In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

Knowledge space theory (KST) is a mathematical framework for modeling and assessing student knowledge. While KST has successfully served as the foundation of several learning systems, recent advancements in machine learning provide an opportunity to improve on purely KST-based approaches to assessing student knowledge. As such, in this work we…

Understanding large-scale patterns in student course enrollment is a problem of great interest to university administrators and educational researchers. Yet important decisions are often made without a good quantitative framework of the process underlying student choices. We propose a probabilistic approach to modelling course enrollment…

This paper explores alternative assessment methods from the perspective of categorizations. It addresses the technologies that support assessment. It discusses initial, formative, and summative assessment, as well as objective and subjective assessment, and formal and informal assessment. It approaches each category of assessment from the…

A fairly large number of different methods exist for evaluating comparisons or null hypothetical contrasts. Because it is difficult to choose among them, this paper develops a 2 by 2 classification of the methods. The first dimension of the classification is decision-based error rate vs. experimentwise error rate. The second dimension is planned…

Methodological issues of using a class of neural networks called Mixture Density Networks (MDN) for discriminant analysis are discussed. MDN models have the advantage of having a rigorous probabilistic interpretation, and they have proven to be a viable alternative as a classification procedure in discrete domains. Both classification and…

This study is an attempt to answer the following research question: can the reliability of a criterion-referenced test be accurately determined according to a multiple classification of the student's performance? Specifically, the study pursues the beta-multinomial model, which postulates the probability distribution of an examinee's degree of…

Continuation ratio logits are used to model the possibilities of obtaining ordered categories in a polytomously scored item. This model is an alternative to other models for ordered category items such as the graded response model and the generalized partial credit model. The discussion includes a theoretical development of the model, a…

A method for comparing the cross validated classification accuracies of linear and quadratic classification rules is presented under varying data conditions for the k-group classification problem. With this method, separate-group as well as total-group proportions of correct classifications can be compared for the two rules. McNemar's test for…

Using computer simulation data, the effect of a single global outlier in two-group classification analysis was explored in terms of the outcome variables of change in classification results (PCHNG), change in misclassification rate (MISDIF), and change in precision of misclassification rate estimation. The precision of misclassification rate…

Some of the different approaches to standard setting are discussed. Brief comments and references are offered concerning strategies that rely primarily on the use of expert judgment. Controversy surrounds methods that use expert judges, as well as those using test groups to set scores empirically. A minimax procedure developed by H. Huynh, an…

This paper focuses on three aspects related to the conceptualization and application of canonical correlation analysis as a dominant statistical model: (1) partial canonical correlation analysis and its application in statistical testing; (2) the relation between canonical correlation analysis and discriminant analysis; and (3) the relation…

The purposes of the present investigation were to illustrate the applicability of categorization methodology for several empirical situations and to draw implications regarding the use of such methodology in examining categorical data. In using three tasks--two designed to measure cognitive dimensions (e.g., categorizing countries and categorizing…

This paper discusses the principles underlying discriminant analysis and constructs a simulated data set to illustrate its methods. Discriminant analysis is a multivariate technique for identifying the best combination of variables to maximally discriminate between groups. Discriminant functions are established on existing groups and used to…

This study compared the model of J. E. Grizzle, C. F. Starmer, and G. G. Koch (GSK, 1969) and log-linear model-based approaches for testing hypotheses in r x c contingency tables. Tables were simulated under various conditions of table, sample, row-effect size, and column-effect size. Test statistics for column (main) and interaction effects were…