In 4 experiments, the authors explored the role of visual layout in rule-based syntactic judgments. Participants judged the validity of a set of algebraic equations that tested their ability to apply the order of operations. In each experiment, a nonmathematical grouping pressure was manipulated to support or interfere with the mathematical…

The purpose of the current article is to examine the impact of laboratory demonstrations and computer visualizations on learning in a third-year fluid mechanics course at Norwegian University of Science and Technology (NTNU). As a first step, on entering the course, students were exposed to a laboratory demonstration focusing on the nature of…

In this study the effectiveness of an arrow diagram which can help students apply the Chain Rule was investigated. Different variations of this diagram were used as mnemonic devices for applying the Chain Rule. For the investigation two instruments were developed, diagnostic test and post-test. The diagnostic test was developed to determine the…

With the help of technology and a basic high school algebra method for finding the vertex of a quadratic polynomial, students can develop and prove the formula for least-squares lines. Students are exposed to the power of a computer algebra system to generalize processes they understand and to see deeper patterns in those processes. (Contains 4…

Experimenters sometimes wish to estimate for a particular dependent variable the proportion of total group variance that is associated with mean differences among fixed treatments or subject classifications. Hays (1981) represents this proportion by the parameter omega squared. A point estimate may be easily computed as a function of the number of…

Bounds are established for log cross-product ratios (log odds ratios) involving pairs of items for item response models. First, expressions for bounds on log cross-product ratios are provided for unidimensional item response models in general. Then, explicit bounds are obtained for the Rasch model and the two-parameter logistic (2PL) model.…

The bilingual dictionary has been adapted from a dictionary originally developed by Teresa Kow and Euphine Cheung in New York to assist Chinese students in their understanding of mathematics vocabulary and concepts in English. A total of 204 terms and definitions are provided in English with Chinese translations directly below the entries. Each…

Formulas are derived for the bias in the maximum likelihood estimators (MLE) of the item parameters in the logistic item response model when examinee abilities are known. Numerical results are given for a typical verbal test for college admission. Most typically the bias of an MLE is about one-tenth of its standard error. It is very seldom more…

There are two general methods of cross-validation: empirical estimation, and formula estimation. In choosing a specific cross-validation procedure, one should consider both costs (e.g., inefficient use of available data in estimating regression parameters) and benefits (e.g., accuracy in estimating population cross-validity). Empirical…

This paper is primarily concerned with determining the statistical bias in the maximum likelihood estimate of the examinee ability parameter in item response theory, and of certain functions of such parameters. Given known item parameters, unbiased estimators are derived for (1) an examinee's ability parameter and proportion-correct true score;…

Four recent indices emphasizing the interrelationships of score distribution shape, modality, mean, and variance were investigated to determine the reliability of mastery tests. Attention was focused on the values of the indices when the cutoff score was near to or far from the modes of distribution. Five types of score distributions were…

Results of operations on the Pythagorean formula are interpreted pictorially to yield interesting art forms. (MP)

A coordinate system is imposed on a geoboard to form a table that leads to the discovery of the formula n[(n+1)(n+1)] (n+2)/12. Proof is by induction. (MP)

Two problems are presented that may be used to determine if a student's understanding of the area concept goes beyond manipulation of formulas. (MP)

A general historical background for the development of some common formulas concerning length, area, and volume is given through a discussion of various written records. (MN)