Presents a dice game that students can use as a basis for exploring mathematical probabilities and making decisions while they also exercise skills in multiplication, pattern identification, proportional thinking, and communication. (ASK)

Describes a project that features a video in the form of a documentary built around a series of six case studies in mathematical thinking: geometry, number, measurement, algebra, chance and data, functions, and calculus. Chooses an example from each area to illustrate inductive and deductive thinking-patterns and proof. (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)

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)

Describes a mathematics lesson using digital sums that allows teachers to assess third grade students' understanding of reasoning, arithmetic, and geometry. (ASK)

Presents a problem suggested for students in grades one through six concerning the concepts of grouping, reasoning, and pattern finding. Discusses the student problem-solving process. (ASK)

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…