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)

From 1984 through 1988, the authors worked with teachers using an inquiry approach to teach high school geometry courses with the aid of the "Geometric Supposers." Problems are a critical component of the approach because they focus attention and energy and guide students in the application, integration, and extension of knowledge.…

This project was designed to: (1) assess 7th-graders' metacognitive beliefs and processes and investigate how they affect problem-solving behaviors; and (2) explore the extent to which these students can be taught to be more strategic and aware of their own problem-solving behaviors. The primary assessment was conducted by analyzing video tapes of…