The use of qualitative graphs of Gibbs energy versus temperature is described in the context of chemical demonstrations involving phase changes and colligative properties at the general chemistry level. (Contains 5 figures and 1 note.)

This study investigated the accuracy of classroom teachers' judgments of the reading progress of their low-performing students. Participants were 36 second grade teachers and students in their lowest reading groups (n = 150). Student progress was monitored weekly using reading-curriculum-based measurement (R-CBM) procedures. After 6 weeks,…

Under the backdrop of the investigation of rational functions and their respective curved asymptotes, the reader is invited to experience the mathematical process alongside the authors and observe the application of the NCTM Process Standards and the use of multiple representations in the investigation and solution of a problem. (Contains 9…

These proceedings contain the papers and posters of the International Conference on e-Learning (EL) 2019, which was organised by the International Association for Development of the Information Society and co-organised by the Instituto Superior de Engenharia do Porto, in Porto, Portugal, July 17-19, 2019. The EL 2019 conference aims to address the…

Authors of principles and price theory textbooks generally illustrate short-run production using a total product curve that displays first increasing and then diminishing marginal returns to employment of the variable input(s). Although it seems reasonable that a temporary range of increasing returns to variable inputs will likely occur as…

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)