We explore how 13 year-olds construct meanings around the notion of curvature in their classroom while working with software that combines symbolic notation to construct geometrical figures with dynamic manipulation of variable. The ideas of curve as intrinsic dynamic construction, and curve as object with properties related to its positioning on…

This illustrated book examines everything having to do with the square. It begins with a basic definition of the square and continues by giving some examples of squares and other interesting historical information. Some ideas addressed include why cities are laid out in square blocks, how buildings are designed from squares and cubes, and how…

According to the Third International Mathematics and Science Study (TIMSS) which compared student performance in mathematics and science in 41 countries in 1995, fourth grade students in the United States perform only slightly above the international average in mathematics. The study showed that most U.S. students are mastering basic arithmetic;…

The Nevada Mathematics Standards provide the framework for a comprehensive K-12 mathematics program and guide curriculum, instruction, and assessment as well as other policies and practices that affect student learning. The standards are intended to serve as a foundation for teachers and curriculum specialists as they create curriculum and adopt…

Although proof and reasoning are seen as fundamental components of learning mathematics, research shows that many students continue to struggle with geometric proofs. In order to relate pedagogical methods to students' understanding of geometric proof, this 3-year project focuses on 2 components of student understanding of proof, namely, students'…

This report is incorporated into "Attaining Excellence: A TIMSS Resource Kit." Released in Fall 1997, the TIMSS resource kit was developed for educators and those interested in using TIMSS data to improve teaching, curricula, and student achievement in state and local communities. This module presents information about the grade 8…

This document outlines the content standards for mathematics in the state of Colorado. The document is organized into six standards, each of which is subdivided into a series of lists defining what is expected of students at each grade level within the standard. The standards relate to number, algebra, data, geometry, measurement, and the linking…

Directions are given for seven activities involving the folding of paper strips to illustrate geometric concepts. Properties of pentagons, triangles, hexagons, and Mobius bands resulting from the various foldings are discussed. (DT)

Describes initial encounter of a fifth grade student with Logo, a computer program language designed to develop in the user a knowledge of programing, geometry, arithmetic, and problem solving. A brief description of Logo, programing examples, and two references are included. (EJS)

Enrichment activities that teach about geometry as they instruct in geometry are given for some significant topics. The facets of geometry included are tessellations, round robin tournaments, geometric theorems on triangles, and connections between geometry and complex numbers. (MNS)

Pascal's Triangle is examined within the context of providing a partial model for the outcomes of dice throws. Several issues are addressed regarding the nature of the pattern. Discussion leads to the development of a general formula for six-sided dice. Modifications for other than six sides are noted. (MP)

The microcomputer has great potential for making high school geometry more stimulating and more easily understood by the students. The microcomputer can facilitate instruction in both the logico-deductive and spatial-visual aspects of geometry through graphics representations, simulation of motion, and its capability of interacting with the…

Some geometric activities are described that teachers can use to give their students experiences that will influence their spatial abilities. It is noted that the goal is to improve spatial abilities, not to increase knowledge, so individual pupil responses should not be used to judge student achievement. (MP)

Presented is a method for finding two triangles that have five pairs of congruent parts, yet fail to be congruent. The solution is thought to involve some creative insights that should challenge both the teacher and students to recall and analyze all the congruence axioms and theorems. (MP)