Mineralogy and geochemistry of the Erongo Granite and interior quartz-tourmaline orbicules and NYF-type miarolitic pegmatites, Namibia

The early Cretaceous anorogenic Erongo Granite of Namibia is known to host abundant boron mineralization in rounded, quartz-tourmaline clusters and in NYF-type miarolitic, pegmatitic cavities. Rock and mineral samples were taken from the bulk granite, tourmaline nests, and miarolitic cavities and analyzed using a variety of modern analytical techniques. Geochemical and mineralogical data suggest substantial input from the metasedimentary rocks of the Damara orogen was important in the genesis of the Erongo Granite magma. The geochemical signature of the Damara orogen is most evident in the tourmaline clusters and miarolitic cavities, where fractional crystallization accumulated volatile and incompatible elements enough to exsolve a second fluid phase and induce drastic textural and mineralogical changes. As a result, the geochemical character of the pegmatitic cavities is far removed from that of classic NYF-type systems, where boron mineralization is usually not observed

Preliminary Investigation of Instructor Effects on Gender Gap in Introductory Physics

Gender differences in student learning in the introductory, calculus-based electricity and magnetism course were assessed by administering the Conceptual Survey of Electricity and Magnetism pre- and postcourse. As expected, male students outgained females in traditionally taught sections as well as sections that incorporated interactive engagement (IE) techniques. In two of the IE course sections, however, the gains of female students were comparable to those of male students. Classroom observations of the course sections involved were made over an extended period. In this paper, we characterize the observed instructor-student interactions using a framework from educational psychology referred to as wise schooling. Results suggest that instructor practices affect differential learning, and that wise schooling techniques may constitute an effective strategy for promoting gender equity in the physics classroom

A framework for the natures of negativity in introductory physics

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects--both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebra contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond

Framework for the natures of negativity in introductory physics

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects—both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebraic contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond

How curriculum developers cognitive theories influence curriculum development

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] When we examined student responses to questions about the direction of the static friction force in various situations, we both had strong ideas about how to write a tutorial to promote deeper understanding. But our ideas were quite different. In this theoretical paper, we present the two contrasting tutorials and show how their differences can be traced to different theoretical orientations toward cognition and learning. We do not claim that one tutorial—or the theoretical framework loosely associated with it—is superior. Instead, we hope to illustrate two claims. One, we show in detail how curriculum designers’ cognitive “theories” (frameworks), even if largely tacit during the act of creation, shape the resulting tutorials. Two, we show how, at least for us, articulating and discussing our respective theoretical orientations and their influence on our tutorial writing enables a rethinking of long-standing tutorial-writing habits. We argue that instructional intuition—shaped by explicit and tacit theoretical assumptions—functions well in guiding the design of curriculum, as our contrasting tutorials illustrate; but more systematic attention to the underlying theoretical assumptions can productively inform refinements

Student Understanding of Control of Variables: Deciding Whether or Not a Variable Influences the Behavior of a System

The ability of adult students to reason on the basis of the control of variables was the subject of an extended investigation. This paper describes the part of the study that focused on the reasoning required to decide whether or not a given variable influences the behavior of a system. The participants were undergraduates taking introductory Physics and K-8 teachers studying physics and physical science in inservice institutes and workshops. Although most of the students recognized the need to control variables, many had significant difficulty with the underlying reasoning. The results indicate serious shortcomings in the preparation of future scientists and in the education of a scientifically literate citizenry. There are also strong implications for the professional development of teachers, many of whom are expected to teach control of variables to young students