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.     

The versatile chemistry of the [B20H18]2- ions: novel reactions and structural motifs

Among the polyhedral [closo-BnHn]2- ion series (n = 5-12 inclusive) the aromatic [closo-B10H10]2- ion is both readily available and quite reactive. Among its many reactions which retain its cage structure one finds the oxidative dimerization reaction in which two [closo-B10H12]2- ions each formally lose a hydride ion and undergo dimerization of the resulting [closo-B10H9]- ions to produce the [trans-B20H18]2- ion. The two-component [closo-B10H9]- ions of the latter are linked together by a pair of unique B-B-B bonds which provide unprecedented reactivity to the structure. Among these reactions are the two-electron reduction to a set of three interconvertible [B20H18]4- ions having intercage B-B bonds and the related reductive substitution reaction in which [trans-B20H18]2- undergoes attack by nucleophile, L, to produce [B20H18L]2-. The latter species is formally a substituted [B20H19]3- (L = H) ion formed by B-B bond protonation of one of the isomeric [B20H18]4- ions. These and a variety of novel reactions are described here along with interrelated reaction mechanisms considered for the first time.     

Core polarization and 5/2+ states in91Nb

The energies and spectroscopic factors ofJ ^π=5/2⁺ states of nucleus⁹¹Nb excited via a reaction transferring a proton to the 2d _5/2 orbit of⁹⁰Zr target state have been calculated. Effective two-body interaction used has been extracted from the experimentally observed two-body energies of (1g ₉ ^2/?1 (n) 2d _5/2(n)), (1g ₉ ^2/?1 (n) 1g _9/2(p)) and (1g _9/2(p)-2d _9/2(n)) multiplets in⁹⁰Zr,⁹⁰Nb and⁹²Nb nuclei respectively. Most of the calculated energies and the strengths ofJ ^π=5/2⁺ levels have reasonably good counterparts in the experimental spectrum, however the calculation shows about 17% strength lying at 6.8 MeV, without having a confirmed counterpart in the observed level scheme. The reduced transition strengthsB(M1) forM l transitions from 5/2^? T>(11/2) state to the various components of 5/2⁺ T<(=9/2) state have also been reported; but the corresponding experimental values are not available. The main feature of the reduced transition strengths is that theM1 transition to the state at 3.69 MeV is inhibited whereas that to the state at 6.79 MeV is enhanced, the relevant core-configuration, interfering destructively in the former case and constructively in the latter.     

Electrical properties of a-antimony selenide

This paper reports conduction mechanism in a-Sb₂Se₃ over a wide range of temperature (238 to 338 K) and frequency (5 Hz to 100 kHz). The d.c. conductivity measured as a function of temperature shows semiconducting behaviour with activation energy ΔE=0.42 eV. Thermally induced changes in the electrical and dielectric properties of a-Sb₂Se₃ have been examined. The a.c. conductivity in the material has been explained using modified CBH model. The band conduction and single polaron hopping is dominant above room temperature. However, in the lower temperature range the bipolaron hopping dominates.     

The benefit of practice for sound localization without sight

An experiment was designed to determine whether normally sighted human subjects would be able to adapt to the handicapping effects of sudden deprivation of visual cues on horizontal plane sound localization. Two groups of sighted normal-hearing young adults participated. One group was allowed the benefit of sight. The other group was blindfolded. Measurements of accuracy and the time to respond were made daily over the course of five consecutive days, in a semi-reverberant sound proof booth that modeled listening in a small office. Sound localization was assessed using an array of eight speakers that surrounded the subject in space. Each day, one block of 120 trials was presented for each of three stimuli, two one-third octave noise bands, centred at 0.5 and 4 kHz, and broadband noise, to assess the utilization of interaural temporal difference cues, interaural level difference cues and binaural and spectral cues in combination. Blindfolded subjects were relatively less accurate than sighted subjects. Both groups showed gains with practice, the blindfolded group to a greater degree, largely due to improvements in the use of spectral cues. The blindfolded group took longer to respond than the sighted group, but showed greater decrements in response time with practice.     

Development of a fluorescence model for the determination of constants associated with binding,quenching, and Förster resonance energy transfer efficiency

Determining accurate dissociation constants for equilibrium processes involving a fluorescent mechanism can prove to be quite challenging. Typically, titration curves and nonlinear least squares fitting of the data using computer programs are employed to obtain such constants. However, these approaches only consider the total fluorescence signal and often ignore other energy transfer processes within the system. The current model considers the impact on fluorescence from equilibrium binding (viz., metal-ligand, ligand-substrate, etc.), quenching, and resonance energy transfer. This model should provide more accurate binding constant as well as insights into other photonic processes. The equations developed for this model are discussed and are applied to experimental data from titrimetric experiments. Since the experimental data are generally in excess of the number of parameters that are needed to define the system, fitting is operated in an overdetermined mode and employs error minimization (either absolute or relative) to define goodness of fit. Examples of how changes in certain parameters affect the shape of the titrimetric curve are also presented. The current model does not consider chelation-enhanced fluorescence.