Game theory is appropriate as a topic for an honors seminar for high school students. Matrices provide a model for analyzing certain situations involving conflict, and probability theory can be used to determine the best strategies for the players. Variations on the ancient game of morra are discussed. (MNS)

Presents created letters and responses from a character representing an authority to develop ways of teaching what constructivism is and ways to address the obstacles that teachers might face in adapting a mathematics reform and constructivist approach in the classroom. Contains 16 references. (ASK)

Describes the use of graph theory and game theory to deepen students' appreciation of Ferdinand Magellan's story and his magnificent contributions as an explorer. (MKR)

The historical development of probability theory is traced from its early origins in games of chance through its mathematical foundations in the work of Pascal and Fermat. The roots of statistics are also presented beginning with early actuarial developments through the work of Laplace, Gauss, and others. (MDH)

Outlines a course on fractal geometry and chaos theory. Discusses how chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum and offers an eight unit course by pulling together units related to chaos theory and fractal geometry. Contains 25 references. (ASK)

Examines research relevant to the debate about the relative emphasis that formal proof should play in high school geometry. Discussion includes establishing truth in geometry, research in students' learning of proof, developing the notion of proof, alternatives to axiomatic approaches, computer construction programs, and classroom recommendations.…

Presents an opportunity for students to become familiar with the fundamental premise of iteration for a new branch of mathematics that is known as chaos theory by using graphing calculators. (ASK)

Describes a spreadsheet model for approximating square roots then extends that model into the intriguing domain of chaos. Focuses on the use of a dynamic model to promote habits of mathematical reasoning, conjecturing, and graphing analysis that support mathematics learning across grade levels. (ASK)

By considering colors as sets of wavelengths and using Boolean Algebra of sets, the effects of combining colors can be represented in a formal mathematical system. (SD)

Some counterintuitive ideas in probability are examined. In particular, for sequential selection procedure, such as drawing cards, it is shown that there is probabilistic advantage to drawing first (or early) relative to drawing last (or late) in the sequence. (Author/MK)

The mathematics of an educational game commonly known as "Frogs" is analyzed to see different mathematical concepts imbedded in it. (MP)

The need for students of engineering to acquire the rational, methodical approaches identified with the "mathematical way of thinking" is discussed. The skill areas in mathematics most critical to engineering majors are pointed out, with proper shaping of student attitudes seen as an important role secondary school mathematics must play.…

The five levels of the van Hiele theory are described. Then interviewing tasks designed to be presented to students in kindergarten through college are presented. Finally, responses from 14 interviews are discussed, with implications for teaching geometry. Extensive references are included. (MNS)

The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

Discussed are several different transformations based on the generation of fractals including self-similar designs, the chaos game, the koch curve, and the Sierpinski Triangle. Three computer programs which illustrate these concepts are provided. (CW)