Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

This article details an exploratory data analysis project using the Common Online Data Analysis Platform (CODAP) based on the "Guidelines for Assessment and Instruction in Statistics Education" (GAISE) four-part statistical problem-solving model. The project goal was to answer what similarities and differences exist within the school…

A growing body of research suggests that accounting for student specific variability in educational data can improve modeling accuracy and may have implications for individualizing instruction. The Additive Factors Model (AFM), a logistic regression model used to fit educational data and discover/refine skill models of learning, contains a…

Online educational technologies offer opportunities for providing individualized feedback and detailed profiles of students' skills. Yet many technologies for mathematics education assess students based only on the correctness of either their final answers or responses to individual steps. In contrast, examining the choices students make for how…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Supplemental Instruction (SI) is a program that seeks to improve student success by targeting classes with high failure rates, as defined with a failure percentage of 30% or more. It is organized by an administrative SI supervisor who supervises SI leaders, which are students that have successfully completed the courses that they have been…

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…

Individuals vary in their responses to incentives and opportunities. For example, additional education will affect one person differently than another. In recent years, econometricians have given increased attention to such heterogeneous responses and to the consequences of such responses for interpreting regression estimates, especially…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

Learning analysts often consider whether learning processes across time are related (1) to one another or (2) to learning outcomes at higher levels. For example, are a group's temporal sequences of talk (e.g., correct evaluation [right arrow] correct, new idea) during its problem solving related to its group solution? I show how to address these…

A long-standing challenge for knowledge tracing is how to update estimates of multiple subskills that underlie a single observable step. We characterize approaches to this problem by how they model knowledge tracing, fit its parameters, predict performance, and update subskill estimates. Previous methods allocated blame or credit among subskills…

In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

Recently, the authors have been exploring the use of propensity score methods for developing evidence of program impact. Specifically, they have been developing evidence (after one year of implementation) of the effects of the Math Science Partnership in New York City ("MSPinNYC2") on high school students' achievement--both in terms of…

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n x 1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a…

This study was designed to forge stronger theoretical and empirical links between achievement goal theory and attribution theory. High school students ("N" = 224) completed a self-report survey that assessed 3 types of achievement goals, 7 types of attributions, and self-efficacy. Results indicated that students' adoption of achievement…