PS-I learning approaches with an initial problem-solving phase (PS) followed by an instruction phase (I) can be optimised by providing adaptive (individualised) instruction that builds on students' problem-solving products. A computer-based implementation of both phases offers the possibility of adaptivity at the transition from the…

The role of common fractions in mathematics education and in applications is discussed in light of the increased importance of calculators and the metric system. (MP)

This discussion of cyclic patterns that appear in repeating decimals includes the use of the calculator in discovering the patterns. (MP)

This discussion centers around the division process and suggests that the method of recording division might cause confusion. The role of fractional notation is discussed. (MP)

Children trained in the clustering-operations approach showed greater achievement than those trained in a traditional approach. The clustering approach presents all four operations simultaneously. (MP)

An array model is discussed as an alternative approach to reviewing the four basic operations with fractions; it could help motivate students. (MP)

Three topics related to teaching mathematics are discussed: a problem with the order of operations, teaching fractions, and an application of the distributive property. (MP)

Grid paper activities are discussed as a way to help students conceptualize fractions. (MP)

A proof is given of the irrationality of the square root of 2 which depends on notions of terminating and repeating decimals. (MP)

An account is given of the use of the calculator and Cuisenaire rods in examining decimals that result from the division of whole numbers. (MP)

This method of teaching the division of fractions emphasizes the use of concrete materials and helps students understand what division of fractions means. (MP)

A process of teaching fractions is detailed that respects pupil ideas and concept images and builds on these in a way that helps children to develop personal algorithms. This approach is an attempt to get away from perceived one-sided views found in most textbooks. (MP)

It is viewed understandable that many teachers consider fractions one of the most difficult mathematical topics to teach. School experiences need careful planning to include sequential activities which develop accurate concepts, and concepts are thought best developed by activities which move along the concrete-to-abstract continuum. (MP)

How graph paper has been used to illustrate the algorithm for division of fractions is presented. The combined use of graph paper and an overhead projector can make the presentation even more convincing. A review of whole number division is recommended prior to the lesson. (MP)