Though statistical testing is commonly practiced, the logic of statistical tests is confusing, thinking about distributions is difficult, and the way statisticians formulate expectations as probability distributions is poorly understood. To support instruction, the statistics education community has increasingly utilized simulation-based…

In the last decades, the development of computerized adaptive testing (CAT) has allowed more precise measurements with a smaller number of items. In this study, we develop an item bank (IB) to generate the adaptive algorithm and simulate the functioning of CAT to assess the domains of mathematical knowledge in Argentinian university students…

A large-scale simulation study of the assessment effectiveness of a particular instantiation of knowledge space theory is described. In this study, data from more than 700,000 actual assessments in mathematics using the ALEKS (Assessment and LEarning in Knowledge Spaces) software were used to determine response probabilities for the same number of…

Due to low cost monte-carlo (MC) simulations have been extensively conducted in the area of educational measurement. However, the results derived from MC studies may not always be generalizable to operational studies. The purpose of this study was to provide a methodological discussion on the other different types of simulation methods, and run…

This mixed-method study aims to explore the feasibility of using the game-based, multimodal representation of mathematical problems to support middle school students' practice and performance of math problem representation and solving. A three-dimensional architectural simulation game, called E-Rebuild, was developed to engage students in…

Classical automated test assembly (ATA) methods assume fixed and known coefficients for the constraints and the objective function. This hypothesis is not true for the estimates of item response theory parameters, which are crucial elements in test assembly classical models. To account for uncertainty in ATA, we propose a chance-constrained…

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap,…

In this study purposes to indicate the effect of the number of DIF items and the distribution of DIF items in these forms, which be equalized on equating error. Mean-mean, mean-standard deviation, Haebara and Stocking-Lord Methods used in common item design equal groups as equalization methods. The study included six different simulation…

This study introduces the signal weighted teacher value-added model (SW VAM), a value-added model that weights student-level observations based on each student's capacity to signal their assigned teacher's quality. Specifically, the model leverages the repeated appearance of a given student to estimate student reliability and sensitivity…

This research proposes a new statistic for testing latent variable distribution fit for unidimensional item response theory (IRT) models. If the typical assumption of normality is violated, then item parameter estimates will be biased, and dependent quantities such as IRT score estimates will be adversely affected. The proposed statistic compares…

Large-scale assessments (LSAs) use Mislevy's "plausible value" (PV) approach to relate student proficiency to noncognitive variables administered in a background questionnaire. This method requires background variables to be completely observed, a requirement that is seldom fulfilled. In this article, we evaluate and compare the…

Participation in international large-scale assessments has grown over time with the largest, the Programme for International Student Assessment (PISA), including more than 70 education systems that are economically and educationally diverse. To help accommodate for large achievement differences among participants, in 2009 PISA offered…

A challenge with flipped instruction is the pre-class preparation, where students independently learn fundamental content outside the classroom. For this pre-class learning, instructors typically assign videos with quizzes. However, this approach is the same for all and does not address differential needs. In a prior National Science Foundation…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…