Mathematically gifted and talented learners: Theory and practice

This is an Author's Accepted Manuscript of an article published in International Journal of Mathematical Education in Science and Technology, 40(2), 213-228, 2009, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/00207390802566907.There is growing recognition of the special needs of mathematically gifted learners. This article reviews policy developments and current research and theory on giftedness in mathematics. It includes a discussion of the nature of mathematical ability as well as the factors that make up giftedness in mathematics. The article is set in the context of current developments in Mathematics Education and Gifted Education in the UK and their implications for Science and Technology. It argues that early identification and appropriate provision for younger mathematically promising pupils capitalizes on an intellectual resource which could provide future mathematicans as well as specialists in Science or Technology. Drawing on a Vygotskian framework, it is suggested that the mathematically gifted require appropriate cognitive challenges as well as attitudinally and motivationally enhancing experiences. In the second half of this article we report on an initiative in which we worked with teachers to identify mathematically gifted pupils and to provide effective enrichment support for them, in a number of London Local Authorities. A number of significant issues are raised relating to the identification of mathematical talent, enrichment provision for students and teachers’ professional development

Fermi Gamma-ray Imaging of a Radio Galaxy

The Fermi Gamma-ray Space Telescope has detected the gamma-ray glow emanating from the giant radio lobes of the radio galaxy Centaurus A. The resolved gamma-ray image shows the lobes clearly separated from the central active source. In contrast to all other active galaxies detected so far in high-energy gamma-rays, the lobe flux constitutes a considerable portion (>1/2) of the total source emission. The gamma-ray emission from the lobes is interpreted as inverse Compton scattered relic radiation from the cosmic microwave background (CMB), with additional contribution at higher energies from the infrared-to-optical extragalactic background light (EBL). These measurements provide gamma-ray constraints on the magnetic field and particle energy content in radio galaxy lobes, and a promising method to probe the cosmic relic photon fields.Comment: 27 pages, includes Supplementary Online Material; corresponding authors: C.C. Cheung, Y. Fukazawa, J. Knodlseder, L. Stawar

Search for Second-Generation Scalar Leptoquarks in ppˉ\bm{p \bar{p}} Collisions at s\sqrt{s}=1.96 TeV

Results on a search for pair production of second generation scalar leptoquark in $p \bar{p}$ collisions at $\sqrt{s}$=1.96 TeV are reported. The data analyzed were collected by the CDF detector during the 2002-2003 Tevatron Run II and correspond to an integrated luminosity of 198 pb$^{-1}$. Leptoquarks (LQ) are sought through their decay into (charged) leptons and quarks, with final state signatures represented by two muons and jets and one muon, large transverse missing energy and jets. We observe no evidence for $LQ$ production and derive 95% C.L. upper limits on the $LQ$ production cross sections as well as lower limits on their mass as a function of $\beta$, where $\beta$ is the branching fraction for $LQ \to \mu q$.Comment: 9 pages (3 author list) 5 figure

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

A change in the optical polarization associated with a gamma-ray flare in the blazar 3C 279

It is widely accepted that strong and variable radiation detected over all accessible energy bands in a number of active galaxies arises from a relativistic, Doppler-boosted jet pointing close to our line of sight. The size of the emitting zone and the location of this region relative to the central supermassive black hole are, however, poorly known, with estimates ranging from light-hours to a light-year or more. Here we report the coincidence of a gamma-ray flare with a dramatic change of optical polarization angle. This provides evidence for co-spatiality of optical and gamma-ray emission regions and indicates a highly ordered jet magnetic field. The results also require a non-axisymmetric structure of the emission zone, implying a curved trajectory for the emitting material within the jet, with the dissipation region located at a considerable distance from the black hole, at about 10^5 gravitational radii.Comment: Published in Nature issued on 18 February 2010. Corresponding authors: Masaaki Hayashida and Greg Madejsk

Measurement of the Dipion Mass Spectrum in X(3872) -> J/Psi Pi+ Pi- Decays

We measure the dipion mass spectrum in X(3872)--> J/Psi Pi+ Pi- decays using 360 pb-1 of pbar-p collisions at 1.96 TeV collected with the CDF II detector. The spectrum is fit with predictions for odd C-parity (3S1, 1P1, and 3DJ) charmonia decaying to J/Psi Pi+ Pi-, as well as even C-parity states in which the pions are from Rho0 decay. The latter case also encompasses exotic interpretations, such as a D0-D*0Bar molecule. Only the 3S1 and J/Psi Rho hypotheses are compatible with our data. Since 3S1 is untenable on other grounds, decay via J/Psi Rho is favored, which implies C=+1 for the X(3872). Models for different J/Psi-Rho angular momenta L are considered. Flexibility in the models, especially the introduction of Rho-Omega interference, enable good descriptions of our data for both L=0 and 1.Comment: 7 pages, 4 figures -- Submitted to Phys. Rev. Let

Search for ZZ and ZW Production in ppbar Collisions at sqrt(s) = 1.96 TeV

We present a search for ZZ and ZW vector boson pair production in ppbar collisions at sqrt(s) = 1.96 TeV using the leptonic decay channels ZZ --> ll nu nu, ZZ --> l l l' l' and ZW --> l l l' nu. In a data sample corresponding to an integrated luminosity of 194 pb-1 collected with the Collider Detector at Fermilab, 3 candidate events are found with an expected background of 1.0 +/- 0.2 events. We set a 95% confidence level upper limit of 15.2 pb on the cross section for ZZ plus ZW production, compared to the standard model prediction of 5.0 +/- 0.4 pb.Comment: 7 pages, 2 figures. This version is accepted for publication by Phys. Rev. D Rapid Communication

Attentional learning helps language acquisition take shape for atypically developing children, not just children with Autism Spectrum Disorders

The shape bias-generalising labels to same shaped objects-has been linked to attentional learning or referential intent. We explore these origins in children with typical development (TD), autism spectrum disorders (ASD) and other developmental disorders (DD). In two conditions, a novel object was presented and either named or described. Children selected another from a shape, colour or texture match. TD children choose the shape match in both conditions, children with DD and 'high-verbal mental age' (VMA) children with ASD (language age > 4.6) did so in the name condition and 'low-VMA' children with ASD never showed the heuristic. Thus, the shape bias arises from attentional learning in atypically developing children and is delayed in ASD

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Binary systems and their nuclear explosions

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