My NASA Data (Chambers et al. 2008) is a teaching tool available on NASA's website that offers microsets of real data in an easily accessible, user-friendly format. In this article, the authors describe a lesson plan based on an activity from My NASA Data, in which students explore parts of the United States where they would want to live if they…

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

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…

This paper provides surface area and volume formulas for surfaces of revolution in R[superscript n]. In addition the authors illustrate how to obtain the formulas for volume and surface areas of revolution about the x- or y-axis in two different ways: a "heuristic" argument and a rigorous calculation using "cylindrical" coordinates. In the last…

This article provides for a fast extremely accurate approach to graphing functions that is based on learning function reference graphs and then applying algebraic transformations to these reference graphs.

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…

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…

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…

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…

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…