About the Transformed Course

The text that follows explains much of the transformation process and rationale behind the transformations. The first part (2006) reports on the state of affairs following the first year of the process, after the course had been taught twice (in the FA05 and SP06 semesters). The second part (2011) details additional changes that were made to the materials as part of Charles Baily's dissertation project on quantum perspectives. Click on the links in the table of contents to go directly to that section in the text.

Contents

I. Transformations, Part 1 (2006)
Reforming a large lecture modern physics course for engineering majors using a PER-based design [McKagan, Perkins, Wieman]

ABSTRACT: We have transformed a large lecture modern physics course for engineering majors by radically changing both the content and the learning techniques implemented in lecture and homework. The content of this course emphasizes reasoning development, model building, and connections to real world applications. In addition, we implemented a variety of PER-based teaching methods, including peer instruction, collaborative homework sessions, and interactive simulations. We have assessed the effectiveness of this curriculum using pre/post surveys on both content and beliefs.

     A. Introduction
     B. Transformation Process
     C. Interactive Engagement Techniques
     D. Conceptual Understanding and Reasoning Development
     E. Real World Applications
     F. Textbook
     G. Assessment of the Course
     H. Conclusions and Next Steps

II. Transformations, Part 2 (2010)
Interpretive Themes in Quantum Physics: Curriculum Development and Outcomes [Baily, Finkelstein]

ABSTRACT: A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our prior work has shown that student perspectives on the physical interpretation of quantum mechanics can be characterized, and are differentially influenced by the myriad ways instructors approach interpretive themes in their introductory courses. We report how a transformed modern physics curriculum (recently implemented at the University of Colorado) has positively impacted student perspectives on quantum physics, by making questions of classical and quantum reality a central theme of the course, but also by making the beliefs of students (and not just those of scientists) an explicit topic of discussion.

     A. Introduction
     B. Course Background and Transformations
     C. Single-Quanta Experiments
     D. Comparative Outcomes
     D. Discussion



I. Transformations, Part 1 (2006)
Reforming a large lecture modern physics course for engineering majors using a PER-based design
[McKagan, Perkins, Wieman]

I.A. Introduction

It is well-documented that PER-based active-engagement techniques improve student learning in introductory physics courses. Some physics instructors who accept the use of interactive engagement techniques in introductory physics courses claim that these techniques are inappropriate for more advanced courses. At the University of Colorado, we have systematically transformed both introductory and advanced courses in physics and other sciences, and documented the results of these reforms. In the fall of 2005 and spring of 2006, Carl Wieman, Kathy Perkins and Sam McKagan transformed and taught a modern physics course for engineering majors. This course is the third semester of our introductory physics sequence, and is typically taken by sophomore mechanical engineering majors and senior electrical engineering majors.

This course has been transformed using a research-based design, based on the following principles learned from Physics Education Research:

  • Using interactive engagement techniques can lead to higher learning gains than traditional lecture. [1]
  • Directly addressing student difficulties can lead to higher learning gains. [2]
  • Unless physics content is presented in a way that explicitly addresses student beliefs about science, these beliefs tend to become more novice-like. [3, 4]
  • People have a limited short term memory, so material should be presented in a manner that reduces cognitive load by focusing on the important points, having a coherent structure, and eliminating nonessential details. [5]
  • For students to gain a conceptual understanding of the material, all aspects of the course, including homework and exams, must address conceptual understanding, not just numerical problem-solving.

I.B. Transformation Process

In order to develop a clear set of learning goals for the course, we interviewed seven physics faculty members about the most important concepts they thought students should learn from this course. These interviews elucidated an important issue in transforming more advanced courses: unlike introductory physics, in which there is a well-established set of topics on which most experts agree, there is no general consensus about what should be taught in more advanced classes. This issue is particularly acute in this course, which by default has often closely resembled the corresponding course for physics majors, who will see the topics in several later courses. To determine how to make our course most relevant to our target audience, we met with a group of engineering professors, to whom we posed the question, “What do your students need to know about modern physics?” The general consensus was that engineering students need to know about applications of quantum mechanics such as electron devices, lasers, STMs, and MRIs; they need to know about the quantum origin of molecular bonding and material structure; and they need some experience solving differential equations describing physical systems. The engineering professors said that their students do not need to know about special relativity or a lot of abstract mathematical formalism, topics that had typically been emphasized in this course.

