Describes a model for geometrical probability. Presents two examples of basic theories of probability using geometrical probability. Provides three problems using the described theorem. (YP)

Describes how five-year-old children responded to the investigation of looking for patterns in a multiplication square. Provides a 10 x 10 multiplication square for the investigation. (YP)

Describes the Calculator-Aware Number (CAN) curriculum developed by the Primary Initiatives in Mathematics Education (PrIME) project. Summarizes the CAN curriculum as it relates to learning by children and use by teachers. (YP)

Reports students were more successful in estimation for a problem in context than for the pure computation. Describes students' strategies to make estimates in context. Discusses how to teach estimation. (YP)

Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)

Presented is a rationale for the importance of estimation. Strategies used by good estimators, and teaching strategies for computational estimation are considered. (PK)

Provides methods of teaching negative number operations, including addition, subtraction, and multiplication. Presents examples and activities for the operations. (YP)

Describes a process of mathematical investigation involving generalized Fibonacci sequences. Provides the derivation using expressions, BASIC programs, and numerical verification. (YP)

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)

This article examines the level of understanding by children (six- to seven-year-olds) of the addition and equality symbols. The article reports that about half of the subjects were unable to write the mathematical expression of simple addition while they were able to do it verbally. (YP)

Proposed is a way for teachers to distinguish between rich, challenging material that encourages mathematical thinking and material that is unsuitable. Included are multistep problems that encourage a broader understanding of mathematics. (KR)

Described are four classroom activities that may be interspersed into a curriculum or offered as homework. Systematic procedures, alternative strategies, and trial and error are emphasized in these counting exercises. (KR)

Discussed are ways in which students can generalize both quadratic or cubic situations. Generalizations are produced using the factor method, repeated linear generalizations, means of the mean, and through the use of differences. (KR)