Planning District‐Wide Professional Development: Insights Gained From Teachers and Students Regarding Mathematics Teaching in a Large Urban District

This paper describes the mechanism used to gain insights into the state of the art of mathematics instruction in a large urban district in order to design meaningful professional development for the teachers in the district. Surveys of close to 2,000 elementary, middle school, and high school students were collected in order to assess the instructional practices used in mathematics classes across the district. Students were questioned about the frequency of use of various instructional practices that support the meaningful learning of mathematics. These included practices such as problem solving, use of calculators and computers, group work, homework, discussions, and projects, among others. Responses were analyzed and comparisons were drawn between elementary and middle school students' responses and between middle school and high school responses. Finally, fifth‐grade student responses were compared to those of their teachers. Student responses indicated that they had fewer inquiry‐based experiences, fewer student‐to‐student interactions, and fewer opportunities to defend their answers and justify their thinking as they moved from elementary to middle school to high school. In the elementary grades students reported an overemphasis on the use of memorization of facts and procedures and sparse use of calculators. Results were interpreted and specific directions for professional development, as reported in this paper, were drawn from these data. The paper illustrates how student surveys can inform the design of professional development experiences for the teachers in a district.     

The Effects of a Study‐Group Process on the Implementation of Reform in Mathematics Education

In each of three consecutive years, 16 teachers were admitted to a program in which they participated in a study group to reform their teaching practices in mathematics. The 48 (total) elementary school teachers in this program were selected to ensure diversity of setting— urban and suburban, as well as public and parochial. Teachers routinely met with the study group for 1 year, engaging in follow‐up activities after that year. Surveys, interviews, and site visits showed that teachers underwent significant changes in their knowledge, beliefs, and teaching practices and were attempting to implement reform consistent with current standards. Teachers with 11 to 25 years of experience demonstrated the greatest changes. Long‐term effects of the program and its impact on colleagues within the building and district have yet to be studied.     

A flexible and generic approach to dynamic modelling of supply chains

In this paper, we present a new modelling approach for realistic supply chain simulation. The model provides an experimental environment for informed comparison between different supply chain policies. A basic simulation model for a generic node, from which a supply chain network can be built, has been developed using an object-oriented approach. This generic model allows the incorporation of the information and physical systems and decision-making policies used by each node. The object-oriented approach gives the flexibility in specifying the supply chain configuration and operation decisions, and policies. Stochastic simulations are achieved by applying Latin Supercube Sampling to the uncertain variables in descending order of importance, which reduces the number of simulations required. We also present a case study to show that the model is applicable to a real-life situation for dynamic stochastic studies.     

Allocating electricity transmission costs through tracing: a game-theoretic rationale

Tracing is a method of assigning flows in an electricity network to particular generators and loads, assuming perfect mixing at each node. It can be used to assign costs to transmission users. We show that the resulting allocation is equal to the Shapley value of an equivalent co-operative game.     

Timelike Minimal Surfaces via Loop Groups

This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces.In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.     

A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle

In this paper, a generalized anti–maximum principle for the second order differential operator with potentials is proved. As an application, we will give a monotone iterative scheme for periodic solutions of nonlinear second order equations. Such a scheme involves the L^p norms of the growth, 1 ≤ p ≤ ∞, while the usual one is just the case p = ∞.     

Dynamic interaction of plasma flow with the hot boundary layer of a geomagnetic trap

The study of the interaction between collisionless plasma flow and stagnant plasma revealed the presence of an outer boundary layer at the border of a geomagnetic trap, where the super-Alfvén subsonic laminar flow changes over to the dynamic regime characterized by the formation of accelerated magnetosonic jets and decelerated Alfvén flows with characteristic relaxation times of 10–20 min. The nonlinear interaction of fluctuations in the initial flow with the waves reflected from an obstacle explains the observed flow chaotization. The Cherenkov resonance of the magnetosonic jet with the fluctuation beats between the boundary layer and the incoming flow is the possible mechanism of its formation. In the flow reference system, the incoming particles are accelerated by the electric fields at the border of boundary layer that arise self-consistently as a result of the preceding wave-particle interactions; the inertial drift of the incoming ions in a transverse electric field increasing toward the border explains quantitatively the observed ion acceleration. The magnetosonic jets may carry away downstream up to a half of the unperturbed flow momentum, and their dynamic pressure is an order of magnitude higher than the magnetic pressure at the obstacle border. The appearance of nonequilibrium jets and the boundary-layer fluctuations are synchronized by the magnetosonic oscillations of the incoming flow at frequencies of 1–2 mHz.     

A power mode approach to estimating vibrational power transmitted by multiple sources

A power mode method for the estimation of the power transmitted to a flexible receiver by an array of point force excitations is described. The vibrational power transmitted by N discrete point forces is regarded as the power transmitted by N independent power modes following eigendecomposition of the mobility matrix of the receiving structure. Approximate expressions for the upper and lower bounds and the mean value of the transmitted power are then developed in terms of these power modes. The approach is extended to more general cases, including that where both force and moment excitations are applied to the structure and where there are velocity source excitations. Numerical examples are presented.