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

Wittmann about the resources framework

Michael C. Wittmann

Research in the Resources Framework: Changing environments, consistent exploration

Wittmann, M.C. (2018). Research in the Resources Framework: Changing environments, consistent exploration. in Reviews in PER Volume 2: Getting Started in Physics Education Research, edited by C. Henderson and K. A. Harper (American Association of Physics Teachers, College Park, MD, 2018).

In this paper, I discuss my personal journey through one research tradition, that of the resources framework, and how it has evolved over time. In my present work, understanding learners' reasoning in physics in terms of the construction of large-scale models from small-scale resources emphasizes the person doing the constructing over the physics they are discussing. In this human-centered approach, I find value not in the correctness or incorrectness of a given response, but in the nature of construction, the individual's evaluation of their own ideas, and the communication between learners as they seek to understand each other. The resources framework has driven my attention toward a human-centered approach, and has had an effect on both my professional and personal life, in the process. In addition, events in my personal life have proven relevant to my professional work in ways that are reflected by my use of the resources framework to understand knowledge and learning.

Schermerhorn Thompson on determining differential area elements

Student determination of differential area elements in upper-division physics

Benjamin P. Schermerhorn and John R. Thompson

Physics Education Research Conference Proceedings 2017

Given the significance of understanding differential area vectors in multivariable coordinate systems to the learning of electricity and magnetism (E&M), students in junior-level E&M were interviewed about E&M tasks involving integration over areas. In one task, students set up an integral for the magnetic flux through a square loop. A second task asked students to set up an integral to solve for the electric field from a circular sheet of charge. Analysis identified several treatments of the differential area: (1) a product of differential lengths, (2) a sum of differential lengths, (3) a product of a constant length with differential length in one direction, (4) a derivative of the expression for a given area, and (5) the full area.

Physics Education Research Conference 2017
Part of the PER Conference series
Cincinnati, OH: July 26-27, 2017
Pages 356-359

DOI: 10.1119/perc.2017.pr.084

Tabachnick Colesworthy Wittmann on teacher knowledge of acceleration

Middle School Physics Teachers' Content Knowledge of Acceleration

Elijah Tabachnick, Peter Colesworthy, and Michael C. Wittmann

Physics Education Research Conference Proceedings 2017

In the "speed model" of accelerated motion, the terms "speeding up" and "slowing down" are equated with positive and negative acceleration, respectively. As part of the Maine Physical Sciences Partnership, we have investigated middle school physical science teachers' understanding of accelerated motion in the context of using vectors as a pictorial tool for kinematics and found a high prevalence of the speed model. Through surveys, interviews, and observation of professional development activities, we have found that the teachers consistently use the correct mathematical tools to talk about displacements and velocities, and correctly use vectors to represent displacements, velocities and accelerations. However, when interpreting the acceleration of an object, teachers often use the speed model, which contradicts their other work. We discuss this result and present two conjectures about its possible origin.

Physics Education Research Conference 2017
Part of the PER Conference series
Cincinnati, OH: July 26-27, 2017
Pages 384-387

DOI: 10.1119/perc.2017.pr.091

Wittmann Rogers Alvarado Medina Millay on survey questions about energy

Using multiple survey questions about energy to uncover elements of middle school student reasoning

M. Wittmann, A. Rogers, C. Alvarado, J. Medina, and L. Millay

Physics Education Research Conference Proceedings 2017, Cincinnati, OH, 2017.

One power of middle school physics teaching is its focus on conceptual understanding, rather than mathematical modeling. Teaching energy in middle school allows one to focus on the conceptual ideas, metaphors, and analogies we use to make sense of the topic. In the Next Generation Science Standards, energy is both a core disciplinary idea in the physical sciences and a crosscutting concept. In this paper, we provide several examples of seeming contradictions in student responses to similar questions. For example, students think differently about energy flow to the air or the ground. They also think differently about energy flow in cold and hot situations, though not necessarily as expected. Analyzing these results carefully, in particular when comparing and contrasting seemingly similar questions, may help both researchers and teachers listen for ideas, target instruction, and recognize learning more effectively.

Physics Education Research Conference 2017
Part of the PER Conference series
Cincinnati, OH: July 26-27, 2017
Pages 440-443

DOI: 10.1119/perc.2017.pr.105

McKay Millay Wittmann and many more write on Teacher Leadership

Susan R. McKay, Laura Millay, Erika Allison, Elizabeth Byerssmall, Michael C. Wittmann, Mickie Flores, Jim Fratini, Bob Kumpa, Cynthia Lambert, Eric A. Pandiscio, Michelle K. Smith

Investing in Teachers’ Leadership Capacity: A Model from STEM Education

Teachers play a key role in the quality of education provided to students. The Maine Center for Research in STEM Education (RiSE Center) at the University of Maine has worked with partners to design, implement, and evaluate several programs in the past eight years to provide professional learning opportunities and support for Maine’s STEM teachers, leading to significant impacts for teachers and students across the state. A strategic investment in developing teacher leadership capacity played a key role in expanding the initial partnership to include teachers and school districts across the state. With support from education researchers and staff at the RiSE Center, STEM teachers have taken on roles as leaders of professional learning opportunities for peers and as decision makers in a statewide professional community for improving STEM education. This article describes the structures that have fostered teacher leadership and how those structures emerged through partnership and collaboration, the ways in which teacher leadership has amplified the resources we have been able to provide to STEM teachers across the state, and the outcomes for Maine students.

