This article reviews current methods for evaluating models in the cognitive sciences, including theoretically based approaches, such as Bayes factors and minimum description length measures; simulation approaches, including model mimicry evaluations; and practical approaches, such as validation and generalization measures. This article argues…

This article describes how sixth-grade students developed concrete models to solve division of fractions story problems. Students developed separate two-step procedures to solve measurement and partitive problems, drawing on invented procedures for division of whole numbers. Errors also tended to be specific to the type of division problem…

U.S. state educational testing programs administer tests to track student progress and hold schools accountable for educational outcomes. Methods from item response theory, especially Rasch models, are usually used to equate different forms of a test. The most popular method for estimating Rasch models yields inconsistent estimates and relies on…

The hierarchical latent regression model (HLRM) is a flexible framework for estimating group-level proficiency while taking into account the complex sample designs often found in large-scale educational surveys. A complex assessment design in which information is collected at different levels (such as student, school, and district), the model also…

"The 2006 Winter Meeting of the AAPT Was Over..."and the flight home from Anchorage to Cleveland was just about to end--eight hours in the air, only two complimentary beverages, no meals, a jump across four time zones, a one-year-old baby daughter, and a wife whose motto for the week was, "Why did they choose to have a winter meeting in Alaska?"…

The interpretation of a Thurstonian model for paired comparisons where the utilities' covariance matrix is unrestricted proved to be difficult due to the comparative nature of the data. We show that under a suitable constraint the utilities' correlation matrix can be estimated, yielding a readily interpretable solution. This set of identification…

Since the publication of [Gelman, R., & Gallistel, C. R. (1978). "The child's understanding of number." Cambridge, MA: Harvard University Press.] seminal work on the development of verbal counting as a representation of number, the nature of the ontogenetic sources of the verbal counting principles has been intensely debated. The present…

K. Rayner, A. Pollatsek, D. Drieghe, T. J. Slattery, and E. D. Reichle argued that the R. Kliegl, A. Nuthmann, and R. Engbert corpus-analytic evidence for distributed processing during reading should not be accepted because (a) there might be problems of multicollinearity, (b) the distinction between content and function words and the skipping…

The four types of ionic equilibria--acid-base, redox, precipitation, and complexation--have certain similarities, which has led some authors to develop a unified treatment of them. These authors have highlighted the common aspects and tried to find a systemization of the equilibria that would facilitate learning them. In this unified treatment,…

Everyday, people face situations that call for adding, subtracting, multiplying, or dividing, and at least half of the time, these calculations are accomplished without the use of pen, paper, or calculators. Because figuring "in your head" is such an important life skill, it should have a regular role in classroom math teaching. This article…

The authors of this article introduce students in their department's construction course to a variety of energy-saving practices and processes. They describe activities that could give students an opportunity to apply design methodology in the creative pursuit of a solution to an open-ended problem. An introductory lecture gives students the…

The teaching of mathematics courses to chemistry students that is strongly based on symbolic computation and allows an instructor to explore a topic or principle is reviewed. The mathematical software available, nominally for symbolic computation associated with numerical and graphical capabilities are highly developed and provides an invaluable…

The authors develop and test generalized versions of take-the-best (TTB) and rational (RAT) models of multiattribute paired-comparison inference. The generalized models make allowances for subjective attribute weighting, probabilistic orders of attribute inspection, and noisy decision making. A key new test involves a response-time (RT)…

Choosing mental, written, or calculator procedures is important for children to learn. Children should be encouraged to be flexible and consider alternatives when doing mental calculation. Developing mental skills, symbols and rules, and numbers in context are each considered. (MNS)

A set of three problem-solving programs designed as drills that give practice in mental arithmetic are reviewed. The programs are viewed to have several weaknesses in style, but are noted as worthy of consideration for purchase. The material is designed to motivate students to practice all four basic operations. (MP)