Planning District‐Wide Professional Development: Insights Gained From Teachers and Students Regarding Mathematics Teaching in a Large Urban District

This paper describes the mechanism used to gain insights into the state of the art of mathematics instruction in a large urban district in order to design meaningful professional development for the teachers in the district. Surveys of close to 2,000 elementary, middle school, and high school students were collected in order to assess the instructional practices used in mathematics classes across the district. Students were questioned about the frequency of use of various instructional practices that support the meaningful learning of mathematics. These included practices such as problem solving, use of calculators and computers, group work, homework, discussions, and projects, among others. Responses were analyzed and comparisons were drawn between elementary and middle school students' responses and between middle school and high school responses. Finally, fifth‐grade student responses were compared to those of their teachers. Student responses indicated that they had fewer inquiry‐based experiences, fewer student‐to‐student interactions, and fewer opportunities to defend their answers and justify their thinking as they moved from elementary to middle school to high school. In the elementary grades students reported an overemphasis on the use of memorization of facts and procedures and sparse use of calculators. Results were interpreted and specific directions for professional development, as reported in this paper, were drawn from these data. The paper illustrates how student surveys can inform the design of professional development experiences for the teachers in a district.     

An Analytic Zariski Structure Over a Field

Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms.     

Comparison of localization and delocalization indices obtained with Hartree-Fock and conventional correlated methods: effect of Coulomb correlation

Atomic populations and localization [lambda(A)] and delocalization [delta(A,B)] indices (LIs and DIs) are calculated for a large set of molecules at the Hartree-Fock (HF), MP2, MP4(SDQ), CISD, and QCISD levels with the 6-311++G(2d,2p) basis set. The HF method and the conventional correlation methods [MP2, MP4(SDQ), CISD, and QCISD] yield distinct sets of LIs and DIs. Yet, within the four conventional correlation methods the differences in atomic populations and LIs and DIs are small. Relative to HF, the conventional correlation methods [MP2, MP4(SDQ), CISD, QCISD] yield virtually the same LIs and DIs for molecules with large charge separations while LIs and DIs that differ significantly from the HF values--the LIs are increased and DIs decreased--are obtained for bonds with no or small charge separations. Such is the case in the archetypal homopolar molecules HC(triple bond)CH, H2C=CH2, CH3-CH3, and "protonated cyclopropane" C(3)H(7) (+), in which case the bonding may be atypical. Relative to HF, the typical effect of the conventional correlation methods is to decrease the DI between atoms.     

Recoil spectrometry: Ion accelerator based elemental characterisation of surface layers

Recoil Spectrometry covers a group of techniques that are very similar to the well known Rutherford backscattering Spectrometry technique, but with the important difference that one measures the recoiling target atom rather than the projectile ion. This makes it possible to determine both the identity of the recoil and its depth of origin from its energy and velocity, using a suitable detector system. The incident ion is typically high-energy (30–100MeV)³⁵C1,⁸¹Br or¹²⁷I. Low concentrations of light elements such as C, O and N can be profiled in a heavy matrix such as Fe or GaAs. Here we present an overview of mass and energy dispersive recoil Spectrometry and illustrate its successful use in some typical applications.     

Acoustic absorption in aqueous potassium phosphate

Measurements of acoustic absorption and velocity as a function of frequency and concentration in KH₂PO₄–K₂HPO₄ buffers at 4°C and pH 5-7 are reported. The dependence of the observed acoustic relaxation parameters on concentration is consistent with that to be expected from perturbation of a monomer-dimer equilibrium with an equilibrium constant [for 2H₂PO ₄ ^– (H₂PO₄)₂ ^2–] of 0.21 M^–1, a bimolecular rate constant of 5×10⁸ M^–1-sec^–1 and a standard volume change of –5 cm³ mole. The equilibrium constant for H₂PO ₄ ^– + HPO₄ ^2–H₃(PO₄)₂ ^3– is estimated to be 0.7 M^–1.     

Analytical TEM examinations of CoPt-TiO2 perpendicular magnetic recording media.

For this analytical TEM study, nonmagnetic oxygen-rich boundaries were introduced into Co-Pt-alloy perpendicular recording media by cosputtering Co and Pt with TiO2. Increasing the TiO2 content resulted in changes to the microstructure and elemental distribution within grains and boundaries in these films. EFTEM imaging was used to generate composition maps spanning many tens of grains, thereby giving an overall depiction of the changes in elemental distribution occurring with increasing TiO2 content. Comparing EFTEM with spectrum-imaging maps created by high-resolution STEM with EDXS and EELS enabled both corroboration of EFTEM results and quantification of the chemical composition within individual grain boundary areas. The difficulty of interpreting data from EDXS for these extremely thin films is discussed. Increasing the TiO2 content of the media was found to create more uniformly wide Ti- and O-rich grain boundaries as well as Ti- and O-rich regions within grains.     

Multifunctional redox catalysts as selective enhancers of oxidative stress

Certain cancer cells proliferate under conditions of oxidative stress (OS) and might therefore be selectively targeted by redox catalysts. Among these catalysts, compounds containing a chalcogen and a quinone redox centre are particularly well suited to respond to the presence of OS. These catalysts combine the specific electrochemical features of quinones and chalcogens. They exhibit high selectivity and efficiency against oxidatively stressed rat PC12, human Jurkat and human Daudi cells in cell culture, where their mode of action most likely involves the catalytic activation of existent and the generation of new reactive oxygen species. The high efficiency and selectivity shown by these catalysts makes them interesting for the development of anti-cancer drugs.