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Differences in children’s mathematics knowledge are evident at kindergarten entry, favoring children who have greater access to economic resources. Fostering preschoolers’ mathematics learning at home and in classroom settings, through games and other developmentally appropriate activities, is of great interest to educators, early childhood leaders, and policymakers. This cluster randomized trial examined the ef- fects of a naturalistic, game-based mathematics intervention implemented in Head Start classrooms and examined whether including a family math component added value. A total of 573 children (64% His- panic; 60% multilingual) were included from 66 classrooms which were randomly assigned to Classroom Math (CM), Classroom Math + Family Math (CM+FM), or business-as-usual (BAU). Results indicated that the family math component did add value to the classroom-based intervention as CM+FM resulted in a significant positive impact on children’s mathematics knowledge relative to BAU, but CM alone did not. For preschoolers age 50+ months, both interventions had significant effects on children’s mathemat- ics knowledge relative to BAU, but CM+FM had a stronger effect (d = .36). The number of math games played was significantly associated with higher mathematics scores and the number of family math mini- books returned had a significant impact on children’s spring scores, over and above the number of games played. The CM+FM intervention also had a significant effect on teachers’ instructional practice (d =.79). Adding a family math component to a game-based classroom intervention resulted in positive impacts for preschoolers and seems to be an effective, ecologically valid intervention that fosters early mathematical competencies. 

Collecting and organizing data to understand and answer real-world questions is an increasingly important skill in our current world. Fostering data collection and analysis (DCA) skills in young children leverages key mathematics skills as well as the data representation, visualization, and interpretation skills of computational thinking (CT), culminating in a problem-solving approach with data. As such, the intervention, comprising investigations and a digital app, supported preschool teachers and children to answer data-focused questions by engaging in each step of the DCA process in order to foster CT and math skills. Teachers appreciated that the app offers a new way for children to visualize data and noted that the app provided learning opportunities for children that would not otherwise be possible or easy to implement. Results also suggest that the app provides a systematic process for data collection, entry, and interpretation. Children in classrooms that completed the intervention had significantly higher scores at post-intervention compared to children in classrooms that did not complete the intervention, controlling for pre-intervention scores, B(SE) = 0.13(0.05), t (6) = 2.48, p = .048. 

Abstract Seasonal cycles within the marginal ice zones in polar regions include large shifts in temperature and salinity that strongly influence microbial abundance and physiology. However, the combined effects of concurrent temperature and salinity change on microbial community structure and biochemical composition during transitions between seawater and sea ice are not well understood. Coastal marine communities along the western Antarctic Peninsula were sampled and surface seawater was incubated at combinations of temperature and salinity mimicking the formation (cold, salty) and melting (warm, fresh) of sea ice to evaluate how these factors may shape community composition and particulate metabolite pools during seasonal transitions. Bacterial and algal community structures were tightly coupled to each other and distinct across sea-ice, seawater, and sea-ice-meltwater field samples, with unique metabolite profiles in each habitat. During short-term (approximately 10-day) incubations of seawater microbial communities under different temperature and salinity conditions, community compositions changed minimally while metabolite pools shifted greatly, strongly accumulating compatible solutes like proline and glycine betaine under cold and salty conditions. Lower salinities reduced total metabolite concentrations in particulate matter, which may indicate a release of metabolites into the labile dissolved organic matter pool. Low salinity also increased acylcarnitine concentrations in particulate matter, suggesting a potential for fatty acid degradation and reduced nutritional value at the base of the food web during freshening. Our findings have consequences for food web dynamics, microbial interactions, and carbon cycling as polar regions undergo rapid climate change. 

Radial basis functions are typically used when discretization schemes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in solving many types of differential equations. However, the weights of the interpolated solution, used in the linear superposition of basis functions to interpolate the solution, and the actual value of the solution are completely different. In fact, these weights mix the value of the solution with the geometrical location of the nodes used to discretize the equation. In this paper, we used nodal radial basis functions, which are interpolants of the impulse function at each node inside the domain. This transformation allows to solve a linear hyperbolic partial differential equation using series expansion rather than the explicit computation of a matrix inverse. This transformation effectively yields an implicit solver which only requires the multiplication of vectors with matrices. Because the solver requires neither matrix inverse nor matrix-matrix products, this approach is numerically more stable and reduces the error by at least two orders of magnitude, compared to solvers using radial basis functions directly. Further, boundary conditions are integrated directly inside the solver, at no extra cost. The method is locally conservative, keeping the error virtually constant throughout the computation. 

Synopsis Intense bottom-ice algal blooms, often dominated by diatoms, are an important source of food for grazers, organic matter for export during sea ice melt, and dissolved organic carbon. Sea-ice diatoms have a number of adaptations, including accumulation of compatible solutes, that allows them to inhabit this highly variable environment characterized by extremes in temperature, salinity, and light. In addition to protecting them from extreme conditions, these compounds present a labile, nutrient-rich source of organic matter, and include precursors to climate active compounds (e.g., dimethyl sulfide [DMS]), which are likely regulated with environmental change. Here, intracellular concentrations of 45 metabolites were quantified in three sea-ice diatom species and were compared to two temperate diatom species, with a focus on compatible solutes and free amino acid pools. There was a large diversity of metabolite concentrations between diatoms with no clear pattern identifiable for sea-ice species. Concentrations of some compatible solutes (isethionic acid, homarine) approached 1 M in the sea-ice diatoms, Fragilariopsis cylindrus and Navicula cf. perminuta, but not in the larger sea-ice diatom, Nitzschia lecointei or in the temperate diatom species. The differential use of compatible solutes in sea-ice diatoms suggests different adaptive strategies and highlights which small organic compounds may be important in polar biogeochemical cycles.