Searcharxiv⌕ Search

arXiv subjects

Michael C. Wittmann

Publications and source records attributed to Michael C. Wittmann.

At least 19 recordsLinked to original sources
arXiv2018

Research in the Resources Framework: Changing environments, consistent exploration

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.

physics.ed-ph↗
arXiv2013

Probing Student Understanding With Alternative Questioning Strategies

Common research tasks ask students to identify a correct answer and justify their answer choice. We propose expanding the array of research tasks to access different knowledge that students might have. By asking students to discuss answers they may not have chosen naturally, we can investigate students' abilities to explain something that is already established or to disprove an incorrect response. The results of these research tasks also provide us with information about how students' responses vary across the different tasks. We discuss three underused question types, their possible benefits and some preliminary results from an electric circuits pretest utilizing these new question types. We find that the answer students most commonly choose as correct is the same choice most commonly eliminated as incorrect. Also, students given the correct answer can provide valuable reasoning to explain it, but they do not spontaneously identify it as the correct answer.

physics.ed-ph↗
arXiv2010

Students' Responses To Different Representations Of A Vector Addition Question

We investigate if the visual representation of vectors can affect which methods students use to add them. We gave students one of four questions with different graphical representations, asking students to add the same two vectors. For students in an algebra-based class the arrangement of the vectors had a statistically significant effect on the vector addition method chosen while the addition or removal of a grid did not.

physics.ed-ph↗
arXiv2010

Using conceptual blending to describe emergent meaning in wave propagation

Students in interviews on a wave physics topic give answers through embodied actions which connect their understanding of the physics to other common experiences. When answering a question about wavepulses propagating along a long taut spring, students' gestures help them recruit information about balls thrown the air. I analyze gestural, perceptual, and verbal information gathered using videotaped interviews and classroom interactions. I use conceptual blending to describe how different elements combine to create new, emergent meaning for the students and compare this to a knowledge-in-pieces approach.

physics.ed-ph↗
arXiv2009

Understanding the use of two integration methods on separable first order differential equations

We present evidence from three student interactions in which two types of common solution methods for solving simple first-order differential equations are used. We describe these using the language of resources, considering epistemic games as particular pathways of solutions along resource graphs containing linked procedural and conceptual resources. Using transcript data, we define several procedural resources, show how they can be organized into two facets of a previously described epistemic game, and produce a resource graph that allows visualization of this portion of the epistemic games. By representing two correct mathematical procedures in terms of shared resources, we help clarify the types of thinking in which students engage when learning to apply mathematical reasoning to physics and illustrate how a "failure to connect" two ideas often hinders students' successful problem solving.

physics.ed-ph↗
arXiv2009

The role of sign in students' modeling of scalar equations

We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students in a sophomore level mechanics class at some point wrote Newton's Second Law as F = -ma; they were using this form to ensure that the sign of the force pointed in a direction consistent with the chosen coordinate system while assuming that some variables have only positive value. We use one student's detailed explanation to suggest that students' issues with variables are context-dependent, and that much of their reasoning is useful for productive instruction.

physics.ed-ph↗
arXiv2008

Visualizing changes in student responses using consistency plots

Traditional methods of reporting changes in student responses have focused on class-wide averages. Such models hide information about the switches in responses by individual students over the course of a semester. We extend unpublished work by Steven Kanim on "escalator diagrams" which show changes in student responses from correct to incorrect (and vice versa) while representing pre- and post-instruction results on questions. Our extension consists of "consistency plots" in which we represent three forms of data: method of solution and correctness of solution both before and after instruction. Our data are from an intermediate mechanics class, and come from (nearly) identical midterm and final examination questions.

physics.ed-ph↗
arXiv2008

Applying a resources framework to analysis of the Force and Motion Conceptual Evaluation

We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation (FMCE). Our goal is to move beyond the expert/novice analysis of student learning based on pre-/post-testing and the correctness of responses (either on the overall test or on clusters of questions defined solely by content). We use a resources framework, taking special note of the contextual and representational dependence of questions with seemingly similar physics content. We analyze clusters in ways that allow the most common incorrect answers to give as much, or more, information as the correctness of responses in that cluster. Furthermore, we show that false positives can be found, especially on questions dealing with Newton's Third Law.

physics.ed-ph↗
arXiv2006

Integrated approaches in physics education: A graduate level course in physics, pedagogy, and education research

We describe a course designed to help future educators build an integrated understanding of the different elements of physics education research (PER), including: research into student learning, content knowledge from the perspective of how it is learned, and reform-based curricula together with evidence of their effectiveness. Course elements include equal parts of studying physics through proven curricula and discussion of research results in the context of the PER literature. We provide examples of the course content and structure as well as representative examples of student learning in the class.

physics.ed-ph↗
arXiv2006

Lab-Tutorials for teaching quantum physics (Lab-Tutorials fuer den Quantenphysik Unterricht)

