Reviews the historic relationship between logic and the mathematics curriculum. Proposes a list of logical elements for modern school mathematics. Checks the current national curriculum against this list and finds it to be deficient, especially in relation to the development of ideas of proof. Presents arguments for reform. (Contains 29…

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)

Presents graphing calculator activities that rely on resolving the magnitude and direction form of vectors into their Cartesian components so that they are suitable as applications for vector or trigonometric relationships for years 10-12. (ASK)

Presents an activity using fractal cards--eye-catching pop-up cards--by applying simple iterative processes to single sheets of paper. This activity incorporates the concepts of measurement, number systems, sequences, series, limits, recursion, iteration, self-similarity, and fractional dimensions. Contains 12 references. (ASK)

Presents an activity for eighth-grade students and beyond to explore relationships between and among the areas of various polygons. Emphasizes that students should be given the opportunity to design their own examples. (ASK)

Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Presents an algebra project in which students build a dance club. Reveals how this project motivates students and makes algebra more accessible, dynamic, and relevant to their society. (ASK)

Presents a problem for students in grades 4-6 on Venn diagrams with or without manipulatives. Lists questions for teachers to reflect upon during the problem-solving process concerning student understanding of problems, problem-solving strategies, assessment, and reasoning skills. (ASK)

Presents a problem on Pythagorean triples and patterns to generate sets of triples. (ASK)

Presents an exercise that introduces students to scientific measurements using only metric units. At the conclusion of the exercise, students eat the experiment. Requires dried refried beans, crackers or chips, and dried instant powder for lemonade. (DDR)

Describes a spreadsheet model for approximating square roots then extends that model into the intriguing domain of chaos. Focuses on the use of a dynamic model to promote habits of mathematical reasoning, conjecturing, and graphing analysis that support mathematics learning across grade levels. (ASK)

Describes two activities that involve thinking of slope as rate of change. Uses a calculator-based laboratory, graphing calculator, appropriate probes, and web sites to make the concepts of slope and y-intercept come alive for middle grade students. (ASK)

Investigated the potentialities of teaching the concept of measuring surfaces to primary school children. Children tested in covering the surface of an object using socially significant materials (e.g., cardboard rectangles vs. car pictures and a drawing of a parking lot) were found to complete the task at ages younger than expected. (JPB)

Presents ways of connecting mathematics to students' lives. Provides information on CamMotion, software that uses video and computer technologies to bring mathematics and students together in innovative ways. (ASK)

Suggests an elementary school activity and questions to promote five types of mathematical thinking including modeling, logical analysis, inference, optimization, and abstraction. Discusses evaluating activities for mathematical reasoning opportunities. (ASK)