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This work-in-progress paper describes the development of an assessment for teachers’ pedagogical content knowledge (PCK) for data fluency – the ability and confidence to actively make sense of and use data. In the context of a project that seeks to develop and pilot test data fluency professional learning for mathematics and science teachers in grades 6–9, researchers constructed a novel instrument for assessing teachers’ specialized knowledge for teaching, which lives at the intersection of data knowledge, domain-specific knowledge, pedagogy, and technology. This online one-hour instrument is a written performance task and is sensitive to three dimensions of PCK: 1) teachers’ ability to analyze student thinking, 2) teachers’ ability to plan instruction, and 3) the degree to which teachers’ responses reflect a learner-centered orientation. The project team is currently developing a scoring rubric for this instrument, which will be revised based on the pretest and posttest data from the pilot study. 

We present high-resolution millimeter continuum ALMA observations of the disks around the T Tauri stars LkCa 15 and 2MASS J16100501-2132318 (hereafter, J1610). These transition disks host dust-depleted inner regions, which have possibly been carved by massive planets, and they are of prime interest to the study of the imprints of planet-disk interactions. While at moderate angular resolution, they appear as a broad ring surrounding a cavity, the continuum emission resolves into multiple rings at a resolution of ~60 × 40 mas (~7.5 au for LkCa 15, ~6 au for J1610) and ~7 μ Jy beam −1 rms at 1.3 mm. In addition to a broad extended component, LkCa 15 and J1610 host three and two narrow rings, respectively, with two bright rings in LkCa 15 being radially resolved. LkCa 15 possibly hosts another faint ring close to the outer edge of the mm emission. The rings look marginally optically thick, with peak optical depths of ~0.5 (neglecting scattering), in agreement with high angular resolution observations of full disks. We performed hydrodynamical simulations with an embedded, sub-Jovian-mass planet and show that the observed multi-ringed substructure can be qualitatively explained as the outcome of the planet-disk interaction. We note, however, that the choice of the disk cooling timescale alone can significantly impact the resulting gas and dust distributions around the planet, leading to different numbers of rings and gaps and different spacings between them. We propose that the massive outer disk regions of transition disks are favorable places for planetesimals, and possibly second-generation planet formation of objects with a lower mass than the planets carving the inner cavity (typically few M Jup ), and that the annular substructures observed in LkCa 15 and J1610 may be indicative of planetary core formation within dust-rich pressure traps. Current observations are compatible with other mechanisms contributing to the origin of the observed substructures, in particular with regard to narrow rings generated (or facilitated) at the edge of the CO and N 2 snowlines. 

Abstract Despite the growing number of binary black hole coalescences confidently observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include the effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that have already been identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total source-frame massM> 70M_⊙) binaries covering eccentricities up to 0.3 at 15 Hz emitted gravitational-wave frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place a conservative upper limit for the merger rate density of high-mass binaries with eccentricities 0 <e≤ 0.3 at 16.9 Gpc⁻³yr⁻¹at the 90% confidence level.