Bashar Zogheib

Confidence interval estimation for the population coefficient of variation using ranked set sampling: a simulation study

In this paper, an evaluation of the performance of several confidence interval estimators of the population coefficient of variation (τ) using ranked set sampling compared to simple random sampling is performed. Two performance measures are used to assess the confidence intervals for τ, namely: width and coverage probabilities. Simulated data were generated from normal, log-normal, skew normal, Gamma, and Weibull distributions with specified population parameters so that the same values of τ are obtained for each distribution, with sample sizes n=15, 20, 25, 50, 100. A real data example representing birth weight of 189 newborns is used for illustration and performance comparison.

A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions

This paper is devoted to develop a new matrix scheme for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions. We first transform these equations into equivalent integro partial differential equations (PDEs). Such these integro-PDEs contain both of the initial and boundary conditions and can be solved numerically in a more appropriate manner. Subsequently, all the existing known and unknown functions in the latter equations are approximated by Bernoulli polynomials and operational matrices of differentiation and integration together with the completeness of these polynomials can be used to reduce the integro-PDEs into the associated algebraic generalized Sylvester equations. For solving these algebraic equations, an efficient Krylov subspace iterative method (i.e., BICGSTAB) is implemented. Two numerical examples are given to demonstrate the efficiency, accuracy, and versatility of the proposed method.

University Student Perceptions of Technology Use in Mathematics Learning.

Although most universities and educators are relying on implementing various technological tools in the curriculum, acceptance of such tools among students is still not sufficient. The Technology Acceptance Model (TAM) has been widely used by researchers to test user’s acceptance of technology in business, education and other domains. This research study is an attempt that tests the integration of TAM and user satisfaction in the educational field. It particularly investigates students’ acceptance to use MyMathLab, a technological tool, in university math classes in the Middle East. Structural equation modelling with various constructs was used. Findings support the theoretical model showing the great influence of user satisfaction on perceived ease of use and subjective norm on behavioural intention. The findings of this study also demonstrate that selfefficacy, user satisfaction, subjective norms, perceived usefulness, perceived ease of use, and students’ attitude constructs all have a positive impact on students’ behavioural intentions to adopt and use technological tools in a mathematics class room. Findings of this research have greater implications for educators and students worldwide. Keyword: TAM, MyMathLab, university, students, math, self-satisfaction. Introduction Higher education institutions have implemented different technologies to provide teachers and students with many interesting tools that can be used to improve the teaching– learning process (Martín-Blas & Serrano-Fernández, 2009). However, despite the strong presences of information and communication technology (ICT) in classrooms, studies have shown that ICT is underused (Ruthven, 2009). For instance, although institutions have made large investments in educational technology, many technologies have Material published as part of this publication, either on-line or in print, is copyrighted by the Informing Science Institute. Permission to make digital or paper copy of part or all of these works for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage AND that copies 1) bear this notice in full and 2) give the full citation on the first page. It is permissible to abstract these works so long as credit is given. To copy in all other cases or to republish or to post on a server or to redistribute to lists requires specific permission and payment of a fee. Contact Publisher@InformingScience.org to request redistribution permission. Technology Use in Mathematics Learning 418 been underutilised or abandoned completely, due to limited user acceptance (Liu, Liao & Pratt, 2009; Teo, 2009), for example, SMART notebook. Similarly, Imtiaz and Mirhashemi (2013, p. 23) argued that many advantages of technology in education have been realized, but there still remain many hindrances and barriers in technology adoption and use in education. Imtiaz and Mirhashemi (2013, p. 23) stipulated that this has led to a less than expected implementation of technology in education. This study tries to bridge the gap identified in prior research (e.g., Liu et al., 2009; Ruthven, 2009; Teo, 2009) in relation to technology adoption and use in education. The current study proposes and empirically tests an integrated theoretical model of university students’ acceptance and intentions to use a technological tool, named MyMathLab, based on an extended version of the technology acceptance model (TAM) and user satisfaction. Recently, researchers argued that the models and theories that developed from the body of research within the business contexts could be applied to understanding technology acceptance in educational contexts (Teo, 2013). Among the most popular models in technology acceptance research, the technology acceptance model (TAM) (Davis, 1989) has been found to be a robust model for understanding the factors that affect users’ intention to use technology in education (Teo, 2012). In fact, TAM has become one of the most widely used models in technology embedded education research (Kiliç, 2014). This study aims at investigating and assessing the factors that determine the adoption of technological tools in mathematics among university students. The main research question this paper explores is, What are the main factors that determine university students’ attitudes toward adopting technological tools in learning? This paper is arranged into six sections. Following the Introduction, the second section provides a brief review of prior studies in technology adoption in general, technology adoption in education, and the exemplar technological tool used for investigation in this study. The third section discusses the research model and hypotheses. Section four describes the research method. The data analysis is presented in section five, and, finally, section six discusses the findings and concludes the paper.

