The Gaussian Radon Transform in Classical Wiener Space

We study the Gaussian Radon transform in the classical Wiener space of Brownian motion. We determine explicit formulas for transforms of Brownian functionals specified by stochastic integrals. A Fock space decomposition is also established for Gaussian measure conditioned to closed affine subspaces in Hilbert spaces

A Gaussian Radon Transform for Banach Spaces

We develop a Radon transform on Banach spaces using Gaussian measure and prove that if a bounded continuous function on a separable Banach space has zero Gaussian integral over all hyperplanes outside a closed bounded convex set in the Hilbert space corresponding to the Gaussian measure then the function is zero outside this set

Examining and contrasting the cognitive activities engaged in undergraduate research experiences and lab courses

While the positive outcomes of undergraduate research experiences (UREs) have been extensively categorized, the mechanisms for those outcomes are less understood. Through lightly structured focus group interviews, we have extracted the cognitive tasks that students identify as engaging in during their UREs. We also use their many comparative statements about their coursework, especially lab courses, to evaluate their experimental physics-related cognitive tasks in those environments. We find there are a number of cognitive tasks consistently encountered in physics UREs that are present in most experimental research. These are seldom encountered in lab or lecture courses, with some notable exceptions. Having time to reflect and fix or revise, and having a sense of autonomy, were both repeatedly cited as key enablers of the benefits of UREs. We also identify tasks encountered in actual experimental research that are not encountered in UREs. We use these findings to identify opportunities for better integration of the cognitive tasks in UREs and lab courses, as well as discussing the barriers that exist. This work responds to extensive calls for science education to better develop students' scientific skills and practices, as well as calls to expose more students to scientific research.Comment: 11 pages, 3 figure

Quantifying critical thinking: Development and validation of the Physics Lab Inventory of Critical thinking (PLIC)

Introductory physics lab instruction is undergoing a transformation, with increasing emphasis on developing experimentation and critical thinking skills. These changes present a need for standardized assessment instruments to determine the degree to which students develop these skills through instructional labs. In this article, we present the development and validation of the Physics Lab Inventory of Critical thinking (PLIC). We define critical thinking as the ability to use data and evidence to decide what to trust and what to do. The PLIC is a 10-question, closed-response assessment that probes student critical thinking skills in the context of physics experimentation. Using interviews and data from 5584 students at 29 institutions, we demonstrate, through qualitative and quantitative means, the validity and reliability of the instrument at measuring student critical thinking skills. This establishes a valuable new assessment instrument for instructional labs.Comment: 16 pages, 4 figure

Toolboxes and handing students a hammer: The effects of cueing and instruction on getting students to think critically

Developing critical thinking skills is a common goal of an undergraduate physics curriculum. How do students make sense of evidence and what do they do with it? In this study, we evaluated students' critical thinking behaviors through their written notebooks in an introductory physics laboratory course. We compared student behaviors in the Structured Quantitative Inquiry Labs (SQILabs) curriculum to a control group and evaluated the fragility of these behaviors through procedural cueing. We found that the SQILabs were generally effective at improving the quality of students' reasoning about data and making decisions from data. These improvements in reasoning and sensemaking were thwarted, however, by a procedural cue. We describe these changes in behavior through the lens of epistemological frames and task orientation, invoked by the instructional moves