Highlights the argument that states that problem solving is much more than just solving problems, by focusing on problem-solving history, George Polya's view of problem solving, Asians' successful use of multiple intuitive solutions, and other examples. (ASK)

Describes an episode involving conditional statements and the notion of logical equivalence that occurred in a 10th-grade college-preparatory geometry class. Illustrates some of the confusion that can arise in connection with this topic, for both students and teachers. (ASK)

Presents an activity to teach piecewise functions using wax paper and rectangular grids. Helps students understand the idea of different pieces by literally "piecing" together a new type of mathematical function. Also describes a followup activity and explains how piecewise functions can be graphed using graphing calculators. (NB)

Presents a trigonometry problem concerning control of the entry of sunlight through a window. (ASK)

Highlights the use of spreadsheets in studying and investigating probabilistic situations with both high school students and preservice mathematics teachers. (ASK)

Discusses the importance of the use of rich problems to challenge gifted students. Highlights the characteristics of challenging problems and projects, and presents examples of these kinds of questions. (ASK)

Presents activities for teaching the logistic growth model using calculators and spreadsheets. (ASK)

NCTM's Curriculum and Evaluation Standards are often invoked to support many kinds of educational practices; however, the Standards were not written as a prescription for teaching and learning. Instead of taking the Standards literally, educators should use common sense to judge how to use them in individual situations. Includes case study…

Addresses a problem originally published in the September 1994 issue in an article entitled "Creative Teaching Will Produce Creative Students" by Krulik and Rudnick. Problem stated: "Find all rectangles with integral dimensions whose area A and perimeter P are numerically equal." Presents solution to a rectangular solid, extends the problem to…

Describes a project combining precalculus and transition mathematics students focusing on popcorn by comparing popping ratios of different brands of popcorn and finding what size box could hold the most popped corn. Project design required group effort and cooperation. Students exhibited growth of positive attitudes toward the study of mathematics…

Argues that proving something begins with an assumption and proceeds logically to a conclusion, thus convincing by offering arguments. Describes some pitfalls involved in proving through examining several case histories. Offers suggestions for teaching the proof process. For example, sometimes an extreme example or counterexample will do more to…

Suggests use of the quadratic formula to build understanding that connections between factors and solutions to equations work both ways. Making use of natural connections among concepts allows students to work more efficiently. Presents four sample problems showing the roots of equations. Messy quadratic equations with rational roots can be solved…

This activity involves students investigating the mathematics of packaging and exploring various concepts in geometry, including area and the Pythagorean theorem. Mathematics comes out of the discussion of packaging cans into six-packs and focuses on the cost-effectiveness of the horizontal storage area used. Students learn how knowledge of…

Describes a project to explore how mathematics teachers can use assessment of students' learning to shape their own instructional practices. The project had two goals: (1) to make sense of what students understand, how they understand it, and what counts as evidence of understanding; and (2) to use analysis of materials that document students'…

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,…