Mathematization and the ‘Boas course’

Loverude, Michael E.

doi:10.1119/perc.2017.juried.004

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…Our results align with Loverude's findings from studying students' use of mathematics in physics. Loverude argues that "experience with mathematical procedures does not necessarily mean students make sense of the meaning of the procedures" [38]. Indeed, our students, who had completed one term of mathematical methods, were proficient at distinguishing modulus squared of complex numbers, but often failed to make sense of the analogous comparison in quantum mechanics.…”

Section: B Many Students Do Not Recognize the Purpose Of Using Complmentioning

confidence: 97%

Probing student reasoning in relating relative phase and quantum phenomena

Wan

Emigh

Shaffer

2019

Phys. Rev. Phys. Educ. Res.

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In quantum mechanics, probability amplitudes are complex numbers and the relative phases between the terms in superposition states have measurable effects. This article describes an investigation into sophomore-and junior-level students' reasoning patterns in relating relative phases and real-world quantum phenomena. The investigation involved one observational experiment and three testing experiments, during which we formulated and tested three hypotheses that allow us to gain insights into why students have difficulty recognizing the measurable effects of relative phases. We found that, in both spin-1=2 and infinite square well contexts, many students do not recognize that quantum states differing only by a relative phase are experimentally distinguishable. Moreover, student ability to recognize the measurable effects of relative phase does not improve when given (i) a task that specifically prompts students to compare the probabilities for a particular observable and (ii) a task that does not require taking inner products or changing basis. We also examined the extent to which lacking proficiency with complex numbers may have hindered student understanding of relative phase. The data indicate that most students are proficient with complex numbers. These findings suggest that many students do not, in fact, recognize the purpose of using complex numbers in superposition states. We discuss possible explanations for why students do not seem to recognize this purpose, and we also provide suggestions for future avenues of research.

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Section: B Many Students Do Not Recognize the Purpose Of Using Complmentioning

confidence: 97%

Probing student reasoning in relating relative phase and quantum phenomena

Wan

Emigh

Shaffer

2019

Phys. Rev. Phys. Educ. Res.

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“…To bridge this gap, physics education researchers have come up with various classroom activities. Loverude [3] discussed different problems related to dice, birth order etc, to help students gain clarity on the concepts of probability, micro-states, macro-states and multiplicity. Later, Michael C LoPresto designed a simple statistical thermodynamical experiment [4], which can be performed with a combination of 2 or 3 dice having four and eight faces to explain the same concepts.…”

Section: Review Of Related Literaturementioning

confidence: 99%

A computer simulation using spreadsheets for learning concept of steady-state equilibrium

et al. 2016

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In this paper, we present a simple spreadsheet based simulation activity that can be performed by students at the undergraduate level. This simulation is implemented in free open source software (FOSS) LibreOffice Calc, which is available for both Windows and Linux platform. This activity aims at building the probability distribution for the possible macro-states of a system. This has been achieved by randomly sampling the configuration space consisting of all the possible microstates and determining the corresponding macrostate for each of the samples, which is akin to Monte-Carlo simulation. This simulation could act as a very useful tool in engaging students for learning the concepts of microstates, macrostates and steady state equilibrium, once the ideas have been introduced in the classroom. Further, the effect of the number of particles on the quality of steady state equilibrium achieved demonstrates the idea of thermodynamic limit.

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“…The blended space may also include utterances that are inseparable by the researchers. Increasingly, physics education researchers are using the term more broadly to refer to the blended nature of mathematical structure and physical meaning [24,25,44,45].…”

Section: Introductionmentioning

confidence: 99%

Toward understanding and characterizing expert physics covariational reasoning

Zimmerman¹,

Olsho²,

Brahmia³

et al. 2020

2019 Physics Education Research Conference Proceedings

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Relating two quantities to describe a physical system or process is at the heart of "doing physics" for novices and experts alike. In this paper, we explore the ways in which experts use covariational reasoning when solving introductory physics graphing problems. Here, graduate students are considered experts for the introductory level material, as they often take the role of instructor at large research universities. Drawing on work from Research in Undergraduate Mathematics Education (RUME), we replicated a study of mathematics experts' covariational reasoning done by Hobson and Moore with physics experts [N. L. F. Hobson and K. C. Moore, in RUME Conference Proceedings, pp. 664-672 (2017)]. We conducted think-aloud interviews with 10 physics graduate students using tasks minimally adapted from the mathematics study. Adaptations were made solely for the purpose of participant understanding of the question, and validated by preliminary interviews. Preliminary findings suggest physics experts approach covariational reasoning problems significantly differently than mathematics experts. In particular, two behaviors are identified in the reasoning of expert physicists that were not seen in the mathematics study. We introduce these two behaviors, which we call Using Compiled Relationships and Neighborhood Analysis, and articulate their differences from the behaviors articulated by Hobson and Moore. Finally, we share implications for instruction and questions for further research.

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Mathematization and the ‘Boas course’

Cited by 4 publications

References 9 publications

Probing student reasoning in relating relative phase and quantum phenomena

Probing student reasoning in relating relative phase and quantum phenomena

A computer simulation using spreadsheets for learning concept of steady-state equilibrium

Toward understanding and characterizing expert physics covariational reasoning

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