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.)

This is the teacher's edition of a text for the first year of a two-year high school geometry course. The course bases plane and solid geometry and trigonometry on the fact that the translations of a Euclidean space constitute a vector space which has an inner product. Volume 1 deals largely with affine geometry, and the notion of dimension is…

The author re-enacted the "Meno's" discussion between Plato and the slave about doubling the size of the square, and found that a six-year-old's answers paralleled those of the slave; neither had formal knowledge of geometry. Plato stated that learning is recollection of knowledge held before birth. (CHK)

This booklet, one of a series, has been developed for the project, A Program for Mathematically Underdeveloped Pupils. A project team, including inservice teachers, is being used to write and develop the materials for this program. The materials developed in this booklet include (1) elementary properties of the exponent, (2) properties of the…

High-ability Jamaican students in grades one, three, five, seven, and nine were asked to draw five three-dimensional objects (cuboid, pyramid, cylinder, cone, cube) from memory, and with the object visible; later they were asked to select the best sketch of each solid from among several presented. Drawings and selections were scored for…

The first chapter, Perpendiculars and Parallels (II), of the ninth unit in this SMSG series includes a discussion of the properties of triangles, circles and perpendiculars, parallels in space, perpendicular lines and planes, and parallel planes. The next chapter, on coordinate geometry, covers distance; midpoints; algebraic descriptions of…

A mathematical derivation is given, developing the cardioid as an epicycloid locus. Curve-stitched designs are given for a family of epicycloids. (MP)

The free-energy change, or binding energy, of an idealized bubble cluster is calculated on the basis of one mole of gas, and on the basis of a single bubble going from sphere to polyhedron. Some new relations of bubble geometry are developed in the course of the calculation. (BB)