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In July 2021, Computer Science (CS) standards were officially added as a subject area within the K-12 Montana content standards. However, due to a lack of professional development and pre-service preparation in CS, schools and teachers in Montana are underprepared to implement these standards. Montana is also a unique state, since AmericanIndian education is mandated by the state constitution in what is known as the IndianEducation for All Act. We are developing elementary and middle school units and teacher training materials that simultaneously address CS, Indian Education, and other Montana content standards. In this paper, we present a unit for fourth through sixth grades using a participatory design approach. Through physical computing, students create a visual narrative of their own stories inspired by ledger art, an American Indian art medium for recording lived experiences. We discuss the affordances and challenges of an integrated approach to CS teaching and learning in elementary and middle schools in Montana. 

In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy equivalent to that of a single path; we call this the trivial space of directed paths. Directed spaces that are topologically trivial may have non-trivial spaces of directed paths, which means that information is lost when the direction of these topological spaces is ignored. We define a notion of directed collapsibility in the setting of a directed Euclidean cubical complex using the spaces of directed paths of the underlying directed topological space, relative to an initial or a final vertex. In addition, we give sufficient conditions for a directed Euclidean cubical complex to have a contractible or a connected space of directed paths from a fixed initial vertex. We also give sufficient conditions for the path space between two vertices in a Euclidean cubical complex to be disconnected. Our results have applications to speeding up the verification process of concurrent programming and to understanding partial executions in concurrent programs. 

We propose a new approach for constructing the underlying map from trajectory data. Our algorithm is based on the idea that road segments can be identified as stable subtrajectory clusters in the data. For this, we consider how subtrajectory clusters evolve for varying distance values, and choose stable values for these. In doing so we avoid a global proximity parameter. Within trajectory clusters, we choose representatives, which are combined to form the map. We experimentally evaluate our algorithm on vehicle and hiking tracking data. These experiments demonstrate that our approach can naturally separate roads that run close to each other and can deal with outliers in the data, two issues that are notoriously difficult in road network reconstruction.