Presents three geometric problems from a workshop for in-service algebra teachers to help them make connections between the mathematical concepts that they know and the drawings that they were required to display on their graphing calculators. (ASK)

The chain rule is one of the hardest ideas to convey to students in Calculus I. It is difficult to motivate, so that most students do not really see where it comes from; it is difficult to express in symbols even after it is developed; and it is awkward to put it into words, so that many students can not remember it and so can not apply it…

Calls for the use of the zoom feature of graphing calculators to help students better understand the concept of derivatives. (MKR)

Discusses the rationale behind the technique of rationalizing the denominator in algebra. Argues that the importance of this technique is greatly exaggerated and is usually unnecessary. Examines an appropriate application of rationalizing the denominator. (ASK)

Discusses areas where teachers may harbor mistaken assumptions about their students' understanding when using graphing calculators: (1) confidence and competence with order of operations, (2) integration of algebraic and graphical knowledge, and (3) scaling a graph. (MKR)

Challenges mathematics instructors to use graphing calculator technology in courses designed for non-mathematics majors and offers three types of open-ended problems that can be integrated into a basic skills mathematics curriculum: simultaneous equations, distance problems, and proportions using real data. (MKR)