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This study used three pairs of problem-posing tasks to examine the impact of different prompts on students’ problem posing. Two kinds of prompts were involved. The first asked students to pose 2–3 different mathematical problems without specifying other requirements for the problems, whereas the second kind of prompt did specify additional requirements. A total of 2124 students’ responses were analyzed to examine the impact of the prompts along multiple dimensions. In response to problem-posing prompts with more specific requirements, students tended to engage in more in-depth mathematical thinking and posed much more linguistically and semantically complex problems with more relationships or steps required to solve them. The findings from this study not only contribute to our understanding of problem-posing processes but also have direct implications for teaching mathematics through problem posing. 

The topic of study in this report is student focusing and noticing. Specifically, we examined a teacher’s goals for student focusing and noticing and the student outcomes for focusing and noticing. The mathematics context for this research was quadratic functions and covariational reasoning. Two whole-class discussion episodes were analyzed. Results showed ways that the teacher’s goals and student outcomes were aligned and three ways that they were misaligned. These results could inform how quadratic functions are taught and how teachers can improve the alignment between their goals for student focusing and noticing and student outcomes for focusing and noticing. 

Liquid xenon (LXe) is a well-studied detector medium to search for rare events in dark matter and neutrino physics. Two-phase xenon time projection chambers (TPCs) can detect electronic and nuclear recoils with energy down to kilo-electron volts (keV). In this paper, we characterize the response of a single-phase liquid xenon proportional scintillation counter (LXePSC), which produces electroluminescence directly in the liquid, to detect electronic recoils at low energies. Our design uses a thin (10–25 μm diameter), central anode wire in a cylindrical LXe target where ionization electrons, created from radiation particles, drift radially towards the anode, and electroluminescence is produced. Both the primary scintillation (S1) and electroluminescence (S2) are detected by photomultiplier tubes (PMTs) surrounding the LXe target. Up to 17 photons are produced per electron, obtained with a 10 μm diameter anode wire, allowing for the highly efficient detection of electronic recoils from beta decays of a tritium source down to ∼ 1 keV. Single electrons, from photoemission of the cathode wires, are observed at a gain of 1.8 photoelectrons (PE) per electron. The delayed signals following the S2 signals are dominated by single-photon-like hits, without evidence for electron signals observed in the two-phase xenon TPCs. We discuss the potential application of such a LXePSC for reactor neutrino detection via Coherent Elastic Neutrino Nucleus Scattering (CEνNS).

 

We propose a framework to convert the protein intrinsic disorder content to structural entropy (H) using Shannon’s information theory (IT). The structural capacity (C), which is the sum of H and structural information (I), is equal to the amino acid sequence length of the protein. The structural entropy of the residues expands a continuous spectrum, ranging from 0 (fully ordered) to 1 (fully disordered), consistent with Shannon’s IT, which scores the fully-determined state 0 and the fully-uncertain state 1. The intrinsically disordered proteins (IDPs) in a living cell may participate in maintaining the high-energy-low-entropy state. In addition, under this framework, the biological functions performed by proteins and associated with the order or disorder of their 3D structures could be explained in terms of information-gains or entropy-losses, or the reverse processes.