In this work, we analyze the results obtained by a group of freshmen students in a test of prior knowledge on technical drawing carried out before and after attending an introductory course on this subject. The aim of this course was to help students to gain knowledge necessary to take full advantage of the CAD software that is regularly used to…

Before the 19th century the idea of more than three dimensions was exceptional. During the 19th century, however, geometry was revolutionized and new branches were developed. This revolution also created the idea of the possibility of a n-dimensional geometry or space; flatland, i.e. n = 2, was a consequence of this new thinking. In 1884 the…

This reprinted "Mathematics Teacher" article gives a brief history of the mathematics of Escher's art. (Contains 9 plates.)

Mathematics begins in human experience thousands of years ago as empirical and intuitive experiences. It takes the deliberate naming of concepts to help crystallize and secure those observations and intuitions as abstract concepts, and to begin separating the concept of number from specific instances of objects. It takes the creation of compact…

As a result of attending a course on moving images, the authors consider the balance between visualising and verbalising geometry. In thinking about the balance between visualising and verbalising (and verbal reasoning), the authors began to appreciate more than before that geometric visualisation is greatly aided by what they know--if everyone…

The purpose of this paper is to provide examples of "non-traditional conjectures" in a dynamic geometry environment that can be used to stimulate students to provide proofs. The author believes that teachers can ask their students to find out if these conjectures are true; if the conjectures are true, then the students can come up with their own…

Research has shown that certain ways of teaching can make a difference in whether students learn standards-based content. Many strategies have proven to be effective in teaching literacy, mathematics, science and social studies. These strategies have facilitated blending academic and career/technical subjects to make learning more meaningful for…

This module, designed to help students find and identify various geometric shapes and solids, contains 26 worksheets. Topics covered by these worksheets include: identification and grouping of objects with particular patterns, work with pentagons, hexagons, spirals, and symmetry. Teaching suggestions are included. (MK)

Montgomery County Public Schools (MCPS) "Special Education at a Glance," which includes a copy of the "Guide to Planning and Assessing School-Based Special Education Programs," provides in a single document, information about the special education population at each Montgomery County (Maryland) public school, including…

A device is suggested for constructing triangles with the same area and the same perimeter. A proof is given as is a proof of necessary conditions for a special case. The question of congruence of the triangles is left to the reader. (LS)

On a triangular grid of equilateral triangles an analytical procedure is presented for solving puzzles that require one to measure out a specified amount of liquid from containers of various volumes. (JP)

The relationship between area and perimeter is presented through a series of laboratory-type activities and demonstrations. (SD)

This is part one of a three-part School Mathematics Study Group (SMSG) textbook. This part contains the first five chapters including: (1) Analytic Geometry, (2) Coordinates and the Line, (3) Vectors and Their Applications, (4) Proof by Analytic Methods, and (5) Graphs and Their Equations. (MK)

This is part one of a three-part teacher's guide for an SMSG text designed to be used as a one-semester course for twelfth-grade students. This guide includes a suggested time schedule, a teacher's commentary, and answers to exercises. (MK)

This is part two of a three-part teacher's guide to an SMSG textbook designed to be used as a one-semester course for twelfth-grade students. For chapters 6 through 10, this guide includes a teacher's commentary and answers to the exercises. (MK)