Presents a strategy for graphing conic sections on the polar plane without using a table of values by beginning with information gained from the graphs of circular functions. (MKR)

Explores many forms of a circle using variations of the distance formula. Metric space is defined and examples of metrics are given, including a "circle" that is a square. Also shown are variations which are not metrics. (MKR)

This is part two of a three-part School Mathematics Study Group (SMSG) textbook. This part includes the index and chapters 6 through 10: (6) Curve Sketching and Locus Problems, (7) Conic Sections, (8) The Line and the Plane in 3-Space, (9) Quadric Surfaces, and (10) Geometric Transformations. (MK)

An investigation using the Pythagorean theorem, the area of a triangle, and some first-year algebra yields a relationship between the radii of inscribed and escribed circles. (MP)

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)

This is part three of a three-part teacher's guide to an SMSG textbook designed to be used as a one-semester course for twelfth-grade students. This guide contains a teacher's commentary and answers to materials that can be used to supplement the regular course found in the first ten chapters of the text. (MK)

Presents an activity in which students draw a picture, analyze each line and curve, and write the symbolic equations represented by the graph. Includes reproducible student worksheets. (MKR)

Describes the Geometer's Sketchpad, a geometric construction kit composed of three manipulatable, dynamic, linked, multiple representation environments: the coordinate system, formulas, and graphs. Examines the use of the environments for studying parameter effects of linear and quadratic functions and for solving linear equations. (MDH)

This is part three of a three-part School Mathematics Study Group (SMSG) textbook. It contains eight chapters of supplements. Four of these are designed to be supplements to the specific chapters 2, 3, 7, and 10. The other four supplements cover the topics: Determinants; Flow Chart for Two Linear Equations in x and y; Graphs with Non-uniform…

Function Probe is a multi-representational software for Apple Macintosh computers. It was designed to allow students to approach problems in different ways and/or use different representations. This case study describes a 16-year-old student as he creates a path among a variety of representations of transformations of functions while using the…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

Entering a value into a calculator and repeatedly performing a function f(x) on the calculator can lead to the solution of the equation f(x)=x. Explores the outcomes of performing this iterative process on the calculator. Discusses how patterns of the resulting sequences converge, diverge, become cyclic, or display chaotic behavior. (MDH)

This proceedings contains 75 research reports, 8 discussion groups, 32 oral reports, and 28 poster presentation entries from the 1996 Annual Meeting of the American Chapter of the International Group for the Psychology of Mathematics Education. A one-page synopsis is included for discussion groups, oral reports, and poster presentations. Topic…