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This descriptive study attended to the extent to which we see evidence of the presence of four practices that promote equity and access in 141 grades 3-8 mathematics lessons in the United States. We found that lessons generally showed evidence of some incorporation of the practices but often not at the highest level. Teachers in this sample engaged in social coaching at a relatively high level, across elementary and middle school classrooms. Teachers tended to do less with respect to supporting connection and engagement between student context and the math learning environment. We also found statistically significant differences between elementary and middle school lessons in positioning students as competent and supporting a nurturing environment by proactively building relationships and productive classroom culture. We offer possible interpretations and a few brief implications of these findings. 

This study examines the utilization of cognitive interviews longitudinally over a one-year period to collectively trace raters’ response processes as they interpreted and scored with observational rubrics designed to measure teaching practices that promote equity and access in elementary and middle school mathematics classrooms. We draw on four rounds of cognitive interviews (totaling 14 interviews) that involved four raters at purposeful time points spread over the year. Findings reported in this study focus on raters’ responses about one rubric, positioning students as competent. The findings point to the complexities of utilizing observational rubrics and the need to track response processes longitudinally at multiple time points during data collection in order to attend to rater calibration and the reliability and validity of resulting rubric scores. 

Abstract CUPID, the CUORE Upgrade with Particle Identification, is a next-generation experiment to search for neutrinoless double beta decay ($$0\mathrm {\nu \beta \beta }$$ $0\nu \beta \beta$) and other rare events using enriched Li$$_{2}$$ $_2^{}$$$^{100}$$ $_{}^{100}$MoO$$_{4}$$ $_4^{}$scintillating bolometers. It will be hosted by the CUORE cryostat located at the Laboratori Nazionali del Gran Sasso in Italy. The main physics goal of CUPID is to search for$$0\mathrm {\nu \beta \beta }$$ $0\nu \beta \beta$of$$^{100}$$ $_{}^{100}$Mo with a discovery sensitivity covering the full neutrino mass regime in the inverted ordering scenario, as well as the portion of the normal ordering regime with lightest neutrino mass larger than 10 meV. With a conservative background index of 10$$^{-4}$$ $_{}^{-4}$ cts$$/($$ $/($keV$$\cdot $$ $·$kg$$\cdot $$ $·$yr$$)$$ $)$, 240 kg isotope mass, 5 keV FWHM energy resolution at 3 MeV and 10 live-years of data taking, CUPID will have a 90% C.L. half-life exclusion sensitivity of$$1.8\cdot 10^{27}$$ $1.8·{10}^{27}$ yr, corresponding to an effective Majorana neutrino mass ($$m_{\beta \beta }$$ $m_{\beta \beta }$) sensitivity of 9–15 meV, and a$$3\sigma $$ $3\sigma$discovery sensitivity of$$1\cdot 10^{27}$$ $1·{10}^{27}$ yr, corresponding to an$$m_{\beta \beta }$$ $m_{\beta \beta }$range of 12–21 meV. 

Puffer and porcupine fishes (families Diodontidae and Tetraodontidae, order Tetradontiformes) are known for their extraordinary ability to triple their body size by swallowing and retaining large amounts of seawater in their accommodating stomachs. This inflation mechanism provides a defence to predation; however, it is associated with the secondary loss of the stomach's digestive function. Ingestion of alkaline seawater during inflation would make acidification inefficient (a potential driver for the loss of gastric digestion), paralleled by the loss of acid–peptic genes. We tested the hypothesis of stomach inflation as a driver for the convergent evolution of stomach loss by investigating the gastric phenotype and genotype of four distantly related stomach inflating gnathostomes: sargassum fish, swellshark, bearded goby and the pygmy leatherjacket. Strikingly, unlike in the puffer/porcupine fishes, we found no evidence for the loss of stomach function in sargassum fish, swellshark and bearded goby. Only the pygmy leatherjacket (Monochanthidae, Tetraodontiformes) lacked the gastric phenotype and genotype. In conclusion, ingestion of seawater for inflation, associated with loss of gastric acid secretion, is restricted to the Tetraodontiformes and is not a selective pressure for gastric loss in other reported gastric inflating fishes.