The precision of item parameter estimates can be increased by taking advantage of dependencies between the latent proficiency variable and auxiliary examinee variables such as age, courses taken, and years of schooling. Score gains roughly equivalent to two to six additional item responses can be expected in typical educational and psychological…

The purpose of this study was to examine the effect that large within-examinee item difficulty variability had on estimates of the proportion of consistent classification of examinees into mastery categories over two test administrations. The classification consistency estimate was based on a single test administration from an estimation procedure…

The critical role of computers in scientific advancement is described in this panel report. With the growing range and complexity of problems that must be solved and with demands of new generations of computers and computer architecture, the importance of computational mathematics is increasing. Multidisciplinary teams are needed; these are found…

The use of new extension of standard Item Response Theory (IRT) modeling of dichotomous items to include external variables is proposed. External variables may appear both as categorical grouping variables and as continuous variables; this requires the formulation of a model for the relationships between the external variables and the response…

Described is the notion of multiple alternative representations of mathematical reasoning, particularly as they relate to algebraic notation and the potential of computers to change representations. Features of a desirable notation for algebraic problem solving are described. This is followed by a description of the RAND Corporation's intelligent…

When learning is taking place, students test their hypotheses and evaluate them, and modify their current theories on the basis of new information. This phenomenon is known as "hypothesis testing view" or "theory changes." Many students change their rules to another while they are taking a test. This study introduced a new…

The purpose of this study was to evaluate the use of log-linear models in detecting test item bias. The evaluation of the log-linear approach in this regard will focussed on the following: (1) the stability of the procedure across replications--the effect of sampling error across random samples of ethnic groups; (2) the amount of artifactual…

Diagnostic testing confronts several challenges at once, among which are issues of test interpretation and immediate modification of the test itself in response to the interpretation. Several methods are available for administering and evaluating a test in real-time, towards optimizing the examiner's chances of isolating a persistent pattern of…

The potential of item response theory (IRT) for solving a number of testing problems in the Maryland Functional Reading Program would appear to be substantial in view of the many other promising applications of the theory. But, it is well-known that the advantages derived from an IRT model cannot be achieved when the fit between an item response…

The use of three remedies for errors in the measurement of ability that arise from differences in rater stringency is discussed. Models contrasted are: (1) Conventional; (2) Handicap; and (3) deterministic Rater Response Theory (RRT). General model requirements, power, bias of measures, computing cost, and complexity are contrasted. Contrasts are…

Statistical models for school effectiveness rankings are assessed. An analysis of linear models with fixed regression parameters and models with separate regression parameters for each school is presented. In the first case, the regression lines are parallel and the ranking of the schools is the same for all student backgrounds. In the second…

A method for estimating the parameters of the Rasch model is examined. The unknown quantities in this method are the item parameters and the distribution function of the latent trait over the population. In this sense, the method is equivalent to marginal maximum likelihood estimation. The new procedure is based on a method suggested by J. Kiefer…

In order to evaluate our methods and approaches of estimating the operating characteristics of discrete item responses, it is necessary to try other comparable methods on similar sets of data. LOGIST 5 was taken up for this reason, and was tried upon the hypothetical test items, which follow the normal ogive model and were used frequently in…

Optimal appropriateness indices, recently introduced by Levine and Drasgow (1984), provide the highest rates of detection of aberrant response patterns that can be obtained from item responses. These optimal appropriateness indices are used to study three important problems in appropriateness measurement. First, the maximum detection rates of two…

Based on the game "Prisoners' Dilemma," a game-theoretical model of the arms race suitable for postsecondary level mathematics and/or political science students is developed in which two players can initially choose any level of arms development. The purpose of the game is to show under what conditions deescalation rather than escalation…