An Investigative Approach to Teaching Mathematics: Excitement and Concerns of K-8 Preservice Teachers

Following from the recommendations of the National Council of Teachers of Mathematics, an Investigative Approach (IA) to teaching mathematics encourages students to explore real-world problems through hands-on activities instead of focusing on rote memorization of facts, formulas, and procedures. This paper discusses thirty-two K-8 preservice teachers‘ responses to questions regarding excitements and concerns about using this method of teaching. Although most preservice teachers are excited about the prospects of using this approach in their future classrooms, some exhibit hesitations related to concerns about time constraints and their own math abilities. A mathematics methods course presently being taught that is centered around the ideas of IA is discussed, and recommendations for the use of IA in preservice math methods courses to help teachers overcome these concerns are made

Providing Real-World Experiences: the Virginia Tech Externship for Mathematics Specialists

We describe the structure and implementation of the yearlong Externship experience associated with the Mathematics Specialist program at Virginia Polytechnic Institute & State University (Virginia Tech). We discuss the assignments and experiences included in the Externship, the alignment of those experiences with the job description developed by the Virginia Mathematics and Science Coalition Task Force, and teacher comments on the effectiveness of their Externship experiences [1]

Management of the Rice Tungro Virus Vector \u3ci\u3eNephotettix virescens\u3c/i\u3e (Homoptera: Cicadellidae) with Controlled-Release Formulations of Carbofuran

Field trials were conducted in lowland flooded rice in the Philippines to evaluate a number of carbofuran controlled-release formulations in comparison with commercial formulations. The test formulations were based on a biodegradable matrix of pine kraft lignin and were used as granules of different sizes and also in the form of small strips. The release rates were assessed under field conditions by bioassaying rice plants in the field, using adult rice green leafhopper, Nephotettix virescens Distant. The lignin formulations with a high level of active ingredient (15–45% by weight) gave as good or better control than the commercial 3% granules in tests based on three application techniques: broadcast into the floodwater, soil incorporation, and root zone injection. The improvements in control levels of green leafhoppers were most marked with soil incorporation and root zone application. The best lignin-based formulation reduced levels of tungro virus infection from 23% for a conventional flowable carbofuran formulation to 1.0% at an application rate of 0.5 kg (AI)/ha. At the same rate, the grain yield was increased from 3.56 t/ha to 5.5 t/ha, using the controlled-released formulation

Effects of morphology on phonons of nanoscopic silver grains

The morphology of nanoscopic Ag grains significantly affects the phonons. Atomistic simulations show that realistic nanograin models display complex vibrational properties. (1) Single-crystalline grains. Nearly-pure torsional and radial phonons appear at low frequencies. For low-energy, faceted models, the breathing mode and acoustic gap (lowest frequency) are about 10% lower than predicted by elasticity theory (ET) for a continuum sphere of the same volume. The sharp edges and the atomic lattice split the ET-acoustic-gap quintet into a doublet and triplet. The surface protrusions associated with nearly spherical, high-energy models produce a smaller acoustic gap and a higher vibrational density of states (DOS) at frequencies \nu<2 THz. (2) Twined icosahedra. In contrast to the single-crystal case, the inherent strain produce a larger acoustic gap, while the core atoms yield a DOS tail extending beyond the highest frequency of single-crystalline grains. (3) Mark's decahedra, in contrast to (1) and (2), do not have a breathing mode; although twined and strained, do not exhibit a high-frequency tail in the DOS. (4) Irregular nanograins. Grain boundaries and surface disorder yield non-degenerate phonon frequencies, and significantly smaller acoustic gap. Only these nanograins exhibit a low-frequency \nu^2 DOS in the interval 1-2 THz.Comment: Version published in Phys. Rev.

Pair tunneling through single molecules

By a polaronic energy shift, the effective charging energy of molecules can become negative, favoring ground states with even numbers of electrons. Here, we show that charge transport through such molecules near ground-state degeneracies is dominated by tunneling of electron pairs which coexists with (featureless) single-electron cotunneling. Due to the restricted phase space for pair tunneling, the current-voltage characteristics exhibits striking differences from the conventional Coulomb blockade. In asymmetric junctions, pair tunneling can be used for gate-controlled current rectification and switching.Comment: 4+ pages, 4 figures; minor changes, version published in Phys. Rev. Let

Inductive algebras and homogeneous shifts

Inductive algebras for the irreducible unitary representations of the universal cover of the group of unimodular two by two matrices are classified. The classification of homogeneous shift operators is obtained as a direct consequence. This gives a new approach to the results of Bagchi and Misra

Universal zero-bias conductance for the single electron transistor. II: Comparison with numerical results

A numerical renormalization-group survey of the zero-bias electrical conductance through a quantum dot embedded in the conduction path of a nanodevice is reported. The results are examined in the light of a recently derived linear mapping between the temperature-dependent conductance and the universal function describing the conductance for the symmetric Anderson model. A gate potential applied to the conduction electrons is known to change markedly the transport properties of a quantum dot side-coupled to the conduction path; in the embedded geometry here discussed, a similar potential is shown to affect only quantitatively the temperature dependence of the conductance. As expected, in the Kondo regime the numerical results are in excellent agreement with the mapped conductances. In the mixed-valence regime, the mapping describes accurately the low-temperature tail of the conductance. The mapping is shown to provide a unified view of conduction in the single-electron transistor.Comment: Sequel to arXiv:0906.4063. 9 pages with 8 figure

Rotated stripe order and its competition with superconductivity in La1.88_{1.88}Sr0.12_{0.12}CuO4_4

We report the observation of a bulk charge modulation in La$_{1.88}$Sr$_{0.12}$CuO$_4$ (LSCO) with a characteristic in-plane wave-vector of (0.236, $\pm \delta$), with $\delta$=0.011 r.l.u. The transverse shift of the ordering wave-vector indicates the presence of rotated charge-stripe ordering, demonstrating that the charge ordering is not pinned to the Cu-O bond direction. On cooling through the superconducting transition, we find an abrupt change in the growth of the charge correlations and a suppression of the charge order parameter indicating competition between the two orderings. Orthorhombic LSCO thus helps bridge the apparent disparities between the behavior previously observed in the tetragonal "214" cuprates and the orthorhombic yttrium and bismuth-based cuprates and thus lends strong support to the idea that there is a common motif to charge order in all cuprate families.Comment: 6 pages, 4 figue