Preferred citation:

McKay, Susan R. , Laura Millay, Erika Allison, Elizabeth Byerssmall, Michael C. Wittmann, Mickie Flores, Jim Fratini, Bob Kumpa, Cynthia Lambert, Eric A. Pandiscio, and Michelle K. Smith. "Investing in Teachers’ Leadership Capacity: A Model from STEM Education." Maine Policy Review 27.1 (2018) : 54 -63, https://digitalcommons.library.umaine.edu/mpr/vol27/iss1/15

Wittmann, Alvarado, and Millay on teacher knowledge of energy

Michael C. Wittmann, Carolina Alvarado, Laura Millay

Teacher awareness of problematic facets of meaningful metaphors of energy

Latin American Journal of Physics Education 11, 2327 (2017).

English Abstract

How teachers respond to students depends, in part, on what they see in their students’ thinking. In a teacher professional development setting, we asked teachers to provide possible incorrect responses and explanations that students might give when discussing the gravitational potential energy of identical hikers walking to the summit of a mountain along different paths, from the same starting point. Teachers were aware of the common difficulties that students might have, including (1) energy is “used up” because of travel time, travel distance, or the effort exerted during travel (2) double-counting work and energy, and (3) energy being an intrinsic property of the hiker. Several of these difficulties use the metaphor of energy as a substance-like quantity, but teachers never made explicit that they were aware of the value of this metaphor in thinking about energy. We discuss the need for teachers to respond to multiple grain sizes of student thinking, including the metaphors they use and the different and at times problematic facets of each.

Keywords: Teacher training, Alternative conceptions, Gravity.

Resumen Espanol

La manera en que los maestros responden a los alumnos depende, en parte, de lo que ven en el pensamiento de los estudiantes. En un curso de capacitación, le pedimos a maestros que proporcionaran la posible respuesta incorrecta y la explicación de qué explicaciones podrían dar al analizar la energía gravitacional potencial de unos excursionistas idénticos caminando hacia la cumbre de una montaña por diferentes veredas, iniciando desde el mismo punto. Los maestros reconocían las dificultades comunes que los estudiantes podrían tener, incluyendo (1) la energía es “usada” en el tiempo viajado, distancia recorrida, o el esfuerzo requerido durante el viaje, (2) contar doblemente el trabajo y la energía, y (3) considerar la energía como una propiedad intrínseca del excursionista. Muchas de esas dificultades utilizan la metáfora de la energía como una cantidad del tipo sustancia, pero los maestros nunca hicieron explícito que ellos estaban al tanto del valor de dicha metáfora la pensar en energía. Discutimos la necesidad de los maestros a responder a las múltiples maneras de pensar de los estudiantes, incluyendo metáforas que usan así como las facetas que pueden ser problemáticas en ocasiones..

Palabras clave: Capacitación de maestros, Concepciones alternativas, Gravedad.

Link to journal: http://www.lajpe.org
Link to article: http://www.lajpe.org/jun17/2327_AAPT_2017.pdf

Ishimoto, Davenport, and Wittmann on cultural differences on the FMCE

M. Ishimoto, G. Davenport, and M. C. Wittmann

Comparing Item Response Curves of Japanese and American Students on the Force and Motion Conceptual Evaluation

Physical Review Physics Education Research 13, 20135 (published Nov 30, 2017)

Student views of force and motion reflect the personal experiences and physics education of the student. With a different language, culture, and educational system, we expect that Japanese students’ views on force and motion might be different from those of American students. The Force and Motion Conceptual Evaluation (FMCE) is an instrument used to probe student views on force and motion. It was designed using research on American students, and, as such, the items might function differently for Japanese students. Preliminary results from a translated version indicated that Japanese students had similar misconceptions as those of American students. In this study, we used item response curves (IRCs) to make more detailed item-by-item comparisons. IRCs show the functioning of individual items across all levels of performance by plotting the proportion of each response as a function of the total score. Most of the IRCs showed very similar patterns on both correct and incorrect responses; however, a few of the plots indicate differences between the populations. The similar patterns indicate that students tend to interact with FMCE items similarly, despite differences in culture, language, and education. We speculate about the possible causes for the differences in some of the IRCs. This report is intended to show how IRCs can be used as a part of the validation process when making comparisons across languages and nationalities. Differences in IRCs can help to pinpoint artifacts of translation, contextual effects because of differences in culture, and perhaps intrinsic differences in student understanding of Newtonian motion.

