Leaping without Bridges: Implementing the Common Core with Students Not Previously Instructed Within Its Expectations

Teachers in most states across the nation are now engaged in transitioning their instruction and content focus to the domains of the Common Core State Standards for Mathematics (CCSSM). They are working very hard to make adaptive decisions about their practice and they are serious about understanding the ways in which the CCSSM “are not intended to be new names for old ways of doing business” (CCSSI, 2010, p. 5). As the states transition to the CCSSM many teachers will be working with students whose mathematics instruction took place under a different set of mathematics learning expectations. In our work with our own students and through the CCSSM professional development that we have provided for other teachers in multiple states, we have observed how difficult this transition can be for both teachers and students. The purpose of this article is to share what we have found to be productive ways for teachers to leap into the CCSSM and overcome the fact that many students are missing curricular and instructional bridges that might have otherwise made the transition smoother

Improving Attitude and Problem Solving Through Mathematics Camps

This poster describes the results of preservice teachers’ involvement in providing mathematics camps to children that focus on enjoyment of problem solving through their teaching program at a university in Southeast Asia

Development of a Model for the Small-Particle Orbital Debris Population Based on the STS Impact Record

In preparation for the release of the Orbital Debris Engineering Model (ORDEM) version 3.1, the NASA Orbital Debris Program Office (ODPO) revisited how orbiting debris populations of characteristic sizes smaller than 1 cm were modeled. The primary contributor to the population of sub-centimeter debris particles is the surface deterioration or erosion of spacecraft materials exposed to the outer-space environment. Because small particulates are not directly trackable by remote sensing, the primary means of detection is via historical counts of small impact features on flown radiator and window surfaces of the U.S. Space Transportation System (STS, also known as the Space Shuttle) from 1995-2011. Historic NASA studies of high-velocity impact tests have related impact-feature size to particle mass and velocity for certain STS surfaces, so that a corresponding particle size may be inferred from each small-impact feature observed. Micro-debris populations are then estimated by modeling the path and orientation of an STS mission through a simulated debris environment, and the densities of this simulated environment are rescaled to approximate the number of observed STS impact features. Monte-Carlo methods are further employed to gauge the estimation uncertainty of the rescaled environment. A description of the chosen methodologies for estimating and adjusting the micro-debris population model, and the results, are presented

Statistical Issues for Uncontrolled Reentry Hazards Empirical Tests of the Predicted Footprint for Uncontrolled Satellite Reentry Hazards

A number of statistical tools have been developed over the years for assessing the risk of reentering objects to human populations. These tools make use of the characteristics (e.g., mass, material, shape, size) of debris that are predicted by aerothermal models to survive reentry. The statistical tools use this information to compute the probability that one or more of the surviving debris might hit a person on the ground and cause one or more casualties. The statistical portion of the analysis relies on a number of assumptions about how the debris footprint and the human population are distributed in latitude and longitude, and how to use that information to arrive at realistic risk numbers. Because this information is used in making policy and engineering decisions, it is important that these assumptions be tested using empirical data. This study uses the latest database of known uncontrolled reentry locations measured by the United States Department of Defense. The predicted ground footprint distributions of these objects are based on the theory that their orbits behave basically like simple Kepler orbits. However, there are a number of factors in the final stages of reentry - including the effects of gravitational harmonics, the effects of the Earth s equatorial bulge on the atmosphere, and the rotation of the Earth and atmosphere - that could cause them to diverge from simple Kepler orbit behavior and possibly change the probability of reentering over a given location. In this paper, the measured latitude and longitude distributions of these objects are directly compared with the predicted distributions, providing a fundamental empirical test of the model assumptions

Statistical Issues for Uncontrolled Reentry Hazards

A number of statistical tools have been developed over the years for assessing the risk of reentering objects to human populations. These tools make use of the characteristics (e.g., mass, shape, size) of debris that are predicted by aerothermal models to survive reentry. The statistical tools use this information to compute the probability that one or more of the surviving debris might hit a person on the ground and cause one or more casualties. The statistical portion of the analysis relies on a number of assumptions about how the debris footprint and the human population are distributed in latitude and longitude, and how to use that information to arrive at realistic risk numbers. This inevitably involves assumptions that simplify the problem and make it tractable, but it is often difficult to test the accuracy and applicability of these assumptions. This paper looks at a number of these theoretical assumptions, examining the mathematical basis for the hazard calculations, and outlining the conditions under which the simplifying assumptions hold. In addition, this paper will also outline some new tools for assessing ground hazard risk in useful ways. Also, this study is able to make use of a database of known uncontrolled reentry locations measured by the United States Department of Defense. By using data from objects that were in orbit more than 30 days before reentry, sufficient time is allowed for the orbital parameters to be randomized in the way the models are designed to compute. The predicted ground footprint distributions of these objects are based on the theory that their orbits behave basically like simple Kepler orbits. However, there are a number of factors - including the effects of gravitational harmonics, the effects of the Earth's equatorial bulge on the atmosphere, and the rotation of the Earth and atmosphere - that could cause them to diverge from simple Kepler orbit behavior and change the ground footprints. The measured latitude and longitude distributions of these objects provide data that can be directly compared with the predicted distributions, providing a fundamental empirical test of the model assumptions

