Categorization of quantum mechanics problems by professors and students

Lin, Shih‐Yin; Singh, Chandralekha

doi:10.1088/0143-0807/31/1/006

Cited by 74 publications

(65 citation statements)

References 18 publications

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“…The table provides only one of the several possible ways to classify the questions. Our prior research shows [13] that different instructors categorize a given QM question in different ways so the categorization shown in Table 1 is only one of them that we found convenient. The group "Other" includes questions about the uncertainty principle, the concept of degeneracy in the context of a free particle, and the Ehrenfest theorem that says that the expectation value of a physical observable obeys the classical laws [1][2][3][4][5][6].…”

Section: The Survey Resultsmentioning

confidence: 99%

Surveying Students’ Understanding of Quantum Mechanics

Zhu¹,

Singh²,

Sabella³

et al. 2010

AIP Conference Proceedings

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Abstract. Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and graduate students have with non-relativistic quantum mechanics of one particle in one spatial dimension. We developed a research-based conceptual multiple-choice survey that targets these issues to obtain information about the common difficulties and administered it to more than a hundred students from seven different institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, time-dependence of wavefunction and timedependence of expectation value. We find that the advanced undergraduate and graduate students have many common difficulties with these concepts and that research-based tutorials and peer-instruction tools can significantly reduce these difficulties. The survey can be administered to assess the effectiveness of various intructional strategies.

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Section: The Survey Resultsmentioning

confidence: 99%

Surveying Students’ Understanding of Quantum Mechanics

Zhu¹,

Singh²,

Sabella³

et al. 2010

AIP Conference Proceedings

Self Cite

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show abstract

“…The most prevalent method for studying how people form categories for physics problems is by using card-sorting tasks [13][14][15][16][17][18][19][20][21]. In most of these studies, textbook-style physics problems are printed onto index cards or listed on a piece of paper and study participants are asked to place the problems into groups based on solution similarity and to assign a name to each group.…”

Section: A Overview Of Research On Categorizationmentioning

confidence: 99%

“…Some students use surface features and some use principles, suggesting that not all undergraduate students are ''novices'' [15,16,18,19,25] and not all graduate students can be classified as ''experts'' [20,21].…”

Section: A Overview Of Research On Categorizationmentioning

confidence: 99%

Impact of a short intervention on novices’ categorization criteria

Docktor

Mestre

Ross

2012

Phys. Rev. ST Phys. Educ. Res.

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Research on physics problem categorization has established that proficient problem solvers are able to group together physics problems that would be solved by similar principles and use conceptual approaches when solving problems, whereas weak solvers rely more heavily upon surface features (objects, contexts, and quantities provided) to identify specific equations that match to the problem situation. This study explores the degree to which novices are able to shift their categorization strategies toward one that is more principle based as a result of a brief, computer-based intervention designed to highlight the role of principles as categorization criteria. Students finishing an introductory algebra-based mechanics course were presented with a sequence of problem pairs, asked to judge whether each pair would be solved similarly, and provided with feedback. Students in one condition received feedback that was very sparse and only indicated correctness, whereas students in a second condition viewed elaborate feedback that linked problem features to the appropriate concepts and principles to solve each problem. We found an increased use of physics principles in the reasoning provided by students who received the elaborate feedback whereas students who did not view this elaboration primarily cited quantities in the problem statement. Although these results suggest it is possible to increase students' attention to principles when approaching problems, poor performance on the items indicates that considering the appropriateness of principles remains a difficult task for beginning physics students.

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“…Therefore, it is important for upper-level undergraduate and PhD students to develop proficiency with the probability distributions of measurement outcomes when different physical observables are measured in a given quantum state of the system. Indeed, several prior studies have found that many advanced students struggle with the foundational issues in quantum mechanics including measurement (e.g., see [1][2][3][4][5][6][7][8][9][10][11][12]). Studies have focused on diverse pedagogical approaches for helping students learn quantum mechanics better (e.g., see [13][14][15][16][17][18][19][20][21][22][23][24][25][26]), and visualization tools such as QuVIS and QuTIP have been developed to help students develop intuition about quantum mechanical phenomena [23,24].…”

Section: Introductionmentioning

confidence: 99%

Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics

Marshman

Singh

2017

Eur. J. Phys.

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A solid grasp of the probability distributions for measuring physical observables is central to connecting the quantum formalism to measurements. However, students often struggle with the probability distributions of measurement outcomes for an observable and have difficulty expressing this concept in different representations. Here we first describe the difficulties that upper-level undergraduate and PhD students have with the probability distributions for measuring physical observables in quantum mechanics. We then discuss how student difficulties found in written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the probability distributions of measurement outcomes for physical observables. The QuILT strives to help students become proficient in expressing the probability distributions for the measurement of physical observables in Dirac notation and in the position representation and be able to convert from Dirac notation to position representation and vice versa. We describe the development and evaluation of the QuILT and findings about the effectiveness of the QuILT from in-class evaluations.

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Categorization of quantum mechanics problems by professors and students

Cited by 74 publications

References 18 publications

Surveying Students’ Understanding of Quantum Mechanics

Surveying Students’ Understanding of Quantum Mechanics

Impact of a short intervention on novices’ categorization criteria

Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics

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