Using Technology as a Vehicle to Appropriately Integrate Mathematics and Science Instruction for the Middle School

At the College of William and Mary, pre-service middle school science and mathematics teachers enroll in their respective methods courses taught in the same time period. Both instructors emphasize the importance of the content pedagogy unique to their disciplines in their individual courses such as strategies for teaching problem solving, computation, proportional reasoning, algebraic and geometric thinking in mathematics, and strategies for teaching students how to investigate or design and conduct experiments in science. However, the two classes come together for sessions in which they examine the relationship of the two disciplines and the proper role of technology, both graphing calculator and computer, in their instruction Starting with resources such as Science in Seconds for Kids by Jean Potter [1], the science students collaborate with the math students to design and conduct brief experiments. The data generated is analyzed using spreadsheets and later graphing calculators. Various classes of mathematical curves are examined using data generated by sensors/probes and CBLs. Through this experience the pre-service teachers learn to work collaboratively with their colleagues on meaningful tasks, strengthening the effectiveness of all participants

Experimental Design at the Intersection of Mathematics, Science, and Technology in Grades K-6

Interdisciplinary courses, highlighting as they do the area(s) the disciplines have in common, often give the misperception of a single body of knowledge and/or way of knowing. However, discipline based courses often leave the equally mistaken notion that the disciplines have nothing in common. The task of the methods courses described in this paper is to reach an appropriate balance so that our pre-service elementary (K-6) teachers have a realistic perception of the independence and interdependence of mathematics and science. At the College of William and Mary each cohort of pre-service elementary teachers enrolls in mathematics and science methods courses taught in consecutive hours. Both instructors emphasize the importance of the content pedagogy unique to their disciplines such as strategies for teaching problem solving, computation, algebraic thinking, and proportional reasoning in mathematics and strategies for teaching students how to investigate and understand the concepts of science. The instructors model interdisciplinary instruction by collaboratively teaching common content pedagogy such as the use of technology, data analysis, and interpretation. Students also identify real-life application of the mathematical principles they are learning that can be applied to science. The concept of simultaneously teaching appropriately selected math and science skills are stressed. Given this approach students are not left with the notion that mathematics is the handmaid of science nor the notion that it is the queen of the sciences. Rather, they view mathematics as a co-equal partner

Cooling dynamics of a dilute gas of inelastic rods: a many particle simulation

We present results of simulations for a dilute gas of inelastically colliding particles. Collisions are modelled as a stochastic process, which on average decreases the translational energy (cooling), but allows for fluctuations in the transfer of energy to internal vibrations. We show that these fluctuations are strong enough to suppress inelastic collapse. This allows us to study large systems for long times in the truely inelastic regime. During the cooling stage we observe complex cluster dynamics, as large clusters of particles form, collide and merge or dissolve. Typical clusters are found to survive long enough to establish local equilibrium within a cluster, but not among different clusters. We extend the model to include net dissipation of energy by damping of the internal vibrations. Inelatic collapse is avoided also in this case but in contrast to the conservative system the translational energy decays according to the mean field scaling law, E(t)\propto t^{-2}, for asymptotically long times.Comment: 10 pages, 12 figures, Latex; extended discussion, accepted for publication in Phys. Rev.

Diffraction in low-energy electron scattering from DNA: bridging gas phase and solid state theory

Using high-quality gas phase electron scattering calculations and multiple scattering theory, we attempt to gain insights on the radiation damage to DNA induced by secondary low-energy electrons in the condensed phase, and to bridge the existing gap with the gas phase theory and experiments. The origin of different resonant features (arising from single molecules or diffraction) is discussed and the calculations are compared to existing experiments in thin films.Comment: 40 pages preprint, 12 figures, submitted to J. Chem. Phy

Generic Modal Cut Elimination Applied to Conditional Logics

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics. For these, we obtain fully internalised calculi which are substantially simpler than those known in the literature, along with leaner proofs of cut elimination and complexity. In one case, conditional logic with modus ponens and conditional excluded middle, cut elimination and complexity were explicitly stated as open in the literature

Simulation for the oblique impact of a lattice system

The oblique collision between an elastic disk and an elastic wall is numerically studied. We investigate the dependency of the tangential coefficient of restitution on the incident angle of impact. From the results of simulation, our model reproduces experimental results and can be explained by a phenomenological theory of the oblique impact.Comment: 30 pages, 9 figures, submitted to J. Phys. Soc. Japa

Interferometry with Bose-Einstein Condensates in Microgravity

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Due to their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this paper we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far-field of a double-slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.Comment: 8 pages, 3 figures; 8 pages of supporting materia

Ab-initio study of model guanine assemblies: The role of pi-pi coupling and band transport

Several assemblies of guanine molecules are investigated by means of first-principle calculations. Such structures include stacked and hydrogen-bonded dimers, as well as vertical columns and planar ribbons, respectively, obtained by periodically replicating the dimers. Our results are in good agreement with experimental data for isolated molecules, isolated dimers, and periodic ribbons. For stacked dimers and columns, the stability is affected by the relative charge distribution of the pi orbitals in adjacent guanine molecules. pi-pi coupling in some stacked columns induces dispersive energy bands, while no dispersion is identified in the planar ribbons along the connections of hydrogen bonds. The implications for different materials comprised of guanine aggregates are discussed. The bandstructure of dispersive configurations may justify a contribution of band transport (Bloch type) in the conduction mechanism of deoxyguanosine fibres, while in DNA-like configurations band transport should be negligible.Comment: 21 pages, 6 figures, 3 tables, to be published in Phys. Rev.

Predicting the Location of Glioma Recurrence After a Resection Surgery

International audienceWe propose a method for estimating the location of glioma recurrence after surgical resection. This method consists of a pipeline including the registration of images at different time points, the estimation of the tumor infiltration map, and the prediction of tumor regrowth using a reaction-diffusion model. A data set acquired on a patient with a low-grade glioma and post surgery MRIs is considered to evaluate the accuracy of the estimated recurrence locations found using our method. We observed good agreement in tumor volume prediction and qualitative matching in regrowth locations. Therefore, the proposed method seems adequate for modeling low-grade glioma recurrence. This tool could help clinicians anticipate tumor regrowth and better characterize the radiologically non-visible infiltrative extent of the tumor. Such information could pave the way for model-based personalization of treatment planning in a near future