This paper describes an investigation of problem sequencing as part of a symposium presenting theoretical concerns and research findings regarding several diverse types of strategies for designing and presenting instructional materials. The first step involved analyzing a set of problems, to determine the knowledge (rules) required for solving the…

A series of problems concerning a geoboard with "holes" is suggested. (SD)

The author provides a detailed example of the use of the circular geoboard in suggesting an hypothesis which is then proven. (SD)

Elucidated is the relationship among three threads of mathematical investigations: Kirkman's schoolgirl problems, finite geometries, and Euler's n-square officer problems. (JP)

A teacher tells how she uses the game of chess to introduce students to formal geometry by drawing analogies between rules of chess and deductive systems. (JP)

This textbook presents the foundation for a second high-school year mathematics course. It aims to teach "how to study" as well as the "content" of a second unit of secondary mathematics through the nature and form of the material, explicit exhibits, formulated tests of both sound and unsound reasoning, through study-helps,…

This is part one of a two-part SMSG mathematics text for elementary school students. One of the goals of the text is the development of mathematical ideas via appropriate experiences with things from the physical world and the immediate environment. The text materials provide an introduction to the study of mathematics in which growth is from the…

This is part two of a two-part SMSG mathematics text for elementary school students. One of the goals of the text is the development of mathematical ideas via appropriate experiences with things from the physical world and the immediate environment. The text materials provide an introduction to the study of mathematics in which growth is from the…

THIS GUIDE OUTLINES THE MINIMUM MATERIAL FOR WHICH STUDENTS OF NINTH YEAR MATHEMATICS - COURSE 1 - ALGEBRA WERE HELD RESPONSIBLE ON THE REGENTS EXAMINATIONS BEGINNING IN JUNE, 1966. THE REPORT ALSO PRESENTS THE SCOPE AND CONTENT OF THE ALGEBRA COURSE AND POSSIBLE SUGGESTIONS FOR TEACHING THE MATERIAL TO STUDENTS. (RP)

This is part two of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include real numbers, similar triangles, variation, non-metric…

This is part two of a two-part SMSG elementary school text for third-grade students. The development of mathematical ideas in the text is grounded in appropriate experiences with things from the physical world and the immediate environment. Chapter topics include: (1) addition and subtraction; (2) length and area; (3) multiplication; (4)…