Grade 4-6 student conceptions and utilization of informal and formal variable representations across mathematically equivalent tasks

Title from PDF of title page (University of Missouri--Columbia, viewed on October 22, 2012).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Dissertation advisor: Dr. John LanninIncludes bibliographical references.Vita.Ph. D. University of Missouri--Columbia 2011.Dissertations, Academic -- University of Missouri--Columbia -- Curriculum and instruction."May 13, 2011"This study reports how 24 grade 4-6 students in one elementary and middle school interpreted formal (e.g., x + y = 12) and informal representations of variables (e.g., □ + ∆ = 12). While interpretations for variables represented as letters (e.g., x and y) have been well established for students in algebra classes and beyond, little research into elementary school students' initial interpretations of variables exists. The students were consistent in their meaning of various representations of variables presented in equations, but did not parallel normative algebraic solutions. For example, students treated the representation of the variables as different variables and consistently produced multiple solutions for each variable (e.g., y + y = 12; a + b = 12; and □ + ∆ = 12). Further, the common misconception that different variables can only take on different values was not a typical response for these students (Fujii, 2003). When these same tasks were presented as word problems, students treated variables in an algebraically normative way. In other words, the students were more “successful” solving the word problems (Koedinger & Nathan, 2004). Students attended to the syntactic and semantic structure of the word problems to determine meanings for the variables that were not evident in the equations

Biological & Chemical Oceanography Data Management Office : a domain-specific repository for oceanographic data from around the world [poster]

Presented at AGU Ocean Sciences, 11 - 16 February 2018, Portland, ORThe Biological and Chemical Oceanography Data Management Office (BCO-DMO) is a domain-specific digital data repository that works with investigators funded under the National Science Foundation’s Division of Ocean Sciences and Office of Polar Programs to manage their data free of charge. Data managers work closely with investigators to satisfy their data sharing requirements and to develop comprehensive Data Management Plans, as well as to ensure that their data will be well described with extensive metadata creation. Additionally, BCO-DMO offers tools to find and reuse these high-quality data and metadata packages, and services such as DOI generation for publication and attribution. These resources are free for all to discover, access, and utilize. As a repository embedded in our research community, BCO-DMO is well positioned to offer knowledge and expertise from both domain trained data managers and the scientific community at large. BCO-DMO is currently home to more than 9000 datasets and 900 projects, all of which are or will be submitted for archive at the National Centers for Environmental Information (NCEI). Our data holdings continue to grow, and encompass a wide range of oceanographic research areas, including biological, chemical, physical, and ecological. These data represent cruises and experiments from around the world, and are managed using community best practices, standards, and technologies to ensure accuracy and promote re-use. BCO-DMO is a repository and tool for investigators, offering both ocean science data and resources for data dissemination and publication.NSF #143557

The Atacama Cosmology Telescope: Dusty Star-Forming Galaxies and Active Galactic Nuclei in the Southern Survey

We present a catalog of 191 extragalactic sources detected by the Atacama Cosmology Telescope (ACT) at 148 GHz and/or 218 GHz in the 2008 Southern survey. Flux densities span 14-1700 mJy, and we use source spectral indices derived using ACT-only data to divide our sources into two sub-populations: 167 radio galaxies powered by central active galactic nuclei (AGN), and 24 dusty star-forming galaxies (DSFGs). We cross-identify 97% of our sources (166 of the AGN and 19 of the DSFGs) with those in currently available catalogs. When combined with flux densities from the Australian Telescope 20 GHz survey and follow-up observations with the Australia Telescope Compact Array, the synchrotron-dominated population is seen to exhibit a steepening of the slope of the spectral energy distribution from 20 to 148 GHz, with the trend continuing to 218 GHz. The ACT dust-dominated source population has a median spectral index of 3.7+0.62-0.86, and includes both local galaxies and sources with redshifts as great as 5.6. Dusty sources with no counterpart in existing catalogs likely belong to a recently discovered subpopulation of DSFGs lensed by foreground galaxies or galaxy groups.Comment: 13 pages, 8 figures, 4 table

The Atacama Cosmology Telescope: A Measurement of the Thermal Sunyaev-Zel'dovich Effect Using the Skewness of the CMB Temperature Distribution

