Preservice Teachers’ Understandings of the Relation Between a Fraction or Integer and Its Decimal Expansion: Strength and Stability of Belief

Abstract

In an earlier study of preservice elementary and middle school teachers’ beliefs about repeating decimals, Weller, Arnon, and Dubinsky (2009) reported on a comparison of the mathematical performance of 77 preservice teachers who completed an APOS-based instructional unit with 127 preservice teachers who completed traditional instruction. The purpose of the current study, based on 47 interviews conducted 4 months after the instruction, during which time there was no further instruction on this topic, is to determine the strength and stability (over time) of the students’ beliefs, to uncover thinking that did not arise in the earlier study, and to see whether the interviews yield similar comparative results. The interviews did uncover changes in student thinking. The students who received the APOS-based instruction developed stronger and more stable (over time) beliefs that a repeating decimal is a number; a repeating decimal has a fraction or integer to which it corresponds; a repeating decimal in general equals its corresponding fraction or integer; and, in particular, In addition, a number of indices and categories were developed that may prove useful in other studies consisting of the comparison of interview and questionnaire data involving a large number of interview subjects.     

The antecedents and consequences of intergroup affective polarisation on social media

Social media platforms enable like-minded users to form online groups, interact and thereby contribute to ideological polarisation. However, online groups also polarise along a continuum of liking or affect for their group compared to other groups. We explore affective polarisation on social media and its implications for online intergroup interaction. Using social identity theory, we investigate the effects of group identification, passion, and affective polarisation on social media users' intergroup approach and avoidance tendencies. We test the research model in the context of political groups on social media. We find group identification contributes to affective polarisation by strengthening favouritism for the ingroup rather than hostility for the outgroup. Although those with greater group identification prefer to confront (approach) the opposition group on social media, the behaviour is a function of inflated feelings for the ingroup more so than animus for the outgroup. Interestingly, users with greater affective polarisation tend to shut out (avoid) the rival group on social media. Our findings imply affective polarisation contributes to group isolation that may exacerbate ideological polarisation.     

Speed scaling with a solar cell

We consider the setting of a device that obtains its energy from a battery and some regenerative source such as a solar cell. We consider the speed scaling problem of scheduling a collection of tasks with release times, deadlines, and sizes, so as to minimize the energy recharge rate of the regenerative source. This is the first theoretical investigation of speed scaling for devices with a regenerative energy source. We show that the problem can be expressed as a polynomial sized convex program. We show that, using the KKT conditions, one can obtain an efficient algorithm to verify the optimality of a schedule. We show that the energy optimal YDS schedule is 2-approximate with respect to the recharge rate. We show that the online algorithm BKP is O(1)$O\left(1\right)$-competitive with respect to recharge rate.     

libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations

In this paper we describe the libMesh (http://libmesh.sourceforge.net) framework for parallel adaptive finite element applications. libMesh is an open-source software library that has been developed to facilitate serial and parallel simulation of multiscale, multiphysics applications using adaptive mesh refinement and coarsening strategies. The main software development is being carried out in the CFDLab (http://cfdlab.ae.utexas.edu) at the University of Texas, but as with other open-source software projects; contributions are being made elsewhere in the US and abroad. The main goals of this article are: (1) to provide a basic reference source that describes libMesh and the underlying philosophy and software design approach; (2) to give sufficient detail and references on the adaptive mesh refinement and coarsening (AMR/C) scheme for applications analysts and developers; and (3) to describe the parallel implementation and data structures with supporting discussion of domain decomposition, message passing, and details related to dynamic repartitioning for parallel AMR/C. Other aspects related to C++ programming paradigms, reusability for diverse applications, adaptive modeling, physics-independent error indicators, and similar concepts are briefly discussed. Finally, results from some applications using the library are presented and areas of future research are discussed.     

Performing Efficient NURBS Modeling Operations on the GPU

We present algorithms for evaluating and performing modeling operations on NURBS surfaces using the programmable fragment processor on the Graphics Processing Unit (GPU). We extend our GPU-based NURBS evaluator that evaluates NURBS surfaces to compute exact normals for either standard or rational B-spline surfaces for use in rendering and geometric modeling. We build on these calculations in our new GPU algorithms to perform standard modeling operations such as inverse evaluations, ray intersections, and surface-surface intersections on the GPU. Our modeling algorithms run in real time, enabling the user to sketch on the actual surface to create new features. In addition, the designer can edit the surface by interactively trimming it without the need for retessellation. Our GPU-accelerated algorithm to perform surface-surface intersection operations with NURBS surfaces can output intersection curves in the model space as well as in the parametric spaces of both the intersecting surfaces at interactive rates. We also extend our surface-surface intersection algorithm to evaluate self-intersections in NURBS surfaces.     

Speed Scaling of Processes with Arbitrary Speedup Curves on a Multiprocessor

We consider the setting of a multiprocessor where the speeds of the m processors can be individually scaled. Jobs arrive over time and have varying degrees of parallelizability. A nonclairvoyant scheduler must assign the processes to processors, and scale the speeds of the processors. We consider the objective of energy plus flow time. We assume that a processor running at speed s uses power s ^α for some constant α>1. For processes that may have side effects or that are not checkpointable, we show an W(m^(a-1)/a2)\Omega(m^{(\alpha -1)/\alpha^{2}}) bound on the competitive ratio of any randomized algorithm. For checkpointable processes without side effects, we give an O(log m)-competitive algorithm. Thus for processes that may have side effects or that are not checkpointable, the achievable competitive ratio grows quickly with the number of processors, but for checkpointable processes without side effects, the achievable competitive ratio grows slowly with the number of processors. We then show a lower bound of Ω(log ^1/α m) on the competitive ratio of any randomized algorithm for checkpointable processes without side effects.     

GPU-accelerated minimum distance and clearance queries

We present practical algorithms for accelerating distance queries on models made of trimmed NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as coprocessors in accelerating CAD operations. By supplementing surface data with a surface bounding-box hierarchy on the GPU, we answer distance queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster and about two orders of magnitude more accurate than the commercial solid modeling kernel ACIS.     

An introduction to TMN

The Telecommunication Management Network standard (ITU-T M.3010), the Network Magagement Forum OMNIPoint program, and many related developments are summarized. TMN and OMNIPoint are presented as a means to achieve integrated network management in the telecommunications industry by calling for all management systems to include an interoperable interface which permits each system to be integrated into a larger management hierarchy. By means of such interfaces, hierarchical integration of management systems can be achieved within the administration of a single service provider. Interoperable interfaces also make possible the interconnection of multiple service providers and the connection of customer to service provider, resulting in the possibility of industry wide integration of management infrastructures at all levels.