One technique for helping students understand the role of variables and parameters in an equation is to explore graphical representations. Several computer programs are commercially available for this purpose including Matlab (http://www.mathworks.com/), Mathmatica (http://www.wolfram.com/), Genplot (http://www.genplot.com/), or Excel (http://serc.carleton.edu/introgeo/models/mathematical/Using...

In [4] we proved that the limit of a weakly convergent sequence of finite graphs can be viewed as a graphing or a continuous field of infinite graphs. Thus one can associate a type II1-von Neumann algebra to such graph sequences. We show that in this case the integrated density of states exists that is the weak limit of the spectra of the graph Laplacians of the finite graphs is the KNS-spectra...

This paper attempts to organize some recent findings in the literature concerning the errors students make on tasks involving graphs and proposes some initial cognitive explanations for patterns in these errurs. Some basic characteristics of a competence model are proposed for knowledge structures used in comprehending and generating graphs. Two types of common misconceptions, treating the grap...

Synopsis: Although there are a number of technologies related to school algebra, it is only the personal technology of the graphics calculator that seems likely to be available widely enough to influence curriculum design and implementation on a large scale. The algebra curriculum of the past is overburdened with symbolic manipulation at the expense of understanding for most students. But algeb...

This article begins by reviewing the relevant research literature concerning the portable revolution in education. It outlines the advantages and disadvantages of portable forms of technology, with an emphasis on their potential impact upon student learning and attitudes. (The focus is on mathematics as far as possible, but writing is touched upon too as it is the main use for computers in scho...

Kinematics, the study of motion, is critical to understanding physics. For that reason it is among the first topics covered in introductory physics classes and it acts as a foundation for much of the rest of the course. Graphs are an important element in the study of kinematics. Interpreting the large amounts of data displayed on graphs is critical to making sense of the field. Because features...

The official inclusion of the teaching of graphing in school curricula has motivated increasing research and innovative pedagogical strategies such as the use of media graphs in school contexts. However, only a few studies have investigated knowledge about graphing among those who will teach this curricular content. We discuss aspects of the interpretation of media graphs among primary school s...

The accessibility of datasets from the Internet coupled with mathematically enabled software and technologies such as graphing calculators which include data analysis capabilities, place in the hands of students and teachers tools that have the potential to create a rich learning environment for the study of statistics. Further, the advent of graphing calculator peripherals such as Texas Instru...

Analysis of the curricula for primary schools in England and Brazil indicates that in both countries while there is emphasis given in policy documents to the importance of problem solving, the materials that are designed to support teachers’ implementation of the curriculum in their classrooms reflects a more passive approach to the teaching of graphing. We draw on research evidence from studie...

A strip plot graphs one dimensional data by displaying each sample point as a point on a one dimensional axis. The main difficulties with this technique is (i) when several samples have identical values they will be printed on top of each other, and (ii) in the case of a large sample the graph will become overly crowded and less informative. The two ways to alleviate these difficulties are: (a)...