Contributes to the emerging picture of children's development of understanding in geometry and the kinds of teaching that can support it. Describes how teachers can use episode writing to capture student thinking and make instructional decisions. (ASK)

Describes an open-ended activity in which students try to determine the factors that contribute to an unusual chemical reaction. Uses a case study approach to show students how the presence of chlorine in tap water can interfere with a pH indicator. Includes assessment guidelines and extension activities. (WRM)

Presents examples of students' work when they are engaged in problem solving and reasoning tasks as they determine how to fill bottles with water to create musical notes by blowing across the tops of the bottles, and as they create mathematical models that represent these notes. (ASK)

Describes vortex tessellation in which an individual tile becomes smaller, and swirls or spirals inward to the center. Provides mathematical uses of this type of tessellation. (ASK)

Features activities for advanced second-year algebra students in grades 11 and 12. Introduces three random variables and considers an empirical and theoretical probability for each. Uses coins, regular dice, decahedral dice, and calculators. (ASK)

Introduces a technique for developing tasks suitable for group investigation where students work from sets of numerical examples toward making generalizations. (ASK)

Describes possible uses of spirographs in mathematics classrooms to study parametric equations and symmetry. (ASK)

Suggests that assessing problem-solving activities is more complex than assessing other activities. Addresses one method of assessment for a particular mathematical problem-solving activity that is an analytic scoring rubric. (ASK)

Presents a set of tasks using a child's invented strategy and a nonstandard algorithm to illustrate one way to facilitate the development of mathematical and pedagogical dispositions. (ASK)

Describes young students' development of mathematical understanding as they dramatize, read, write, and draw about mathematics after reading the story "Benny's Pennies." (ASK)

Extends a counting activity described in the April 1997 issue of "The Mathematics Teacher" entitled, "The Pyramid Question: A Problem Solving Adventure." In this activity, students must find all triangles with positive integral sides and a perimeter of 36. Considers triangles with perimeters other than 36 for this activity and…

Explores some of the principles of and presents several constructions in hyperbolic geometry using script tools created for the Geometer's Sketchpad. (ASK)

Introduces a model of differential equations for students--a very real overpopulation problem is occurring in the Ndumu Game Reserve in KwaZulu-Natal, South Africa, where one species of antelope, the Nyala, is crowding out another species, the Bushbuck. Constructs a competing species model to mathematically describe what is occurring in Ndumu.…

Adds a cropping or harvesting term to the animal overpopulation model developed in Part I of this article. Investigates various harvesting strategies that might suggest a solution to the overpopulation problem without actually culling any animals. (ASK)

Describes a rich, investigative approach to multivariable calculus. Introduces a project in which students construct physical models of surfaces that represent real-life applications of their choice. The models, along with student-selected datasets, serve as vehicles to study most of the concepts of the course from both continuous and discrete…