An Overview of NASA's Oribital Debris Environment Model

Using updated measurement data, analysis tools, and modeling techniques; the NASA Orbital Debris Program Office has created a new Orbital Debris Environment Model. This model extends the coverage of orbital debris flux throughout the Earth orbit environment, and includes information on the mass density of the debris as well as the uncertainties in the model environment. This paper will give an overview of this model and its implications for spacecraft risk analysis

THE USE OF PERCUSSION IN THERAPY: A REALIST SYNTHESIS

Background: Percussion use is common in both music therapy clinical practice and in publications. However, no comprehensive review regarding the use of percussion instruments in music interventions appears to exist. The investigator examined the various literature review types available in order to address the complex and contextual nature of percussion-related interventions. The purpose of this study was to conduct a realist synthesis-type systematic review of the literature regarding the use of percussion in therapy in order to answer the following research questions. Research Questions: 1. When using published tools designed to evaluate quality of research, what was the outcome of this appraisal process when reviewing identified studies? 2. What are the context-mechanism-outcome configurations within percussion-related interventions as found through the systematic review process? Methods: Literature review types were examined in order to locate a systematic review type that best fit the research questions. The investigator used a prior database from Matney (in press), and employed inclusion/exclusion criteria to locate studies with reduced bias and increased study rigor. Eligible studies were examined using methodological evaluation tools, which were corroborated through inter-rater reliability. The investigator created evidence tables that included context-mechanism-outcome configurations (CMOC’s). These configurations were examined for larger patterns that may inform theory development. The investigator linked chains of evidence in accordance with the realist synthesis methodology, and offered CMOC propositions. Results: Results revealed that 30.91% of studies prior to eligibility screening did not report internal review board or consent procedures. Regarding experimental studies evaluated after screening, 34.79% did not report the type of randomization procedure used, and 43.48% were unclear regarding concealment of allocation. Reporting within qualitative and mixed-methods studies also lacked transparent reporting. The investigator presented CMOC’s for each individual study, and proposed evidence linkage that may promote theory development regarding percussion interventions. Conclusions: The percussion-related intervention literature that was evaluated demonstrates a lack of study rigor (internal review board and/or consent procedures, intention to treat principle), a lack of transparent and detailed reporting (randomization details, allocation concealment, treatment consistency amongst groups), as well as a lack of replication and transferability. While context-mechanism-outcome configurations can only provide tentative theory development due to the paucity of connections available, the literature suggests that particular mechanisms may promote effective outcomes in particular situations. The investigator provides implications for future research, clinical practice, and pedagogy

Determination of CTV-to-ITV margin for free-breathing respiratory-gated treatments using 4DCT and the Novalis ExacTrac Gating System with implanted fiducials

The purpose of this project was to investigate the interplay between gating window characteristics and target margin required to compensate for residual motion during the gating window. This project investigated the accuracy of ExacTrac and 4DCT imaging localizing an implanted coil at various phases of respiration. Radiochromic film measured delivered dose patterns for selected gating intervals over a variety of respiratory patterns. In order to establish accurate dosimetry, this project implemented and tested an EBT radiochromic film dosimetry system. Film testing showed that the performance of a medical grade Vidar Dosimetry Pro radiographic film scanner and an Epson V700 Photo flatbed scanner were very similar. Both scanners showed nearly the same performance in terms of measurement repeatability, noise, vertical and horizontal uniformity over a range of doses from 11.5-511.9 cGy. The Vidar was selected for these studies due to clinical availability. Even at the greatest coil velocities observed, ExacTrac coil localization agreed with calculated coil motion to within 0.8 mm. 4DCT showed errors up to 5.5 mm resolving coil position during large respiratory-induced velocities. 4DCT accurately measured the coil length within 1 mm of actual coil length at end expiration/inhalation. 4DCT can provide an accurate representation of the phantom at end-respiration for treatment planning purposes, and ExacTrac can accurately localize the coil to determine target motion in all phases For patient treatments it is suggested that target margins should be set using the residual motion during gating. For patients without implanted coils, the residual motion can be computed based on the target motion measured from 4DCT and the size of the gating window. For patients with implanted coils, the ExacTrac system can be used to directly measure residual tumor motion during gating. The hypothesis of this work was that gated delivery combined with 4DCT could limit internal margins to less than 3 mm while maintaining 95% prescription dose coverage of moving targets. The hypothesis was found to be true for gating windows of 10% and 20% for target motions up to 25 mm and was true with gating windows up to 50% for smaller motions (5 & 10 mm)