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Mathematics teachers make numerous decisions that form lessons that in turn greatly influence what students learn. In making these decisions, teachers rely on their curricular reasoning (CR) to decide on what mathematics to teach, how to structure their lesson, and what problems or tasks to use to achieve their lesson goals. However, teachers differ with respect to the sophistication of their CR and the diversity of CR aspects used in their reasoning. In this paper, we detail two ways to classify teachers’ CR: a leveled approach to capture the increasing sophistication of teachers’ CR, and a heat map approach that highlights the extent to which teacher use various CR aspects in their planning. These methods provide stakeholders avenues by which CR can be studied and that teachers’ CR abilities can be further developed. 

The flux of cosmic ray muons at the Earth’s surface exhibits seasonal variations due to changes in the temperature of the atmosphere affecting the production and decay of mesons in the upper atmosphere. Using 1473 live days of data collected by the NuMI Off-axis ${\nu }_e$Appearance (NOvA) Near Detector during 2018–2022, we studied the seasonal pattern in the multiple-muon event rate. The data confirm an anticorrelation between the multiple-muon event rate and effective atmospheric temperature, consistent across all the years of data. Previous analyses from MINOS and NOvA saw a similar anticorrelation but did not include an explanation. We find that this anticorrelation is driven by altitude–geometry effects as the average muon production height changes with the season. This has been studied with a CORSIKA cosmic ray simulation package by varying atmospheric parameters, and provides an explanation to a longstanding discrepancy between the seasonal phases of single and multiple-muon events. 

This Letter reports measurements of muon-neutrino disappearance and electron-neutrino appearance and the corresponding antineutrino processes between the two NOvA detectors in the NuMI neutrino beam. These measurements use a dataset with double the neutrino mode beam exposure that was previously analyzed, along with improved simulation and analysis techniques. A joint fit to these samples in the three-flavor paradigm results in the most precise single-experiment constraint on the atmospheric neutrino mass splitting, $\mathrm{\Delta }{m}_{32}^2=2.431_{-0.034}^{+0.036}(-2.479_{-0.036}^{+0.036})\times {10}^{-3}{\mathrm{eV}}^2$if the mass ordering is normal (inverted). In both orderings, a region close to maximal mixing with ${\sin }^2{\theta }_{23}=0.55_{-0.06}^{+0.02}$is preferred. The NOvA data show a mild preference for the normal mass ordering with a Bayes factor of 2.4 (corresponding to 70% of the posterior probability), indicating that the normal ordering is 2.4 times more probable than the inverted ordering. When incorporating a 2D $\mathrm{\Delta }{m}_{32}^2-{\sin }^{2}2{\theta }_{13}$constraint based on Daya Bay data, this preference strengthens to a Bayes factor of 6.6 (87%). 

We present the measurement of ${\pi }^{+}$-argon inelastic cross sections using the ProtoDUNE single-phase liquid argon time projection chamber in the incident ${\pi }^{+}$kinetic energy range of 500–800 MeV in multiple exclusive channels (absorption, charge exchange, and the remaining inelastic interactions). The results of this analysis are important inputs to simulations of liquid argon neutrino experiments such as the Deep Underground Neutrino Experiment and the Short Baseline Neutrino program at Fermi National Accelerator Laboratory. They will be employed to improve the modeling of final state interactions within neutrino event generators used by these experiments, as well as the modeling of ${\pi }^{+}$-argon secondary interactions within the liquid argon. This is the first measurement of ${\pi }^{+}$-argon absorption at this kinetic energy range as well as the first ever measurement of ${\pi }^{+}$-argon charge exchange. 

Double- and single-differential cross sections for inclusive charged-current ${\nu }_{\mu }$-nucleus scattering are reported for the kinematic domain 0 to $2\mathrm{GeV}/c$in three-momentum transfer and 0 to 2 GeV in available energy, at a mean ${\nu }_{\mu }$energy of 1.86 GeV. The measurements are based on an estimated 995,760 ${\nu }_{\mu }$charged-current (CC) interactions in the scintillator medium of the NOvA Near Detector. The subdomain populated by 2-particle-2-hole (2p2h) reactions is identified by the cross section excess relative to predictions for ${\nu }_{\mu }$-nucleus scattering that are constrained by a data control sample. Models for 2-particle-2-hole processes are rated by ${\chi }^2$comparisons of the predicted-versus-measured ${\nu }_{\mu }$CC inclusive cross section over the full phase space and in the restricted subdomain. Shortfalls are observed in neutrino generator predictions obtained using the theory-based València and SuSAv2 2p2h models. Published by the American Physical Society2025 

The 2x2 Demonstrator, a prototype for the Deep Underground Neutrino Experiment (DUNE) liquid argon (LAr) Near Detector, was exposed to the Neutrinos from the Main Injector (NuMI) neutrino beam at Fermi National Accelerator Laboratory (Fermilab). This detector is a prototype of a new modular design for a liquid argon time-projection chamber (LArTPC), comprising a two-by-two array of four modules, each further segmented into two optically isolated LArTPCs. The 2x2 Demonstrator features a number of pioneering technologies, including a low-profile resistive field shell to establish drift fields, native 3D ionization pixelated imaging, and a high-coverage dielectric light readout system. The 2.4-tonne active mass detector is flanked upstream and downstream by supplemental solid-scintillator tracking planes, repurposed from the MINERvA experiment, which track ionizing particles exiting the argon volume. The antineutrino beam data collected by the detector over a 4.5 day period in 2024 include over 30,000 neutrino interactions in the LAr active volume—the first neutrino interactions reported by a DUNE detector prototype. During its physics-quality run, the 2x2 Demonstrator operated at a nominal drift field of 500 V/cm and maintained good LAr purity, with a stable electron lifetime of approximately 1.25 ms. This paper describes the detector and supporting systems, summarizes the installation and commissioning, and presents the initial validation of collected NuMI beam and off-beam self-triggers. In addition, it highlights observed interactions in the detector volume, including candidate muon antineutrino events.