Arvind Kumar’s research while affiliated with Tata Institute of Fundamental Research and other places

Dimensional analysis is a familiar tool for most physics students. Yet some aspects of the topic remain under-emphasized, which we highlight in this article through some select examples.

In this first article of the two-article series, we focus on the major systems of units in physics. Different systems of units, besides the SI, are commonly used, depending on the domain of interest. Conversion of equations and units across systems that differ in the number of base dimensions often poses learning difficulties. This article aims to clarify this somewhat neglected topic in college physics instruction.

In this article, we briefly review and illustrate the evolution of reasoning modes in science, from the pre-modern to the modern era, with particular reference to physics. This can help students demarcate explanations that are unacceptable in modern science from those that are possible explanations subject to experimental confirmation. The discussion bears directly on some common learning pitfalls in physics.

In this part of the article, we briefly review and illustrate the different explanatory frameworks used in modern physics within the acceptable reasoning modes in science (reviewed in the first part). This can help students improve their appreciation of the nature of physics.

Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in a variety of contexts. The questionnaire was finalized after a trial of its pilot version on 7 students on the basis of their written scripts and interviews. After content validation by three external experts, the test was administered to a sample of 141 senior undergraduate physics students from a diverse set of colleges and national institutes. Data analysis reveals several significant student pitfalls in the topic related principally to (i) the identification of a dimensionless ratio to characterize an approximation, (ii) the notion of the order of approximation and consistent handling of a problem up to the required order, and (iii) the notion of the order of infinitesimal in calculus-based derivations. The findings are of direct pedagogic relevance.

This article reviews and illustrates some simple aspects of approximations in physics, which should be useful to students at the undergraduate level.

We elaborate on a new approach of assessing content-based epistemic clarity of college physics students in terms of their ability to discriminate between different epistemic warrants for propositions in a chained argument in physics. A threefold classification (nominal, physical, and mathematical) of warrants is used, with each class split into a number of distinct epistemic categories. The assessment tool consists of a questionnaire, illustrated here for a standard undergraduate physics derivation, in which the student chooses the appropriate epistemic category (from an appended list) for each proposition in the given derivation. The tool includes a brief supplementary orientation note for clarifying the meaning of different categories. It is tested for reliability and internal consistency. Correlation of content knowledge, ascertained independently, with epistemic clarity is investigated. Surveys on large and diverse samples of physics undergraduates carried out with or without the orientation note reveal a variety of epistemic errors, some common among all groups of students, and some that are good discriminators. The epistemic measure obtained from such a tool is, however, limited in scope by its narrow definition. The construct validity of the tool and the pedagogic relevance of the work are discussed.

We propose an epistemic measure of physics in terms of the ability to discriminate between the purely mathematical, physical (i.e. dependent on empirical inputs) and nominal (i.e. empty of mathematical or physical content) propositions appearing in a typical derivation in physics. The measure can be relevant in understanding the maths-physics link hurdles among college students. To illustrate the idea, we construct a tool for a familiar derivation (involving specific heats of an ideal gas), and use it for a sample of students from three different institutes. The reliability of the tool is examined. The results indicate, as intuitively expected, that epistemic clarity correlates with content clarity. Data yield several significant trends on the extent and kinds of epistemic pitfalls prevalent among physics undergraduates.