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This paper explores the addition of AI into ChangeMaker K-12, a set of experiences and materials designed to support teacher candidates (TC) in learning to teach engineering design. The ChangeMaker K-12 model and materials consist of four progressive stages: design awareness, design for function, design with empathy, and design for change. This new research explores the introduction of AI assistance into these four stages. 

Abstract Observations of GeV gamma-ray emission from the well-studied mixed-morphology supernova remnant (SNR) W44 by Fermi-Large Area Telescope and AGILE imply that it is a site of significant cosmic-ray acceleration. The spectral energy distribution (SED) derived from the GeV data suggests that the gamma-ray emission likely originates from the decay of neutral pions generated by cosmic-ray interactions. It is essential to measure the SED of W44 in the X-ray and very-high-energy (VHE) gamma-ray bands to verify the hadronic origin of the emission and to gauge the potential contributions from leptonic emission. We report an upper limit of the nonthermal X-ray flux from W44 of 5  × 10⁻¹³erg cm⁻²s⁻¹in the 0.5–8.0 keV band based on  ∼300 ks of XMM-Newton observations. The X-ray upper limit is consistent with previously estimated hadronic models, but in tension with the leptonic models. We estimate the VHE flux upper limit of  ∼1.2  × 10⁻¹²erg s⁻¹cm⁻²in the 0.5–5.0 TeV range from W44 using data from the Very Energetic Radiation Imaging Telescope Array System. Our nondetection of W44 at VHE wavelengths is in agreement with observations from other imaging atmospheric Cherenkov telescopes and is perhaps consistent with the evolutionary stage of the SNR. 

Although "developmental math" is widely discussed in higher-education circles, exactly what developmental math encompasses is often underdeveloped. In this theoretical report, we use a sample of highly cited works on developmental math to identify common characterizations of the term "developmental math" in the literature. We then interrogate and problematize each characterization, particularly in terms of whether they serve equity-related goals such as access to college credentials and math learning. We close by proposing an alternative characterization of developmental math and discuss the theoretical implications. We see this as a first step towards conversations about how developmental math could be conceptualized. 

In this theoretical paper, our aim is to start a conversation about how "levels" in mathematics are operationalized and defined, with a specific focus on "college level." We approach this from a lens of developmental stages, using this to propose an initial framework for describing how learners might progress along a developmental continuum delineated by the kinds of reasoning/justification, generalization/abstraction, and types of conceptions that they hold, rather than by the particular computations learners are able to do, or the kinds of mathematical objects with which learners are engaging. 

Context.Blazars, which include BL Lacs and flat-spectrum radio quasars, represent the brightest persistent extragalactic sources in the high-energy (HE; 10 MeV–100 GeV) and very-high-energy (VHE;E > 100 GeV)γ-ray sky. Due to their almost featureless optical/UV spectra, it is challenging to measure the redshifts of BL Lacs. As a result, about 50% ofγ-ray BL Lacs lack a firm measurement of this property, which is fundamental for population studies, indirect estimates of the extragalactic background light, and fundamental physics probes (e.g., searches for Lorentz-invariance violation or axion-like particles). Aims.This paper is the third in a series of papers aimed at determining the redshift of a sample of blazars selected as prime targets for future observations with the next generation, ground-based VHEγ-ray astronomy observatory, Cherenkov Telescope Array Observatory (CTAO). The accurate determination of the redshift of these objects is an important aid in source selection and planning of future CTAO observations. Methods.Promising targets were selected following a sample selection obtained with Monte Carlo simulations of CTAO observations. The selected targets were expected to be detectable with CTAO in observations of 30 h or less. We performed deep spectroscopic observations of 41 of these blazars using the Keck II, Lick, SALT, GTC, and ESO/VLT telescopes. We carefully searched for spectral lines in the spectra and whenever features of the host galaxy were detected, we attempted to model the properties of the host galaxy. The magnitudes of the targets at the time of the observations were also compared to their long-term light curves. Results.Spectra from 24 objects display spectral features or a high signal-to-noise ratio (S/N). From these, 12 spectroscopic redshifts were determined, ranging from 0.2223 to 0.7018. Furthermore, 1 tentative redshift (0.6622) and 2 redshift lower limits atz > 0.6185 andz > 0.6347 were obtained. The other 9 BL Lacs showed featureless spectra, despite the high S/N (≥100) observations. Our comparisons with long-term optical light curves tentatively suggest that redshift measurements are more straightforward during an optical low state of the active galactic nucleus. Overall, we have determined 37 redshifts and 6 spectroscopic lower limits as part of our programme thus far. 

Abstract Pulsar halos are regions around middle-aged pulsars extending out to tens of parsecs. The large extent of the halos and well-defined central cosmic-ray accelerators make this new class of Galactic sources an ideal laboratory for studying cosmic-ray transport. LHAASO J0621+3755 is a candidate pulsar halo associated with the middle-aged gamma-ray pulsar PSR J0622+3749. We observed LHAASO J0621+3755 with VERITAS and XMM-Newton in the TeV and X-ray bands, respectively. For this work, we developed a novel background estimation technique for imaging atmospheric Cherenkov telescope observations of such extended sources. No halo emission was detected with VERITAS (0.3–10 TeV) or XMM-Newton (2–7 keV) within 1^∘and $10^{\prime }$around PSR J0622+3749, respectively. Combined with the LHAASO Kilometer Square Array (KM2A) and Fermi-LAT data, VERITAS flux upper limits establish a spectral break at  ∼1–10 TeV, a unique feature compared with Geminga, the most studied pulsar halo. We model the gamma-ray spectrum and LHAASO-KM2A surface brightness as inverse Compton emission and find suppressed diffusion around the pulsar, similar to Geminga. A smaller diffusion suppression zone and harder electron injection spectrum than Geminga are necessary to reproduce the spectral cutoff. A magnetic field ≤1μG is required by our XMM-Newton observation and synchrotron spectral modeling, consistent with Geminga. Our findings support slower diffusion and lower magnetic field around pulsar halos than the Galactic averages, hinting at magnetohydrodynamic turbulence around pulsars. Additionally, we report the detection of an X-ray point source spatially coincident with PSR J0622+3749, whose periodicity is consistent with the gamma-ray spin period of 333.2 ms. The soft spectrum of this source suggests a thermal origin. 

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.