Abstract
A central goal of physics education is to teach problem-solving competency, but the description of the nature of this competency is somehwat fragmentary and implicit in the literature. The present article uses recent historical scholarship on Arnold Sommerfeld and Enrico Fermi to identify and characterize two positions on the nature of physics problem-solving competency. The first, Sommerfeld’s, is a “theory first, phenomenon second” approach. Here, the relevant problems originate in one of the theories of physics and the goal of the problem-solver is to make a mathematical analysis of the relevant equation(s) and then give a qualitative analysis of the phenomenon that arise from these mathematical results. Fermi’s position is a “phenomenon first, theory second” approach, where the starting point is a physical phenomenon that is analyzed and then brought into the realm of a physics theory. The two positions are illustrated with solutions to two problems and it is shown that the two positions are reflected in problem collections of university educations in physics.
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Notes
Lev Landau often used a “phenomenon first” approach in his research, but the problems he assigned in his famous theoretical minimum were oriented towards a “theory-first” approach. Ioffe (2013) gave an example of problem and the famous Landau and Lifschitz textbooks give other problems, which according to Hall (2006), stem from the theoretical minimum.
Fermi is the inventor of Fermi problems. However, one should note that while the above approach in general accords with Fermi problems, the latter, such as the famous number of Piano Tuners in Chicago, often do not require physical reasoning, in contrast to the crucial steps involving physics of the above approach.
The procedure is to use the definition of angular momentum l, which is conserved in central force motion, and substitute \( \left(\frac{l}{{\mathrm{mr}}^2}\right)\left(\frac{l}{{\mathrm{mr}}^2}\right) \) for \( \frac{d}{dt} \).
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Acknowledgements
The author wishes to thank Jens Højgaard Jensen for numerous discussions on problem-solving in physics as well as comments to a draft of the article.
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Niss, M. What Is Physics Problem-Solving Competency? The Views of Arnold Sommerfeld and Enrico Fermi. Sci & Educ 27, 357–369 (2018). https://doi.org/10.1007/s11191-018-9973-z
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DOI: https://doi.org/10.1007/s11191-018-9973-z