The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

Explored are various aspects of drawing graphs on surfaces. The Euler's formula, Kuratowski's theorem and the drawing of graphs in the plane with as few crossings as possible are discussed. Some applications including embedding of graphs and coloring of maps are included. (YP)

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)