17 research outputs found
Teaching the Process of Science: Faculty Perceptions and an Effective Methodology
Most scientific endeavors require science process skills such as data interpretation, problem solving, experimental design, scientific writing, oral communication, collaborative work, and critical analysis of primary literature. These are the fundamental skills upon which the conceptual framework of scientific expertise is built. Unfortunately, most college science departments lack a formalized curriculum for teaching undergraduates science process skills. However, evidence strongly suggests that explicitly teaching undergraduates skills early in their education may enhance their understanding of science content. Our research reveals that faculty overwhelming support teaching undergraduates science process skills but typically do not spend enough time teaching skills due to the perceived need to cover content. To encourage faculty to address this issue, we provide our pedagogical philosophies, methods, and materials for teaching science process skills to freshman pursuing life science majors. We build upon previous work, showing student learning gains in both reading primary literature and scientific writing, and share student perspectives about a course where teaching the process of science, not content, was the focus. We recommend a wider implementation of courses that teach undergraduates science process skills early in their studies with the goals of improving student success and retention in the sciences and enhancing general science literacy
A convergence result for discreet steepest decent in weighted sobolev spaces
A convergence result is given for discrete descent based on Sobolev gradients arising from differential equations which may be expressed as quadratic forms. The argument is an extension of the result of David G. Luenberger on Euclidean descent and compliments the work of John W. Neuberger on Sobolev descent
Seeing the Potential in Students\u27 Questions
Rich mathematical questions emerge from online dialogues between high school algebra students and prospective teachers
Inverse limits of upper semi-continuous set valued functions
Abstract. In this article we define the inverse limit of an inverse sequence (X1, f1), (X2, f2), (X3, f3),... where each Xi is a compact Hausdorff space and each fi is an upper semi-continuous function from Xi+1 into 2 X i. Conditions are given under which the inverse limit is a Hausdorff continuum and examples are given to illustrate the nature of these inverse limits. 1