Beginning with a construction problem admitting a classical solution, the authors provide other solutions based on algorithmic estimation and transformational geometry. The latter methods are generalized to suggest solutions to other problems; hints to these solutions are provided. Teacher-student discussion could lead in many directions. (SD)

Four problems are given and discussed involving reflection about a line or the reflection properties of conic sections. Solutions are given. (MP)

A procedure using calculators is described to test Ulam's conjecture that all positive integers converge to 1, if subject to certain iterated transformations. (MNS)

Adults' geometric analogy solution was investigated as a function of systematic variations in the information structure of items. Latency data from verification of true and false items were recorded. A model incorporating assumptions about the form of item representation, working memory factors, and processing components and strategies was…

Presents an activity on transformations that employs a story from children's literature. Emphasizes that books and stories that use mathematical problem solving not only engage children in the narrative but also give them opportunities to see how mathematics is used in everyday life. (ASK)

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…

This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…

Presents a geometric problem and illustrates four different ways to solve it: (1) a synthetic approach; (2) a coordinate approach; (3) a vector approach; and (4) a transformation approach. (KHR)

The authors present 3 experiments demonstrating ways to reduce illegal moves in problem-solving tasks. They propose a 3-stage framework for the rejection of illegal moves. An illegal move must come to mind and be selected, checked for legality, and correctly rejected. Illegal move reduction can occur at any stage. Control group participants…

This extension of Harris' classification system permits classification of the interval-scale properties of any 2 x 2 (two person, two choice) game. The system is compared to taxonomies developed by various previous researchers. It is shown to permit compact description of any 2 x 2 game as an octet of numbers. It also permits rapid classification…

Certain properties of lenses provide a physical model of the mathematical concepts of multiplication of integral numbers and of similarity transformations in geometry. Further, they can provide a realistic concrete representation for rules governing multiplication of signed numbers. Suggestions for problems and classroom demonstrations involving…

The last 13 of 32 exercises of a course designed to give a wide range of skills in deductive, inductive, and indirect methods of proof in geometry are presented. (MP)

An approach to the instruction of maxima and minima problems that works with tools of geometry and algebra is presented. The focus is on a classic pie-cutting problem, which is viewed as an interesting and instructive task that is an excellent application of transformation geometry. (MP)

Presented is a method for solving certain types of problems, with the goal of piquing students' interest in studying affine geometry, which underlines the method. (MNS)