To address the second education principle listed above, we reviewed the existing PER literature on student difficulties in modern physics and quantum mechanics. In addition, one of us (SBM) hosted a weekly problem-solving session for students in the semester before our transformations began. Field notes from this session provided insights into common problems for our student population.

Concurrently with our efforts, we developed the Quantum Mechanics Conceptual Survey (QMCS), a multiple choice survey designed to test student understanding of the fundamental concepts of quantum mechanics. [6] The questions in the QMCS are based on faculty interviews, studies of textbooks and syllabi, existing conceptual tests of quantum mechanics, [7, 8] research studies of student misconceptions, informal observations of students in problem-solving sessions and class, and formal interviews with students. The student interviews conducted to validate this survey were also useful in gaining a better understanding of student misconceptions. [9-11]

The content of the course was chosen to reflect the concepts most commonly cited in faculty interviews (fundamental principles of quantum mechanics), the priorities of the engineering faculty (real world applications and the relationship of microscopic principles to macroscopic properties of materials), and expert beliefs about the relevance and coherence of physics (real world applications, grounding in experiment, conceptual understanding, and reasoning development).

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I.C. Interactive Engagement Techniques

We encouraged interactive engagement in class by assigning students to 3-person consensus groups for peer instruction. We asked an average of about 5 questions per 50 minute class, to which students submitted their answers using clickers. Most of the questions included a period of group discussion. We used several different kinds of clicker questions, including interactive lecture demos in which we asked students to predict the results of an experiment, usually demonstrated with a simulation; eliciting misconceptions in order to address them; polling students to find out more about their background or what they wanted us to address; asking students to work through difficult multi-step problems; and quizzes on the assigned reading. During clicker questions, the three instructors as well as three undergraduate learning assistants circulated through the room in order to facilitate group discussions and to listen and report back on what students were thinking.We occasionally used other interactive engagement techniques in class, for example working through a tutorial on quantum tunneling.

Outside of class, we encouraged interactive engagement by hosting collaborative problem solving sessions where students could work together on homework. These sessions were staffed by instructors, undergraduate learning assistants, and graduate teaching assistants, all of whom were trained to facilitate discussion and help students figure out answers on their own, rather than telling students the answers. These sessions were voluntary, but attendance was encouraged by advertising their value and making the homework sufficiently difficult that students could seldom complete it on their own. According to the end of term survey, one third of the students attended the problem-solving sessions at least 80% of the time, and another third attended 20-60% of the time.

We have developed a suite of interactive computer simulations on quantum mechanics specifically for this course as part of the Physics Education Technology (PhET) Project. [12] These simulations follow research-based design principles and are extensively tested through student interviews and classroom studies. In the course, we incorporated simulations into lecture, clicker questions, and homework. The homework included a large number of guided inquiry activities designed to help students explore and learn from the simulations. By providing visual representations of abstract concepts and microscopic processes that cannot be directly observed, these simulations help students to build mental models of phenomena that are often difficult to understand.

The simulations incorporate many of the principles listed in the introduction, such as reducing cognitive load by focusing student attention only on essential features. For example, many students have difficulty understanding the circuit diagram for the variable voltage supply in the photoelectric effect experiment, which distracts them from seeing the main point of the experiment. By illustrating the variable voltage supply as a battery with a slider, our Photoelectric Effect simulation eliminates this distraction.

I.D. Conceptual Understanding and Reasoning Development

Throughout the course, we focused on helping students develop conceptual understanding and reasoning skills, such as making inferences from observations and understanding why we believe the ideas of quantum mechanics. This was emphasized in all aspects of the course. We wrote all our own homework, which was online and composed of computer-graded multiple choice and numeric questions, and TA-graded essay questions. The homework was designed to be extremely difficult conceptually, though only moderately difficult mathematically. Thus students were required to write essays explaining a conceptual model or to determine the underlying reasons for a complex physical phenomenon.

