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Describing and measuring instructional quality of mathematics lessons is a common goal amongst mathematics education researchers. Such work takes several forms such as classifying and coding instructional moves and student activity or providing high-level rubric-based scores in relation to categories. In this work, we share an innovative mixed methods approach to analyzing lesson data that includes both a time-based classification of instruction and an overall scoring component. Using the Math Habits framework, our project team analyzed a set of 97 fourth-eighth grade mathematics lessons including overall scores. From this qualitative analysis, we developed quantitative models to predict overall scores and better understand the ways that individual codes do or do not contribute to overall lesson score characterizations. 

Daily oscillations in photosynthetically active radiation strongly influence the timing of metabolic processes in picocyanobacteria, but it is less clear how the light-dark cycle affects the activities of their consumers. We investigated the relationship between marine picocyanobacteria and nanoplanktonic consumers throughout the diel cycle to determine whether heterotrophic and mixotrophic protists (algae with phagotrophic ability) display significant periodicity in grazing pressure. Carbon biomass of Prochlorococcus and Synechococcus was estimated continuously from abundances and cell size measurements made by flow cytometry. Picocyanobacterial dynamics were then compared to nanoplankton abundances and ingestion of fluorescently labeled bacteria measured every 4 h during a 4 d survey in the North Pacific Subtropical Gyre. Grazing of the labeled bacteria by heterotrophic nanoplankton was significantly greater at night than during the day. The grazing activity of mixotrophic nanoplankton showed no diel periodicity, suggesting that they may feed continuously, albeit at lower rates than heterotrophic nanoplankton, to alleviate nutrient limitation in this oligotrophic environment. Diel changes in Prochlorococcus biomass indicated that they could support substantial growth of nanoplankton if those grazers are the main source of picocyanobacterial mortality, and that grazers may contribute to temporally stable abundances of picocyanobacteria. 

Following sea‐ice retreat, surface waters of Arctic marginal seas become nutrient‐limited and subsurface chlorophyll maxima (SCM) develop below the pycnocline where nutrients and light conditions are favorable. However, the importance of these “hidden” features for regional productivity is not well constrained. Here, we use a unique combination of high‐resolution biogeochemical and physical observations collected on the Chukchi shelf in 2017 to constrain the fine‐scale structure of nutrients, O₂, particles, SCM, and turbulence. We find large O₂excess at middepth, identified by positive saturation () maxima of 15%–20% that unambiguously indicate significant production occurring in middepth waters. Themaxima coincided with a complete depletion of dissolved inorganic nitrogen (DIN = NO₃⁻ + NO₂⁻ + NH₄⁺). Nitracline depths aligned with SCM depths and the lowest extent ofmaxima, suggesting this horizon represents a compensation point for balanced growth and loss. Furthermore, SCM were also associated with turbulence minima and sat just above a high turbidity bottom layer where light attenuation increased significantly. Spatially, the largestmaxima were associated with high nutrient winter‐origin water masses (14.8% ± 2.4%), under a shallower pycnocline associated with seasonal melt while lower values were associated with summer‐origin water masses (7.4% ± 3.9%). Integrated O₂excesses of 800–1,200 mmol m⁻²in regions overlying winter water are consistent with primary production rates that are 12%–40% of previously reported regional primary production. These data implicate short‐term and long‐term control of SCM and associated productivity by stratification, turbulence, light, and seasonal water mass formation, with corresponding potential for climate‐related sensitivities.

 

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.