An important issue in personalized learning is to provide learners with customized learning according to their learning characteristics. This paper focused attention on scheming learning map as follows. The learning goal can be achieved via different pathways based on alternative materials, which have the relationships of prerequisite, dependence,…

This study compares the performance of two estimation algorithms of new usage, the Metropolis-Hastings Robins-Monro (MHRM) and the Hamiltonian MCMC (HMC), with two consolidated algorithms in the psychometric literature, the marginal likelihood via EM algorithm (MML-EM) and the Markov chain Monte Carlo (MCMC), in the estimation of multidimensional…

To further understand the properties of data-generation algorithms for multivariate, nonnormal data, two Monte Carlo simulation studies comparing the Vale and Maurelli method and the Headrick fifth-order polynomial method were implemented. Combinations of skewness and kurtosis found in four published articles were run and attention was…

Most computerized adaptive tests (CATs) have been studied using the framework of unidimensional item response theory. However, many psychological variables are multidimensional and might benefit from using a multidimensional approach to CATs. This study investigated the accuracy, fidelity, and efficiency of a fully multidimensional CAT algorithm…

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

Steinley and Brusco (2011) presented the results of a huge simulation study aimed at evaluating cluster recovery of mixture model clustering (MMC) both for the situation where the number of clusters is known and is unknown. They derived rather strong conclusions on the basis of this study, especially with regard to the good performance of…

Although problem-based learning (PBL) has many advantages, it often fails to connect to the real world outside the classroom. The integration with the laboratory setting and the use of information and communication technologies (ICTs) have been proposed to address this deficiency. Multi-user virtual environments (MUVEs) like Second Life (SL) are…

The order of problems presented to students is an important variable that affects learning effectiveness. Previous studies have shown that solving problems in a blocked order, in which all problems of one type are completed before the student is switched to the next problem type, results in less effective performance than does solving the problems…

The purpose of this embedded quasi-experimental mixed methods research was to use solving simple linear equations as the lens for looking at the effectiveness of concrete and virtual manipulatives as compared to a control group using learning methods without manipulatives. Further, the researcher wanted to investigate unique benefits and drawbacks…

Automated test assembly (ATA) has been an area of prolific psychometric research. Although ATA methodology is well developed for unidimensional models, its application alongside cognitive diagnosis models (CDMs) is a burgeoning topic. Two suggested procedures for combining ATA and CDMs are to maximize the cognitive diagnostic index and to use a…

Item factor analysis (IFA), already well established in educational measurement, is increasingly applied to psychological measurement in research settings. However, high-dimensional confirmatory IFA remains a numerical challenge. The current research extends the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm, initially proposed for…

Perhaps the most common criterion for partitioning a data set is the minimization of the within-cluster sums of squared deviation from cluster centroids. Although optimal solution procedures for within-cluster sums of squares (WCSS) partitioning are computationally feasible for small data sets, heuristic procedures are required for most practical…

In this paper, two emerging learning and teaching methods have been studied: collaboration in concert with algorithm visualization. When visualizations have been employed in collaborative learning, collaboration introduces new challenges for the visualization tools. In addition, new theories are needed to guide the development and research of the…

This article provides technical descriptions of five fixed parameter calibration (FPC) methods, which were based on marginal maximum likelihood estimation via the EM algorithm, and evaluates them through simulation. The five FPC methods described are distinguished from each other by how many times they update the prior ability distribution and by…

In psychometrics, it is often the case that one encounters data that may not be considered random but selected in a systematic way according to some explanatory variable. In this article, maximum likelihood estimation is considered when data are supposed to arise from a bivariate normal distribution that is truncated in an extreme way. Two methods…