In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…

In this article, the authors present the results of a research study in which they used two national datasets to construct and examine a model that estimates relative faculty instructional costs for specific undergraduate degree programs and also identifies differences in these costs by region and institutional type. They conducted this research…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…

We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…

Autonomously developing organisms face several challenges when learning reaching movements. First, motor control is learned unsupervised or self-supervised. Second, knowledge of sensorimotor contingencies is acquired in contexts in which action consequences unfold in time. Third, motor redundancies must be resolved. To solve all 3 of these…

Traditional approaches to the investigation of the objectivity of ratings for constructed-response items are based on classical test theory, which is item-dependent and sample-dependent. Item response theory overcomes this drawback by decomposing item difficulties into genuine difficulties and rater severity. In so doing, objectivity of ability…

In the last decade, several attempts have been made to relate item response theory (IRT) models to latent class analysis (LCA) models. One of these attempts is the solution-error response-error (SERS) model, an LCA model in which the structure of the latent class probabilities is explained by a one-dimensional loglinear Rasch model. In this paper,…

Bayesian methods for estimating dose response curves in quantal bioassay are studied. A linearized multi-stage model is assumed for the shape of the curves. A Gibbs sampling approach with data augmentation is employed to compute the Bayes estimates. In addition, estimation of the "relative additional risk" and the "risk specific…

Various classical approaches to evaluating test bias are reviewed, and their conceptual underpinnings are discussed. Bias is examined as it relates to predictive validity, rather than construct validity. One of the first test bias models was developed by T. A. Cleary (1968). Cleary's work with test bias and regression stimulated others to develop…

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques…

The normal curve has long been important in statistics. Most interval variables yield normal or quasi-normal distributions when data are collected from large samples, and the normal "Z" distribution is also used as a test statistic (e.g., to test differences between two means when sample size is large, since "t" approaches…

New multivariate permutation tests are proposed that may be effectively substituted for Hotelling's T-Square test in situations commonly arising in educational research. The new tests: (1) are distribution-free; (2) provide tests of directional as well as non-directional hypotheses; (3) may be tailored for sensitivity to specific treatment…

Test items are designed to be representative of the subject areas that they measure and to reflect the importance of specific domains or item types within those subject areas. Content validity is achieved by content specification and number of items in each content domain included in the design of the test. However, largely due to the normal…

A study compared a parallel distributed processing (PDP) model with a more traditional symbolic information processing model that accounts for early reading acquisition by human subjects. Two experimental paradigms were simulated. In one paradigm (a "savings" paradigm) subjects were divided into two groups and trained with two sets of…

In 1992 N. S. Raju and others proposed a general procedure for assessing differential test functioning (DTF) and item bias (differential item functioning or DIF) in tests developed with unidimensional, multidimensional, or polytomous item response theory (IRT) models. The purpose of this paper is to assess the adequacy and validity of their…