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]

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

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

Mineralogical evidence for multiple dust sources in an early Triassic loessite.

Loessite present in a borehole into the Smith Bank Formation (early Triassic age, Central North Sea) differentiates five coeval source terranes for aerosol dust, three long distance sources and two local sources. All were active immediately following the end Permian mass extinction. Long distance sources are sedimentary, basic magmatic and acid–intermediate volcanic. Although predominantly silt‐sized and dominated by quartz with subordinate feldspars, muscovite and illite, evidence of basic and acid–intermediate magmatic/volcanic sources are pervasive. Baddeleyite is diagnostic of basic magmatism, an origin supported by enrichment of plagioclase relative to potassium feldspar. Deduction of acid–intermediate volcanism comes from the collective occurrence of irregular geometry quartz, volcanic shards, Ti‐mineralization, euhedral biotite, sanidine, the co‐occurrence of apatite and zircon, and the common occurrence of a tosuditic clay mineral. The tosuditic phase occurs as an unusual diagenetic dioctahedral chlorite/smectite formed at low temperature (<45°C), during very shallow burial by the decomposition of unstable rhyo‐dacitic and andesitic grains in alkaline pore water from an adjacent lake that yielded pore fluids with a high Al:Si ratio. The Siberian Traps large igneous province is the likely source terrane for the magmatic and volcanic silt. Locally sourced clay pellets and kaolinite booklets formed from aeolian erosion of an adjacent, periodically desiccated lake‐floor and a kaolinitic regolith, respectively. Inference of a prolonged harsh, arid climate leaves no evidence of any periods of sustained humidity or climatic fluctuation, such as pedogenesis. The association between the end Permian mass extinction, emplacement and aeolian erosion of the Siberian Traps large igneous province, and location of the Smith Bank Formation in a large lacustrine endorheic basin, combine to preserve a record of prolonged harsh climate in the early Triassic

Visual discomfort from flash afterimages of riloid patterns

Op-art-based stimuli have been shown to be uncomfortable, possibly due to a combination of fixational eye movements (microsaccades) and excessive cortical responses. Efforts have been made to measure illusory phenomena arising from these stimuli in the absence of microsaccades, but there has been no attempt thus far to decouple the effects of the cortical response from the effect of fixational eye movements. This study uses flash afterimages to stablise the image on the retina and thus reduce the systematic effect of eye movements, in order to investigate the role of the brain in discomfort from op-art-based stimuli. There was a relationship between spatial frequency and the magnitude of the P300 response, showing a similar pattern to that of discomfort judgements, which suggests there might be a role of discomfort and excessive neural responses independently from the effects of microsaccades

Recent advances in pulmonary arterial hypertension [version 1; referees: 2 approved]

Pulmonary arterial hypertension (PAH) is a rare disorder with a high mortality rate. Treatment options have improved in the last 20 years, but patients still die prematurely of right heart failure. Though rare, it is heterogeneous at the genetic and molecular level, and understanding and exploiting this is key to the development of more effective treatments. BMPR2 , encoding bone morphogenetic receptor type 2, is the most commonly affected gene in both familial and non-familial PAH, but rare mutations have been identified in other genes. Transcriptomic, proteomic, and metabolomic studies looking for endophenotypes are under way. There is no shortage of candidate new drug targets for PAH, but the selection and prioritisation of these are challenges for the research community

Motion and Trajectories of Particles Around Three-Dimensional Black Holes

The motion of relativistic particles around three dimensional black holes following the Hamilton-Jacobi formalism is studied. It follows that the Hamilton-Jacobi equation can be separated and reduced to quadratures in analogy with the four dimensional case. It is shown that: a) particles are trapped by the black hole independently of their energy and angular momentum, b) matter alway falls to the centre of the black hole and cannot understake a motion with stables orbits as in four dimensions. For the extreme values of the angular momentum of the black hole, we were able to find exact solutions of the equations of motion and trajectories of a test particle.Comment: Plain TeX, 9pp, IPNO-TH 93/06, DFTUZ 93/0