Springuel Wittmann and Thompson on the encoding of quantitative data

R. Padraic Springuel, Michael C. Wittmann, and John R. Thompson

Reconsidering the encoding of data in physics education research

Phys. Rev. Phys. Educ. Res. 15, 020103 – Published 3 July 2019

[This paper is part of the Focused Collection on Quantitative Methods in PER: A Critical Examination.] How data are collected and how they are analyzed is typically described in the literature, but how the data are encoded is often not described in detail. In this paper, we discuss how data typically gathered in PER are encoded and how the choice of encoding plays a role in data analysis. We describe the kinds of data that are found when using short answer, multiple choice, Likert-scale, ranking task, and free response questions in terms of nominal, ordinal, interval, and ratio data. We discuss the mathematical operations that are available for each kind of data and how this affects ways that similarity and difference between student responses can be determined, a topic we discuss in terms of measures of distances and correlation. Finally, we use several papers from the literature to discuss ways in which data have been encoded and analyzed, with examples of normalized gain, factor analysis, model analysis, cluster analysis, and the investigation of epistemological agreement. We highlight both strengths and weaknesses of the data encoding approaches used in these studies. Our goal is not a comprehensive review, but one that is illustrative and can help researchers understand their own and each other’s work more deeply.

Wittmann Millay Alvarado Lucy Medina and Rogers on the resources framework and middle school students

Michael C. Wittmann, Laura A. Millay, Carolina Alvarado, Levi Lucy, Joshua Medina, Adam Rogers

Applying the resources framework of teaching and learning to issues in middle school physics instruction on energy

American Journal of Physics 87, 535 (2019); https://doi.org/10.1119/1.5110285

Our choice of model affects how we interpret what we observe. Students often have difficulties with the ideas of energy, but not all their difficulties are about energy, alone. We present two examples. In the first, student difficulties with mechanical energy seem to be with the system in which energy flows, not energy itself. In the second, students seem to use a substance metaphor of energy, which has been shown to be very productive, but use the “wrong” substance. Accounting for the nuances of student responses suggests the use of a model of knowledge and learning, the resources framework, that takes into account context dependence and the ways in which incorrect answers often contain substantial amounts of correct information.

Gray Wittmann Vokos and Scherr on energy diagrams and the NGSS

Kara E. Gray, Michael C. Wittmann, Stamatis Vokos, and Rachel E. Scherr

Drawings of energy: Evidence of the Next Generation Science Standards model of energy in diagrams

Physical Review Physics Education Research 15, 010129.

The Next Generation Science Standards (NGSS) provide a succession of objectives for energy learning and set an expectation for teachers to assess learners’ representations of energy in a variety of science contexts. To support teachers in evaluating the extent to which representations of energy display NGSS objectives, we have (i) discerned the constituent ideas that comprise the NGSS model of energy in the physical sciences and (ii) developed a checklist for assessing the extent to which an energy diagram provides evidence of the NGSS energy model. This energy diagram checklist is representation independent (so that diverse diagrams in a course may all be evaluated) and scenario independent (so that it can be applied throughout the physical science curriculum). We demonstrate the use of the checklist for assessing both pedagogical energy diagrams and learner-invented energy diagrams, including measuring a class’s increased facility with energy diagrams.

Schermerhorn & Thompson about differential volume elements

Benjamin P. Schermerhorn and John R. Thompson

Physics students’ construction and checking of differential volume elements in an unconventional spherical coordinate system


Phys. Rev. Phys. Educ. Res. 15, 010112

In upper-division physics courses, students’ use of differential line, area, and volume elements and their facility with the various multivariable coordinate systems consistently go hand in hand. As part of an effort to investigate student understanding of the structure of non-Cartesian coordinate systems and the associated differential elements, we interviewed students (mostly in pairs) in junior-level electricity and magnetism courses at two universities. In a sequence of tasks, students were asked to construct a differential length vector and a differential volume element in an unconventional spherical coordinate system. None of the students were able to arrive at a correct differential length element initially. This work addresses the construction and checking of the volume element. Volume element construction occurred by either combining associated lengths, an attempt to determine sides of a differential cube, or mapping from the existing spherical coordinate system. Students who constructed volume elements from differential length components corrected their length element terms as a result of checking the volume element expression by integration. Other students who relied heavily on spherical coordinates displayed further difficulty connecting dimensionality and projection ideas to differential construction.

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.15.010112

Schermerhorn and Thompson on differential length vectors

Benjamin P. Schermerhorn and John R. Thompson

Physics students’ construction of differential length vectors in an unconventional spherical coordinate system

Phys. Rev. Phys. Educ. Res. 15, 010111

Vector calculus and multivariable coordinate systems play a large role in the understanding and calculation of much of the physics in upper-division electricity and magnetism. Differential vector elements represent one key mathematical piece of students’ use of vector calculus. In an effort to examine students’ understanding of non-Cartesian differential length elements, students in junior-level electricity and magnetism were interviewed in pairs and asked to construct a differential length vector for an unconventional spherical coordinate system. One aspect of this study identified symbolic forms invoked by students when building these vector expressions, some previously identified and some novel, given the vector calculus context. Analysis also highlighted several common ideas in students’ concept images of a non-Cartesian differential length vector as they determined their expressions. As no interview initially resulted in the construction of an appropriate differential, analysis addresses the role of the evoked concept images and symbolic forms on students’ performance.

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.15.010111