Helping students learn to “think like a physicist” is a major goal of most physics courses from the introductory to advanced level (Van Heuvelen 1991a, Reif 1986, Reif 1981, Larkin and Reif 1979, Reif 1995, Larkin 1981). Expert physicists monitor their own learning and use problem solving as an opportunity for learning, and extending and organizing their knowledge (Maloney 1994, Heller and Reif 1984). Prior research has focused on how introductory physics students differ from physics experts (Chi et al. 1981, Larkin et al. 1980, Singh 2002, Dufresne et al. 2005, Hardiman et al. 1989) and strategies that may help introductory students learn to learn (Eylon and Reif 1984, Van Heuvelen 1991b, Elby 2001, Meltzer 2005, Ozimek et al. 2004). By comparison, few investigations have focused on the learning skills of advanced physics students although some investigations have been carried out on the difficulties advanced students have with various advanced topics, e.g., in quantum mechanics (Singh 2001, Bao and Redish 2002, Wittmann et al. 2002, Singh et al. 2006, Singh 2008).
It is commonly assumed that most students who have made it through an entire undergraduate physics curriculum have not only learned a wide body of physics content but also have picked up the habits of mind and self-monitoring skills needed to build a robust knowledge structure (e.g. Chi et al. 1981). Instructors take for granted that advanced physics students will learn from their own mistakes in problem solving without explicit prompting, especially if students are given access to clear solutions. It is implicitly assumed that, unlike introductory students, advanced students have become independent learners and they will take the time out to learn from their mistakes, even if the instructors do not reward them for fixing their mistakes, e.g., by explicitly asking them to turn in, for course credit, a summary of the mistakes they made
and writing down how those mistakes can be corrected (Mason et al. 2008, Cohen et al. 2008, Yerushalmi et al. 2008, Yerushalmi et al. 2007, Singh et al. 2007).
However, such assumptions about advanced students’ superior learning and self- monitoring skills have not been substantiated by research. Very little is known about whether the development of these skills from the introductory level until the time the students become physics professors is a continuous process of development or whether there are some discontinuous “boosts” in this process for many students, e.g., when they become involved in graduate research or when they ultimately independently start teaching and researching. There is also no research data on the fraction of students who have gone through the “traditional” physics curriculum and have been unable to develop sufficient learning and self-monitoring skills that are the hallmark of a physicist.
Moreover, investigations in which advanced physics students are asked to perform tasks related to simple introductory physics content do not properly assess their learning and self- monitoring skills. Advanced students may have a large amount of “compiled knowledge” about introductory physics and may not need to do much self-monitoring or learning while dealing with introductory problems. For example, when physics graduate students were asked to group together introductory physics problems based upon similarity of solution, their categorization was better than that of introductory physics students, even though there is a distribution overlap (see chapter 2). While such tasks may be used to compare the grasp that introductory and advanced students have of introductory physics content, tasks involving introductory level content do not shed much light on advanced physics students’ learning and self-monitoring skills.
The task of evaluating advanced physics students’ learning and self-monitoring skills should involve advanced level physics topics at the periphery of advanced students’ own understanding. While tracking the same student’s learning and self-monitoring skills longitudinally is an extremely difficult task, taking snapshots of advanced students’ learning and self-monitoring skills can be very valuable. Here, we investigate whether students in an advanced quantum mechanics course learn automatically from their own mistakes without explicit intervention.
At the University of Pittsburgh, honors-level quantum mechanics is a two-semester course sequence which is mandatory only for those students who want to obtain an honors degree in physics. It is often one of the last courses an undergraduate physics major takes. Here, we discuss a study in which we administered four quantum physics problems in the same semester both in the midterm and final exams to students enrolled in the honors-level quantum mechanics. Solutions to all of the midterm questions were available to students on a course website. Moreover, written feedback was provided to students after their midterm performance, indicating on the exams where mistakes were made and how they can be corrected.
Our goal was to explore the extent to which these advanced physics students use their mistakes as a learning opportunity (Chi et al. 1989) and whether their performance on the problems administered a second time (in the final exam) is significantly better than the performance on those problems in the midterm exams. We also interviewed a subset of students individually within two months using a think-aloud protocol (Chi 1994, Chi 1997, Ericsson and Simon 1993) to get a deeper understanding of their attitudes and approaches to problem solving and learning (Cummings et al. 2004, Marx and Cummings 2007). Moreover, an evaluation of how well students were able to retrieve relevant knowledge to solve the quantum mechanics
problems during the interviews that took place a couple of months after the final exam gives us a glimpse of the robustness of students’ knowledge structure (Francis et al. 1998).
We found that students’ average performance in the final exam on the problems that were given a second time was not significantly better than the average performance on those problems on the midterm exams. While some students improved, others deteriorated. We conclude that advanced physics students do not routinely exploit their mistakes in problem solving as a learning opportunity. Our study suggests that many advanced physics students may be employing inferior learning strategies, e.g., “cramming” before an exam and selective memorization of content based upon their expectation that those problems are likely to show up on the exam; most do not give a high priority to building a robust knowledge structure. Prior research shows that introductory physics students benefit from explicit interventions to help them develop useful learning and self-monitoring skills (Singh et al. 2006, Singh 2008, Mason et al. 2008, Cohen et al. 2008, Yerushalmi et al. 2008, Yerushalmi et al. 2007, Singh et al. 2007, Karelina and Etkina 2007, Etkina et al. 2008). We hypothesize that similar explicit interventions will also prove useful in advanced courses and will help advanced physics students in developing habits of mind.