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…

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…

Three multidimensional item response theory (IRT) models for testlet-based tests are described. In the bifactor model (Gibbons & Hedeker, 1992), each item measures a general dimension in addition to a testlet-specific dimension. The testlet model (Bradlow, Wainer, & Wang, 1999) is a bifactor model in which the loadings on the specific dimensions…

The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just…

Over 10 years have passed since the publication of Carr and Burkholder's (1998) technical article on how to construct single-subject graphs using Microsoft Excel. Over the course of the past decade, the Excel program has undergone a series of revisions that make the Carr and Burkholder paper somewhat difficult to follow with newer versions. The…

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 "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…

Algebra progress monitoring is a research-based practice that extends a long history of research in curriculum-based measurement (CBM). This article describes the theoretical foundations and research evidence for algebra progress monitoring, along with critical features of the practice. A detailed description of one practitioner's implementation…

The inquiry-based approach to learning has gained popularity in recent times. Those who promote this approach maintain that mathematical investigation should be used to engage students. The National Council of Teachers of Mathematics (NCTM) recommends that problem solving be the center of mathematics teaching in promoting student learning through…

This paper addresses the difficulties experienced by first-grade students studying rigid body motion at Sofia University. Most quantities describing the rigid body are in relations that the students find hard to visualize and understand. They also lose the notion of cause-result relations between vector quantities, such as the relation between…