This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse.

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

A new general procedure for deriving the Gibbs energy of mixing is developed through general thermodynamic considerations, and the ideal-solution model is obtained as a special particular case of the general one. The deduction of the Gibbs energy of mixing for the ideal-solution model is a rational one and viewed suitable for advanced students who…

Simulations make it possible to explore physical and biological phenomena, where conducting the real experiment is impracticable or difficult. The implementation of a software program describing and simulating a given physical situation encourages the understanding of a phenomenon itself. Fifty-nine students, enrolled at the Mathematical Methods…

This article describes a lesson unit in which students constructed tables and graphs to represent the growth of different trees. Students then compared the graphs to develop an understanding of slope.

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…