For example, students worked through a series of homework questions using the Lasers simulation to build up an understanding of how a laser works, at the end of which they had to write essays on questions such as why a population inversion is necessary to build a laser and why this requires atoms with three levels instead of two.

I.E. Real-World Applications

We incorporated applications into every aspect of the course, presenting at least one application of each major concept discussed. We presented photomultiplier tubes as an application of the photoelectric effect; discharge lamps, fluorescent lights, and lasers as applications of atomic structure and transitions, alpha decay and STMs and applications of quantum tunneling, LEDs and CCDs as applications of the quantum theory of conductivity, and MRIs as an application of spin. A lecture on Bose Einstein Condensation tied together many of the concepts introduced throughout the course.

I.F. Textbook

Finding a textbook appropriate for this course was difficult, given the focus on conceptual understanding and applications, which are not suitably covered in standard texts. The first semester we used Tipler and Llewellyn, [13] a popular modern physics textbook that was consistent with our level of math and contained most topics we covered. Students complained about the text on a weekly basis, both verbally and in feedback forms, and our top students reported that they stopped reading the textbook because they couldn’t understand it. Many students used our power point lecture notes, which were posted online, as an alternative to the textbook. The second semester we switched to portions of volumes 3 and 5 of Knight’s introductory physics textbook based on physics education research. [14] This textbook is at a lower level than our course mathematically, and it does not include many of our topics such as the time-independent Schrodinger equation. However, the pedagogical focus for the topics it does include is much more consistent with our with our approach. There were almost no complaints about the textbook second semester, and the average student ranking of the usefulness of the textbook for their learning on a scale of 1 (not useful) to 5 (a great deal) went up from 2.1 to 3.2. The usefulness rankings for other aspects of the course did not change significantly between the two semesters, and were between 3.5 and 4.3, with the posted lecture notes receiving the highest ranking.

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I.G. Assessment of the Course

We used several methods for assessing the effectiveness of instruction in this course, including giving the QMCS pre/post as measure of conceptual learning and the Colorado Learning and Attitudes about Science Survey (CLASS) as a measure of the change in student beliefs about science. We have also done several studies to assess learning in particular content areas of the course, the results of which can be found in the Associated Research tab.

We gave the QMCS as a pretest and posttest during the two semesters in which we taught this course (FA05 and SP06) both to our students (engineering majors) and to the students in the corresponding course for physics majors. We also gave it as posttest to both the engineering and physics majors’ courses the semester before our reforms (SP05). We use the other four modern physics as baseline “traditional” courses. It is worth noting that our class size was approximately 180 students both semesters, more than double the typical size of this course in previous semesters, about 80. The physics majors’ course ranges in size from about 30 to 80.

Table I shows the QMCS results. We calculate the average normalized gain <g> for each course, which measures how much students learned as a fraction of how much they could have learned. The values of <g> for the transformed courses are consistent with typical normalized gains on the Force Concept Inventory (FCI) in transformed introductory physics courses [1]. There are wide variations in <g> for the traditional courses, but all are consistently lower than in the reformed courses. It is interesting to note that the physics majors started consistently higher than the engineering majors, but ended up lower than the engineering majors in the transformed courses.



CoursePrePost<g>Δ<g>N
Trans. Eng. SP0630650.490.04156
Trans. Eng. FA0532690.540.05162
Trad. Eng. SP05(30)510.300.0568
Trad. Phys. SP0644640.370.1523
Trad. Phys. FA0540520.210.0654
Trad. Phys. SP05(44)630.340.0864
Table I. Average percent correct responses and normalized gains on 12 common questions on QMCS for six modern physics courses. We do not have pretest data for Spring 2005, so in the analysis of these courses, we have assumed that the average pretest scores would have been the same as the following spring. Because the survey is still under development, different versions were used different semesters. This analysis includes only the 12 common questions that were asked all three semesters.


