Two decades ago, in an award-winning paper, Dan Kennedy (1995) likened learning mathematics to climbing a tree, for which there was only one way to climb: up a large and solid trunk. In the limited time that is available, many students give up the climb, impede others, fall off the trunk, or fail to climb the tree sufficiently well. In the case of…

Describes computer or calculator-graphing technology to develop parametric representations which help students connect mathematical topics from algebra and trigonometry through algebraic, graphical, and numerical representations. Computer or calculator graphing utilities instantly transform algebraic expressions into visual and numerical displays…

How the use of calculators can illuminate mathematics and improve the level of problem-solving discussion in classes is presented. (MP)

Consideration of a definite integral in an advanced calculus class led to a great deal of mathematical thinking and to the joy of discovery. Graphing calculators allowed students to investigate quick solutions which should be regarded as stepping stones to additional investigation and rigorous proof. With slight modifications to their proofs,…

Discussed is the place and teaching of trigonometry in a NCTM Standards-based mathematics curriculum. Presented is how these standards can be implemented in a technology-rich environment that encourages reasoning, communication, problem solving, and confidence building. Examples focus on functions, graphical sense, modeling, and identities. (KR)