Portland Public Schools

In this collaborative analysis, we (a philosopher of education and an experienced public school educator) examine the experience of demoralization and remoralization in the context of the COVID-19 pandemic. We overlay the context of the pandemic with the context of institutional racism and their interwoven impact for educators of colour. We use one educator’s narratives about teaching during the pandemic as a launching point about where philosophical research on teacher demoralization needs to go next. We argue that the pandemic presents an opportunity for teachers to gain clarity about their moral centres and for school and district leaders to create space for teachers to enact their professional values and thus access the moral rewards of their work. Teachers of colour encounter distinct challenges in having their moral centres recognized, but their prior experiences with moral friction may present them with unique resources in these challenging times. Teachers’ energy and agency are squandered, leading to demoralization, if they are not given sufficient space to enact their professional values.

Abstract Background: Following the shooting at Sandy Hook Elementary School, the Hartford Consensus produced the Stop the Bleed program to train bystanders in hemorrhage control. In our region, the police bureau delivers critical incident training to public schools, offering instruction in responding to violent or dangerous situations. Until now, widespread training in hemorrhage control has been lacking. Our group developed, implemented and evaluated a novel program integrating hemorrhage control into critical incident training for school staff in order to blunt the impact of mass casualty events on children.Methods: The staff of 25 elementary and middle schools attended a 90-minute course incorporating Stop the Bleed into the critical incident training curriculum, delivered on-site by police officers, nurses and doctors over a three-day period. The joint program was named Protect Our Kids. At the conclusion of the course, hemorrhage control kits and educational materials were provided and a four-question survey to assess the quality of training using a ten-point Likert scale was completed by participants and trainers. Results: 1018 educators underwent training. A majority were teachers (78.2%), followed by para-educators (5.8%), counselors (4.4%) and principals (2%). Widely covered by local and state media, the Protect Our Kids program was rated as excellent and effective by a majority of trainees and all trainers rated the program as excellent. Conclusions: Through collaboration between trauma centers, police and school systems, a large-scale training program for hemorrhage control and critical incident response can be effectively delivered to schools.

Manipulatives are a common tool in mathematics teaching and learning, including for students with disabilities. The most common manipulatives are concrete manipulatives, yet app-based manipulatives are a viable age-appropriate option for secondary students with disabilities. Through an adapted alternating treatment design with three middle school students—two with mild intellectual disability and one with a learning disability, researchers explored the impact of virtual and concrete manipulatives on students’ accuracy, independence, and task completion time for solving addition of fractions with unlike denominators. Students were equally successful in terms of accuracy and differences with independence were minimal. When comparing the two manipulative types, the results were idiosyncratic; two students were more independent with the concrete manipulative and one with the app-based manipulative. Implications for research regarding mathematics instruction and use of concrete and app-based manipulatives are discussed.

Mathematics education is an important but underexplored area of research for secondary students with mild intellectual disability. In this multiple probe across behaviors replicated across two participants study, the researchers explored the effectiveness of the virtual–representational–abstract (VRA) instructional sequence to support two students’ acquisition of three mathematical behaviors. Each student was able to acquire his or her three mathematical behaviors (i.e., place value, single-digit addition with regrouping, subtraction with regrouping, and single-digit multiplication) following instruction with the VRA sequence. However, each student struggled with maintenance with at least one behavior. Implications for practice relative to the VRA instructional sequence are discussed.

We present a so-called labelling method to insert cost annotations in a higher-order functional program, to certify their correctness with respect to a standard compilation chain to assembly code including safe memory management, and to reason on them in a higher-order Hoare logic.

We prove that the folk model structure on strict $\infty$-categories transfers to the category of strict $\infty$-groupoids (and more generally to the category of strict $(\infty, n)$-categories), and that the resulting model structure on strict $\infty$-groupoids coincides with the one defined by Brown and Golasinski via crossed complexes.

Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps. First, we recall definitions of finiteness spaces and describe their basic properties deduced from the general theory of linearly topologised spaces. Then we give an interpretation of LL based on linear algebra. Second, thanks to separation properties, we can introduce an algebraic notion of totality candidate in the framework of linearly topologised spaces: a totality candidate is a closed affine subspace which does not contain 0. We show that finiteness spaces with totality candidates constitute a model of classical LL. Finally, we give a barycentric simply typed lambda-calculus, with booleans ${\mathcal{B}}$ and a conditional operator, which can be interpreted in this model. We prove completeness at type ${\mathcal{B}}^n\to{\mathcal{B}}$ for every n by an algebraic method.

We develop new methods to statically bound the resources needed for the execution of systems of concurrent, interactive threads. Our study is concerned with a \emph{synchronous} model of interaction based on cooperative threads whose execution proceeds in synchronous rounds called instants. Our contribution is a system of compositional static analyses to guarantee that each instant terminates and to bound the size of the values computed by the system as a function of the size of its parameters at the beginning of the instant. Our method generalises an approach designed for first-order functional languages that relies on a combination of standard termination techniques for term rewriting systems and an analysis of the size of the computed values based on the notion of quasi-interpretation. We show that these two methods can be combined to obtain an explicit polynomial bound on the resources needed for the execution of the system during an instant. As a second contribution, we introduce a virtual machine and a related bytecode thus producing a precise description of the resources needed for the execution of a system. In this context, we present a suitable control flow analysis that allows to formulte the static analyses for resource control at byte code level.