This paper attempts to quantify the accuracy limit of "nextitem-correct" prediction by using numerical optimization to estimate the student's probability of getting each question correct given a complete sequence of item responses. This optimization is performed without an explicit parameterized model of student behavior, but with the…

Latent variable models, such as the popular Knowledge Tracing method, are often used to enable adaptive tutoring systems to personalize education. However, finding optimal model parameters is usually a difficult non-convex optimization problem when considering latent variable models. Prior work has reported that latent variable models obtained…

In recent years, the usefulness of affect detection for educational software has become clear. Accurate detection of student affect can support a wide range of interventions with the potential to improve student affect, increase engagement, and improve learning. In addition, accurate detection of student affect could play an essential role in…

This article seeks to address a pedagogical theory of introducing the classicist and the frequentist approach to probability, by investigating important elements in 9th grade students' learning process while working with a "TinkerPlots2" combinatorial problem. Results from this research study indicate that, after the students had seen…

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, "TinkerPlots." Initial responses indicated that the students were aware of…

This paper presents a method designed to assist practitioners in the interpretation of the practical significance of a statistically significant logistic regression coefficient is presented. To avoid the interpretation problems encountered when using the traditionally reported change in either the log odds or odds values, this method centers the…

This research aims to study the ways in which "local" events of randomness, based on experiencing the outcome of individual events, can be developed into "global" understandings that focus on an aggregated view of probability (e.g. probability of an event). The findings reported in the paper are part of a broader study that adopted a strategy of…

A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…

A pivotal theorem which is of critical importance to statistical inference in probability and statistics is the Central Limit Theorem (CLT). The theorem concerns the sampling distribution of random samples taken from a population, including population distributions that do not have to be normal distributions. This paper contains a brief history of…

A method of generating common statistical tables using canned statistical computer software is presented. This method allows instructors to provide statistical tables for their students, tailored to their needs. The four most common tables used in elementary college statistics courses are z (standard normal), t, F, and chi square. Specific…

This paper addresses the problem of probabilistic reasoning as it applies to Truth Maintenance Systems (TMS). A computer-based Belief Maintenance System (BMS) has been constructed which manages a current set of probabilistic beliefs in much the same way that a TMS manages a set of true/false beliefs. It may be thought of as a generalization of a…