Describes how the concept of similar triangles was taught using an optical method of estimating large distances as a corresponding activity. Includes the derivation of a formula to calculate one source of measurement error and is a nice exercise in the use of the properties of similar triangles. (Author/NB)

Presents an active way for students to learn about SAS, SSS, ASA, AAS, and HL in determining congruent triangles. (Author/NB)

Teaching mathematics with games and puzzles goes back in history. Presents an example with the set theory game called Subset Takeaway in which two players can play. Creates a geometric representation of Subset Takeaway starting with a triangle and going to a three-dimensional simplex. Illustrates the winning strategy in the game and features a…

In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…

This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. This module, intended to present a treatment of congruent triangles which is not totally axiomatic, contains six sections: (1) Draw vs. Construct; (2) Triangle Construction; (3) Arguing for Congruence; (4) Parallel Line Construction; (5)…

Geometry is the study of shape and space. Without spatial ability, students cannot fully appreciate the natural world. Spatial ability is also very important for work in various fields such as computer graphics, engineering, architecture, and cartography. A number of studies have demonstrated that technology has an important potential to develop…

The author drew the 2008 Easter conference to a close. During the final address, the author chose to focus on the domain of perimeter and area both because it is a topic accessible to teachers of all ages and because learners display considerable confusion between them. The core difficulty seems to lie in the necessity to attend either to the…

When the author first used "VisiCalc," the author thought it a very useful tool when he had the formulas. But how could he design a spreadsheet if there was no known formula for the quantities he was trying to predict? A few months later, the author relates he learned to use multiple linear regression software and suddenly it all clicked into…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

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…