As a part of the increasing emphasis among schools on meeting important statewide academic goals, schools are focusing more closely on the progress of individual students. Parents have a similar goal--to monitor the progress of their child. Frequent student progress monitoring accomplishes this common goal, in that it is used to track the progress…

When conducting an exploratory factor analysis, the decision regarding the number of factors to retain following factor extraction is one that the researcher should consider very carefully, as the decision can have a dramatic effect on results. Although there are numerous strategies that can and should be utilized when making this decision,…

The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

Rapid cognitive diagnosis allows measuring current levels of learner domain-specific knowledge in online learning environments. Such measures are required for individualizing instructional support in real time, as students progress through a learning session. This article describes 2 experiments designed to validate a rapid online diagnostic…

Students often struggle with the connection between algebraic and graphical representations of functions. This overview of the history of the Cartesian coordinate system helps the classroom teacher consider new ways to aid students in making the "Cartesian connection." (Contains 7 figures.)

In this paper we derive an expression for the dynamic electric polarizability of a particle bound by a double delta potential for frequencies below and above the absolute value of the particle's ground state energy. The derived expression will be used to study some of the fundamental features of the system and its representation of real systems.…

This article describes an activity for developing the notion of association between two quantitative variables. By exploring a collection of scatter plots, the authors propose a nonstandard "intuitive" measure of association; and by examining properties of this measure, they develop the more standard measure, Pearson's Correlation Coefficient. The…

This article provides an overview of vertex-edge graphs as an essential topic in the high school mathematics curriculum, including rationale, recommendations, and sample applications. A classroom-ready activity with full teacher notes is also included. (Contains 1 table and 9 figures.)

Mobile phones may provide a useful and engaging platform for supporting therapeutic services working with adolescents. This paper examines the potential benefits of the mobile phone for self-charting moods in comparison to existing methods in current practice. The paper describes a mobile phone application designed by the authors which allows…

A theorem is proved stating that the set of all "minimax links," defined as links minimizing, over paths, the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph, comprises the union of all minimum spanning trees of that graph. (Author/SLD)

This article describes a graphical method for visualizing compositions of functions; this method is used to find domains and ranges of compositions.

The usage and disappearance of the Central Ibero-Romance future subjunctive have been extensively researched through Old Spanish texts. Studies on the future subjunctive as it evolved in the farther Western Ibero-Romance languages, represented by Galician and Portuguese, have been scarce, if not incomplete. This dissertation partially fills the…

Each year, well over a million students take college algebra and related courses. Very few of these students take the courses to prepare for calculus, but rather because they are required by other disciplines or to fulfill Gen Ed requirements. The present article discusses what the current mathematical needs are in most of those disciplines,…

Over the past decade, research on the use of technology in the mathematics classroom has focused primarily on issues of student learning and engagement. In this article, we focus on middle grades mathematics teachers' use of The Geometer's Sketchpad, and study both the decisions they make about when to use technology, and their motivations for…

This article is about the students' investigation about the relationship between the diameter of the view tubes (x) of constant lengths and the viewable vertical distance (y) on the wall while keeping the perpendicular distance from the eyeball to the wall constant. The students collected data and used and represented it in tabular and graphical…