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The National Council of Teachers of Mathematics' Illuminations Project provides electronic resources to illuminate the Principles and Standards for School Mathematics and to improve the teaching and learning of mathematics for all students. This paper describes the types of resources that are available and discusses how the Principles and Standards document has guided work on the project. Organized around the six principles, this paper provides a vehicle for further discussion of the vision put forth in the Principles and Standards.

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Secondary school geometry is perhaps most succinctly described as the study of shape. Many aspects of shape are studied, such as properties of and relationships among shapes, location of shapes, transformations of shapes, and reasoning about shape. Consider an important counterpoint to this shape story or perhaps chapter zero in the story—the study of vertex-edge graphs, which are geometric objects for which shape is not an essential characteristic.