A Districtwide Study of Automaticity When Included in Concept‐Based Elementary School Mathematics Instruction

While conceptual understanding of properties, operations, and the base‐ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three elementary schools in a school district implements mandatory automaticity drills for 10 minutes each day while the remaining two elementary schools, with the same curriculum and very similar demographics, do not. This study looks at (a) the impact that schoolwide implementation of automaticity drills has on schoolwide computational math skills as measured by the ITBS and (b) the relationship between automaticity and conceptual understanding as measured by statewide standardized testing. The results suggest that while there may be an association between automaticity and higher performance on standardized tests, caution should be taken before assuming there are benefits to promoting automaticity drills. These results are consistent with those that support a process‐driven approach to automaticity based on familiarity with properties and strategies associated with the base‐ten number system; they are not consistent with those that support an answer‐driven approach to automaticity based on memorization of answers.     

Structural dynamics and stability analysis of 2D-FG microbeams with two-directional porosity distribution and variable material length scale parameter

Abstract

Since the two-directional functionally graded (2D-FG) materials can satisfy the new requirements raised based on the elimination of the stress concentration, delamination and cracking problems accompanying with the low cost and lightweight on the structures without sacrificing the stiffness and strength, the structural analyses of these structures become more important than ever. Moreover, the usage of the micro-electromechanical systems composed of 2D-FG materials has been increasing in automotive, military, space, biomedical, and nuclear energy industries. Within this study, the free vibration and buckling behaviors of 2D-FG porous microbeams are investigated based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory and using finite element method. The effects of the thickness to material length scale parameter (MLSP) accompanying with the micro-porosity volume fraction ratio, boundary condition, aspect ratio, and gradient index on the dimensionless fundamental frequencies and dimensionless critical buckling loads of the 2D-FG porous microbeams are investigated. Moreover, with assumption of the variable material length scale parameters (VMLSP), the computed results are compared with ones obtained by employing constant MLSP. It is found that VMLSP increases the stiffness of the 2D-FG porous microbeams and effects the free vibration and buckling responses of these structures.     

A step toward the wet surface chemistry of glycine and alanine on Cu{110}: destabilization and decomposition in the presence of near-ambient water vapor

The coadsorption of water with organic molecules under near-ambient pressure and temperature conditions opens up new reaction pathways on model catalyst surfaces that are not accessible in conventional ultrahigh-vacuum surface-science experiments. The surface chemistry of glycine and alanine at the water-exposed Cu{110} interface was studied in situ using ambient-pressure photoemission and X-ray absorption spectroscopy techniques. At water pressures above 10(-5) Torr a significant pressure-dependent decrease in the temperature for dissociative desorption was observed for both amino acids, accompanied by the appearance of a new CN intermediate, which is not observed for lower pressures. The most likely reaction mechanisms involve dehydrogenation induced by O and/or OH surface species resulting from the dissociative adsorption of water. The linear relationship between the inverse decomposition temperature and the logarithm of water pressure enables determination of the activation energy for the surface reaction, between 213 and 232 kJ/mol, and a prediction of the decomposition temperature at the solid-liquid interface by extrapolating toward the equilibrium vapor pressure. Such experiments near the equilibrium vapor pressure provide important information about elementary surface processes at the solid-liquid interface, which can be retrieved neither under ultrahigh vacuum conditions nor from interfaces immersed in a solution.     

Double direct templating of periodically nanostructured ZnS hollow microspheres

We introduce a "double direct templating" method for obtaining hollow microspheres with periodically nanostructured walls. Silica or polystyrene colloids are dispersed in a self-assembled hexagonal lyotropic liquid crystal containing precursors for ZnS. The semiconductor ZnS mineralizes on the surface of the colloid, expressing a pore morphology that is a copy of the structure of the liquid crystal. After etching of the sacrificial colloids, hollow capsules with templated and uniform mesoporous shells are obtained.     

On some constacyclic codes over $$\mathbb {Z}_{4}\left[ u\right] /\left\langle u^{2}-1\right\rangle $$, their $$\mathbb {Z}_4$$Z4 images,and new codes

In this paper, we study \(\lambda \)-constacyclic codes over the ring \(R=\mathbb {Z}_4+u\mathbb {Z}_4\) where \(u^{2}=1\), for \(\lambda =3+2u\) and \(2+3u\). Two new Gray maps from R to \(\mathbb {Z}_4^{3}\) are defined with the goal of obtaining new linear codes over \(\mathbb {Z}_4\). The Gray images of \(\lambda \)-constacyclic codes over R are determined. We then conducted a computer search and obtained many \(\lambda \)-constacyclic codes over R whose \(\mathbb {Z}_4\)-images have better parameters than currently best-known linear codes over \(\mathbb {Z}_4\).     

Convergence of Solutions of Nonhomogeneous Linear Difference Systems with Delays

Sufficient conditions are given for the asymptotic constancy of the solutions of a linear system of difference equations with delays. Moreover, it is shown that the limits of the solutions, as t→∞, can be computed in terms of the initial function and a special matrix solution of the corresponding adjoint equation.     

A Confidence Region Approach to Tuning for Variable Selection

We develop an approach to tuning of penalized regression variable selection methods by calculating the sparsest estimator contained in a confidence region of a specified level. Because confidence intervals/regions are generally understood, tuning penalized regression methods in this way is intuitive and more easily understood by scientists and practitioners. More importantly, our work shows that tuning to a fixed confidence level often performs better than tuning via the common methods based on Akaike information criterion (AIC), Bayesian information criterion (BIC), or cross-validation (CV) over a wide range of sample sizes and levels of sparsity. Additionally, we prove that by tuning with a sequence of confidence levels converging to one, asymptotic selection consistency is obtained, and with a simple two-stage procedure, an oracle property is achieved. The confidence-region-based tuning parameter is easily calculated using output from existing penalized regression computer packages. Our work also shows how to map any penalty parameter to a corresponding confidence coefficient. This mapping facilitates comparisons of tuning parameter selection methods such as AIC, BIC, and CV, and reveals that the resulting tuning parameters correspond to confidence levels that are extremely low, and can vary greatly across datasets. Supplemental materials for the article are available online.     

A multi-objective mathematical model for the industrial hazardous waste location-routing problem

Industrial hazardous waste management involves the collection, transportation, treatment, recycling and disposal of industrial hazardous materials that pose risk to their surroundings. In this paper, a new multi-objective location-routing model is developed, and implemented in the Marmara region of Turkey. The aim of the model is to help decision makers decide on locations of treatment centers utilizing different technologies, routing different types of industrial hazardous wastes to compatible treatment centers, locations of recycling centers and routing hazardous waste and waste residues to those centers, and locations of disposal centers and routing waste residues there. In the mathematical model, three criteria are considered: minimizing total cost, which includes total transportation cost of hazardous materials and waste residues and fixed cost of establishing treatment, disposal and recycling centers; minimizing total transportation risk related to the population exposure along transportation routes of hazardous materials and waste residues; and minimizing total risk for the population around treatment and disposal centers, also called site risk. A lexicographic weighted Tchebycheff formulation is developed and computed with CPLEX software to find representative efficient solutions to the problem. Data related to the Marmara region is obtained by utilizing Arcview 9.3 GIS software and Marmara region geographical database.