What Does It Mean to Understand a Physics Equation? A Study of Undergraduate Answers in Three Countries

Airey, John; Lindqvist, Josefine Grundström; Kung, Rebecca Lippmann

doi:10.1007/978-3-030-17219-0_14

Cited by 3 publications

(4 citation statements)

References 16 publications

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“…Some of the proponents of this work have suggested a set of scientific thinking skills (epistemic games) that students engage with when they use mathematics in physics problem solving [4,5,10]. Taking a different tack, other authors have explored what students mean when they say they understand a physics equation, from an epistemological perspective [13,14]. Expanding on these ideas, Uhden et al [9] claim that it is not appropriate to separate physical (conceptual) and mathematical (quantitative) models in physics education.…”

Section: Physics Reasoning or Calculating?mentioning

confidence: 99%

“…In a few rare cases in the literature, however, we can find examples where students suggest that rearranging equations is not only a tool for calculating, but also a marker of conceptual understanding. Airey et al found that many students believe they understand an equation when they can rearrange it and use it in different formats [13]. An even more in-depth treatment can be found in Eichenlaub and Redish, in a student's answer about using the equation of nuclear decay of a sample of particles over time [5].…”

Section: Rearranging Equationsmentioning

confidence: 99%

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Rearranging equations to develop physics reasoning

Kapodistrias,

Airey

2024

Eur. J. Phys.

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Researchers generally agree that physics experts use mathematics in a way that blends mathematical knowledge with physics intuition. However, the use of mathematics in physics education has traditionally tended to focus more on the computational aspect (manipulating mathematical operations to get numerical solutions) to the detriment of building conceptual understanding and physics intuition. Several solutions to this problem have been suggested; some authors have suggested building conceptual understanding before mathematics is introduced, while others have argued for the inseparability of the two, claiming instead that mathematics and conceptual physics need to be taught simultaneously. Although there is a body of work looking into how students employ mathematical reasoning when working with equations, the specifics of how physics experts use mathematics blended with physics intuition remain relatively underexplored. In this paper, we describe some components of this blending, by analyzing how physicists perform the rearrangement of a specific equation in cosmology. Our data consist of five consecutive forms of rearrangement of the equation, as observed in three separate higher education cosmology courses. This rearrangement was analyzed from a conceptual reasoning perspective using Sherin’s framework of symbolic forms. Our analysis clearly demonstrates how the number of potential symbolic forms associated with each subsequent rearrangement of the equation decreases as we move from line to line. Drawing on this result, we suggest an underlying mechanism for how physicists reason with equations. This mechanism seems to consist of three components: narrowing down meaning potential, moving aspects between the background and the foreground and purposefully transforming the equation according to the discipline’s questions of interest. In the discussion section we highlight the potential that our work has for generalizability and how being aware of the components of this underlying mechanism can potentially affect physics teachers’ practice when using mathematics in the physics classroom.

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Section: Physics Reasoning or Calculating?mentioning

confidence: 99%

Section: Rearranging Equationsmentioning

confidence: 99%

Rearranging equations to develop physics reasoning

Kapodistrias,

Airey

2024

Eur. J. Phys.

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“…Multiple representations are the expression of a concept in many ways, such as using text (verbal descriptions), sketches, diagrams, graphs, and mathematical equations (Airey et al, 2019;Eichenlaub & Redish, 2019;Euler & Gregorcic, 2018;Franke et al, 2019;Geyer & Kuske-Janßen, 2019). Using MRs can even help students improve their creative thinking during problem-solving (Bicer, 2021).…”

Section: Introductionmentioning

confidence: 99%

The effects of the multiple representation approach on undergraduate students understanding of Archimedes Principle

Kriek,

Legesse

2023

JPR

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Students often face difficulties to understand Archimedes' principle and to apply it in everyday life. It is therefore necessary to explore a different teaching approach that addresses students' visual and auditory senses in a unique manner. The aim of this study was to determine the effect of using multiple representations on undergraduate physics students' understanding of Archimedes' principle. A quasiexperimental approach was employed, involving the random selection of four groups of students (experimental and control) with two iterations, each involving two groups of students. A sample of 128 students completed an open-ended questionnaire based on the Thermal Transport Conceptual Inventory, and the Fluid Mechanics Concept Inventory. Lesson plans were presented for both iterations. Quantitative analysis involved the use of t-tests to assess the comparability of the groups, prior to the intervention and ANCOVA after the intervention to determine the effect. Qualitative data analysis involved identifying and comparing themes to establish student understanding before and after the two iterations. The findings indicated that the use of six different representations did not yield a significant effect compared to traditional teaching, while the use of eight representations proved significantly effective where the static pictures were replaced by animation pictures as well as adding videos and virtual labs. Careful planning is crucial not only for selecting the most suitable representation in a particular teaching situation, but also for determining which technology to use when addressing students' understanding of Archimedes' principle.

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“…Research on physics equations can be found mostly on two areas i.e. use of equations in problem-solving and student attitudes and beliefs about physics equations (Airey et al, 2019). Here we performed a study to identify the students' understanding of the physics equations.…”

Section: Introductionmentioning

confidence: 99%

Students’ Understanding on Physics Equations Used in the Experiment

Santosa

2019

JPF

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This study investigates the students’ understanding of physics equations used in the experiment. Here 91 students participated in this qualitative study. All of them worked on the experiment to determine the specific charge of an electron e/m. In this case, physics equations are derived to provide the basis of the experimental method in order to obtain the desired value of e/m. Students’ understanding of physics equations was observed through an initial test, their experimental report, and a final test. The final test reveals that many students perceive the equations as a mathematical tool. As a result, about 64 % of the participant states that e/m depends on the variable in the experiment e.g. the current or the accelerating potential. They do not realize that e/m is a constant.

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What Does It Mean to Understand a Physics Equation? A Study of Undergraduate Answers in Three Countries

Cited by 3 publications

References 16 publications

Rearranging equations to develop physics reasoning

Rearranging equations to develop physics reasoning

The effects of the multiple representation approach on undergraduate students understanding of Archimedes Principle

Students’ Understanding on Physics Equations Used in the Experiment

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