Education Commons^™

Designing Research-Based Instructional Materials That Leverage Dual-Process Theories Of Reasoning: Insights From Testing One Specific, Theory-Driven Intervention, Mila Kryjevskaia, Mackenzie R. Stetzer, Beth A. Lindsey, Alistair Mcinerny, Paula R. L. Heron, Andrew Boudreaux

Physics & Astronomy

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] Research in physics education has contributed substantively to improvements in the learning and teaching of university physics by informing the development of research-based instructional materials for physics courses. Reports on the design of these materials have tended to focus on overall improvements in student performance, while the role of theory in informing the development, refinement, and assessment of the materials is often not clearly articulated. In this article, we illustrate how dual-process theories of reasoning and decision making have guided the ongoing development, testing, and analysis …

Toward A Framework For The Natures Of Proportional Reasoning In Introductory Physics, Andrew Boudreaux, Stephen E. Kanim, Alexis Olsho, Suzanne W. Brahmia, Charlotte Zimmerman, Trevor I. Smith

Physics & Astronomy

We present a set of modes of reasoning about ratio and proportion as a means of operationalizing expert practice in physics. These modes, or natures of proportional reasoning, stem from consideration of how physicists reason in context and are informed by prior work in physics and mathematics education. We frame the natures as the core of an emerging framework for proportional reasoning in introductory physics, that will categorize the uses of proportional reasoning in introductory physics contexts, and provide guidance for the development of reliable assessments. We share results from preliminary assessment items indicating that university physics students have difficulty …

Framework For The Natures Of Negativity In Introductory Physics, Suzanne W. Brahmia, Alexis Olsho, Trevor I. Smith, Andrew Boudreaux

Physics & Astronomy

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 …

Nimbleknow User Documentation, Camille Estee Ottaway

WWU Honors College Senior Projects

NimbleKnow User Documentation is an Honors Project by Camille Ottaway

NimbleKnow is a simple web application that teachers can use to pose questions which students can then answer using their basic smartphones or tablets. In order to accommodate ESL learners our application includes translation features. Having a user-friendly classroom technology can promote more engagement and collaboration between students and faculty alike in a classroom environment.

Conformal Geometry Of Polygons, Michael Albert

WWU Honors College Senior Projects

Conformal maps are functions from subsets of the complex plane to the complex plane that locally preserve angles. Our goal is to understand conformal maps that pass to and from polygonal domains. In order to do so, we derive some of the basic theory of harmonic functions on simply connected domains. In particular, our goal with the first few sections is to prove the Schwarz Reflection principle. Using this, as well as other tools from complex analysis, we give an in-depth explanation of Tao’s proof of the Schwarz-Christoffel formula. This is a differential equation that allows one to compute a …