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.Comment: 5 pages, 1 figure, to be published in The Physics Teache

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.Comment: 23 pages, 4 figures, 3 tables, 28 references, 7 notes. Accepted for publication in the International Journal of Science Educatio

The Case for Dynamic Models of Learners' Ontologies in Physics

In a series of well-known papers, Chi and Slotta (Chi, 1992; Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Slotta, Chi & Joram, 1995; Chi, 2005; Slotta & Chi, 2006) have contended that a reason for students' difficulties in learning physics is that they think about concepts as things rather than as processes, and that there is a significant barrier between these two ontological categories. We contest this view, arguing that expert and novice reasoning often and productively traverses ontological categories. We cite examples from everyday, classroom, and professional contexts to illustrate this. We agree with Chi and Slotta that instruction should attend to learners' ontologies; but we find these ontologies are better understood as dynamic and context-dependent, rather than as static constraints. To promote one ontological description in physics instruction, as suggested by Slotta and Chi, could undermine novices' access to productive cognitive resources they bring to their studies and inhibit their transition to the dynamic ontological flexibility required of experts.Comment: The Journal of the Learning Sciences (In Press

Students’ analogical reasoning in novel situations: theory-like misconceptions or p-prims?

Over the past 50 years there has been much research in the area of students' misconceptions. Whilst this research has been useful in helping to inform the design of instructional approaches and curriculum development it has not provided much insight into how students reason when presented with a novel situation and, in particular, the knowledge they draw upon in an attempt to make predictions about that novel situation. This article reports on a study of Greek students, aged from 10 to 17 years old, who were asked to make predictions in novel situations and to then provide, without being told whether their predictions were correct or incorrect, explanations about their predictions. Indeed, their explanations in such novel situations have the potential to reveal how their ideas, as articulated as predictions, are formed as well as the sources they draw upon to make those predictions. We also consider in this article the extent to which student ideas can be seen either as theory-like misconceptions or, alternatively, as situated acts of construction involving the activation of fragmented pieces of knowledge referred to as phenomenological primitives (p-prims). Our findings suggest that in most cases students' reasoning in novel situations can be better understood in terms of their use of p-prims and that teaching might be made more effective if teachers were more aware of the p-prims that students were likely to be using when presented with new situations in physics

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.Comment: 27 pages, 14 figures, no tables. Submitted for publication to the Physical Review Special Topics Physics Education Research on March 8, 200

Development of quantum perspectives in modern physics

Introductory undergraduate courses in classical physics stress a perspective that can be characterized as realist; from this perspective, all physical properties of a classical system can be simultaneously specified and thus determined at all future times. Such a perspective can be problematic for introductory quantum physics students, who must develop new perspectives in order to properly interpret what it means to have knowledge of quantum systems. We document this evolution in student thinking in part through pre- and post-instruction evaluations using the Colorado Learning Attitudes about Science Survey. We further characterize variations in student epistemic and ontological commitments by examining responses to two essay questions, coupled with responses to supplemental quantum attitude statements. We find that, after instruction in modern physics, many students are still exhibiting a realist perspective in contexts where a quantum-mechanical perspective is needed. We further find that this effect can be significantly influenced by instruction, where we observe variations for courses with differing learning goals. We also note that students generally do not employ either a realist or a quantum perspective in a consistent manner.Comment: 18 pages, plus references; 3 figures; 9 tables. PACS: 01.40.Fk, 03.65._

Quantized gravitational waves in the Milne universe

The quantization of gravitational waves in the Milne universe is discussed. The relation between positive frequency functions of the gravitational waves in the Milne universe and those in the Minkowski universe is clarified. Implications to the one-bubble open inflation scenario are also discussed.Comment: 26 pages, 1 figure, revtex. submitted to Phys. Rev. D1

Learning physics in context: a study of student learning about electricity and magnetism

This paper re-centres the discussion of student learning in physics to focus on context. In order to do so, a theoretically-motivated understanding of context is developed. Given a well-defined notion of context, data from a novel university class in electricity and magnetism are analyzed to demonstrate the central and inextricable role of context in student learning. This work sits within a broader effort to create and analyze environments which support student learning in the sciencesComment: 36 pages, 4 Figure