The role of mathematical modelling pertains several disciplines, both STEM and non-STEM, and various fields: education, academy, work, everyday and social life. Despite its importance, it is not uncommon to see university students facing difficulties with the use of Mathematics to create models, even when mathematical entities that play a role in…

Many national science frameworks (e.g., Next Generation Science Standards) argue that developing mathematical modeling competencies is critical for students' deep understanding of science. However, science teachers may be unprepared to assess these competencies. We are addressing this need by developing virtual lab performance assessments that…

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…

An adaptive test can usually match or exceed the measurement precision of conventional tests several times its length. This increased efficiency is not without costs, however, as the models underlying adaptive testing make strong assumptions about examinees and items. Most troublesome is the assumption that item pools are unidimensional. Truly…

An approach to scoring reading comprehension based on the concept of the testlet is described, using models developed for items in multiple categories. The model is illustrated using data from 3,866 examinees. Application of testlet scoring to multiple category models developed for individual items is discussed. (SLD)

A method of automatically selecting items for inclusion in a test with constraints on item content and statistical properties was applied to real data. Tests constructed manually from the same data and constraints were compared to tests constructed automatically. Results show areas in which automated assembly can improve test construction. (SLD)

Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributions. The focus is on the conditions under which stochastic order in families of conditional distributions is transferred to their inverse distributions,…

The symposium, "Taming the Rasch Tiger: Using Item Response Theory in Practical Educational Measurement," was organized to deemphasize the technical complexities of item response theory (IRT) and to show the audience how IRT can be used in practical educational measurement. Four papers from the symposium are summarized and comments are…

Computerized adaptive testing procedures (CATPs) based on the graded response method (GRM) of F. Samejima (1969) and the partial credit model (PCM) of G. Masters (1982) were developed and compared. Both programs used maximum likelihood estimation of ability, and item selection was conducted on the basis of information. Two simulated data sets, one…

This simulation study involved the design of two two-stage tests in which the routing tests and the second-stage measurement testlets took the form of a multidimensional knapsack problem with prespecified target informations and constraints to be enumerated using the algorithm of E. Balas. Two conventional tests of similar length to the two-stage…

A nominal response model-based computerized adaptive testing procedure (nominal CAT) was implemented using simulated data. Ability estimates from the nominal CAT were compared to those from a CAT based upon the three-parameter logistic model (3PL CAT). Furthermore, estimates from both CAT procedures were compared with the known true abilities used…

In the answer-until-correct mode of multiple-choice testing, respondents are directed to continue choosing among the alternatives to each item until they find the correct response. There is no consensus as to how to convert the resulting pattern of responses into a measure because of two conflicting models of item response behavior. The first…

The graded response model for two-stage testing was applied to an attitudes toward science scale using real-data simulation. The 48-item scale was administered to 920 students at a grade-8 equivalent in Singapore. A two-stage 16-item computerized adaptive test was developed. In two-stage testing an initial, or routing, test is followed by a…

One important and promising application of item response theory (IRT) is computerized adaptive testing (CAT). The implementation of a nominal response model-based CAT (NRCAT) was studied. Item pool characteristics for the NRCAT as well as the comparative performance of the NRCAT and a CAT based on the three-parameter logistic (3PL) model were…

The robustness of a partial credit (PC) model-based computerized adaptive test's (CAT's) ability estimation to items that did not fit the PC model was investigated. A CAT program was written based on the PC model. The program used maximum likelihood estimation of ability. Item selection was on the basis of information. The simulation terminated…