A penalty scheme for academic dishonesty

This work contributes to better understanding of the optimal penalties for the deterrence of academic dishonesty. Academic dishonesty has recently become one of the most prevalent issues in higher education [1]. In order to address this issue, researches have focused on understanding cheating methods and techniques, determinants, punishment, and consequences. Unlike common descriptive, exploratory or regression-based approaches proposed in the literature, this work proposes a mathematical framework for analyzing the optimal academic dishonesty penalties. Results suggest that expected penalties should be more than the possible gain in grades obtained by committing an offense. Moreover, it shows that increasing penalties are not always optimal for dealing with repeat cheats.

Modal Hermite spectral collocation method for solving multi-dimensional hyperbolic telegraph equations

Abstract The present research is contemplated proposing a numerical solution of multi-dimensional hyperbolic telegraph equations with appropriate initial time and boundary space conditions. The truncated Hermite series with unknown coefficients are used for approximating the solution in both of the spatial and temporal variables. The basic idea for discretizing the considered one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) telegraph equations is based on the collocation method together with the Hermite operational matrices of derivatives. The resulted systems of linear algebraic equations are solved by some efficient methods such as LU factorization. The solution of the algebraic system contains the coefficients of the truncated Hermite series. Numerical experiments are provided to illustrate the accuracy and efficiency of the presented numerical scheme. Comparisons of numerical results associated to the proposed method with some of the existing numerical methods confirm that the method is accurate and fast experimentally.

Bernoulli Collocation Method for Solving Linear Multidimensional Diffusion and Wave Equations with Dirichlet Boundary Conditions

A numerical approach is proposed for solving multidimensional parabolic diffusion and hyperbolic wave equations subject to the appropriate initial and boundary conditions. The considered numerical solutions of the these equations are considered as linear combinations of the shifted Bernoulli polynomials with unknown coefficients. By collocating the main equations together with the initial and boundary conditions at some special points (i.e., CGL collocation points), equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. Operational matrices of differentiation are implemented for speeding up the operations. In both of the one-dimensional and two-dimensional diffusion and wave equations, the geometrical distributions of the collocation points are depicted for clarity of presentation. Several numerical examples are provided to show the efficiency and spectral (exponential) accuracy of the proposed method.

On the optimality of escalating penalties for repeat offences against the academic honour code

Abstract Although academic dishonesty has a long history in academia, its pervasiveness has recently reached an alarming level. Academic dishonesty not only undermines the purpose of education and the assessment process but also threatens the creditability of academic records. We propose a framework for analysing students’ behaviour with respect to academic policies and honour codes. We draw an analogy between law enforcement and academic integrity enforcement and highlight similarities and differences. The proposed framework captures major determinants of academic dishonesty reported in the literature, namely detection probability, punishment severity, class average and record of academic deviance. The framework models both students’ development of nonacademic skills to improve their grades and teaching assistants’ development of detection skills, which both affect the detection probability. Our analysis demonstrates that the optimality of escalating penalties is conditional on the offenders and academic policy enforcers learning. Use-case scenarios are presented to facilitate the implementation of our results in classrooms.

Optimal penalties for misbehavior deterrence in communication networks

The communication among entities in any network is administered by a set of rules and technical specifications detailed in the communication protocol. All communicating entities adhere to the same protocol to successfully exchange data. Most of the rules are expressed in an algorithm format that computes a decision based on a set of inputs provided by communicating entities or collected by a central controller. Due to the increasing number of communicating entities and large bandwidth required to exchange the set of inputs generated at each entity, distributed implementations have been favorable to reduce the control overhead. In such implementations, each entity self-computes crucial protocol decisions; therefore, can alter these decisions to gain unfair share of the resources managed by the protocol. Misbehaving users degrade the performance of the whole network in-addition to starving well-behaving users. In this work we develop a framework to derive the optimal penalty strategy for penalizing misbehaving users. The proposed framework considers users learning of the detection mechanism techniques and the detection mechanism tracking of the users behavior and history of protocol offenses. Analysis indicate that escalating penalties are optimal for deterring repeat protocol offenses.

Effects of some design factors on the distribution of similarity indices in cluster analysis

ABSTRACT This article investigates the effects of number of clusters, cluster size, and correction for chance agreement on the distribution of two similarity indices, namely, Jaccard and Rand indices. Skewness and kurtosis are calculated for the two indices and their corrected forms then compared with those of the normal distribution. Three clustering algorithms are implemented: complete linkage, Ward, and K-means. Data were randomly generated from bivariate normal distributions with specified means and variance covariance matrices. Three-way ANOVA is performed to assess the significance of the design factors using skewness and kurtosis of the indices as responses. Test statistics for testing skewness and kurtosis and observed power are calculated. Simulation results showed that independent of the clustering algorithms or the similarity indices used, the interaction effect cluster size x number of clusters and the main effects of cluster size and number of clusters were found always significant for skewness and kurtosis. The three way interaction of cluster size x correction x number of clusters was significant for skewness of Rand and Jaccard indices using all clustering algorithms, but was not significant using Wards method for both Rand and Jaccard indices, while significant for Jaccard only using complete linkage and K-means algorithms. The correction for chance agreement was significant for skewness and kurtosis using Rand and Jaccard indices when complete linkage method is used. Hence, such design factors must be taken into consideration when studying distribution of such indices.