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.13.020135

van de Bogart, Stetzer, and more on metacognition, troubleshooting, and circuits

Kevin L. Van De Bogart, Dimitri R. Dounas-Frazer, H. J. Lewandowski, and MacKenzie R. Stetzer

Investigating the role of socially mediated metacognition during collaborative troubleshooting of electric circuits

Phys. Rev. Phys. Educ. Res. 13, 020116 – Published 12 September 2017

Developing students’ ability to troubleshoot is an important learning outcome for many undergraduate physics lab courses, especially electronics courses. In other work, metacognition has been identified as an important feature of troubleshooting. However, that work has focused primarily on individual students’ metacognitive processes or troubleshooting abilities. In contrast, electronics courses often require students to work in pairs, and hence students’ in-class experiences likely have significant social dimensions that are not well understood. In this work, we use an existing framework for socially mediated metacognition to analyze audiovisual data from think-aloud activities in which eight pairs of students from two institutions attempted to diagnose and repair a malfunctioning electric circuit. In doing so, we provide insight into some of the social metacognitive dynamics that arise during collaborative troubleshooting. We find that students engaged in socially mediated metacognition at multiple key transitions during the troubleshooting process. Reciprocated metacognitive dialogue arose when students were collectively strategizing about which measurements to perform, or reaching a shared understanding of the circuit’s behavior. Our research demonstrates the value of the framework of socially mediated metacognition in providing insight into the nature of collaborative student troubleshooting in the context of electronics. As such, this framework may be a useful resource for future efforts to examine and support the development of student troubleshooting skills in other upper-division laboratory courses.

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.13.020116

Lodge-Scharff on mental models in mathematics and physics

Savannah E. Lodge-Scharff

Investigating Student Mental Models at the Intersection of Mathematics and Physical Reasoning in Physics

Thesis for the Master's of Science in Teaching (MST)

A significant challenge in learning science and mathematics is coordinating different types of mental models, such as mathematical and physical mental models, that represent different aspects of a given phenomenon. This challenge is illustrated in the present study, in which we observed a small number of college students reasoning about forces as both physical and mathematical quantities as they reasoned about a physical system. Using video analysis of the students’ gesture and as they reasoned qualitatively and mathematically about the system, we documented the construction and coordination of participants’ mental models. We found that participants constructed mathematical mental models as imagined lines uniquely to physical mental models as imagined pulls. Moreover, students rarely exhibited the coordination of these two mental models. These findings suggest that instructors that they cannot assume that students generate models, even circumstances designed to support them.

Recommended Citation
Lodge-Scharff, Savannah E., "Investigating Student Mental Models at the Intersection of Mathematics and Physical Reasoning in Physics" (2017). Electronic Theses and Dissertations. 2718.
http://digitalcommons.library.umaine.edu/etd/2718

Ferm MST on following and using inferential reasoning chains

William N. Ferm (Billy)

Examining Student Ability to Follow and Interact with Qualitative Inferential Reasoning Chains

Thesis for Master's of Science in Teaching (MST)


The effectiveness of scaffolded, research-based instruction in physics has been extensively documented in the literature. However, even after such instruction, students who demonstrate a solid conceptual understanding on one physics task may subsequently perform poorly on another, closely related task requiring the application of that same conceptual understanding. Research on such inconsistencies has suggested that poor performance may primarily be attributed to difficulties related to reasoning rather than those of a conceptual nature. To gain insight into this phenomenon, further work is required, specifically focusing on the design and testing of tasks that may be used to document the extent to which students are able to follow, replicate, evaluate, and generate coherent chains of qualitative inferential reasoning before, during, and after scaffolded, research-based instruction.

In response to this need, we have designed and implemented tasks to assess the extent to which introductory physics students are able to logically follow and interact with the reasoning chains of hypothetical students in a variety of physics contexts. In this thesis, we describe several of these tasks, including a “Follow Reasoning” task in which students are asked to infer the conclusions that would be drawn from different lines of reasoning articulated by hypothetical students and to provide justification for those inferences. We also share work from an experiment in which students were first prompted to answer a physics question before completing a “Follow Reasoning” task, which itself contained reasoning associated with the same physics question (leading to either the correct or an incorrect answer). Finally, we describe the construction, implementation, and analysis of a pair of isomorphic “Follow Reasoning” tasks in which the same lines of reasoning are articulated by hypothetical students but the physics context in which the reasoning is presented is different.

Results show that the majority of students were able to predict the logical concluding statement when provided with a hypothetical student reasoning chain (HSRC), suggesting that they were in fact capable of following the reasoning of others. Several overall trends were identified, and they provided insight into how students interact with HSRCs. In addition, we found that students who demonstrated requisite conceptual understanding were better able to follow correct reasoning leading to the correct answer but showed no such enhancement when considering incorrect reasoning leading to a common incorrect answer. Finally, data collected from isomorphic “Follow Reasoning” tasks suggest that student ability to follow particular lines of reasoning may, in fact, be independent of physics context and content. Key findings from this work have numerous important implications for instruction.

Recommended Citation
Ferm, William N. Jr., "Examining Student Ability to Follow and Interact with Qualitative Inferential Reasoning Chains" (2017). Electronic Theses and Dissertations. 2662.
http://digitalcommons.library.umaine.edu/etd/2662