In this article, the author suggests a framework for developing lesson ideas involving variation. This idea was demonstrated by Rebecca Davey at a conference bringing together teachers from the seven schools participating in the TI-"n"spire pilot research project overseen by Alison Clark-Wilson of the University of Chichester. It uses information…

Collecting and graphing performance data are important parts of the educational process. Such procedures help educators, caregivers, and other important stakeholders make data-based decisions to accelerate child progress. With school-age children, collecting and graphing data have been associated with more frequent instructional changes to better…

Examining data provides a unique opportunity to have students work actively with various technologies, such as computers or graphing calculators. Students can import data into spreadsheet software, execute mathematical calculations, create data graphs, and use this material in reports to present the results of their inquiry. Reinforcing the use of…

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…

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…

Often the differences students see in science and mathematics classrooms are in perspective, approach, or application. Understanding those differences can help teachers to present a unified picture of mathematics and science to their students. In this article, the science teacher is given a glimpse of the treatment of topics shared by both…

It has long been known that when a cable of specified length is hung between two poles, it takes the shape of a catenary--a hyperbolic cosine function. In this paper, we study a variation of this problem. First, we consider a cable hanging between two poles in which one end of the cable is fixed to one pole; the other end of the cable runs over a…

Since the dawn of civilization, pictorial representations and symbols have been used to communicate simple statistics. Efficient and effective, they are still used today in the form of pictures and graphs to record and present data. Who can tie their shoes? How many calories are in your favorite food? Make data and graphs relevant and interesting…

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.)