Presents a qualitative and global method of graphing functions that involves transformations of the graph of a known function in the cartesian coordinate system referred to as graphic operators. Explains how the method has been taught to students and some comments about the results obtained. (MDH)

Two trigonometry problems are presented. The first compares the graphs of the functions arcsin[sin(x)], arccos[cos(x)], and the identity function f(x)=x. The second, using the law of cosines, demonstrates that the solution of a triangle knowing two sides and the excluded angle is no longer ambiguous. (MDH)

Discusses a method of graphing polar equations using information from the Cartesian graphs of trigonometric functions. (MKR)

Emphasizes how to express the breadth of mathematics itself. Addresses other missing dimensions which make mathematics attractive to a larger number of students by making it appear less isolated and more tied to thoughts and experiences that students find familiar and congenial. (ASK)

Describes an activity that allows students to investigate families of linear functions and families of quadratic functions. Offers an opportunity for students to conjecture, explain, and justify in an environment based on Euclidean geometry. Includes a teacher's guide, answers, and student worksheets. (KHR)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

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)

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)

Provides activities that deal with Fibonacci-like sequences and guide students' thinking as they explore mathematical induction. Investigation leads to a discovery of an interesting relation that involves all Fibonacci-like sequences. (DDR)

Describes an activity for making the connection between triangle ratios and graphs of circular functions which helps middle school students understand the concept of a sine curve. (ASK)

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)

Study of circular transformation and its associated properties is proposed as review and reinforcement of familiar concepts and for developing broader understanding of transformations. Inversion on a circle is discussed in some detail. (MNS)

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)