There are many uses for the shortest path algorithm presented which are limited only by our ability to recognize when a problem may be converted into the shortest path in a graph representation. (Author/TG)

Results showed that only 32 percent of adult female shoppers in a supermarket were able to use a proportional reasoning strategy to determine which of two sizes of a common item (size ratio 2:3) was the better buy. Performance declined when the ratio was more complex. (JMB)

The article presents a general test for divisibility that includes composite numbers and shows that such a test can be used to determine divisibility by several numbers simultaneously. (MK)

Concepts of probability and statistics are discussed in terms of common occurrences and objects. (MK)

Suggestions for teaching the concept of division by zero are given. (MK)

Gives ways of applying the associative and commutative laws in the addition of one- and two-digit numbers. (MK)

Derivations of elementary trigonometric identities involving constants (namely, particular values of the sine function) are presented. (MK)

Twenty-four children in kindergarten through fourth grade were interviewed and asked to share a pancake fairly among three dolls. The context was chosen to allow children to use out-of-school intuition and understanding if preferred. Four levels of development were identified leading to the understanding of fair fractions as those where each part…

Proposes using the reform documents from the National Council of Teachers of Mathematics (NCTM), a theory-based multidimensional assessment framework, to help expand the scope of assessment in mathematics. Presents a framework using a context based on mathematical reasoning and components that comprise mathematical concepts, procedures,…

Using Taxi-Cab Geometry (a non-Euclidean geometry program) as the starting point, 14 mathematically gifted British secondary students (ages 12-14) were asked to consider the differences between Euclidean and Non-Euclidean geometries, then to construct their own geometry and to consider the non-Euclidean elements within it. The positive effects of…

Illustrates how mathematicians work and do mathematical research through the use of a puzzle. Demonstrates how general rules, then theorems develop from special cases. This approach may be used as a research project in high school classrooms or math club settings with the teacher helping to formulate questions, set goals, and avoid becoming…

Presents activities that engage students and promote discussion emphasizing the history of mathematics, diversity, and multiculturalism. Six activities included are Crossword Puzzle, Date of Event, Quotes Matching, Famous Mathematical Expressions, Calendar Scramble, and Map Puzzle. Also lists related World Wide Web sites. Contains 15 references.…

This study investigated the understanding of and reasoning about geometry of 120 mathematically talented students in the sixth through eight grades prior to taking a course in geometry. Results found that, although the students were able to deduce meaning from context, they lacked understanding of basic definitions, concepts, and properties.…

Discusses the language used in mathematics classrooms and states that appropriate language is based not only on the words we say but also on how those words are being perceived. Indicates that teachers should give students time to develop the meaning of numbers, operations, or problems. (ASK)