The authors use a relatively simple diagram accompanied by mathematical analysis to compare two pricing strategies: price-quantity packages and a two-part tariff. This is done both from the monopolist's point of view and from the welfare point of view. The authors show that in the case of two consumer types, the price-quantity packages strategy…

The variety and complexity of potentially-related data resources available for querying--webpages, databases, data warehouses--has been growing ever more rapidly. There is a growing need to pose integrative queries "across" multiple such sources, exploiting foreign keys and other means of interlinking data to merge information from diverse…

When teaching mathematics with technology, the author does so in the belief that technology enables students to experience mathematical ideas in a way that might not otherwise be possible. However, teachers must be careful: Sometimes technology does not produce results in the way that they or their students expect. Rather than allowing unexpected…

This study examined the written work of students in the introductory calculus-based electricity and magnetism course at the University of Arkansas. The students' solutions to hourly exams were divided into a small set of countable features organized into three major categories, mathematics, language, and graphics. Each category was further divided…

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…

The aims of this cross-grade study were (1) to determine the level of understanding of energy concepts of students at different academic grades and the differences in understanding between these grades and (2) to analyse the conceptual development of these students. Two hundred and forty-three students at 3 different levels (high school,…

One of the major roles of a school psychologist is psychoeducational testing and the preparation of psychoeducational reports. Unfortunately, parents often have difficulty understanding psychoeducational reports. This difficulty might be ameliorated by supplementing psychoeducational reports with graphs. This hypothesis was tested with 144 parents…

Ms. Beyer's first graders have been working for several weeks on solving problems that encourage the use of such multiple representations as ten frames and number lines. The class is using Math Trailblazers, a National Science Foundation-supported elementary school math curriculum developed to reflect recent reform efforts in mathematics…

This article presents a web-based tool designed to compute certified equations and graphs of geometric loci specified using standard Dynamic Geometry Systems (DGS). Complementing the graphing abilities of the considered DGS, the equations of the loci produced by the application are remotely computed using symbolic algebraic techniques from the…

The 2008 presidential election is a great backdrop for analyzing graphs, learning about population distributions, and studying the effect on the electoral voting process. To take advantage of the enthusiasm surrounding the election, the authors conducted two activities in the months leading up to the 2008 presidential elections with several groups…

This article is a guide to the NBER-Rensselaer Scientific Papers Database, which includes more than 2.5 million scientific publications and over 21 million citations to those papers. The data cover an important sample of 110 top U.S. universities and 200 top U.S.-based R&D-performing firms during the period 1981-1999. This article describes the…

Descriptive statistics and appropriate visual representations of scores are important for all test developers, whether they are experienced testers working on large-scale projects, or novices working on small-scale local tests. Many teachers put in charge of testing projects do not know "why" they are important, however, and are utterly convinced…

Research on the counterintuitive Monty Hall dilemma (MHD) and analogous problems has shown that correct reasoning is rarely observed, even with the help of certain hints. Making the causal structure explicit or presenting probabilities by means of natural frequencies seem to enhance performance, but only to a moderate degree. The present…

Students' collaboration while learning could provide better learning environments. Collaboration assumes social interactions which occur in student groups. Social theories emphasize positive influence of such interactions on learning. In order to create an appropriate learning environment that enables social interactions, it is important to…

The "Almanac of American Education" helps users understand and compare the quality of education at the national, state, and county levels. Compiled from official U.S. government and reliable private sources, the book contains historical and current data, insightful analysis, and useful graphs that provide compelling insights into the…