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Although a wide variety of reports on developmental math exist, to date there has not been a large-scale examination of existing work from a math education point of view. Towards this goal, we analyzed 426 reports and peer-reviewed journal articles relating to developmental math published between 2000 and 2020. In report, we quantify the publishers and intended audience, examine the types of outcomes reported on and, where possible, examine the type of developmental math model discussed. We find that over the last decade, less than 20% of reports on developmental math have been aimed at math education audiences. While math education publications more frequently examine math knowledge and student experiences, the overall number of reports, compared to those examining pass rates, is relatively small. 

Active galactic nuclei (AGNs) make up about 35 per cent of the more than 250 sources detected in very high-energy (VHE) gamma rays to date with the imaging atmospheric Cherenkov telescopes. Apart from four nearby radio galaxies and two AGNs of unknown type, all known VHE AGNs are blazars. Knowledge of the cosmological redshift of gamma-ray blazars is key to enabling the study of their intrinsic emission properties, as the interaction between gamma rays and the extragalactic background light (EBL) results in a spectral softening. Therefore, the redshift determination exercise is crucial to indirectly placing tight constraints on the EBL density, and to studying blazar population evolution across cosmic time. Due to the powerful relativistic jets in blazars, most of their host galaxies’ spectral features are outshined, and dedicated high signal-to-noise (S/N) spectroscopic observations are required. Deep medium- to high-resolution spectroscopy of 33 gamma-ray blazar optical counterparts was performed with the European Southern Observatory, New Technology Telescope, Keck II telescope, Shane 3-metre telescope, and the Southern African Large Telescope. From the sample, spectra from 25 objects display spectral features or are featureless and have high S/N. The other eight objects have low-quality featureless spectra. We systematically searched for absorption and emission features and estimated, when possible, the fractional host galaxy flux in the measured total flux. Our measurements yielded 14 firm spectroscopic redshifts, ranging from 0.0838 to 0.8125, one tentative redshift, and two lower limits: one at $z > 0.382$ and the other at z > 0.629.

 

Abstract Dark matter is a key piece of the current cosmological scenario, with weakly interacting massive particles (WIMPs) a leading dark matter candidate. WIMPs have not been detected in their conventional parameter space (100 GeV ≲ M χ ≲ 100 TeV), a mass range accessible with current Imaging Atmospheric Cherenkov Telescopes. As ultraheavy dark matter (UHDM; M χ ≳ 100 TeV) has been suggested as an underexplored alternative to the WIMP paradigm, we search for an indirect dark matter annihilation signal in a higher mass range (up to 30 PeV) with the VERITAS γ -ray observatory. With 216 hr of observations of four dwarf spheroidal galaxies, we perform an unbinned likelihood analysis. We find no evidence of a γ -ray signal from UHDM annihilation above the background fluctuation for any individual dwarf galaxy nor for a joint-fit analysis, and consequently constrain the velocity-weighted annihilation cross section of UHDM for dark matter particle masses between 1 TeV and 30 PeV. We additionally set constraints on the allowed radius of a composite UHDM particle. 

The Breakthrough Listen Initiative is conducting a program using multiple telescopes around the world to search for “technosignatures”: artificial transmitters of extraterrestrial origin from beyond our solar system. The Very Energetic Radiation Imaging Telescope Array System (VERITAS) Collaboration joined this program in 2018 and provides the capability to search for one particular technosignature: optical pulses of a few nanoseconds in duration detectable over interstellar distances. We report here on the analysis and results of dedicated VERITAS observations of Breakthrough Listen targets conducted in 2019 and 2020 and of archival VERITAS data collected since 2012. Thirty hours of dedicated observations of 136 targets and 249 archival observations of 140 targets were analyzed and did not reveal any signals consistent with a technosignature. The results are used to place limits on the fraction of stars hosting transmitting civilizations. We also discuss the minimum pulse sensitivity of our observations and present VERITAS observations of CALIOP: a space-based pulsed laser on board the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations. The detection of these pulses with VERITAS, using the analysis techniques developed for our technosignature search, allows a test of our analysis efficiency and serves as an important proof of principle.