It should be noted that the QMCS covers only the fundamental concepts of quantum mechanics, and not any of the applications that constituted a substantial fraction of our course. However, all six courses spent a comparable amount of time on the material covered by the QMCS, since the engineering majors’ course in Sp05 covered statistical mechanics and the physics majors’ courses covered special relativity, neither of which were covered in the transformed courses or tested in the QMCS.

It is difficult to evaluate the relative success of our treatment of the real world applications that constituted a major part of our course, because this material is simply not covered in other courses. However, this is likely to impact students beliefs about science, and this can be compared with other classes.

We gave the CLASS to assess student beliefs. It is a well known result [3, 4] that in a typical physics course, these beliefs tend to shift towards novice-like. In other words, students leave most physics courses believing that physics is less coherent, less logical, and less relevant to their everyday lives than when they started the course. There is some evidence that, because the subject is so abstract and counterintuitive, teaching modern physics can have a negative impact even in courses where special efforts are taken to address beliefs. [16]

Table II shows that while the traditional modern physics courses had large shifts towards novice-like beliefs, there were no statistically significant shifts in the overall beliefs of students in the reformed courses. While it is difficult to pinpoint a single cause of this difference, it seems reasonable that the emphasis on real world applications and reasoning development helped students to see the subject as more relevant and coherent.



CoursePrePostshiftΔshiftN
Trans. Eng. SP0666.167.1+1.01.1135
Trans. Eng. FA0570.268.0-2.11.1150
Trad. Eng. SP0568.560.5-8.01.955
Trad. Phys. SP0672.167.2-4.92.425
Trad. Phys. FA0578.672.9-5.71.547
Trad. Phys. SP0578.574.8-3.71.561
Table II. Average percent favorable (expert-like) responses on CLASS for the same six modern physics courses shown in Table I. The shifts for the transformed courses are not statistically significant, unlike the traditional courses, which all have large statistically significant shifts down.

I.H. Conclusions and Next Steps

We have transformed a large lecture modern physics course for engineering majors by implementing peer instruction, collaborative homework sessions, and interactive simulations, and by emphasizing real world applications, conceptual understanding, and reasoning development. These transformations have been successful in producing increased learning gains and eliminating the substantial decline in student beliefs. We are now working on the next step, archiving and sustaining these reforms. This course will be taught next semester by a different professor in the PER group, who will use our materials. We will continue to work to improve the course and package it in a way that is easy to pass on to other instructors.

 1. R. Hake, Am. J. Phys 66, 64-74 (1998). [back]

 2. L. C. McDermott, Am. J. Phys 69, 1127-1137 (2001). [back]

 3. E. Redish, J. Saul, and R. Steinber, Am. J. Phys 66, 212-224 (1998). [back]

 4. K. K. Perkins, et al., PERC Proceedings 2004, AIP (2005). [back]

 5. R. E. Mayer, Learning and Instruction, Merrill (Upper Saddle River, NJ 2005). [back]

 6. http://per.colorado.edu/QMCS (2006) [back]

 7. E. Cataloglu and R. W. Robinett, Am. J. Phys 70, 238-251 (2002). [back]

 8. C. Singh, Am. J. Phys 69, 885-895 (2001). [back]

 9. B. Ambrose, PhD thesis, University of Washington (1999). [back]

10. D. Styer, Am. J. Phys 64, 31-34 (1996). [back]

11. P. R. Fletcher, PhD thesis, University of Sydney (2004). [back]

12. PhET simulations can be downloaded for free from http://phet.colorado.edu [back]

13. P. A. Tipler and R. A. Llewellyn, Modern Physics, 4th Ed. W. H. Freeman & Co. (2002) [back]

14. R. Knight, Physics for Scientists and Engineers, 1st Ed. Pearson (2004). [back]

15. W. K. Adams et al., Phys. Rev ST: Phys. Ed. Res. 2 010101-1-14 (2006). [back]

16. T. McCaskey and A. Elby, Contributed poster at Foundations and Frontiers of PER Conference, Bar Harbor, ME, 15-19 August 2005. [back]




