Presents a technique for teaching logarithms using function notation. (MKR)

Presents research findings and teaching implications of mathematics as reasoning and students' reasoning abilities in mathematics. (20 references) (MKR)

Describes four projects that support the transition from an abstract to a concrete notion of the effective use of technology in the secondary school classroom: The Interactive Mathematics Program, Systemic Initiative for Montana Mathematics and Science, University of Chicago School Mathematics Project, and Connected Geometry. (MKR)

Describes some student explorations of angle rotations and of reasonable and unreasonable conjectures using the Geometer's Sketchpad. (MKR)

Discusses mathematics as analogous to a tree with many branches. Contends that technology, especially the graphing calculator, can help students see the sun and sky through the many branches and leaves. (MKR)

Proposes that the value of open-ended questions to enhance learning rests not only with the format and content of the questions themselves but also with the settings in which teachers pose such questions and the procedures used to evaluate students' responses to them. (MKR)

Presents an investigation of a third-degree polynomial using a TI-82 graphing calculator. Also includes an algebraic solution. (MKR)

Shares guidelines for identifying and structuring worthwhile mathematical tasks and gives suggestions for successful classroom approaches in light of the NCTM Standards documents. (MKR)

Focuses on the fascinating topic of soap films to allow students to use practical methods during their investigations into the underlying mathematics of soap film geometry. Provides directions and illustrations for the investigative mechanisms, as well as describing the mathematical equations involved. (JJK)

Describes hands-on class activities in which high school geometry students can create nested Platonic solids from posterboard. Includes discussion of the algebraic and pictorial relationships between pairs of Platonic polyhedra. (MKR)

Fractal geometry is introduced through examples of computational exploration of coastlines, self-similar curves, random walks, and population growth. These explorations, which include the construction of algorithms and the subsequent development and application of simple computer programs, lend themselves to self-directed study and advanced…

Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

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)

Geometric interpretations and derivations of the six trigonometric relationships are demonstrated. Selected for discussion are limiting values, geometric verification of trigonometric identities, a one-dimensional illustration of the Pythagorean relationships, and the geometric derivation of infinite-series relationships. (DE)

Discusses two teaching ideas: (1) copying and distributing anonymous student mathematics homework to the class to increase student responsibility and their ability to communicate and read mathematics, and (2) using maximum/minimum applications of calculus to investigate the most economical dimensions for manufactured metal cans. (MKR)