Kindergarten and first-grade students´ understandings and representations of arithmetic properties

We present a study that explores Kindergarten and first-grade students’ understandings and representations of arithmetic properties. Sixteen students participated in a classroom teaching experiment designed to explore children’s algebraic understandings, including their understandings and symbolic representations of three arithmetic properties: additive identity, additive inverse, and commutativity. We characterized students’ understandings in terms of Skemp’s framework of understandings: rules without reason (instrumental) and knowing what to do and why (relational). Then, following Vergnaud, we analyzed the types of additive relationships (transformation, comparison, or combination) and representations used by students. Our findings show that students’ understandings developed in sophistication over time. We observed the least sophisticated understandings for the commutative property, particularly among Kindergarten students who exhibited instrumental understandings even after instruction

Second graders articulating ideas about linear functional relationships

In this paper, we explore the ideas that second grade students articulate about functional relationships. We adopt a function-based approach to introduce elementary school children to algebraic content. We present results from a design-based research study carried out with 21 second-grade students (approximately 7 years of age). We focus on a lesson from our classroom teaching experiment in which the students were working on a problem that involved a linear functional relationship (y=2x). From the analysis of students’ written work and classroom video, we illustrate two different approaches that students adopt to express the relationship between two quantities. Students show fluency recontextualizing the problem posed, moving between extra-mathematical and intra-mathematical contexts

Tidal Torquing of Elliptical Galaxies in Cluster Environments

Observational studies of galaxy isophotal shapes have shown that galaxy orientations are anisotropic: a galaxy's long axis tends to be oriented toward the center of its host. This radial alignment is seen across a wide range of scales, from galaxies in massive clusters to small Milky Way type satellite systems. Recently, this effect has also been detected in dark matter simulations of cosmological structure, but the degree of alignment of dark matter substructures in these studies is significantly stronger than seen in observations. In this paper we attempt to reconcile these two results by performing high-resolution numerical experiments on N-body multi-component models of triaxial galaxies orbiting in an external analytical potential. The large number of particles employed allows us to probe deep into the inner structure of the galaxy: we show that the discrepancy between observed galaxies and simulated dark matter halos is a natural consequence of induced radial shape twisting in the galaxy by the external potential. The degree of twisting depends strongly on the orbital phase and eccentricity of the satellite, and it can, under certain conditions, be significant at radii smaller than the dark matter scale radius. Such internal misalignments will have important consequences, both for the dynamical evolution of the galaxy itself, and for mass modeling of galaxies in clustered environments.Comment: 19 pages, 22 figures, published in Ap

Allergies and Diabetes as Risk Factors for Dengue Hemorrhagic Fever: Results of a Case Control Study

Dengue is an arboviral disease that affects large areas of countries in tropical and subtropical regions of the world. Around 500,000 cases and 22,000 deaths of dengue hemorrhagic fever (DHF)/Dengue Shock Syndrome (DSS), the most severe presentations of this disease, occur annually. It is unclear why some cases of dengue fever (0.5% to 4%) progress to DHF/DSS. There is weak evidence that some diseases could have a role in this process, such as diabetes, hypertension, and allergies. In epidemics most dengue fever cases are sent home as there are too many to be kept in observation, but if it were possible to identify those with a higher risk of progression to DHF, they could be kept for observation, for early detection of signs, symptoms and alterations in laboratory tests suggestive of DHF, to enable timely and effective clinical management and early intervention. We study this issue and we believe that the evidence produced in this study, when confirmed in other studies, suggests that screening criteria might be used to identify adult patients at a greater risk of developing DHF with a recommendation that they remain under observation and monitoring in a hospital

Probability for chance coincidence of a gamma-ray burst with a galaxy on the sky

The nearby long GRB 060614 was not accompanied by a supernova, challenging the collapsar model for long-duration GRBs and the traditional classification scheme for GRBs. However, Cobb et al. have argued that the association of GRB 060614 and its host galaxy could be chance coincidence. In this work we calculate the probability for a GRB to be randomly coincident with a galaxy on the sky, using a galaxy luminosity function obtained from current galaxy surveys. We find that, with a magnitude limit that current telescopes can reach and an evolving galaxy luminosity function obtained from VVDS, the probability for chance coincidence of a GRB with a galaxy of redshift <1.5 is about several percent. These results agree with previous estimates based on observed galaxies. For the case of GRB 060614, the probability for it to be coincident with a z<0.125 galaxy by angular separation <0.5" is ~0.02%, indicating that the association of GRB 060614 and its host galaxy is secure. If the telescope magnitude limit is significantly improved in future, the probability for GRB-galaxy association will be considerably large, making it very problematic to identify a GRB host based only on the superposition of a GRB and a galaxy on the sky.Comment: 8 pages, 5 figures. Accepted by MNRA