II. Transformations, Part 2 (2010)
Interpretive Themes in Quantum Physics: Curriculum Development and Outcomes
[Baily, Finkelstein]

II.A. Introduction

Like expert physicists, introductory students differ in their physical interpretations of quantum mechanics. [1-4] We have previously shown how the intuitively realist (classical) perspectives of modern physics students can significantly influence their stances on questions central to the so-called measurement problem: Is the wave function physically real, or simply a mathematical tool? Does the collapse of the wave function represent a change in information, or a physical transition not described by any equation? Do electrons exist as localized particles at all times? [2] These questions are of both personal and academic interest to students, but are mostly only superficially addressed in introductory courses, often for fear of generating further confusion in an already abstract and challenging topic area. We have found that introductory students are indeed capable of developing sophisticated and nuanced stances on such interpretive questions, but are often lacking the conceptual resources to articulate their beliefs. [2, 4]

Our prior work has sought to understand and characterize student perspectives on the physical interpretation of quantum mechanics, and in doing so, we have demonstrated various impacts on student thinking from myriad instructional approaches with respect to interpretive themes. [3] Interpretive themes in quantum mechanics are an often hidden aspect of modern physics instruction, according to three criteria: A) Students develop stances on these interpretive themes, regardless of whether instructors adequately attend to them; B) Those beliefs tend to be more novice-like (intuitively realist) in contexts where instruction is less explicit; and C) Explicit instruction is typically not meaningful for students beyond the specific contexts in which they arise. [3, 4]

We have recently implemented further research-based transformations to an introductory modern physics curriculum developed at the University of Colorado, with an aim to have students not only be consciously aware of their own (often intuitive and tacit) beliefs about classical and quantum reality, but also for them to acquire the necessary language and tools to identify and articulate those beliefs in a variety of contexts. We describe here the nature of this transformed curriculum, and show how it has positively impacted students’ personal interest in quantum mechanics, and their attitudes on indeterminacy and wave-particle duality.

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II.B. Course Background and Transformations

Each semester, the University of Colorado (CU) offers two introductory calculus-based modern physics courses; one section is intended for engineering majors (ENG), and the other for physics majors (PHYS). Both versions traditionally cover topics from special relativity and quantum mechanics, with variations from semester to semester according to instructor preferences, and both courses typically enroll ~ 50-100 students. A team from the physics education research (PER) group at CU began developing in 2005 a transformed curriculum for the engineering course [5] that incorporated interactive engagement techniques (in-class concept questions, peer instruction, and computer simulations[6]), as well as revised content intended to emphasize reasoning development, model building, and connections to real-world problems. The progression of quantum physics topics in this course can be broken into three main sections: classical and semi-classical physics; the development of quantum theory; and its application to physical systems.

Informed by our own research into student perspectives, we recently introduced further transformations to this modern physics curriculum, primarily in the middle section of the course. The objectives of these transformations were to: (a) make realist expectations explicit; (b) provide evidence against those expectations; and (c) attend to student attitudes on interpretive themes across a broad selection of topics. The weekly homework assignments consisted of online submissions and written, long-answer problems; there was a broad mixture of conceptual and calculation problems, both requiring short-essay, multiple-choice, and numerical answers. An online discussion board was created to allow students to anonymously ask questions and provide answers to each other (which afforded us many opportunities to gauge the accessibility of the new material to students). In lieu of a long answer section on the final exam, students were asked to write a 2-3 page (minimum) final essay on a topic from quantum mechanics of their choosing, or to write a personal reflection on their experience of learning about quantum mechanics (an option chosen by ~40% of students). As opposed to a formal term paper, this assignment was meant to give students the opportunity to explore an aspect of quantum mechanics that was of personal interest to them.

