Informal Geometry in the Preparation of Teachers: A New Mathematics Course at the University of Virginia

Students require a rich variety of hands-on geometric experiences before they progress to more formal traditional geometric instruction. This fact has often been ignored in the mathematics preparation of today’s teachers. At the University of Virginia a new general education geometry course, The Shape of Space, is being developed that focuses on obtaining deep understandings of elementary geometry through physical and visual activities

A Mathematician\u27s Overview of the Virginia Elementary Mathematics Specialist Program

This article discusses the mathematics component of the Mathematics Specialist master\u27s degree program in the Virginia Mathematics Specialist Project (VMSP). It includes my personal views on the significant mathematical knowledge and skills that Mathematics Specialists need, the mathematics that is taught in the Mathematics Specialist courses, and my thoughts on what appear to be the substantial mathematical abilities and aptitudes that are required by successful Mathematics Specialists in their work. The interpretations I present are highly personal and are undoubtedly dependent on my personal history, a short description of which is given (see Appendix A)

The Resistive-Plate WELL with Argon mixtures - a robust gaseous radiation detector

A thin single-element THGEM-based, Resistive-Plate WELL (RPWELL) detector was operated with 150 GeV/c muon and pion beams in Ne/(5%CH$_4$), Ar/(5%CH$_4$) and Ar/(7%CO$_2$); signals were recorded with 1 cm$^2$ square pads and SRS/APV25 electronics. Detection efficiency values greater than 98% were reached in all the gas mixtures, at average pad multiplicity of 1.2. The use of the 10$^9${\Omega}cm resistive plate resulted in a completely discharge-free operation also in intense pion beams. The efficiency remained essentially constant at 98-99% up to fluxes of $\sim$10$^4$Hz/cm$^2$, dropping by a few % when approaching 10$^5$ Hz/cm$^2$. These results pave the way towards cost-effective, robust, efficient, large-scale detectors for a variety of applications in future particle, astro-particle and applied fields. A potential target application is digital hadron calorimetry.Comment: presented at the 2016 VIenna Conf. On instrumentation. Submitted to the Conference proceeding

Observation of enhanced rate coefficients in the H2+_2^+ + H2_2 →\rightarrow H3+_3^+ + H reaction at low collision energies

The energy dependence of the rate coefficient of the H$_2^+\ + {\rm H}_2 \rightarrow {\rm H}_3^+ + {\rm H}$ reaction has been measured in the range of collision energies between $k_\mathrm{B}\cdot 10$ K and $k_\mathrm{B}\cdot 300$ mK. A clear deviation of the rate coefficient from the value expected on the basis of the classical Langevin-capture behavior has been observed at collision energies below $k_\mathrm{B}\cdot 1$ K, which is attributed to the joint effects of the ion-quadrupole and Coriolis interactions in collisions involving ortho-H$_2$ molecules in the $j = 1$ rotational level, which make up 75% of the population of the neutral H$_2$ molecules in the experiments. The experimental results are compared to very recent predictions by Dashevskaya, Litvin, Nikitin and Troe (J. Chem. Phys., in press), with which they are in agreement.Comment: 14 pages, 3 figure

First in-beam studies of a Resistive-Plate WELL gaseous multiplier

We present the results of the first in-beam studies of a medium size (10$\times$10 cm$^2$) Resistive-Plate WELL (RPWELL): a single-sided THGEM coupled to a pad anode through a resistive layer of high bulk resistivity ($\sim$10$^9 \Omega$cm). The 6.2~mm thick (excluding readout electronics) single-stage detector was studied with 150~GeV muons and pions. Signals were recorded from 1$\times$1 cm$^2$ square copper pads with APV25-SRS readout electronics. The single-element detector was operated in Ne\(5% $\mathrm{CH_{4}}$) at a gas gain of a few times 10$^4$, reaching 99$\%$ detection efficiency at average pad multiplicity of $\sim$1.2. Operation at particle fluxes up to $\sim$10$^4$ Hz/cm$^2$ resulted in $\sim$23$\%$ gain drop leading to $\sim$5$\%$ efficiency loss. The striking feature was the discharge-free operation, also in intense pion beams. These results pave the way towards robust, efficient large-scale detectors for applications requiring economic solutions at moderate spatial and energy resolutions.Comment: Accepted by JINS