Discusses a meaningful experience, conceptually, of multiplication of fractions. (Author/YDS)

Presents an activity, "Lisa's Lemonade Stand," that actively engages students in algebraic thinking as they analyze change by investigating relationships between variables and gain experience describing and representing these relationships graphically. (YDS)

Focuses on the importance of building from mistakes in mathematics instruction to develop better reasoning and problem-solving abilities. (Contains 11 references.) (YDS)

Focuses on children making sense of multiplication. In an activity called "Silent Multiplication," students use what they know about easier multiplication problems to solve increasingly difficult, related problems mentally. (Author/NB)

Develops computational fluency using a game format. Activities involve a standard deck of playing cards. (Author/NB)

Describes a series of lessons in which 6th grade students explore notions of rates of change and their effect on the shapes of graphs. Addresses aspects of the algebra content standard for the middle grades. (YDS)

Previews this special issue of "Mathematical Thinking and Learning," which describes models and modeling perspective toward mathematics problem solving, learning, and teaching. Discusses its characteristics and foundations and provides an example of a model-eliciting activity. (KHR)

Interrelationships between problem solving and number sense are discussed. Suggestions are given on helping children to search for a solution process and to reject unreasonable answers. The teacher's role in developing number-sense skills with problem-solving tasks is also discussed. (MNS)

Advantages and disadvantages of common ways to justify the answer to a probability problem are discussed. One explanation appears superior to the others because it is easy to understand, mathematically rigorous, generalizes to a broader class of problems, and avoids the deficiencies of the other explanations. (MNS)

Describes a course in problem solving for undergraduates not majoring in mathematics or science. The course was unusually successful in bringing average students to mathematical thinking. (Author/MKR)

Teaching which does not in any significant way address the genesis of mathematical ideas hides the fact that mathematics is created by people; that it involves intuition, exploring, conjecturing, and reasoning; and that it is purposeful. Such teaching can give students appearance that much of mathematics is very arbitrary; it just falls from the…

Discusses the relationship between areas of learning skills and metacognitive monitoring processes by focusing on mathematics. Examines the success level in standardized mathematical testing and awareness regarding control processes during the test execution of third grade (N=397) and fourth grade (N=394) children. Concludes that numerical and…

Presents an educational game on probability that can be the starting point for an open-ended statistical project. (ASK)

Presents a mathematical problem on calculating the length of a groove on a long-playing record. Analyzes the problem-solving stages by using two methods of estimation or calculation. (ASK)

Discusses the advantages of teaching with open-ended tasks and compares students' responses to open-ended, closed-area, and perimeter tasks. (ASK)