Following our treatment of the Bohr model of hydrogen (where the localized existence of electrons is assumed), we developed a semi-classical model of atomic magnetic moments, and their classically expected behavior in magnetic fields (Stern-Gerlach experiments). This topic naturally invokes ample discussion on the counter-intuitive results of repeated spin-projection measurements, the need for probabilistic descriptions in quantum mechanics, and the physical meaning of superposition states. Progressing into distant correlated measurements (quantum entanglement, locality, completeness, hidden-variables), we developed working definitions of multiple quantum interpretations (e.g. Realist, Copenhagen, Matter-Wave [2, 4]), framed in terms of the historic debate between Albert Einstein and Niels Bohr. [8] We then proceeded to engage students in an extended argument (with us, and amongst themselves) against realist interpretations of quantum phenomena. This argument was extended in two senses: 1) We were able to augment a number of standard topics (e.g., the uncertainty principle, atomic models) with discussions of interpretive themes; and 2) We introduced several entirely new topics (e.g., delayedchoice experiments) that created additional opportunities for students to explore the differences between data, interpretation, and scientific theory. In their end-of-term reflective essays, the topics most frequently cited by students as having influenced their perspectives on quantum physics were the single-quanta experiments with light and matter.

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II.C. Single-Quanta Experiments

Single-photon and delayed-choice experiments demonstrate the dualistic nature of light, and provide strong evidence for non-local interpretations, but are only meaningful to students if the details and results of the experiments are accessible to them. We therefore omitted from our lectures extraneous technical details, while still focusing on the process of designing the experiments and creating an adequate photon source. A guiding principle for this course was to avoid (as much as possible) the expectation for students to accept our assertions as a matter of faith. And so rather than simply describing what the experimentalists had meant to demonstrate, and then informing students of their success, we presented them with actual data from original sources. [9-12] Student discussions on the implications of each of three singlephoton experiments were inspired by “clicker questions” interspersed throughout lecture. [Fig. 1]

Figure 1. This sample concept question can serve to generate in-class discussion on the differences between experimental data and a physical interpretation of that data. [BS = Beam Splitter; M = Mirror; PM = Photomultiplier; N = Counter.]

Double-slit experiments with electrons demonstrate the dualistic nature of matter, in that they are individually detected as localized particles, but collectively form an interference pattern over time. When only one electron is present in the apparatus at a time, we observe the same results, and may interpret this as each electron interfering with itself as a delocalized wave, and then collapsing to a point in its interaction with the detector. Although this phenomenon may be adequately demonstrated in class using the Quantum Wave Interference PhET simulation, [13] we sought in this course to emphasize connections between theory, interpretation, and experimental evidence, and so augmented these lectures with data from some recently realized doubleslit experiments. In 2008, Frabboni, et al. reported their fabrication of a double-slit opening in gold foil on a scale of tens of nanometers (including TEM images thereof), and demonstrated electron diffraction with both slits open, as well as its absence with one slit covered. [14] Tonomura, et al. produced a movie [15] that literally shows single-electron detection and the gradual buildup of a fringe pattern. [11] Students from prior modern physics courses had often been skeptical as to whether this experiment (where only a single particle passes through the apparatus at a time) could actually be done in practice – in this way, they were able to observe the phenomenon with their own eyes.

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II.D. Comparative Outcomes

In order to gauge the impact on student thinking, we compare several outcomes from this course incorporating interpretive themes [ENG-INT] with three other recent modern physics offerings at CU. All four courses were large-lecture (N=60–100 for each), utilized interactive engagement in class, and varied in their instructional approaches with respect to interpretation in quantum mechanics. These differences may be best illustrated by how each instructor addressed in class the double-slit experiment with electrons. The Realist/Statistical instructor [ENG-R/S] taught that each particle passes through one slit or the other, but that determining which one will disrupt the interference pattern. The Matter-Wave instructor [ENG-MW] promoted a wave-packet description where each electron propagates through both slits and then becomes localized upon detection. The Copenhagen/Agnostic instructor [PHYS-C/A] touched on interpretive questions, but ultimately emphasized predicting features of the interference pattern (mathematical calculation). ENG-MW is the engineering course most similar to ENG-INT (and to the original transformed curriculum), in that similar lecture materials were used, and interpretive themes were discussed near the end, but in that course without specific reference to atomic systems. PHYS-C/A is a class for physics majors that also used many of the same lecture materials, but with less emphasis on interpretation.

