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Recently, there has been a growing emphasis on training teachers to integrate computational thinking (CT) practices into disciplinary instruction. However, many current approaches involve a "top-down" method, where CT concepts and teacher training are dictated by external CT “experts,” often in an abstract and generalized manner, rather than being developed collaboratively or contextually with the teachers. These approaches typically treat CT as a set of abstract concepts, which can fail to promote a holistic understanding of the purposes and disciplinary value of CT. Consequently, teachers may feel less inclined to integrate CT into their regular teaching practice beyond the confines of professional development sessions. Furthermore, teachers are frequently positioned as novices awaiting the transmission of relevant CT knowledge rather than as agentive knowledge-builders with valuable expertise. This can undermine their autonomy, ownership, adaptability, and long-term commitment to implementing CT effectively in their teaching practice. We propose an alternative, “bottom-up” approach to supporting teachers in CT integration through a collaborative partnership between researchers and practitioners. We share evidence that this partnership led to understanding CT as inherently contextualized and productive for disciplinary problem-solving. 

Traditional professional development aimed at integrating computational thinking (CT) into K-12 classrooms frequently fails to link abstract technical terminology with teachers' personal experiences or real-world situations, which can impede overall teacher understanding and effective classroom implementation. This paper investigates an alternative method that employs personal storytelling to introduce CT to educators. We discovered that storytelling helped build emotional connections and prompted deeper reflections on CT concepts. Participants shared how CT appears in various settings, including teaching, parenting, and outdoor activities, which transformed their understanding and forged significant connections between theory and practice. 

Paraproducts are a special subclass of the multilinear Calderón-Zygmund operators, and their Lebesgue space estimates in the full multilinear range are characterized by the norm of the symbol. In this note, we characterize the Sobolev space boundedness properties of multilinear paraproducts in terms of a suitable family of Triebel-Lizorkin type norms of the symbol. Coupled with a suitable wavelet representation theorem, this characterization leads to a new family of Sobolev space T(1)-type theorems for multilinear Calderón-Zygmund operators. 

We quantify the Sobolev space norm of the Beltrami resolvent \((I- \mu S)^{-1}\), where \(S\) is the Beurling–Ahlfors transform, in terms of the corresponding Sobolev space norm of the dilatation \(\mu\) in the critical and supercritical ranges. Our estimate entails as a consequence quantitative self-improvement inequalities of Caccioppoli type for quasiregular distributions with dilatations in \(W^{1,p}\), \(p \ge 2\). Our proof strategy is then adapted to yield quantitative estimates for the resolvent \((I-\mu S_\Omega)^{-1}\) of the Beltrami equation on a sufficiently regular domain \(\Omega\), with \(\mu\in W^{1,p}(\Omega)\). Here, \(S_\Omega\) is the compression of \(S\) to a domain \(\Omega\). Our proofs do not rely on the compactness or commutator arguments previously employed in related literature. Instead, they leverage the weighted Sobolev estimates for compressions of Calderón–Zygmund operators to domains, recently obtained by the authors, to extend the Astala–Iwaniec–Saksman technique to higher regularities. 

Context. The fundamental process of star formation in galaxies involves the intricate interplay between the fueling of star formation via molecular gas and the feedback from recently formed massive stars that can, in turn, hinder the conversion of gas into stars. This process, by which galaxies evolve, is also closely connected to the intrinsic properties of the interstellar medium (ISM), such as structure, density, pressure, and metallicity. Aims. To study the role that different molecular and atomic phases of the ISM play in star formation, and to characterize their physical conditions, we zoom into our nearest neighboring galaxy, the Large Magellanic Cloud (LMC; 50 kpc), the most convenient laboratory in which to study the effects of the lower metal abundance on the properties of the ISM. The LMC offers a view of the ISM and star formation conditions in a low-metallicity (Z~ 0.5 Z_⊙) environment similar, in that regard, to the epoch of the peak of star formation in the earlier Universe (z~ 1.5). Following up on studies carried out at galactic scales in low-Z galaxies, we present an unprecedentedly detailed analysis of well-known star-forming regions (SFRs) at a spatial resolution of a few parsecs. Methods. We mapped a 610pc× 260pc region in the LMC molecular ridge in [C II]λ158 µm and the [O III]λ88 µm using the FIFI-LS instrument on the SOFIA telescope. We compared the data with the distribution of the CO(2−1) emission from ALMA, the modeled total infrared luminosity, and the Spitzer/MIPS 24 µm continuum and Hα. Results. We present new large maps of [CII] and [OIII] and perform a first comparison with CO(2−1) line and LTIR emission. We also provide a detailed description of the observing strategy with SOFIA/FIFI-LS and the data reduction process. Conclusions. We find that [CII] and [OIII] emission is associated with the SFRs in the molecular ridge, but also extends throughout the mapped region, and is not obviously associated with ongoing star formation. The CO emission is clumpier than the [C II] emission and we find plentiful [C II] present where there is little CO emission, possibly holding important implications for “CO-dark” gas. We find a clear trend of the L_[C II]/L_TIRratio decreasing with increasing L_TIRin the full range. This suggests a strong link between the “[C II]-deficit” and the local physical conditions instead of global properties.