Archimedes viewed the method of centroids as a valuable tool for intuitive discoveries. This article presents several uses of this technique and discusses how the method of centroids could be used in secondary schools. (Author/MK)

Solid polyominoes are formed by gluing cubes together so that the two faces of adjacent cubes are wholly in contact. Tessellations of a three-dimensional space with solid pentominoes are discussed and illustrated. (MP)

Presents an activity to identify some square-differences on the multiplication table. Discusses these properties using the Pythagorean triangle. (ASK)

Offers an alternative instructional method of constructing cubes based on the use of linking smaller cubes to form triangles. Offers learners insight into algebra by clearly exposing the underlying structure of the problem-solving process. (ASK)

This document presents a summary of changes made to the 2008 Mathematics Standard for grade 8. The table presented in this document offers a summary of the: (1) Removed Performance Objectives (POs); (2) POs Moved to a Different Grade Level; (3) POs Moved within the Grade Level or from another Grade Level; and (4) New POs.

Despite widespread agreement that the activity of "reasoning-and-proving" should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that…

The participants in this study were high school Hispanic students from four geometry classes. All students were taught by the same teacher, and the duration of the experiment was for one term or six weeks. Two classes were placed in the control group and another two classes in the experimental group. In the control group, students took weekly…

This article details the results of a written test designed to reveal how education majors construct and evaluate histograms and frequency polygons. Included is a description of the mistakes made by the students which shows how they tend to confuse histograms with bar diagrams, incorrectly assign data along the Cartesian axes and experience…

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 the teacher's edition of a text for the second 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. Congruence is a geometric topic reserved for Volume 2. Volume 2 opens with an…

Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…

Many educators believe that solid modeling software has made teaching two- and three-dimensional visualization skills obsolete. They claim that the visual tools built into the solid modeling software serve as a replacement for the CAD operator's personal visualization skills. They also claim that because solid modeling software can produce…

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

In this note, a simple proof of the Generalized Ceva Theorem in plane geometry is presented. The approach is based on the principle of equilibrium in mechanics. (Contains 2 figures.)