We present a detection of the unnormalized skewness induced by the thermal Sunyaev-Zel'dovich (tSZ) effect in filtered Atacama Cosmology Telescope (ACT) 148 GHz cosmic microwave background temperature maps. Contamination due to infrared and radio sources is minimized by template subtraction of resolved sources and by constructing a mask using outlying values in the 218 GHz (tSZ-null) ACT maps. We measure = -31 +- 6 \mu K^3 (measurement error only) or +- 14 \mu K^3 (including cosmic variance error) in the filtered ACT data, a 5-sigma detection. We show that the skewness is a sensitive probe of sigma_8, and use analytic calculations and tSZ simulations to obtain cosmological constraints from this measurement. From this signal alone we infer a value of sigma_8= 0.79 +0.03 -0.03 (68 % C.L.) +0.06 -0.06 (95 % C.L.). Our results demonstrate that measurements of non-Gaussianity can be a useful method for characterizing the tSZ effect and extracting the underlying cosmological information.Comment: 9 pages, 5 figures. Replaced with version accepted by Phys. Rev. D, with improvements to the likelihood function and the IR source treatment; only minor changes in the result

The Atacama Cosmology Telescope: Temperature and Gravitational Lensing Power Spectrum Measurements from Three Seasons of Data

We present the temperature power spectra of the cosmic microwave background (CMB) derived from the three seasons of data from the Atacama Cosmology Telescope (ACT) at 148 GHz and 218 GHz, as well as the cross-frequency spectrum between the two channels. We detect and correct for contamination due to the Galactic cirrus in our equatorial maps. We present the results of a number of tests for possible systematic error and conclude that any effects are not significant compared to the statistical errors we quote. Where they overlap, we cross-correlate the ACT and the South Pole Telescope (SPT) maps and show they are consistent. The measurements of higher-order peaks in the CMB power spectrum provide an additional test of the Lambda CDM cosmological model, and help constrain extensions beyond the standard model. The small angular scale power spectrum also provides constraining power on the Sunyaev-Zel'dovich effects and extragalactic foregrounds. We also present a measurement of the CMB gravitational lensing convergence power spectrum at 4.6-sigma detection significance.Comment: 21 pages; 20 figures, Submitted to JCAP, some typos correcte

The Atacama Cosmology Telescope: Sunyaev-Zel'dovich Selected Galaxy Clusters at 148 GHz from Three Seasons of Data

[Abridged] We present a catalog of 68 galaxy clusters, of which 19 are new discoveries, detected via the Sunyaev-Zel'dovich effect (SZ) at 148 GHz in the Atacama Cosmology Telescope (ACT) survey of 504 square degrees on the celestial equator. A subsample of 48 clusters within the 270 square degree region overlapping SDSS Stripe 82 is estimated to be 90% complete for M_500c > 4.5e14 Msun and 0.15 < z < 0.8. While matched filters are used to detect the clusters, the sample is studied further through a "Profile Based Amplitude Analysis" using a single filter at a fixed \theta_500 = 5.9' angular scale. This new approach takes advantage of the "Universal Pressure Profile" (UPP) to fix the relationship between the cluster characteristic size (R_500) and the integrated Compton parameter (Y_500). The UPP scalings are found to be nearly identical to an adiabatic model, while a model incorporating non-thermal pressure better matches dynamical mass measurements and masses from the South Pole Telescope. A high signal to noise ratio subsample of 15 ACT clusters is used to obtain cosmological constraints. We first confirm that constraints from SZ data are limited by uncertainty in the scaling relation parameters rather than sample size or measurement uncertainty. We next add in seven clusters from the ACT Southern survey, including their dynamical mass measurements based on galaxy velocity dispersions. In combination with WMAP7 these data simultaneously constrain the scaling relation and cosmological parameters, yielding \sigma_8 = 0.829 \pm 0.024 and \Omega_m = 0.292 \pm 0.025. The results include marginalization over a 15% bias in dynamical mass relative to the true halo mass. In an extension to LCDM that incorporates non-zero neutrino mass density, we combine our data with WMAP7+BAO+Hubble constant measurements to constrain \Sigma m_\nu < 0.29 eV (95% C. L.).Comment: 32 pages, 21 figures To appear in J. Cosmology and Astroparticle Physic

