Examples from some area tasks indicate that misconceptions about linear measurement can be carried over to area measurement; children will occasionally count points rather than length units or area units. (MP)

Different types of understandings are presented as different facets of the development of the mental processes. (MP)

Arguing that the teaching of stochastic processes should reflect the experience and reality of the student, the author urges concentration on fundamental ideas. The development of intuition should be encouraged, and to this end continuity in teaching and a spiralled curriculum are important. (SD)

The inclusion of probability in the school curriculum is argued to be justified on mathematical, psychological, and social grounds. Contemporary teaching approaches are suggested as sufficient. (MP)

This essay discusses the sketching and transformation of parabolas and other curves as areas where learners can exercise and develop control of their mental imagery. (MN)

Suggested are activities that might stimulate cognitive thought in students and which can be performed both in school and at home. (EB)

A criterion for development of syllabi for mathematics courses is discussed. This criterion is based on the biogenetic law that individuals develop through all the stages of the development of the species. (SD)

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)

Investigates several key statements from Piaget's cognitive psychology and their meaning for science education. Concludes that teaching must be conducted as reversibly as possible so that when the teacher presents his own assimilation schemata it will be equilibrated by the pupils' schemata. (GA)

The author argues that mathematics educators are not optimistic enough about their own professionalism as teachers or the learning capacities of their pupils. He expands on the negative effects of pessimism in relation to education. (MN)

Questions Piagetian theory that dismisses the idea of accelerating cognitive development through classroom activities. (CP)

This discussion is primarily designed to increase teachers' awareness of Piaget's theory of cognitive development and implications for mathematics in the middle school. It is hoped such awareness will compel instructors to adopt strategies that help pupils gain more from mathematical experiences, by providing impetus for innovation and…

Five steps described by Dienes by which mathematics is learned are illustrated through the use of the topic of direct proportion. (MP)

Reports a procedure for training fifth and seventh grade students to substantially improve their understanding and use of controlled experimentation procedures. (SL)

Briefly explains Piaget's theory of intellectual development and its implications for teachers. (LS)