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

Reinventing College Physics for Biologists: Explicating an epistemological curriculum

The University of Maryland Physics Education Research Group (UMd-PERG) carried out a five-year research project to rethink, observe, and reform introductory algebra-based (college) physics. This class is one of the Maryland Physics Department's large service courses, serving primarily life-science majors. After consultation with biologists, we re-focused the class on helping the students learn to think scientifically -- to build coherence, think in terms of mechanism, and to follow the implications of assumptions. We designed the course to tap into students' productive conceptual and epistemological resources, based on a theoretical framework from research on learning. The reformed class retains its traditional structure in terms of time and instructional personnel, but we modified existing best-practices curricular materials, including Peer Instruction, Interactive Lecture Demonstrations, and Tutorials. We provided class-controlled spaces for student collaboration, which allowed us to observe and record students learning directly. We also scanned all written homework and examinations, and we administered pre-post conceptual and epistemological surveys. The reformed class enhanced the strong gains on pre-post conceptual tests produced by the best-practices materials while obtaining unprecedented pre-post gains on epistemological surveys instead of the traditional losses.Comment: 35 pages including a 15 page appendix of supplementary material

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

Protocols for calibrating multibeam sonar

Development of protocols for calibrating multibeam sonar by means of the standard-target method is documented. Particular systems used in the development work included three that provide the water-column signals, namely the SIMRAD SM2000/90- and 200-kHz sonars and RESON SeaBat 8101 sonar, with operating frequency of 240 kHz. Two facilities were instrumented specifically for the work: a sea well at the Woods Hole Oceanographic Institution and a large, indoor freshwater tank at the University of New Hampshire. Methods for measuring the transfer characteristics of each sonar, with transducers attached, are described and illustrated with measurement results. The principal results, however, are the protocols themselves. These are elaborated for positioning the target, choosing the receiver gain function, quantifying the system stability, mapping the directionality in the plane of the receiving array and in the plane normal to the central axis, measuring the directionality of individual beams, and measuring the nearfield response. General preparations for calibrating multibeam sonars and a method for measuring the receiver response electronically are outlined. Advantages of multibeam sonar calibration and outstanding problems, such as that of validation of the performance of multibeam sonars as configured for use, are mentioned

Quantifying Economic Dependency

In this paper we compare several types of economic dependency ratios for a selection of European countries. These dependency ratios take into account not only the demographic structure of the population, but also the differences in age-specific economic behaviour such as labour market activity, income and consumption as well as age-specific public transfers. In selected simulations where we combine patterns of age-specific economic behaviour and transfers with population projections, we show that in all countries population ageing would lead to a pronounced increase in dependency ratios if present age-specific patterns were not to change. Our analysis of cross-country differences in economic dependency demonstrates that these differences are driven by both differences in age-specific economic behaviour and in the age composition of the populations. The choice of which dependency ratio to use in a specific policy context is determined by the nature of the question to be answered. The comparison of our various dependency ratios across countries gives insights into which strategies might be effective in mitigating the expected increase in economic dependency due to demographic change