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Informal mathematics learning has been far less studied than informal science learning – but youth can experience and learn about mathematics in their homes and communities. “Math walks” where students learn about how mathematics appears in the world around them, and have the opportunity to create their own math walk stops in their communities, can be a particularly powerful approach to informal mathematics learning. This study implemented an explanatory sequential mixed-method research design to investigate the impact of problem-posing activities in the math walks program on high school students' mathematical outcomes. The program was implemented during the pandemic and was modified to an online program where students met with instructors via online meetings. The researchers analyzed students' problem-posing work, surveyed students' interest in mathematics before and after the program, and compared the complexity of self-generated problems in pre- and post-assessments and different learning activities in the program. The results of the study suggest that students posed more complex problems in free problem-posing activities than in semi-structured problem-posing. Students also posed more complex problems in the post-survey than in the pre-survey. Students' mathematical dispositions did not significantly change from the pre-survey to post-survey, but the qualitative analysis showed that they began thinking more deeply, asking questions, and connecting school content to real-world scenarios. This study provides evidence that the math walks program is an effective approach to informal mathematics learning. The program was successful in helping students develop problem-posing skills and connect mathematical concepts to the world around them. Overall, “math walks” provide a powerful opportunity for informal mathematics learning.more » « less
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Abstract In this paper, we propose a sparse Bayesian procedure with global and local (GL) shrinkage priors for the problems of variable selection and classification in high‐dimensional logistic regression models. In particular, we consider two types of GL shrinkage priors for the regression coefficients, the horseshoe (HS) prior and the normal‐gamma (NG) prior, and then specify a correlated prior for the binary vector to distinguish models with the same size. The GL priors are then combined with mixture representations of logistic distribution to construct a hierarchical Bayes model that allows efficient implementation of a Markov chain Monte Carlo (MCMC) to generate samples from posterior distribution. We carry out simulations to compare the finite sample performances of the proposed Bayesian method with the existing Bayesian methods in terms of the accuracy of variable selection and prediction. Finally, two real‐data applications are provided for illustrative purposes.
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Abstract Background Annually reoccurring microbial populations with strong spatial and temporal variations have been identified in estuarine environments, especially in those with long residence time such as the Chesapeake Bay (CB). However, it is unclear how microbial taxa cooccurr and how the inter-taxa networks respond to the strong environmental gradients in the estuaries.
Results Here, we constructed co-occurrence networks on prokaryotic microbial communities in the CB, which included seasonal samples from seven spatial stations along the salinity gradients for three consecutive years. Our results showed that spatiotemporal variations of planktonic microbiomes promoted differentiations of the characteristics and stability of prokaryotic microbial networks in the CB estuary. Prokaryotic microbial networks exhibited a clear seasonal pattern where microbes were more closely connected during warm season compared to the associations during cold season. In addition, microbial networks were more stable in the lower Bay (ocean side) than those in the upper Bay (freshwater side). Multivariate regression tree (MRT) analysis and piecewise structural equation modeling (SEM) indicated that temperature, salinity and total suspended substances along with nutrient availability, particulate carbon and Chl
a , affected the distribution and co-occurrence of microbial groups, such as Actinobacteria, Bacteroidetes, Cyanobacteria, Planctomycetes, Proteobacteria, and Verrucomicrobia. Interestingly, compared to the abundant groups (such as SAR11, Saprospiraceae and Actinomarinaceae), the rare taxa including OM60 (NOR5) clade (Gammaproteobacteria), Micrococcales (Actinobacteria), and NS11-12 marine group (Bacteroidetes) contributed greatly to the stability of microbial co-occurrence in the Bay. Modularity and cluster structures of microbial networks varied spatiotemporally, which provided valuable insights into the ‘small world’ (a group of more interconnected species), network stability, and habitat partitioning/preferences.Conclusion Our results shed light on how estuarine gradients alter the spatiotemporal variations of prokaryotic microbial networks in the estuarine ecosystem, as well as their adaptability to environmental disturbances and co-occurrence network complexity and stability.
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