Student Understanding Of The Physics And Mathematics Of Process Variables In P-V Diagrams

Phys. Rev. ST Phys. Educ. Res.

2012

Self Cite

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a physics context. As an extension from this work on students' mathematical competency at the upper level in physics, we report on a preliminary investigation of mathematical understanding of fundamental concepts of slope and derivative among students in a thirdsemester multivariable calculus course. Among the first published findings of physics education research are investigations on students' understanding of kinematics, with particular attention to graphical representations of position-, velocity-, and acceleration-versus-time graphs. Underlying these physical quantities are relationships that depend on derivatives and slopes. We report on our findings as we attempt to isolate students' understanding of these mathematical concepts.

Section: Discussionsupporting

confidence: 80%

Section: Methodsmentioning

confidence: 80%

Investigating graphical representations of slope and derivative without a physics context

Christensen

Phys. Rev. ST Phys. Educ. Res.

2012

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“…[44], pp. [4][5][6][7][8][9]. Students who ranked the probabilities as simply P A ð1Þ > P A ð2Þ > P A ð3Þ also made claims that are consistent with some of Smith's other classifications.…”

Section: Incorrect Reasoning About Probability Ratiosmentioning

confidence: 54%

“…The study of student understanding of advanced topics is becoming increasingly prevalent in physics education research [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Investigating upper-division undergraduate students provides a snapshot of the intellectual journey from novice introductory student to expert physicist that may reveal key components of this transition [19].…”

Section: Introductionmentioning

confidence: 99%

Student understanding of the Boltzmann factor

Smith

Mountcastle

Phys. Rev. ST Phys. Educ. Res.

2015

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[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.

“…Previous studies have shown a positive correlation between student difficulties with physics concepts and those with either the mathematics concepts, application of those concepts, or the representations used to connect the mathematics and the physics. Students lacking and/or failing to apply relevant mathematical knowledge and skills have shown difficulties with reasoning and/or solving problems in physics contexts [2,3,12,13].…”

Section: Introductionmentioning

confidence: 99%

Analytical derivation: An epistemic game for solving mathematically based physics problems

Bajracharya

Phys. Rev. Phys. Educ. Res.

2016

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Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.