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  1. 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
    Free, publicly-accessible full text available April 1, 2023
  2. 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
    Free, publicly-accessible full text available April 1, 2023
  3. Free, publicly-accessible full text available August 9, 2023
  4. Free, publicly-accessible full text available February 1, 2023
  5. 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.