Several excerpts from Euclid's "Elements" are cited, and their applications to the natural, positive rational, and positive real number systems are discussed. (SD)

In a series of exercises students develop designs in which nodes are labelled according to the isolation rules defined. Strategies for creating new designs from known ones, finding the maximum number of isolation designs on a given configuration, and developing larger isolation designs are encouraged. Sample worksheets are included. (SD)

Examples of topics and problems which demand Piaget's formal operational thought at an early stage in the secondary school are provided. (DT)

Activities that are helpful for teachers and pupils alike in getting the feel for how big a million really is are suggested. (DT)

The author has written an unpublished summary of his reactions to an earlier article on number patterns used to provoke mathematical investigations. His work is an additional demonstration of the potential mathematics that can be stimulated from such investigations. (JP)

The development of the ability to associate numerals with sets of appropriate size was studied in children, ages 4 to 5-1/2. (ST)

Represented are notes that have been compiled from meetings between teachers and members of the SMSG staff, discussing kinds of pre-school activities that might be appropriate for the development of various mathematical concepts. The sequence of concepts presented are in the same order as they are developed in the SMSG kindergarten program. Some…

This volume is designed to provide information for teachers and prospective teachers who will teach the basic concepts of algebra normally taught in grade 9. Each section of the book contains background information, suggestions for instruction, and problems. Sections in the book include: (1) Numerals and Variables; (2) Open Sentences and English…

This is one of a series of publications written to supplement the secondary school School Mathematics Study Group program. This booklet will be most useful for enrichment at the eleventh and twelfth grade levels. It treats algebraic structures as abstract mathematical systems and introduces such important ideas as group, non-abelian group, field,…

Presents three experiments which investigated: (1) the nature of the processes by which preschool and kindergarten children estimate small numbers; and (2) the generality of the number-relevant versus number-irrelevant categorization scheme in the child's operative thinking about small numbers. (Author/ED)

Reported are the findings of a study of over seven hundred fourth-, sixth-, and eighth-grade pupils' ability to understand division involving zero. Implications for the classroom are discussed, including suggested teaching strategies. (JP)