 

We report the detection of very high energy gamma-ray emission from the blazar S3 1227+25 (VER J1230+253) with the Very Energetic Radiation Imaging Telescope Array System (VERITAS). VERITAS observations of the source were triggered by the detection of a hard-spectrum GeV flare on 2015 May 15 with the Fermi-Large Area Telescope (LAT). A combined 5 hr VERITAS exposure on May 16 and 18 resulted in a strong 13σdetection with a differential photon spectral index, Γ = 3.8 ± 0.4, and a flux level at 9% of the Crab Nebula above 120 GeV. This also triggered target-of-opportunity observations with Swift, optical photometry, polarimetry, and radio measurements, also presented in this work, in addition to the VERITAS and Fermi-LAT data. A temporal analysis of the gamma-ray flux during this period finds evidence of a shortest variability timescale ofτ_obs= 6.2 ± 0.9 hr, indicating emission from compact regions within the jet, and the combined gamma-ray spectrum shows no strong evidence of a spectral cutoff. An investigation into correlations between the multiwavelength observations found evidence of optical and gamma-ray correlations, suggesting a single-zone model of emission. Finally, the multiwavelength spectral energy distribution is well described by a simple one-zone leptonic synchrotron self-Compton radiation model.

 

Context. Blazars are the most numerous class of high-energy (HE; E ∼ 50 MeV−100 GeV) and very high-energy (VHE; E ∼ 100 GeV−10 TeV) gamma-ray emitters. Currently, a measured spectroscopic redshift is available for only about 50% of gamma-ray BL Lacertae objects (BL Lacs), mainly due to the difficulty in measuring reliable redshifts from their nearly featureless continuum-dominated optical spectra. The knowledge of the redshift is fundamental for understanding the emission from blazars, for population studies and also for indirect studies of the extragalactic background light and searches for Lorentz invariance violation and axion-like particles using blazars. Aims. This paper is the first in a series of papers that aim to measure the redshift of a sample of blazars likely to be detected with the upcoming Cherenkov Telescope Array (CTA), a ground-based gamma-ray observatory. Methods. Monte Carlo simulations were performed to select those hard spectrum gamma-ray blazars detected with the Fermi -LAT telescope still lacking redshift measurements, but likely to be detected by CTA in 30 hours of observing time or less. Optical observing campaigns involving deep imaging and spectroscopic observations were organised to efficiently constrain their redshifts. We performed deep medium- to high-resolution spectroscopy of 19 blazar optical counterparts with the Keck II, SALT, and ESO NTT telescopes. We searched systematically for spectral features and, when possible, we estimated the contribution of the host galaxy to the total flux. Results. We measured eleven firm spectroscopic redshifts with values ranging from 0.1116 to 0.482, one tentative redshift, three redshift lower limits including one at z ≥ 0.449 and another at z ≥ 0.868. Four BL Lacs show featureless spectra. 

Abstract We report on multiwavelength target-of-opportunity observations of the blazar PKS 0735+178, located 2.°2 away from the best-fit position of the IceCube neutrino event IceCube-211208A detected on 2021 December 8. The source was in a high-flux state in the optical, ultraviolet, X-ray, and GeV γ -ray bands around the time of the neutrino event, exhibiting daily variability in the soft X-ray flux. The X-ray data from Swift-XRT and NuSTAR characterize the transition between the low-energy and high-energy components of the broadband spectral energy distribution (SED), and the γ -ray data from Fermi-LAT, VERITAS, and H.E.S.S. require a spectral cutoff near 100 GeV. Both the X-ray and γ -ray measurements provide strong constraints on the leptonic and hadronic models. We analytically explore a synchrotron self-Compton model, an external Compton model, and a lepto-hadronic model. Models that are entirely based on internal photon fields face serious difficulties in matching the observed SED. The existence of an external photon field in the source would instead explain the observed γ -ray spectral cutoff in both the leptonic and lepto-hadronic models and allow a proton jet power that marginally agrees with the Eddington limit in the lepto-hadronic model. We show a numerical lepto-hadronic model with external target photons that reproduces the observed SED and is reasonably consistent with the neutrino event despite requiring a high jet power.