on in the Six Ideas development process that how one grades student work is crucial for motivating desired student behaviors and shaping students' attitudes. For example, if one wants students to take the conceptual questions in the text seriously, similar questions must appear on the course's exams.

For an activity-based Six Ideas course to work well, students must read the textbook before coming to class. We know from experience that students will not do this without strong motivation. The Instructor's Manual provides several proven methods for doing so, each of which provides a certain kind of grading reward for good behavior.

This issue is especially acute with regard to homework, and this is one area where a poor design can actually cause the course to fail. The modeling and rich-context problems in Six Ideas are deliberately designed to be intellectually challenging: one cannot generally solve them simply by hunting for a formula or by slavishly copying an example. This means that even good students may have trouble getting the right answers all the time. If such problems are graded in a traditional, answer-oriented manner, then many students will be frustrated and unhappy.

The emphasis should instead be on encouraging and motivating students to make a serious initial effort, and then give them an opportunity to evaluate their own work by comparing it to expert solutions, and learn from their mistakes, all while minimizing both the time and skill required for grading. Over the years (by trial and error), we have developed a unique but practical homework grading system that does this. This system involves students correcting their own work after comparing that work to expert solutions posted online. Graders evaluate students' final corrected work using a simple 10-point rubric that rewards both initial effort and correction effort, a process that takes literally seconds per problem (and that even undergraduate graders can do well).

You can learn more about this system by pressing the button below. But we hope it is clear from this brief description that this approach allows students to practice solving challenging problems without anxiety, exposes them to expert problem-solving styles, and helps build their skills in self-criticism. This system has proved practical even in very large classes (for example, at Washington University where nearly a thousand students in several sections take the course at a time).

Even so, teams are developing an online homework system keyed to the fourth edition of Six Ideas that offers a more automated approach to evaluation and feedback. We will provide more information about this effort as it becomes available.




The Six Ideas course uses computer applications in a number of crucial places to support a particular line of argument in the text and/or allow students to explore more realistic applications than would otherwise be possible. For example, in unit N, students first learn a graphical method of predicting a particle's future trajectory, and then, after seeing that the Newton app simply automates this process, use that app to predict trajectories even in situations (such as projectile motion with drag and non-circular orbits) where mathematical solutions are impractical. Other apps play analogous roles in other units. These apps are built-in to the text and homework, and so represent a core part of the Six Ideas infrastructure. They provide a crucial stepping-stone for students to go beyond the boundaries of traditional courses. But these apps are all designed to be simple, intuitive, and easy to use, requiring no computer-programming skills.

To learn more about the philosophy behind these apps and where to find them, press the "Learn More" button below. We are currently in the process of converting the old standalone desktop applications to updated and entirely web-based applications.




We have carefully evaluated the Six Ideas course over the years at Pomona and a number of other institutions using a variety of modern instruments, including the Force Concept Inventory (FCI), the Basic Electricity and Magnetism Assessment (BEMA), the Colorado Learning Attitudes about Science Survey (CLASS). Six Ideas courses at multiple institutions and in quite different contexts consistently earn better scores in these assessments than comparable traditional courses, even though a Six Ideas course typically spends significantly less time on the subjects being evaluated. Press the button below for the details.


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