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)…

The Schools and Staffing Survey (SASS) is conducted by the National Center for Education Statistics (NCES) on behalf of the United States Department of Education in order to collect extensive data on American public and private elementary and secondary schools. SASS provides data on the characteristics and qualifications of teachers and…

This book, written by participants of a joint Japan-United States seminar, drawing upon years of classroom and research experience, examines how computation applies in basic and far-reaching ways, starting in early childhood and continuing throughout individuals' lives. The book presents both the Japanese and American views of computational…

This case study examined the performance of a 13-year-old highly skilled mental calculator on mental multiplication tasks. She solved difficult tasks by using various ingenious calculation methods, including distributing, factoring, and recalling the product directly. Implications for instruction are reported. (Author/RH)

Studied for three years were eight Swedish classes with pupils aged 10-12 using calculators whenever they could be of use, along with experimental textbooks. The experimental classes were as competent as control classes in mental arithmetic and calculations with simple algorithms, and had better understanding of numbers and problem solving. (MNS)

This report consists of two volumes, the first takes an in-depth look at the various graduation indicators, with a description of the computational formulas, the data required for each indicator, the assumptions underlying each formula, the strengths and weaknesses of each indicator, and a consideration of the conditions under which each indicator…

Included in this section are brief articles outlining an approach to teaching mental computation, an inductive approach to algebra, and using football to teach probability. (MNS)

Focuses on mental strategies for computing in the middle grades. Describes what they are and why they are important. Refers to relevant research and presents some teaching ideas for developing these strategies beyond the primary grades. Includes a discussion of the role of mental calculation in everyday life both past and future. Contains 27…