Flathead Valley Community College

ABSTRACT This mixed methods exploratory case study illuminates work of educational governance in a rural school district that has experienced dramatic improvement over a five-year period between 2017 and 2021. As such, we offer practical insights about how these leaders support continuous improvement, and theoretical insights about rurality, leadership, and governance from an organizational system thinking perspective.

Chronic obstructive pulmonary disease (COPD) comprises multiple phenotypes such as airflow obstruction, emphysema, and frequent episodes of acute worsening of respiratory symptoms, known as exacerbations. The goal of this pilot study was to test the usefulness of unbiased metabolomics and transcriptomics approaches to delineate biological pathways associated with COPD phenotypes and outcomes. Blood was collected from 149 current or former smokers with or without COPD and separated into peripheral blood mononuclear cells (PBMC) and plasma. PBMCs and plasma were analyzed using microarray and liquid chromatography mass spectrometry, respectively. Statistically significant transcripts and compounds were mapped to pathways using IMPaLA. Results showed that glycerophospholipid metabolism was associated with worse airflow obstruction and more COPD exacerbations. Sphingolipid metabolism was associated with worse lung function outcomes and exacerbation severity requiring hospitalizations. The strongest associations between a pathway and a certain COPD outcome were: fat digestion and absorption and T cell receptor signaling with lung function outcomes; antigen processing with exacerbation frequency; arginine and proline metabolism with exacerbation severity; and oxidative phosphorylation with emphysema. Overlaying transcriptomic and metabolomics datasets across pathways enabled outcome and phenotypic differences to be determined. Findings are relevant for identifying molecular targets for animal intervention studies and early intervention markers in human cohorts.

A natural digraph analogue of the graph-theoretic concept of an `independent set' is that of an `acyclic set', namely a set of vertices not spanning a directed cycle. Hence a digraph analogue of a graph coloring is a decomposition of the vertex set into acyclic sets and we say a digraph is uniquely $n$-colorable when this decomposition is unique up to relabeling. It was shown probabilistically in [A. Harutyunyan et al., Uniquely $D$-colorable digraphs with large girth, Canad. J. Math., 64(6): 1310-1328, 2012] that there exist uniquely $n$-colorable digraphs with arbitrarily large girth. Here we give a construction of such digraphs and prove that they have circular chromatic number $n$. The graph-theoretic notion of `homomorphism' also gives rise to a digraph analogue. An acyclic homomorphism from a digraph $D$ to a digraph $H$ is a mapping $\varphi: V(D) \rightarrow V(H)$ such that $uv \in A(D)$ implies that either $\varphi(u)\varphi(v) \in A(H)$ or $\varphi(u)=\varphi(v)$, and all the `fibers' $\varphi^{-1}(v)$, for $v \in V(H)$, of $\varphi$ are acyclic. In this language, a core is a digraph $D$ for which there does not exist an acyclic homomorphism from $D$ to a proper subdigraph of itself. Here we prove some basic results about digraph cores and construct highly chromatic cores without short cycles.

First-year general chemistry classes at large universities typically enroll students with diverse backgrounds. The vast majority of these students are not chemistry majors. NMR instrumentation was introduced to this class to engage these students in their learning and to represent modern chemistry to students for whom this course might be their only chemistry experience. We have incorporated NMR spectroscopy into the general chemistry laboratory experiments at the University of Technology Sydney in Sydney, Australia. Benchtop NMR spectrometers now mean that students can have close and frequent access to instrumentation. This chapter describes the use of the picoSpin-45 NMR spectrometer in the introductory laboratory, the types of experiments performed, quiz and survey results, and implementation challenges and successes.

The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds. Recent approaches using decomposition to define a covariant derivative on null hypersurfaces are investigated, with examples demonstrating the limitations of the methods. Motivated by Geroch's work on asymptotically flat spacetimes, conformal transformations are used to construct a covariant derivative on null hypersurfaces, and a condition on the Ricci tensor is given to determine when this construction can be used. Several examples are given, including the construction of a covariant derivative operator for the class of spherically symmetric hypersurfaces.

There are two fundamental ways to approach the use of gaming in education: playing games or designing games. In this chapter, we take the second path and discuss how to use an almost ubiquitous software tool in the schools — PowerPoint — with children in the design of original games. In these games, students put school’s content to use in ways perceived to be meaningful and authentie to them. Game design capitalizes on the natural design instincts of children. Children are natural game designers who tacitly know at deep levels what makes a good game and what makes agame fun. Turning over to them the challenge of designing agame that also teaches something is a worthy design goal and is aligned with the goals of schools and teachers. We discuss the balance between learning and motivation that must occur in the act of design and use play theory and flow theory to help explain this. Good games provide among the best exampies of cognitive psychology in action: authentie goals situated in a meaningful and motivating activity with clear and consistent feedback. However, ideas and approaches, no matter how innovative, which cannot meet the practical demands and limitations of a typical school are doomed to failure. Consequently, our approach meets head-on the issue of scalability, that is, having the idea take hold and flourish within the limited resources of a typical school with teachers who already have too many expectations placed on them.