For more publications by NC State authors, visit the .

For more publications by NC State authors, visit the .

For more publications by NC State authors, visit the .

Most of our students, however, will not have the opportunity to study physics beyond a single course. More than 95% of students in introductory physics will never take another physics class. Even engineers, many of whom will study the behavior of physical systems in their engineering classes, often use a distinctly different approach, and one which does not necessarily bridge the gaps that remain after introductory physics. The adage that "they need to see the material several times and then they will understand it when they teach it" is just not relevant to most of our students. Fortunately, evidence suggests that with the right kind of learning environment, a single pass through physics can be a valuable learning experience for the majority of students.

For more publications by NC State authors, visit the .

For more publications by NC State authors, visit the .

In response to the elucidation of specific student difficulties learning introductory physics, a number of physicists have produced curricula that specifically focus on teaching more effectively. In building these research-based curricula, developers combine two elements. They use their understanding, learned from PER, as to what difficulties students really face. These are combined with educational structures and environments influenced by scholars of education and cognitive psychology who find that most students learn more effectively in active-engagement environments in which social interaction takes place. Finally these are refined through successive delivery, research, and redesign.

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McDermott and other physics education researchers have documented that even after studying physics, student understanding of fundamental concepts is often weak. For example, the study detailed in Sidebar 1 shows some of the difficulties students have in making sense of the concept of a photon. (See references and for further details.) Note that the interviewed students might well be able to answer standard problems on the photoelectric or the Compton effect. However, the way they think about the photon inhibits the way they make sense of the nature of light.

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The studies of expert problem solvers indicate that there is much more to being a good problem solver than agility with mathematical manipulations and a good knowledge of concepts. For many students in introductory physics, the idea that concepts are relevant to problems or that physics is more than a set of facts and equations to be memorized is missing. These difficulties do not necessarily go away, even given our "ideal" situation physics majors trained for graduate school. We have heard numerous (but anecdotal) complaints from advisors of physics Ph.D. students who approach their research by "turning the crank" without thinking about the physics.

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In our study of student expectations, we find that after three semesters of traditional instruction in calculus-based physics, half of our engineering physics students agree with the following statement from the MPEX survey:

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Our instructors carefully present critical derivations in lecture. They use them to show the applicability of the resulting formula and its relation with fundamental principles. Nonetheless, many of our students choose to ignore the teacher's explicit emphasis. Their view of what they expect to get out of the class is the use of formulas, not an understanding of the limitations of those formulas or the relation of the formula to fundamental principles and concepts.

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It is important to note that the student difficulties that we observe are not limited to their performance on multiple choice items. In fact, looking merely at student performance on multiple-choice diagnostics can be very misleading. However, results comparable to those described in the previous paragraph have been observed using other tools, including open-ended questions, problems, and interviews.