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The Carnegie Classification sorts institutions by their different styles of education. Two prominent types of institutions are high research activity universities (R1) and liberal arts focused colleges (LA). Institutional characteristics may positively (e.g. Eide et al., 1998) or negatively (e.g. Astin, 1997) affect graduate school aspirations. We analyzed responses from a national undergraduate mathematics major sample using chi-squared and Mann-Whitney U tests to identify differences between students’ knowledge about graduate school and its application process by these two types of institutions. Using this same sample, we used chi-squared tests to explore the differences between departmental (professors, advisors, and mentors) support by institution type. We interpret these results with the theories of social and cultural capital and offer suggestions for future research investigations. 

Applying to graduate school in mathematics requires both a desire to attend graduate school, but also an understanding of the application process. The more students know about the process, the more successful they are in their pursuit of admission to a graduate program. We examined mathematics majors’ knowledge of both graduate school and the graduate school application process as part of a larger study examining barriers to students applying to graduate school in mathematics. We also examined the impact of mentors on student interest in graduate school and whether having a mentor has an impact on student knowledge of graduate school. We frame and explain our results using the theory of social capital. 

Abstract Coronae, which are weak electrical discharges, have long been hypothesized to form on trees under thunderstorms, though never directly observed, characterized, or quantified. Using a newly developed instrument that measures ultraviolet emissions from coronae, the first direct observations and quantifications of coronae are presented for two trees under a thunderstorm in North Carolina. Coronae moved sporadically among leaves on every tree branch in a narrow field of view while the thunderstorm was directly overhead. Coronae emitted ∼10¹¹photons at 260 nm, corresponding to electrical currents of ∼1 μA, derived from unique measurements relating corona intensity to tree electrical current. Similar results across four additional storm intercepts from Florida to Pennsylvania give rise to a vision of swaths of scintillating corona glow as thunderstorms pass over forests. Such widespread coronae have implications for the removal of hydrocarbons emitted by trees, subtle tree leaf damage, and limited thunderstorm electrification. 

Computational chemistry is no longer seen as just an academic exercise. Researchers in academia and industry are now aware of the benefits associated with theoretical predictions of molecules. However, there is a skills-gap associated with teaching/learning the basics and the applications of computational chemistry. Herein, we describe the development and utilization of several quantum chemical exercises for educational purposes. 

Argumentation is a core disciplinary practice in mathematics and science that is important for both content understanding and everyday reasoning. In this report, we investigate how the National Science Foundation’s (NSF’s) recent research investments have advanced understanding and supported the development of interventions that improve the teaching and learning of argumentation in mathematics and science education. In the 5 years spanning 2011 to 2015, NSF’s Discovery Research PreK–12 (DRK-12) program funded or cofunded 23 projects relating to argumentation, with more than $40 million awarded. These 23 DRK-12 projects primarily focused on argumentation in high school and middle school and applied correlational/observational and longitudinal methods (rather than quasiexperimental or experimental methods), often reporting on the design and implementation of technological supports for the teaching and learning of argumentation. Our synthesis of empirical findings focused on how these projects studied both teacher- and student-facing interventions that improved the teaching and learning of argumentation, as well as naturalistic observations of argumentation in classroom settings that helped inform the design and development of future argumentation interventions. Link to PDF: https://www.air.org/sites/default/files/2022-05/Mathematical-and-Scientific-Argumentation-in-PreK-12-April-2022.pdf 

Teachers’ pedagogical content knowledge (PCK) is a complex, multifaceted construct that is widely seen as foundational to the act of teaching. In this synthesis, we investigated how the National Science Foundation’s (NSF’s) recent research investments have advanced understanding and supported the development of teachers’ PCK in PK–12 mathematics and science education. In the 5 years from 2011 to 2015, NSF’s Discovery Research PK–12 program (DRK-12) funded or cofunded 27 projects relating to PCK, totaling $62 million awarded. These 27 DRK-12 projects primarily applied correlational/observational and longitudinal methods (rather than quasi-experimental or experimental methods), often targeting teaching in the middle school grades. Our synthesis of empirical findings focused on how these projects studied PCK, including its measurement, development, and relationship to teaching and student learning. Link to PDF: https://www.air.org/sites/default/files/2022-05/Teachers-Pedagogical-Content-Knowledge-in-Math-and-Science-April-2022.pdf 

We improve the attack of Durak and Vaudenay (CRYPTO'17) on NIST Format-Preserving Encryption standard FF3, reducing the running time from $O(N^5)$ to $$O(N^{17/6})$$ for domain $$Z_N \times Z_N$$. Concretely, DV's attack needs about $$2^{50}$$ operations to recover encrypted 6-digit PINs, whereas ours only spends about $$2^{30}$$ operations. In realizing this goal, we provide a pedagogical example of how to use distinguishing attacks to speed up slide attacks. In addition, we improve the running time of DV's known-plaintext attack on 4-round Feistel of domain $$Z_N \times Z_N$$ from $O(N^3)$ time to just $$O(N^{5/3})$$ time. We also generalize our attacks to a general domain $$Z_M \times Z_N$$, allowing one to recover encrypted SSNs using about $$2^{50}$$ operations. Finally, we provide some proof-of-concept implementations to empirically validate our results.