Existing studies have defined and assessed disciplinary literacy, mathematical literacy, and general academic language. However, there is a need to define and assess mathematics discipline-specific language (MDL), particularly for elementary school teachers. Therefore, the purpose of this study was to develop a research instrument to assess the…

At their core, Intelligent Tutoring Systems consist of a student model and a policy. The student model captures the state of the student and the policy uses the student model to individualize instruction. Policies require different properties from the student model. For example, a mastery threshold policy requires the student model to have a way…

This paper describes a model that integrates an item response theory (IRT) Rasch model and a hierarchical linear model and presents a method of estimating model parameter values that does not rely on large-sample theory and normal approximations. The model resulting from the integration of a hierarchical linear model and the Rasch model allows one…

Introduces Rene Thom's catastrophe theory, which is based upon complex theorems in multidimensional geometry. Catastrophe theory analysis begins by identifying the occurrence of major discontinuities, or catastrophes, in a system such as civil service exams, resulting in catastrophic change. (KS)

Multivariate methods are being used with increasing frequency in educational research because these methods control "experimentwise" error rate inflation, and because the methods best honor the nature of the reality to which the researcher wishes to generalize. This paper: explains the basic logic of canonical analysis; illustrates that…

An objective method based on the likelihood ratio procedure is presented for use in selecting a measurement model from among the RASCH, 2-parameter and 3-parameter logistic latent trait models. The procedure may be applied in a straightforward manner to aid in choosing between the 2-parameter and the Rasch models. When choosing between the 3- and…

Measurement is prescriptive in that the model required to produce the numbers from the phenomena is known in advance. Statistical theory is descriptive because the model required to explain the numbers is inferred from the numbers and any other information the researcher can bring to bear. There are well-known families of measurement models and…

Needs assessment almost always focuses on the assessment of change, change from the real to the ideal, present to future, actual to expected, and so on. As a result, most definitions of need can be represented by a mathematical-style change formula. However, most presentations of the concept of change do not completely represent the complexity of…

Stochastic models are developed in this article to examine the rate of test misgrading in educational and psychological measurement. The estimation of inadvertent grading errors can serve as a basis for quality control in measurement. Limitations of traditional Poisson models have been reviewed to highlight the need to introduce new models using…

The ordered partition model is described as an extension of the partial credit model, its relationship to other models is discussed, and two examples are presented. The model is designed for a measurement context in which categories of response to an item cannot be completely ordered. (SLD)

Some basic concepts of the one-parameter logistic latent-trait model, or the Rasch model, are presented. This model assumes that the probability of a correct answer to an item is a function of two parameters, one representing the difficulty of the item and one representing the ability of the subject. The purpose of this paper is to explain a…

The validity of inferences based on achievement test scores is dependent on the amount of effort that examinees put forth while taking the test. With low-stakes tests, for which this problem is particularly prevalent, there is a consequent need for psychometric models that can take into account different levels of examinee effort. This article…

The application and utility of confirmatory second-order factor analytic methods are discussed. Factor analysis is central to concerns regarding measurement validity. Confirmatory methods are especially useful because they explicitly consider measurement error influences and because the methods are inherently theory-driven and theory-oriented.…

The usefulness of the general Rasch model for multidimensional data, from the most simple formulations to the more complex versions of the model, is explored. Also investigated was whether the parameters of the models could be readily interpreted. Models investigated included: (1) the vector model; (2) the product term model; (3) the vector and…

In three lectures, Benjamin D. Wright of the University of Chicago introduces the Rasch model and its basic concepts. The first lecture, March 30, 1994 discusses the model created by Georg Rasch, a Danish mathematician, which Dr. Wright initially saw as merely a way to make raw scores into measures. Eventually, the model developed into a…