The philosophy behind the Nuffield Mathematics Project, the process of curriculum development, and evaluation of the project are discussed. (SD)

Through a mathematical analysis, Piaget's grouping concept can be formally interpreted as being a hybrid between the mathematical concepts of a group and a lattice. Some relevant pedagogical models are presented. Activities with Cuisenaire Rods, Dienes Blocks, and Papy's Minicomputer are shown to take place in groupings. (LS)

Examination of models for representing integers demonstrates that formal operational thought is required for establishing the operations on integers. Advocated is the use of many models for introducing negative numbers but, apart from addition, it is recommended that operations on integers be delayed until the formal operations stage. (JP)

This paper, after analyzing the meaning of "applied mathematics," seeks to explore and set forth some broad outlines of the pedagogical implications of studies in the application of mathematics. (Author/MP)

The new, and prevalent, raised-dash notation (for subtraction) appearing in school mathematics texts is examined, especially for its effects on students' computational skills. Reasons for a return to the standard notation of the centered dash are presented. (Author/MN)

The author argues that many who speak to the issues of elementary-school mathematics are not aware of the real problems. The clear objective of the teacher of young children is to provide them with experiences which will enhance their development. (SD)

The author argues that mathematics instruction should start with real, complex, non-mathematical problems and describes a teacher education program which is consistent with this belief. (JLH)

The author develops a four-stage model for concept-internalization. The stages are: (1) concrete structure; (2) linguistic structure; (3) algorithm; and (4) mastery. The model is related to teaching methods and the teaching of long division is examined in detail. (SD)

The author outlines seven types of learning and teaching, and briefly discusses related literature on learning theories. He provides examples, and discusses teaching hierarchies. (SD)

A summary with examples of the use of the environment in the teaching of mathematics in British elementary schools. (MM)

A discussion of the importance and procedures for including probability in the elementary through secondary mathematics curriculum is presented. Many examples and problems are presented which the author feels students can understand and will be motivated to do. Random digits, Monte Carlo methods, combinatorial theory, and Markov chains are…