The Atacama Cosmology Telescope: Data Characterization and Map Making

We present a description of the data reduction and mapmaking pipeline used for the 2008 observing season of the Atacama Cosmology Telescope (ACT). The data presented here at 148 GHz represent 12% of the 90 TB collected by ACT from 2007 to 2010. In 2008 we observed for 136 days, producing a total of 1423 hours of data (11 TB for the 148 GHz band only), with a daily average of 10.5 hours of observation. From these, 1085 hours were devoted to a 850 deg^2 stripe (11.2 hours by 9.1 deg) centered on a declination of -52.7 deg, while 175 hours were devoted to a 280 deg^2 stripe (4.5 hours by 4.8 deg) centered at the celestial equator. We discuss sources of statistical and systematic noise, calibration, telescope pointing, and data selection. Out of 1260 survey hours and 1024 detectors per array, 816 hours and 593 effective detectors remain after data selection for this frequency band, yielding a 38% survey efficiency. The total sensitivity in 2008, determined from the noise level between 5 Hz and 20 Hz in the time-ordered data stream (TOD), is 32 micro-Kelvin sqrt{s} in CMB units. Atmospheric brightness fluctuations constitute the main contaminant in the data and dominate the detector noise covariance at low frequencies in the TOD. The maps were made by solving the least-squares problem using the Preconditioned Conjugate Gradient method, incorporating the details of the detector and noise correlations. Cross-correlation with WMAP sky maps, as well as analysis from simulations, reveal that our maps are unbiased at multipoles ell > 300. This paper accompanies the public release of the 148 GHz southern stripe maps from 2008. The techniques described here will be applied to future maps and data releases.Comment: 20 pages, 18 figures, 6 tables, an ACT Collaboration pape

The Atacama Cosmology Telescope: Physical Properties and Purity of a Galaxy Cluster Sample Selected via the Sunyaev-Zel'dovich Effect

We present optical and X-ray properties for the first confirmed galaxy cluster sample selected by the Sunyaev-Zel'dovich Effect from 148 GHz maps over 455 square degrees of sky made with the Atacama Cosmology Telescope. These maps, coupled with multi-band imaging on 4-meter-class optical telescopes, have yielded a sample of 23 galaxy clusters with redshifts between 0.118 and 1.066. Of these 23 clusters, 10 are newly discovered. The selection of this sample is approximately mass limited and essentially independent of redshift. We provide optical positions, images, redshifts and X-ray fluxes and luminosities for the full sample, and X-ray temperatures of an important subset. The mass limit of the full sample is around 8e14 Msun, with a number distribution that peaks around a redshift of 0.4. For the 10 highest significance SZE-selected cluster candidates, all of which are optically confirmed, the mass threshold is 1e15 Msun and the redshift range is 0.167 to 1.066. Archival observations from Chandra, XMM-Newton, and ROSAT provide X-ray luminosities and temperatures that are broadly consistent with this mass threshold. Our optical follow-up procedure also allowed us to assess the purity of the ACT cluster sample. Eighty (one hundred) percent of the 148 GHz candidates with signal-to-noise ratios greater than 5.1 (5.7) are confirmed as massive clusters. The reported sample represents one of the largest SZE-selected sample of massive clusters over all redshifts within a cosmologically-significant survey volume, which will enable cosmological studies as well as future studies on the evolution, morphology, and stellar populations in the most massive clusters in the Universe.Comment: 20 pages, 15 figures, 6 tables. Accepted for publication in ApJ. Higher resolution figures available at: http://peumo.rutgers.edu/~felipe/e-prints

The Atacama Cosmology Telescope: Two-Season ACTPol Spectra and Parameters

We present the temperature and polarization angular power spectra measured by the Atacama Cosmology Telescope Polarimeter (ACTPol). We analyze night-time data collected during 2013-14 using two detector arrays at 149 GHz, from 548 deg$^2$ of sky on the celestial equator. We use these spectra, and the spectra measured with the MBAC camera on ACT from 2008-10, in combination with Planck and WMAP data to estimate cosmological parameters from the temperature, polarization, and temperature-polarization cross-correlations. We find the new ACTPol data to be consistent with the LCDM model. The ACTPol temperature-polarization cross-spectrum now provides stronger constraints on multiple parameters than the ACTPol temperature spectrum, including the baryon density, the acoustic peak angular scale, and the derived Hubble constant. Adding the new data to planck temperature data tightens the limits on damping tail parameters, for example reducing the joint uncertainty on the number of neutrino species and the primordial helium fraction by 20%.Comment: 23 pages, 25 figure