Student interest in quantum mechanics at CU before instruction in modern physics is moderately high, at an average between 75-80% favorable. [Fig. 2] However, their post-instruction interest typically decreases (to below 70%), with negative responses increasing significantly (p < 0.001) – nearly 1/3 of our engineering students would not agree that quantum mechanics is an interesting subject after having learned about it in modern physics! This alone seems sufficient reason for introducing further transformations to our typical curriculum. Students from ENG-INT were nearly unanimous (98%) in their reported interest in quantum physics, and not one student responded with a negative opinion. [Relative to the number of students who completed the final exam, the response rate for the ENG-INT postinstruction survey was ~90%.]

Figure 2. Average pre- and post-instruction student responses to the statement: I think quantum mechanics is an interesting subject. N ~ 50-100 for each semester; error bars represent the standard error on the proportion.

ENG-MW, PHYS-C/A and ENG-INT all offered similar discussions of the Schrödinger model of hydrogen, with a few notable exceptions. Like the first two courses, ENG-INT showed how Schrödinger predicted zero orbital angular momentum for an electron in the ground state, and contrasted this result with the predictions of Bohr and de Broglie. But we continued by arguing how this has implications for the physical interpretation of the wave function – for (as the argument goes) how could conservation of angular momentum allow a localized particle to exist in a state of zero angular momentum in its orbit about the nucleus? More importantly, having already established language and concepts specific to interpretive themes in quantum mechanics, we were able to identify the position of an atomic electron as yet another example of a hidden variable, which we had argued throughout don’t exist as a matter of principle. ENG-INT is the only course among these four where a significant majority of students chose at the end of the semester to disagree with the idea of localized atomic electrons. [Fig. 3]

Figure 3. Post-instruction student responses to the statement: When not being observed, an electron in an atom still exists at a definite (but unknown) position at each moment in time. N ~ 50-100 for each course, as denoted in the text; error bars represent the standard error on the proportion.

Even if the physical interpretation of atomic wave functions is not of primary importance for every modern physics instructor, a common learning goal is for students to recognize a difference between the experimental uncertainty of classical mechanics and the fundamental uncertainty of quantum physics. Realist expectations might lead pre-instruction students to favor agreement with the statement: The probabilistic nature of quantum mechanics is mostly due to the limitations of our measurement instruments. The incoming percentage of students from all three of the engineering courses who agreed with this statement was nearly identical (~45%) while incoming attitudes for the physics majors were significantly more favorable (with only a quarter of them agreeing, and over half disagreeing before instruction).

The differential impact on student responses from these four modern physics courses is most dramatically illustrated by normalizing shifts in student agreement, according to their rate of agreement at the start of the course. [Fig. 4; we define favorable gain as the negative of this, since a decrease in agreement with this statement is considered favorable. This definition is equivalent to the usual normalized gain = (post – pre)/(1 – pre), except the target response rate for agreement is zero instead of 100%.] By this measure, ENG-INT had the greatest positive impact on engineering student attitudes regarding the relationship between fundamental uncertainty in quantum mechanics and classical experimental uncertainty, comparable with the course for physics majors.

Figure 4. Favorable gain = (post-pre)/(0-pre) in student agreement with the statement: The probabilistic nature of quantum mechanics is mostly due to the limitations of our measurement instruments; where agreement is considered unfavorable. N ~ 50-100 for each course, as denoted in the text; error bars represent the standard error on the proportion.
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Discussion

A common lament among educators and researchers is that we are losing students in our introductory classical courses by only teaching them physics from the 19th century; similar issues may arise when modern physics instructors limit course content to the state of knowledge in the first half of the last century, when questions of classical and quantum reality were considered to be philosophical in nature. Addressing modern experiments on the foundations of quantum mechanics was overwhelmingly popular among students, and had a demonstrably positive impact on student thinking. We encourage instructors to consider these results when designing their own courses.

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15. http://rdg.ext.hitachi.co.jp/rd/moviee/doubleslite.wmv [back]