Michael C. Wittmann

Understanding and affecting student reasoning about sound waves

Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in our university physics classes often used sets of resources that were different from the ones we wish them to use. By designing curriculum materials that ask students to think about the physics from a different view, we bring about improvement in student understanding of sound waves. Our curriculum modifications are specific to our own classes, but our description of student learning is more generally useful for teachers. We describe how students can use multiple sets of resources in their thinking, and raise questions that should be considered by both instructors and researchers.

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.

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 Newtons Third Law.

Epistemic Games in Integration: Modeling Resource Choice

As part of an ongoing project to understand how mathematics is used in advanced physics to guide ones conceptual understanding of physics, we focus on students interpretation and use of boundary and initial conditions when solving integrals. We discuss an interaction between two students working on a group quiz problem. After describing the interaction, we briefly discuss the procedural resources that we use to model the students solutions. We then use the procedural resources introduced earlier to draw resources graphs describing the two epistemic game facets used by the students in our transcript.

Student Understanding of Tunneling in Quantum Mechanics: Examining Interview and Survey Results for Clues to Student Reasoning

Members of the University of Maine Physics Education Research Laboratory are studying student understanding of the phenomenon of quantum tunneling through a potential barrier, a standard topic in most introductory quantum physics courses. When a series of interviews revealed that many students believe energy is lost in the tunneling process, a survey was designed to investigate the prevalence of the energy‐loss idea. This survey was administered to populations of physics majors at the sophomore and senior levels. Data indicate that interview results are shared by a somewhat larger population of students and give insight into additional models of reasoning (e.g. analogies to macroscopic tunnels) not found in the interviews.

Resource Plasticity: Detailing a Common Chain of Reasoning with Damped Harmonic Motion

As part of ongoing research into cognitive processes and student thought, we have investigated the interplay between mathematics and physics resources in intermediate mechanics students. We present evidence from a reformed sophomore‐level mechanics class which contains both tutorial and lecture components. In the context of writing Newton’s Second Law for damped harmonic motion, students discuss the signs of the spring and damping forces. Using a grounded theory approach, we identify a common chain of reasoning in which a request for reasoning is followed by elaborative sense‐making and checks for consistency, finishing with an optional appeal for group consensus. Our analysis provides evidence for a description of student thinking in terms of Plasticity, an extension of Resource Theory.

Procedural Resource Creation in Intermediate Mechanics

A problem in resource theory is describing the creation of new, high‐level resources. We model resource creation by analyzing four student groups separating variables during a group quiz on air resistance. We assess each group’s fluency and two observables: use of overt (such as divide, subtract, equals) and covert (such as moving, bringing, or pulling over) mathematical language and use of accompanying gestures (such as circling, grabbing, or sliding). For each group, the type of language and gesture used corresponds to how easily they carry out separation of variables. We create resource graphs for each group to organize our observations and use these graphs to model the creation of the procedural resource Separate Variables.

Resource Selection in Nearly‐Novel Situations

We developed an iterative survey to study the process of resource selection in a specific nearly‐novel situation — the design of vacuum tube diodes. Preliminary data from upper‐level undergraduate physics majors suggest that the ability to identify diode function in simple circuits predicts the ability to construct diodes.

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

We describe a course designed to help future educators develop an integrated understanding of 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 physics study through proven curricula and discussion of research results in the context of the PER literature. We provide examples of the course content and structure and representative examples of student learning in the class.

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 gamblers 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 curriculums success.