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

Results to be expected from light scattering dust analyzer during a rendezvous mission

The light scattering principle for particle detection is customary for the measurement of aerosols. Light scattering techniques can be applied to mixtures of particles (nephelometers) and to single particles as well. Measuring particle mixtures simplify detection because of the higher intensity level, however, information concerning the individual particle is lost. To provide well defined conditions over the whole rendezvous period, i.e., constant illumination beam and unchangeable scattering angle, the use of an artificial light source (instead of the sun) and a scattering volume located within the S/C is desirable. Considering this and the relatively low particle densities to be expected, the measurement of particle mixtures must be excluded

Economic development efforts in the seventh district

Economic development - North Central states ; Federal Reserve District, 7th

Hydrogen-bonded liquid crystals with broad-range blue phases

We report a modular supramolecular approach for the investigation of chirality induction in hydrogen-bonded liquid crystals. An exceptionally broad blue phase with a temperature range of 25 °C was found, which enabled its structural investigation by solid state 19F-NMR studies and allowed us to report order parameters of the blue phase I for the first time

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.

A Tableaux Calculus for Reducing Proof Size

A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It is shown that the obtained proof procedure is sound, refutationally complete and allows to reduce the size of the tableau by an exponential factor. The approach is compatible with all usual refinements of tableaux.Comment: Technical Repor