English abstract: In the "Intuitive Quantum Physics" course, we use graphical interpretations of mathematical equations and qualitative reasoning to develop and teach a simplified model of quantum physics. Our course contains three units: Wave physics, Development of a conceptual toolbox, and quantum physics. It also contains three key themes: wave-particle duality, the Schroedinger equation, and tunneling of quantum particles. Students learn most new material in lab-tutorials in which students work in small groups (3 to 3 people) on specially designed worksheets. Lecture reinforces the lab-tutorial content and focuses more on issues about the nature of science. Data show that students are able to learn some of the most difficult concepts in the course, and also that students learn to believe that there is a conceptually accessible structure to the physics in the course. German abstract: Im Kurs "Intuitive Quantum Physics" werden graphische Interpretationen mathematischer Gleichungen und qualitatives Denken durch ein vereinfachtes Modell der Quantenphysik gelehrt. Unser Kurs besteht aus drei wichtigen Abschnitten: Wellenphysik, Aufbau eines Werkzeugkastens ("Toolbox") und Quantenphysik, sowie drei Schluesselthemen: Welle-Teilchen-Dualitaet, die Schroedinger-Gleichung und Tunneln von Quantenteilchen. Wir unterrichten vorwiegend mit Lab-Tutorials, in denen StudentInnen in kleinen Gruppen (3 bis 4 Personen) anwendungsspezifische Arbeitsblaetter durcharbeiten. In den Diskussionen werden auch Auseinandersetzungen ueber das "Bild der Physik", bei uns "Nature of Science" genannt, gefuehrt. Ueberpruefungen haben ergeben, dass StudentInnen nicht nur die schwierigsten Konzepte des Kurses lernen koennen sondern auch lernen, dass die Quantenphysik begrifflich verstaendlich ist.

physics.ed-ph↗
arXiv2006

Using resource graphs to represent conceptual change

We introduce resource graphs, a representation of linked ideas used when reasoning about specific contexts in physics. Our model is consistent with previous descriptions of resources and coordination classes. It can represent mesoscopic scales that are neither knowledge-in-pieces or large-scale concepts. We use resource graphs to describe several forms of conceptual change: incremental, cascade, wholesale, and dual construction. For each, we give evidence from the physics education research literature to show examples of each form of conceptual change. Where possible, we compare our representation to models used by other researchers. Building on our representation, we introduce a new form of conceptual change, differentiation, and suggest several experimental studies that would help understand the differences between reform-based curricula.

physics.ed-ph↗
arXiv2006

Laboratory-Tutorial activities for teaching probability

We report on the development of students' ideas of probability and probability density in a University of Maine laboratory-based general education physics course called Intuitive Quantum Physics. Students in the course are generally math phobic with unfavorable expectations about the nature of physics and their ability to do it. We describe a set of activities used to teach concepts of probability and probability density. Rudimentary knowledge of mechanics is needed for one activity, but otherwise the material requires no additional preparation. Extensions of the activities include relating probability density to potential energy graphs for certain "touchstone" examples. Students have difficulties learning the target concepts, such as comparing the ratio of time in a region to total time in all regions. Instead, they often focus on edge effects, pattern match to previously studied situations, reason about necessary but incomplete macroscopic elements of the system, use the gambler's fallacy, and use expectations about ensemble results rather than expectation values to predict future events. We map the development of their thinking to provide examples of problems rather than evidence of a curriculum's success.

physics.ed-ph↗
arXiv2002

Limitations in predicting student performance on standardized tests

The Maryland Physics Expectations Survey (MPEX) describes student attitudes and expectations toward learning, and might be used to predict normalized gains on tests such as the Force and Motion Concept Evaluation (FMCE). These predictions are incomplete, though, due to limitations of the standardized tests themselves. I illustrate the problems involved in using the MPEX to predict productive attitudes toward learning physics by focusing on two students, both with seemingly appropriate expectations toward learning. While one had high normalized gains, the other did not, due to "false favorable" responses on the MPEX.

physics.ed-ph↗
arXiv2002

Mathematical Tutorials in Introductory Physics

Students in introductory calculus-based physics not only have difficulty understanding the fundamental physical concepts, they often have difficulty relating those concepts to the mathematics they have learned in math courses. This produces a barrier to their robust use of concepts in complex problem solving. As a part of the Activity-Based Physics project, we are carrying out research on these difficulties and are developing instructional materials in the tutorial framework developed at the University of Washington by Lillian C. McDermott and her collaborators. In this paper, we present a discussion of student difficulties and the development of a mathematical tutorial on the subject of pulses moving on strings.

physics.ed-ph↗
arXiv2002

Making Sense of How Students Make Sense of Mechanical Waves

We report on our study of student understanding of the physics of mechanical waves, specifically the propagation and superposition of simple wavepulses traveling on long, taut strings. We introduce the terms "particle pulses mental model" to describe the reasoning approach that students use to guide their thinking in wave propagation and superposition. Student responses on free response and multiple-choice, multiple response questions dealing with the same physics show inconsistent student thinking, where they may have both correct and incorrect ideas about the concepts.

physics.ed-ph↗
arXiv2002

Epistemology mediating conceptual knowledge: Constraints on data accessible from interviews

A student's epistemological stance (be it knowledge as memorized information, knowledge from authority, or knowledge as invented stuff) may constrain that student from reasoning in productive ways while also shaping the inferences a researcher can make about how that student reasons about a particular phenomenon. We discuss both cases in the context of an individual student interview on charge flow in wires. In the first part of the interview, her focus on memorized knowledge prevents the researcher from learning about her detailed reasoning about current. In the second part of the interview, her focus on constructed knowledge provides the researcher with a picture of her reasoning about the physical mechanisms of charge flow.

physics.ed-ph↗
arXiv2002

The Object Coordination Class Applied to Wavepulses: Analysing Student Reasoning in Wave Physics

Detailed investigations of student reasoning show that students approach the topic of wave physics using both event-like and object-like descriptions of wavepulses, but primarily focus on object properties in their reasoning. Student responses to interview and written questions are analysed using diSessa and Sherin's coordination class model which suggests that student use of specific reasoning resources is guided by possibly unconscious cues. Here, the term reasoning resources is used in a general fashion to describe any of the smaller grain size models of reasoning (p-prims, facets of knowledge, intuitive rules, etc) rather than theoretically ambiguous (mis)conceptions. Student applications of reasoning resources, including one previously undocumented, are described. Though the coordination class model is extremely helpful in organising the research data, problematic aspects of the model are also discussed.

physics.ed-ph↗