Graphs equations in two variables using a BASIC screen-sweep program that generates solutions to equations by applying the intermediate value theorem. Provides suggestions for investigations that result in graphs of a butterfly, the Cheshire cat, the Trisectrix of Catalna, E. T. waving goodbye, a praying mantis, and others. (MDH)

Presented are eight student worksheets of block problems. Included are diagrams of the squares and hollow squares involved and a separate answer sheet for the problems. (CW)

Presents a mathematics activity that illustrates how such adjectives as elegant, surprising, concise, and challenging can be, and in fact are, attributed to proofs by a not very expert audience. (ASK)

Discusses solving inequality problems involving linear programing. Describes the usual and alternative approaches. Presents an intuitive approach for finding a feasible solution by maximizing the objective function. (YP)

Describes two thought experiments, involving visualizing the behavior of functions, that can be turned into computer experiments. (MKR)

Provides illustrated problem settings that serve as models for generating new investigations of the three-dimensional figures that result from a transformation of two-dimensional patterns. (JJK)

Presented is a method for factoring quadratic equations that helps the teacher demonstrate how to eliminate guessing through establishment of the connection between multiplication and factoring. Included are examples that allow the student to understand the link between the algebraic and the pictorial representations of quadratic equations. (JJK)

Discusses how different meanings can be given to the proof at different levels and branches of mathematics education. (ASK)

Presents an activity that utilizes a digital camera to capture a stream of water from a faucet to study quadratic behavior using graphing calculators. (ASK)

Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Describes a spreadsheet model for approximating square roots then extends that model into the intriguing domain of chaos. Focuses on the use of a dynamic model to promote habits of mathematical reasoning, conjecturing, and graphing analysis that support mathematics learning across grade levels. (ASK)

Presents five lessons to demonstrate how graphing calculators can be used to teach the slope-intercept concept of linear equations and to establish more general principles about two-dimensional graphs. Contains a reproducible student quiz. (MKR)

Discusses the use of technology to investigate what graphs represent as well as how to interpret graphs. (MKR)

Presents algebraic and geometric solutions with surprising twists to a word problem involving linear functions and postal rates. (MKR)

Discussed are the rationale for, and the benefits accrued from, the use of graphing calculators within all aspects of the secondary mathematics curriculum. Examples are included that highlight specific features of graphing calculators. (JJK)