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In this article, we overview a professional learn- ing task that involves drawing one’s vision for high-quality, equitable mathematics instruction (HQEMI). The task is part of the ongoing work of a statewide research practice partnership that supports a shared vision of mathematics across the state K–12 system. Our work of HQEMI is rooted in the development of Munter’s (2014) four dimensions for visions of high-quality mathematics instruction (VHQMI): the role of the teacher, classroom discourse, mathematical tasks, and student engagement. The first three dimensions are particularly useful in the work of the drawing task. In this article, we share an overview of the drawing task, its implementa- tion with educators, and sample drawings, de- tailing how personal drawings were made visible across participants and the conversations result- ing from viewing and reflecting on one another’s drawings. These conversations helped surface disparities in notions of ideal mathematics in- struction and provided space for negotiation of shared meaning. We provide themes and over- arching considerations from these conversations to highlight discussions that might be elicited through this task in future iterations. Finally, we provide recommendations for implementing the task and consider how the task might be adapt- ed for others’ contexts to support professional learning about and development of a shared vision for mathematics. 

The University of Indianapolis Teach (STEM)3 (UIndy TS3) program is a clinical residency teacher preparation program in which candidates earn a Master of Arts in Teaching degree with licensure in Chemistry, Biology, or Math. UIndy TS3 consists of multiple layers of support, including a clinical residency with clinical mentor teachers and clinical faculty who also serve as university supervisors, integrated and scaffolded university coursework, which includes clinical seminars and classroom observations, and two years of in-service mentoring. Evaluation and retention results indicate that candidates are well-supported in their high-need classrooms by these program components, and our 3-year retention rate of 93% over eight cohorts is higher than the national average. Moreover, the clinical mentor teacher (CMT) is enriched by the candidate’s presence in the classroom, as the candidate imports new teaching methodologies (such as project-based learning) and technologies to the classroom that in turn inform the practice of the CMT. School administrators are also positively impacted by interacting with the candidates, both by keeping apprised of the challenges that new teachers face and by learning new ways to engage students. The efficacy of UIndy TS3 is proven by our 100% placement rate, long-term retention of program graduates, and their recognition as teacher leaders. 

Abstract We report the observation of gravitational waves from two binary black hole coalescences during the fourth observing run of the LIGO–Virgo–KAGRA detector network, GW241011 and GW241110. The sources of these two signals are characterized by rapid and precisely measured primary spins, nonnegligible spin–orbit misalignment, and unequal mass ratios between their constituent black holes. These properties are characteristic of binaries in which the more massive object was itself formed from a previous binary black hole merger and suggest that the sources of GW241011 and GW241110 may have formed in dense stellar environments in which repeated mergers can take place. As the third-loudest gravitational-wave event published to date, with a median network signal-to-noise ratio of 36.0, GW241011 furthermore yields stringent constraints on the Kerr nature of black holes, the multipolar structure of gravitational-wave generation, and the existence of ultralight bosons within the mass range 10⁻¹³–10⁻¹²eV. 

Abstract On 2023 November 23, the two LIGO observatories both detected GW231123, a gravitational-wave signal consistent with the merger of two black holes with masses $137_{-18}^{+23}{M}_{\odot }$and $101_{-50}^{+22}{M}_{\odot }$(90% credible intervals), at a luminosity distance of 0.7–4.1 Gpc, a redshift of $0.40_{-0.25}^{+0.27}$, and with a network signal-to-noise ratio of ∼20.7. Both black holes exhibit high spins— $0.90_{-0.19}^{+0.10}$and $0.80_{-0.52}^{+0.20}$, respectively. A massive black hole remnant is supported by an independent ringdown analysis. Some properties of GW231123 are subject to large systematic uncertainties, as indicated by differences in the inferred parameters between signal models. The primary black hole lies within or above the theorized mass gap where black holes between 60–130M_⊙should be rare, due to pair-instability mechanisms, while the secondary spans the gap. The observation of GW231123 therefore suggests the formation of black holes from channels beyond standard stellar collapse and that intermediate-mass black holes of mass ∼200M_⊙form through gravitational-wave-driven mergers. 

The gravitational-wave signal GW250114 was observed by the two LIGO detectors with a network matched-filter signal-to-noise ratio of 80. The signal was emitted by the coalescence of two black holes with near-equal masses $m_1={33.6}_{-0.8}^{+1.2}{M}_{\odot }$and $m_2={32.2}_{-1.3}^{+0.8}{M}_{\odot }$, and small spins ${\chi }_{1,2}\le 0.26$(90% credibility) and negligible eccentricity $e\le 0.03$. Postmerger data excluding the peak region are consistent with the dominant quadrupolar $(\ell =|m|=2)$mode of a Kerr black hole and its first overtone. We constrain the modes’ frequencies to $\pm 30\%$of the Kerr spectrum, providing a test of the remnant’s Kerr nature. We also examine Hawking’s area law, also known as the second law of black hole mechanics, which states that the total area of the black hole event horizons cannot decrease with time. A range of analyses that exclude up to five of the strongest merger cycles confirm that the remnant area is larger than the sum of the initial areas to high credibility.