Choosing mental, written, or calculator procedures is important for children to learn. Children should be encouraged to be flexible and consider alternatives when doing mental calculation. Developing mental skills, symbols and rules, and numbers in context are each considered. (MNS)

A model is offered which can be used for teaching addition, subtraction, multiplication, and division with directed numbers. Illustrations for all operations are given. (MNS)

Discusses a number series made from the multiplication of numbers to digits. Presents a number series for diverse multiplication numbers. (YP)

Exercises are used when beginning work with calculators to help pupils think about what they are doing. Four worksheets are included, with discussion of their objectives. (MNS)

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)

The first aim in school might be to help children become more aware of the algorithmic processes they use; then, ensure that they can devise algorithms and define them. Many examples of how these aims can be met are given, including the use of calculators and computers. (MNS)

Discusses the calculation of pi by means of experimental methods. Polygon circle ratios, Archimedes' method, Buffon's needles, a Monte Carlo method, and prime number approaches are used. Presents three BASIC programs for the calculations. (YP)

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

Outlined is the "nine complements" method of subtraction. This activity was used by students to generate proofs that explained why the subtraction method worked. Reasoning and inquiry skills are emphasized. Other examples are offered that have been successful in stimulating inquiry. (KR)

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)