Describes a combinatorics problem involving pizza toppings. Includes three activity sheets. (Author/NB)

A situation is presented that is intended to lead to open-ended mathematical discussions that allow students to conjecture, discover, and prove mathematical statements. (MP)

Presents a question designed to launch a discovery journey through conjecture, research, serendipitous encounters, proof, answers, and new questions. Reports some discoveries and suggests ways in which to incorporate this strategy into classrooms. Presents a geometry project that incorporates this problem-solving approach to mathematics. (JRH)

The idea of "complete permutations" of n distinct objects is explored in order to investigate an application of the concept that arises in Rex Stout's mystery novel, Too Many Cooks. (MN)

An exploratory problem is presented which involves the identification of all the ways a unit fraction with prime denominator can be written as a sum of two unit fractions. (MN)

A discussion on the general equation of a line shows how students can be lead to discover mathematical properties, find how one discovery leads to another, see how different branches of mathematics can lead to a solution, and be provided with a starting point for studying special mathematical topics. (MP)

Activities designed to aid pupils explore the Fibonacci sequence are presented in worksheets. (MP)

Discusses the mathematics education philosophy of J. W. A. Young and how it compares to the principles in the National Council of Teachers of Mathematic's "Curriculum and Evaluation Standards for School Mathematics." Elaborates on Young's views concerning rote learning, establishing connections between mathematics and other disciplines,…

The use of trial-and-error strategies to solve problems is endorsed. Types of problems with which trial and error is effective are discussed, with examples of how it is used, and teaching considerations are briefly considered. A computer program for one problem is included. (MNS)

An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (MP)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

Originally marketed as a personal organizer for mobile business executives and ardent technophiles, the handheld computer is beginning to catch educators' notice. A handful of school districts are piloting large-scale use of these portable devices, ranging in price from $149 to $450. (MLH)

An activity-based unit on congruence and similarity is described. The themes underlying the unit are the usefulness of analogy in determining mathematical principles, and the notion that the number of conditions imposed on figures affects the number of factors which must be specified to insure congruence or similarity. (SD)

Some functions on digits of positive integers are presented as possible sources for useful investigations by students, particularly through the use of calculators and computers or in the writing of small proofs. The material is designed to encourage students to conduct their own investigations. (MP)

The use of a ruler with two parallel Straight edges as a tool in geometric constructions is presented, based on ideas that are fairly standard in high school geometry courses. The constructions are seen as potential challenges that provide opportunities for inventiveness by students. (MP)