Presents a Monte Carlo simulation on probability using a telephone directory as a pseudorandom-number generator. Claims that Monte Carlo simulations offer a way to teach probability concretely and with understanding and that students enjoy the probability experiments. (ASK)

Presents an activity to teach piecewise functions using wax paper and rectangular grids. Helps students understand the idea of different pieces by literally "piecing" together a new type of mathematical function. Also describes a followup activity and explains how piecewise functions can be graphed using graphing calculators. (NB)

Discusses the new Advanced Placement course in statistics as an alternative to calculus for high school seniors. Broad conceptual themes of the course are exploring data, planning a study, anticipating patterns in advance, and statistical inference. Provides a list of College Board regional offices to contact for more information. (MKR)

Presents reasons for, and examples of, addressing environmental issues in secondary mathematics classrooms. (Author/MKR)

Discusses how a teacher might bridge the gap between the professional mathematician (and finished mathematics) and the learner who sees only a small part of mathematics. Includes suggestions about basic rules of inference and a few elementary examples of simple proofs using these rules. (Author/MKR)

Uses probability and Pascal's triangle to analyze the game Plinko from the game show "The Price Is Right." (MKR)

Presents a solution to the problem of finding the probability that a needle would cross a crack in a tile floor when dropped. (MKR)

Recollections of an eighth grade mathematics teacher who represented teaching that takes into account an accurate understanding of the physical, social, emotional, and intellectual changes that are experienced by young adolescents. (six references) (MLF)

Analyzes how each of the three opponents could win on the game show "Jeopardy" regardless of their relative standing when they enter the Final Jeopardy round. Analyzes optimal strategies for each contestant using probabilities. (MKR)

This in-depth examination of a line explores several ways that the infinite nature and finite representation of a line can be perceived. These attempts to understand the nature of the line give insights into the nature of understanding itself. (MDH)

Utilizes the notion of a students' proof schemes and outlines categories of proof schemes to evaluate the justifications given by students so that teachers can plan instruction to move them toward more sophisticated ways of reasoning. Contains 22 references. (ASK)

Presents a set of activities in which students explore how complex models can be generated using a small and simple set of rules. (ASK)

Discusses the characteristics of students' responses in terms of mathematical sophistication demonstrated that might be expected as they engage in a rich mathematical task that requires them to justify their solutions. (ASK)

Presents four related problems that provide examples of ways to include justifications of interesting mathematics in courses taught prior to a geometry course. (ASK)

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)