Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)

Presents a logical reasoning problem pivotal to the novel "Harry Potter and the Sorcerer's Stone" and discusses it at two levels. (Author/NB)

Presents a discovery activity that connects mathematics and the world of entertainment. Combines geometric transformations with a calculator's DRAW, MATRIX, and PRGM features to generate visual reinforcement of mathematical concepts. (Author/NB)

Introduces human graphing by having students standing on certain coordinates instead of points plotted in ink. Includes teacher tips for success and possible graphing explorations. (KHR)

Investigates the effects of inquiry activities on a dynamic geometry environment designed to confront students with contradictions and uncertainties. Characterizes epistemological, didactic, and cognitive aspects of the activities. Analyzes the interplay among these three aspects, students' investigations, and their explanations. (Author/KHR)

Describes an activity in which students examine bicycle chain-rings, cogs, and gear ratios as a means of exploring algebraic relationships, data collection, scatter plots, and lines of best fit. (KHR)

Presents a mathematics activity that introduces proof by contradiction in a nonformal setting. This activity has the added benefit of helping students gain a greater understanding of the electoral college. (ASK)

The 16 units of this book are designed as textbook supplements to encourage students to think mathematically and as mathematicians. Each unit begins with an orientation session which raises general concerns that always occur within mathematical exploration. This is followed by a short, original text in which a mathematician creates a particular…

Guides students through the process of designing a window. Allows them to use technology and a variety of representations while maximizing and minimizing the dimensions based on cost and light. Includes activity sheets. (Author/NB)

Describes an activity, The Spaghetti Problem, that shows how statistics could be used to introduce many topics in the secondary mathematics curriculum. (KHR)

Presents a game in which if player is playing a match of this game with an opponent, at each step in the game he has to decide whether to continue or to stop. Helps students to develop a strategy for making such a decision based on the expected gain and related probabilities. (Author/ASK)

Examines existing research literature which suggests that introducing computing tools can help students focus on the relevant aspects of a problem, function at higher levels of geometric understanding, distinguish between drawings and constructions, and develop and reason about conjectures on the basis of generalization of patterns. (KHR)

Investigates the use of mathematical modeling tasks in 11- and 12-year-old students and the development of mathematical thinking skills using practical modeling activities. Analyzes the development of students' mathematical thinking with interviews of a form of dynamic assessment. Reports that some students proved to be naturally mindful and…

Presents materials and methods that maintain student interest and encourage them to think creatively, develop mathematical reasoning, and look at problems from different perspectives, all within an open-ended approach to problem solving. Includes questions for discussion. (KHR)

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)