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…

Task analytic theories of graph comprehension account for the perceptual and conceptual processes required to extract specific information from graphs. Comparatively, the processes underlying information integration have received less attention. We propose a new framework for information integration that highlights visual integration and cognitive…

Brain images are believed to have a particularly persuasive influence on the public perception of research on cognition. Three experiments are reported showing that presenting brain images with articles summarizing cognitive neuroscience research resulted in higher ratings of scientific reasoning for arguments made in those articles, as compared…

Visual inspection is the primary method used to analyze graphed behavioral data produced by functional analyses of problem behavior. The purpose of this study was to examine rater reliability of functional analysis graphs using visual inspection. Forty-three participants responded to a one-time anonymous survey (N = 454) mailed to graduate…

The revolution of technology in education has heralded a new wave of learning styles and in some cases total dependence on technology. Yet, statistics reveal no significant improvement in student performance in Mathematics and a downward trend in basic algebra skills. The major impediment in the learning process is lack of understanding of the…

In this article we consider an example suitable for investigation in many mid and upper level undergraduate mathematics courses. Fourier series provide an excellent example of the differences between uniform and non-uniform convergence. We use Dirichlet's test to investigate the convergence of the Fourier series for a simple periodic saw tooth…

In this article, the authors discuss the importance of unexpected graphs as a vehicle for encouraging critical classroom dialogue. By examining such graphs more critically, teachers and their students can reexamine beliefs about the authority of technology in their classrooms. (Contains 15 figures.)

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…

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…

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…