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In this paper, we present findings of the entering mathematics identities and visions of high-quality mathematics teaching of Black freshman undergraduate preservice elementary teachers. Evidence suggests that race and racialized experiences impacted both their MIs and their vision for mathematics teaching, highlighting the need to attend to these constructs as we support the preparation of Black teachers who can flourish in their humanity and brilliance. 

In this paper, we present findings of the entering mathematics identities and visions of high-quality mathematics teaching of Black freshman undergraduate preservice elementary teachers. Evidence suggests that race and racialized experiences impacted both their MIs and their vision for mathematics teaching, highlighting the need to attend to these constructs as we support the preparation of Black teachers who can flourish in their humanity and brilliance. 

Key Points We compared tools for describing streamflow timeseries, including streamflow metrics, wavelet, and Fourier analysis Each method indicated streamflow data are structured: variability at short timescales is negatively correlated with long timescales Globally, dams were less correlated with streamflow regime than catchment size and climate were 

Many higher education institutions in the United States provide mathematics tutoring services for undergraduate students. These informal learning experiences generally result in increased final course grades (Byerly & Rickard, 2018; Rickard & Mills, 2018; Xu et al., 2014) and improved student attitudes toward mathematics (Bressoud et al., 2015). In recent years, research has explored the beliefs and practices of undergraduate and, sometimes graduate, peer tutors, both prior to (Bjorkman, 2018; Johns, 2019; Pilgrim et al., 2020) and during the COVID19 pandemic (Gyampoh et al., 2020; Mullen et al., 2021; Van Maaren et al., 2021). Additionally, Burks and James (2019) proposed a framework for Mathematical Knowledge for Tutoring Undergraduate Mathematics adapted from Ball et al. (2008) Mathematical Knowledge for Teaching, highlighting the distinction between tutor and teacher. The current study builds on this body of work on tutors’ beliefs by focusing on mathematical sciences graduate teaching assistants (GTAs) who tutored in an online setting during the 2020-2021 academic year due to the COVID-19 pandemic. Specifically, this study addresses the following research question: What were the mathematical teaching beliefs and practices of graduate student tutors participating in online tutoring sessions through the mathematics learning center (MLC) during the COVID-19 pandemic? 

We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings. Using these outcome distribution functions, we present in this paper a self-consistent statistical mechanics-based analytic model obtained using the Fokker–Planck limit of the Boltzmann equation. Our model quantifies the dominant gravitational physics, combining both strong and weak single–binary interactions, which drives the time evolution of binary orbital parameter distributions in dense stellar environments. We focus in particular the distributions of binary orbital energies and eccentricities. We find a novel steady-state distribution of binary eccentricities, featuring strong depletions of both the highest and the lowest eccentricity binaries. In energy space, we compare the predictions of our analytic model to the results of numerical N-body simulations, and find that the agreement is good for the initial conditions considered here. This work is a first step towards the development of a fully self-consistent semi-analytic model for dynamically evolving binary star populations in dense stellar environments due to direct few-body interactions.