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)

Good teaching is responsive to individual differences, tailoring instruction to meet the needs of individual learners. In gifted education, students need a curriculum that is differentiated (by level, complexity, breadth, and depth), developmentally appropriate, and conducted at a more rapid rate. This collection of essays from experts in the…

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…

The project reported here is conducting repeated randomized control trials of an approach to high school geometry that utilizes Dynamic Geometry (DG) software to supplement ordinary instructional practices. It compares effects of that intervention with standard instruction that does not make use of computer drawing/exploration tools. The basic…

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…

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 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…