This study explores the performance of two mathematically gifted Korean 7th-grade students in tasks involving local organization in geometry. The students understood the necessity of definitions and starting points in defining terms and organizing geometrical properties. They improved the clarity of their definitions and arranged the properties…

What makes Dynamic Geometry Environment (DGE) a powerful mathematical knowledge acquisition microworld is its ability to visually make explicit the implicit dynamism of thinking about mathematical geometrical concepts. One of DGE's powers is to equip us with the ability to retain the background of a geometrical configuration while we can…

This article describes how teachers can use students' conversations to assess their mathematical understanding. The authors draw on their own classroom experiences to show what they learned about planning for future lessons based on discussions in their own classrooms.

The Varignon parallelogram has always provided a simple geometric investigation for students that gives rise to a surprising result. It is possible to extend the Varignon investigation by looking at special quadrilaterals or by considering different dissection points along the sides. In the second of his two-part series, the author offers some…

This article provides an overview of vertex-edge graphs as an essential topic in the high school mathematics curriculum, including rationale, recommendations, and sample applications. A classroom-ready activity with full teacher notes is also included. (Contains 1 table and 9 figures.)

These Proceedings are a written record of the research presented at the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2011) held in Reno, Nevada, October 20-23, 2011. The theme of the conference is Transformative Mathematics Teaching and Learning. The Proceedings…

Two studies investigated the effects of a storytelling-context for teaching geometry skills to kindergarten girls and boys. In Study 1, the story+geometry intervention consisted of an adventure story teaching geometry through part-whole-relations puzzles. Learning was assessed through transfer of skills, using a pre-/post design comparing…

A globe, in a school or university yard, which simulates the Earth's orientation in space, could be a very useful and helpful device for teaching physics, geometry, astronomy and the history of science. It would be very useful for science education to utilize the forthcoming International Year of the Planet Earth 2008 and the International Year of…

Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…

Geometry, classification, and the classification of geometrical objects are integral aspects of recent curriculum documents in mathematics education. Such curriculum documents, however, leave open how the "work" of classifying objects according to geometrical properties can be accomplished given that the knowledge of these properties is the…

Within the study of geometry in the middle school curriculum is the natural development of students' spatial visualization, the ability to visualize two- and three-dimensional objects. The national mathematics standards call specifically for the development of such skills through hands-on experiences. A commonly accepted method is through the…

This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. This module includes: (1) Pythagorean Theorem (with review of radicals); (2) Basic Coordinate Geometry (distance and midpoint, slope, slope of parallels and perpendiculars, and equation of a line); (3) Selecting Coordinates; (4) Coordinate…

The effects of nonexamples on the acquisition of the geometrical concept of semiregular polyhedra were examined. Results favored the treatments containing both examples and nonexamples. (TG).