The Seventh Data Release of the Sloan Digital Sky Survey

This paper describes the Seventh Data Release of the Sloan Digital Sky Survey (SDSS), marking the completion of the original goals of the SDSS and the end of the phase known as SDSS-II. It includes 11663 deg^2 of imaging data, with most of the roughly 2000 deg^2 increment over the previous data release lying in regions of low Galactic latitude. The catalog contains five-band photometry for 357 million distinct objects. The survey also includes repeat photometry over 250 deg^2 along the Celestial Equator in the Southern Galactic Cap. A coaddition of these data goes roughly two magnitudes fainter than the main survey. The spectroscopy is now complete over a contiguous area of 7500 deg^2 in the Northern Galactic Cap, closing the gap that was present in previous data releases. There are over 1.6 million spectra in total, including 930,000 galaxies, 120,000 quasars, and 460,000 stars. The data release includes improved stellar photometry at low Galactic latitude. The astrometry has all been recalibrated with the second version of the USNO CCD Astrograph Catalog (UCAC-2), reducing the rms statistical errors at the bright end to 45 milli-arcseconds per coordinate. A systematic error in bright galaxy photometr is less severe than previously reported for the majority of galaxies. Finally, we describe a series of improvements to the spectroscopic reductions, including better flat-fielding and improved wavelength calibration at the blue end, better processing of objects with extremely strong narrow emission lines, and an improved determination of stellar metallicities. (Abridged)Comment: 20 pages, 10 embedded figures. Accepted to ApJS after minor correction

The Fifth Data Release of the Sloan Digital Sky Survey

This paper describes the Fifth Data Release (DR5) of the Sloan Digital Sky Survey (SDSS). DR5 includes all survey quality data taken through June 2005 and represents the completion of the SDSS-I project (whose successor, SDSS-II will continue through mid-2008). It includes five-band photometric data for 217 million objects selected over 8000 square degrees, and 1,048,960 spectra of galaxies, quasars, and stars selected from 5713 square degrees of that imaging data. These numbers represent a roughly 20% increment over those of the Fourth Data Release; all the data from previous data releases are included in the present release. In addition to "standard" SDSS observations, DR5 includes repeat scans of the southern equatorial stripe, imaging scans across M31 and the core of the Perseus cluster of galaxies, and the first spectroscopic data from SEGUE, a survey to explore the kinematics and chemical evolution of the Galaxy. The catalog database incorporates several new features, including photometric redshifts of galaxies, tables of matched objects in overlap regions of the imaging survey, and tools that allow precise computations of survey geometry for statistical investigations.Comment: ApJ Supp, in press, October 2007. This paper describes DR5. The SDSS Sixth Data Release (DR6) is now public, available from http://www.sdss.or

The Fourteenth Data Release of the Sloan Digital Sky Survey: First Spectroscopic Data from the extended Baryon Oscillation Spectroscopic Survey and from the second phase of the Apache Point Observatory Galactic Evolution Experiment

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since July 2014. This paper describes the second data release from this phase, and the fourteenth from SDSS overall (making this, Data Release Fourteen or DR14). This release makes public data taken by SDSS-IV in its first two years of operation (July 2014-2016). Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey (eBOSS); the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data driven machine learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS website (www.sdss.org) has been updated for this release, and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020, and will be followed by SDSS-V.Comment: SDSS-IV collaboration alphabetical author data release paper. DR14 happened on 31st July 2017. 19 pages, 5 figures. Accepted by ApJS on 28th Nov 2017 (this is the "post-print" and "post-proofs" version; minor corrections only from v1, and most of errors found in proofs corrected

Developing the Enquiring Student and Enhancing the Research-Teaching Interface: Student-led Pedagogical Research and Educational Initiatives in Enquiry Based Learning

This paper describes the progress of a project running at the University of Glasgow to develop elements of Enquiry Based Learning (EBL) in undergraduate degree courses across a range of disciplines. It focuses on the second part of the project but an overview of the first part is also given. During phase 1 of the project, in the summer of 2007, seven undergraduate students spent four weeks working together exploring enquiry based learning (EBL) in the institution’s central, educational development unit. This phase was approached as an EBL exercise itself; the student groups were given full responsibility for the process with the proviso that by the end of this phase they would have developed a guide for staff and students about EBL. The second phase of the project continues throughout the academic year 07/08. Here, each student worked alongside a member of staff from their department of study to develop discipline specific EBL activities taking a research-informed approach to this development. All pairings were charged with introducing EBL such that no major course change procedures had to be followed; this hopefully ensured the sustainability of such adjustments. Staff and students involved in the project represent dentistry, chemistry, biology, theology, law and psychology and the courses under development range from large first year classes to small honours level courses. An overview of the range of enquiry-based learning developments within the courses will be described