This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and…

Children need more than activities to help them see that the relationship expressed in a formula is true. Giving them the underlying principles will contribute to better comprehension, retention, and transfer. (MNS)

The article describes the Mental Mathematics System, a number of formulas designed to develop mathematical skills in elementary and junior high school gifted and talented students. Formulas are provided for multiplication. The formulas for mental mathematics are noted to promote student interest in the subject. (SBH)

Describes a way of using multiple representations to help students learn data analysis and make sense out of a large amount of data. Includes an activity for a group-learning environment. (KHR)

Describes numerical differentiation and the central difference formula in numerical analysis. Presents three computer programs that approximate the first derivative of a function utilizing the central difference formula. Analyzes conditions under which the approximation formula is exact. (MDH)

Argues that the derivation of the area of a circle using integral calculus is invalid. Describes the derivation of the area of a circle when the formula is not known by inscribing and circumscribing the circle with regular polygons whose areas converge to the same number. (MDH)

In this paper we analyze excerpts of "Paradoxes of the Infinite", the posthumous work of Bernard Bolzano (1781-1848), in order to show that Georg Cantor's (1845-1918) approach to the problem of defining actual mathematical infinity is not the most natural. In fact, Bolzano's approach to the paradoxes of infinity is more intuitive, while remaining…

The general combinatorial problem of counting the number of regions into which the interior of a circle is divided by a family of lines is considered. A general formula is developed and its use is illustrated in two situations. (PK)

Classroom ideas for teaching area and perimeter concepts are presented. Squares, circles and other shapes are examined. Further explorations are suggested. (PK)

Flow diagrams developing cube roots and formulas for the square, sphere, cube, circle and sector, oblong, and cylinder are presented. Some comments on their use, along with calculators, are included. (MNS)

In this reprint from the "Australian Journal of Remedial Education," the author examines the importance of the ability to read mathematics statements meaningfully and discusses remediation strategies for children who can not do this. (MKM)

Describes a way for students to learn to solve linear equations using physical objects (pan balances), diagrams, and symbols. Provides diagrams illustrating the method and five problems. Nine references are listed. (YP)

Activities that illustrate a problem-solving approach to teaching grouping symbols, such as parentheses and brackets, are described. Suggested exercises, answers to those exercises, and variations of this activity are included. (KR)

A lawn-mowing problem is discussed in terms of clarifying the problem; making initial conjectures; experimenting; developing a solution; and supporting formulas, theorems, and corollaries. (MNS)