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

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

Earning Legitimacy: Participation, Intellectual Property and Informed Consent

A booklet linking politics and practice aimed at museum practitioners and researchers working with museum

From 2D Integrable Systems to Self-Dual Gravity

We explain how to construct solutions to the self-dual Einstein vacuum equations from solutions of various two-dimensional integrable systems by exploiting the fact that the Lax formulations of both systems can be embedded in that of the self-dual Yang--Mills equations. We illustrate this by constructing explicit self-dual vacuum metrics on $\R^2\times \Sigma$, where $\Sigma$ is a homogeneous space for a real subgroup of SL(2, \C) associated with the two-dimensional system.Comment: 9 pages, LaTex, no figure

The measurement errors in the Swift-UVOT and XMM-OM

The probability of photon measurement in some photon counting instrumentation, such as the Optical Monitor on the XMM-Newton satellite, and the UVOT on the Swift satellite, does not follow a Poisson distribution due to the detector characteristics, but a Binomial distribution. For a single-pixel approximation, an expression was derived for the incident countrate as a function of the measured count rate by Fordham, Moorhead and Galbraith (2000). We show that the measured countrate error is binomial, and extend their formalism to derive the error in the incident count rate. The error on the incident count rate at large count rates is larger than the Poisson-error of the incident count rate.Comment: 4 pages, 2 postscript figures, submitted to MNRA

Cooperating Agents for 3D Scientific Data Interpretation

Many organizations collect vast quantities of three-dimensional (3-D) scientific data in volumetric form for a range of purposes, including resource exploration, market forecasting, and process modelling. Traditionally, these data have been interpreted by human experts with only minimal software assistance. However, such manual interpretation is a painstakingly slow and tedious process. Moreover, since interpretation involves subjective judgements and each interpreter has different scientific knowledge and experience, formulation of an effective interpretation often requires the cooperation of numerous such experts. Hence, there is a pressing need for a software system in which individual interpretations can be generated automatically and then refined through the use of cooperative reasoning and information sharing. To this end, a prototype system, SurfaceMapper, has been developed in which a community of cooperating software agents automatically locate and display interpretations in a volume of 3-D scientific data. The challenges and experiences in designing and building such a system are discussed. Particular emphasis is given to the agents' interactions and an empirical evaluation of the effectiveness of different cooperation strategies is presented

Mechanisms and Observations of Coronal Dimming for the 2010 August 7 Event

Coronal dimming of extreme ultraviolet (EUV) emission has the potential to be a useful forecaster of coronal mass ejections (CMEs). As emitting material leaves the corona, a temporary void is left behind which can be observed in spectral images and irradiance measurements. The velocity and mass of the CMEs should impact the character of those observations. However, other physical processes can confuse the observations. We describe these processes and the expected observational signature, with special emphasis placed on the differences. We then apply this understanding to a coronal dimming event with an associated CME that occurred on 2010 August 7. Data from the Solar Dynamics Observatory's (SDO) Atmospheric Imaging Assembly (AIA) and EUV Variability Experiment (EVE) are used for observations of the dimming, while the Solar and Heliospheric Observatory's (SOHO) Large Angle and Spectrometric Coronagraph (LASCO) and the Solar Terrestrial Relations Observatory's (STEREO) COR1 and COR2 are used to obtain velocity and mass estimates for the associated CME. We develop a technique for mitigating temperature effects in coronal dimming from full-disk irradiance measurements taken by EVE. We find that for this event, nearly 100% of the dimming is due to mass loss in the corona

Response to nitrogen fertilisers of wheat, oats, and barley in Western Australia

Trials were mainly sited in areas normally receiving more than 450 mm average annual rainfall. Response curves were fitted to each set of data and then averaged to give overall response curves for each crop. There was little difference between the crops in absolute or percentage response to nitrogen fertiliser but the nitrogen fertiliser rate required for maximum yield was highest for wheat and lowest for oats

Unification of Residues and Grassmannian Dualities

The conjectured duality relating all-loop leading singularities of n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM to a simple contour integral over the Grassmannian G(k,n) makes all the symmetries of the theory manifest. Every residue is individually Yangian invariant, but does not have a local space-time interpretation--only a special sum over residues gives physical amplitudes. In this paper we show that the sum over residues giving tree amplitudes can be unified into a single algebraic variety, which we explicitly construct for all NMHV and N^2MHV amplitudes. Remarkably, this allows the contour integral to have a "particle interpretation" in the Grassmannian, where higher-point amplitudes can be constructed from lower-point ones by adding one particle at a time, with soft limits manifest. We move on to show that the connected prescription for tree amplitudes in Witten's twistor string theory also admits a Grassmannian particle interpretation, where the integral over the Grassmannian localizes over the Veronese map from G(2,n) to G(k,n). These apparently very different theories are related by a natural deformation with a parameter t that smoothly interpolates between them. For NMHV amplitudes, we use a simple residue theorem to prove t-independence of the result, thus establishing a novel kind of duality between these theories.Comment: 56 pages, 11 figures; v2: typos corrected, minor improvement

The Momentum Amplituhedron

In this paper we define a new object, the momentum amplituhedron, which is the long sought-after positive geometry for tree-level scattering amplitudes in N = 4 super Yang-Mills theory in spinor helicity space. Inspired by the construction of the ordinary amplituhedron, we introduce bosonized spinor helicity variables to represent our external kinematical data, and restrict them to a particular positive region. The momentum amplituhedron M n,k is then the image of the positive Grassmannian via a map determined by such kinematics. The scattering amplitudes are extracted from the canonical form with logarithmic singularities on the boundaries of this geometry.Peer reviewedFinal Published versio