A generalization of the golden ratio is made, called the silver ratio. Some examples where the golden ratio appears are provided so that the silver ratio appears. (MNS)

Third graders decided to collect 10,000 objects, first determining how many each child would bring. Grouping and other activities were involved, and each child wrote about the experience. (MNS)

Describes how teachers can present their students with a variety of experiences that promote the thoughtful use of calculators and a positive attitude in students and parents. Discusses using classroom banks, problem solving, writing word problems, holiday catalog ordering, and parent education. Includes sample activity pages. (MKR)

Students (n=61) in an experimental course stressing active student involvement and the use of a computer algebra system scored higher than students (n=76) in a traditional college algebra course on final measures of inductive reasoning, visualization, and problem solving while maintaining equivalent manipulation and computation skills. (Author/MLB)

Presents three investigations related to the game Bulgarian Solitaire. Investigations ask students to find and represent optimal solutions to the problem, to identify cyclical solution patterns for different numbers, and to respond to questions involving the number and nature of the cyclical solutions. An appendix provides answers to questions.…

Utilizes a computer-generated graph to solve an equation for methods using trigonometric tables or less sophisticated calculators would likely fail because of round-off errors and limitations of the instruments. Discusses how this new technology can be utilized in mathematics instruction. (MDH)

Presented is a concrete, realistic way of representing concepts of coordinate geometry. Students represent the coordinates in a living version of a five-by-five square geoboard. Procedures and examples for using this activity are included. (KR)

Using the notion of the difference between a number and its cube as a starting point, this article presents a wide range of mathematical activities at varying levels of sophistication utilizing numerical, intuitive, and graphical approaches. (JJK)

Discusses elementary school mathematics instruction and describes the design and construction of a database with nonroutine problem-solving situations. A classification for the problems is explained, and use of the database at Indiana University and its potential use by elementary school teachers are described. (four references) (LRW)

Considers children's literature as a tool for teaching mathematics. Ways that children's literature can help achieve the goals established by the National Council of Teachers of Mathematics are discussed, and use of children's books to explore topics such as measurement, multiplication, estimation, and subtraction is examined. A bibliography of 41…

Discusses effectiveness of hints given to (n=100) ninth-grade students solving nonstandard problems on functions. Hints that stimulated concrete action were effective if the action modeled the required solution method. Hints that only warned against certain mistakes were ineffective. Appendix includes problems and hints. (MKR/Author)

Reports a case study exploring how 2 16-year olds were enabled to capitalize on the potential of errors to stimulate and support mathematical inquiry. Discusses variations within the strategy of using errors to enhance mathematics instruction. Appendix includes list of instructional episodes and error activities. (Contains 56 references.) (MKR)

The purpose of this paper is to show, by computer examples, that very different results can be obtained by rearranging selected conditionally convergent series. Computer programs allow the students to select the real number to which they wish the rearrangement to converge. Two computer programs are appended. (KR)

Described are the variations found between the western and African versions of the same logic puzzle. It is demonstrated that mathematical ideas are of concern in traditional non-Western cultures as well as in the West. (KR)

Explored are the distributions of residual components in two model systems. A system of components with exponentially distributed lifetimes and the two-dimensional "leaf model" in which objects fall on a plane with positions independent and normally distributed are discussed. Included are the definition, application, computations, and theorem. (KR)