This paper describes a classroom, instructor-led activity designed to show how graphic calculators can be used to explore coordinate geometry. The activity involves digitizing an image of a hand and transforming the image through geometrical transformations. Teaching notes and calculator instructions are included as are blackline masters. Also…

Discussed is an approach in which algebra and geometry are interwoven in a series of problems that develop one from another. The two main concepts are the algebraic concept of function and the geometric concept of the "family of quadrilaterals." (MNS)

Presents examples which help students think visually about algebraic operations on vectors and the associated mappings of the plane. The pictures help students actively participate in defining new functions by enabling them to compose simpler known functions. Conversely, functions can be factored into the composition of simple functions. (JN)

This volume contains the full text of 2 plenary papers and 26 research reports. In addition, brief, usually one-page, reports are provided for 6 discussion groups, 10 technology focus groups, 7 symposiums, 7 oral presentations, and 17 position sessions. The two full plenary reports are: (1) "Problems of Reification: Representations and…

This book features a set of problems assembled to reflect the criteria of the mathematics portion of the North Carolina High School Comprehensive Test. The problems are not necessarily suited to timed situations but rather are intended for classroom use by teachers to review high school mathematics and build upon concepts and skills developed in…

Gives a lesson plan for a mathematics activity using balloons which shows connections between the algebraic concepts of slope, linear functions, and power functions and the geometric concepts of circle, sphere, volume, and pi. 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)

Discussed are the idea, examples, problems, and applications of convexity. Topics include historical examples, definitions, the John-Loewner ellipsoid, convex functions, polytopes, the algebraic operation of duality and addition, and topology of convex bodies. (KR)

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 review guide, prepared as an aid to teachers of Course III, starts with a pre-test review of Course II topics found again in Course III. The five units of Course III, as outlined in the New York State Syllabus, are then separated into nine smaller units. These include: real numbers; complex numbers; functions; logarithms; trigonometry;…

This book was developed for teachers, youth group leaders, after-school child care providers, and parents, who may not have the time or the expertise to develop strategies for preparing students to be effective problem solvers. The content is organized in a pyramid style to make it easy to locate and grasp the information provided. Information on…

Discusses the interconnection among the various modes of the TI-92 calculator (geometry, data graphing, function graphing, and algebra) and how the power of visualization is extended to provide multiple approaches to complex problem situations. Provides a graphing problem with illustrations and results. (AIM)

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)

Three sequences of coursework are detailed in the curriculum development guidelines provided in this document. The 4-year sequence, structured around problem-solving, applications, and the acquisition of theory, is designed for the college-bound student who plans to enter a mathematics-based field of study. The 3-year sequence is designed for…

Presented is a lesson in which the patterns that occur within and between sequences of polygonal numbers present an opportunity for students to analyze, represent, and generalize relationships. Materials, objectives, levels, and directions for this activity are discussed. Worksheets to accompany the activities are provided. (CW)