Describes a mathematics trail created on the campus of Exeter Academy and in the town of Exeter, New Hampshire. A series of problems and puzzles enabled teachers to teach mathematics outdoors. Novel questions were created to permit students to look at things from a different perspective. Participants were often inspired to create questions of…

Data were analyzed to see if a correlation or relationship existed between students' grades in a course and students' rankings of the professor's teaching. Graphing calculators allowed students to visualize relationships between the data and to compute the equation of the regression line, compute the correlation coefficient, and test statistical…

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)

Describes a project that involves students working with Pascal's triangle. Includes using computation involving Pascal's triangle to understand Plinko, a game on a well-known television show. (JRH)

Describes the use of data sets from ultraracing--foot races that are longer than a marathon--with second-year algebra students in data-analysis projects. (JRH)

Describes an exploration involving parabolas that was prompted by a routine exercise undertaken in a graphing-calculator workshop with high school mathematics teachers. Appendices contain instructions for using the TI-85 SIMULT menu and matrices to solve the system. (JRH)

Presents examples of using a tic-tac-toe format to practice finding the slope and identifying parallel and perpendicular lines from various equation formats. Reports the successful use of this format as a review in both precalculus and calculus classes before students work with applications of analytic geometry. (JRH)

Presents activities that use toy balloons to offer students interesting opportunities to connect algebra and geometry. Involves students measuring the speed of a released balloon and investigating the subtle relationship between the volume of a sphere and its surface area. Prompts a rich and revealing discussion about why the experimental results…

Presents recently developed generalizations to the sieve of Eratosthenes, showing the principles underlying these improvements, which increase its efficiency without changing too much of its simplicity. Offers several possibilities to propose good investigations for students to explore, find patterns, and make generalizations. (JRH)

Highlights the power of writing in the mathematics curriculum. Discusses expository writing, journal writing, and metacognitive development. Presents writing samples that demonstrate the usefulness of writing exercises as an alternative tool for mathematics education. Concludes that writing can be a viable force both as a learning tool and as a…

Describes an experimental approach to determining the speed of light in water using some simple observations and Fermat's principle. Enables students to integrate mathematical techniques and encourages mathematical exploration in which the students have control over what mathematics and technology to use and when to use them. Presents extensions…

Discusses the behavior of functions under reciprocal mappings, focusing on the horizontal reciprocal transformation. Offers suggestions for using the graphing calculator, for extending the concepts, and for teaching about reciprocal mappings. (JRH)

Discusses the use of a dynamic geometry software package to improve teaching of graph theory in basic graph sketching and in isomorphic, bipartite, and planar graphs. (JRH)

Describes the solution to a geometric problem by two ninth-grade mathematicians using The Geometer's Sketchpad computer software program. The problem was to divide any line segment into a regular partition of any number of parts, a variation on a problem by Euclid. The solution yielded two constructions, one a GLaD construction and the other using…

Describes a lesson that uses the graphing calculator to prompt the proof of the mean-value theorem. Students, through guided questioning, proposed the idea of using a difference function to find where a tangent line is parallel to a secant line. Through the use of graphing technology, students conjectured the essential fact that the constructed…