Focuses mainly on a common example in technology-rich mathematics curricula, namely the line of best fit, followed by a discussion of two additional examples, interpolating polynomials and complete graphs. (ASK)

Uses statistical graphs and charts of 33rd annual poll results to support conclusions on implications for educational policy. (PKP)

Phase changes and intermolecular forces are important physical science concepts but are not always easy to present in an active learning format. This article presents several interactive activities in which students plot the melting points of some fatty acids and explore the effect that the nanoscale size and shape of molecules have on the…

The idea of a graphing portfolio and its implementation in two levels of traditional university calculus courses is described. The activity of graphing helps students to gain a broader and deeper understanding of the connection between a function and its graph.

Graphing data and/or results from quantitative studies have been noted in the social sciences and the field of education as a means toward employing solid methodological practices. The publication rate in the JCSD of six specified graphs was examined under two editor ships from 1999 to 2003 and 2004. Preliminary results from the review suggested…

Hierarchical graphs represent relationships between objects (like computer file systems, family trees etc.). Graph nodes represent the objects and interconnecting lines represent the relationships. In two experiments we investigated what concepts are necessary for understanding hierarchical graphs, what misconceptions evolve when some of the…

This case study covers several exploratory data analysis ideas, the histogram and boxplot, kernel density estimates, the recently introduced bagplot--a two-dimensional extension of the boxplot--as well as the violin plot, which combines a boxplot with a density shape plot. We apply these ideas and demonstrate how to interpret the output from these…

A survey was administered to calculus students who had previously been exposed to a course on integral calculus. The purpose of the survey was to explore students' understanding of the definition of a definite integral, their abilities to evaluate definite integrals, and their graphical interpretations of definite integrals. The analysis of…

In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…

This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

It is recommended that schools incorporate literacy in all aspects of the curriculum. In this way, students begin to understand that reading and writing are not just for English class--they are skills that are important for many parts of daily life. This does not mean that teachers need to take time away from their other subjects to achieve this…

This book presents a description of the major curriculum philosophies that have influenced educators and schooling over the last century. The author analyzes four educational visions (Scholar Academic, Social Efficiency, Learner Centered, and Social Reconstruction) to enable readers to reflect on their own educational beliefs and allow them to…

The purpose of this study was to examine the effects of an intervention involving reciprocal peer tutoring and self-graphing of reading data on the disruptive behavior, active responding, and reading fluency of students with emotional or behavioral disorders (EBD). Four middle school students with EBD participated in this research. Results…

Using data to redesign instruction is a means of increasing student achievement. Educators in Camden County (Georgia) Schools have used data from benchmark testing since 1999. They hired a commercial vendor to design a benchmark test that is administered four times a year and use the data to generate subject-area reports that can be further…

The integration of history into educational practice can lead to the development of activities through the use of genetic "moments" in the history of mathematics. In the present paper, we utilize Oresme's genetic ideas--developed during the fourteenth century, including ideas on the velocity-time graphical representation as well as geometric…