This syllabus presents a fused course in plane, solid, and coordinate geometry for secondary school students. Elementary set theory, logic, and the principles of separation provide unifying threads throughout this approach to geometry. There are actually two curriculum guides included; one for each of two different texts--Henderson, Pingry, and…

In earlier work a programing language, LOGO, was developed to teach mathematics in the framework of computer programs. Using LOGO a few programs were tested in both elementary and junior high school mathematics classrooms with excellent results. The work reported here is the first effort to systematically develop extensive curriculum materials…

The limitations of the ledger method in writing formal proofs are discussed. Details are given of a flow-proof method, with an attempt made to describe how to deal with most special situations involving the structuring of proofs. Nine examples of flow proofs in gemoetry are included. (DT)

Pick's Theorem, a statement of the relationship between the area of a polygonal region on a lattice and its interior and boundary lattice points, is familiar to those whose students have participated in activities and discovery lessons using the geoboard. The proof presented, although rather long, is well within the grasp of the average geometry…

Instructions are given for building a flexible model used for illustrating an elliptic paraboloid, a parabolic cylinder, and a hyperbolic paraboloid. (DT)

Concludes that the significant difference found between responses made to displayed drawings and those made to models suggests that, independently of the complexity of stimulus, encoding will not influence responses if the very economical process of simple coding can be used. (Author/AM)

Describes levels of thinking in geometry defined by Pierre van Hiele and Dina van Hiele-Geldof and discusses recent research on geometry learning levels among sixth and ninth graders. (GC)

Focuses on improving geometry teaching by: (1) identifying the meaning of "transforming spatial operations into logical ones;" (2) embodying this meaning in several exemplary experiences; and (3) commenting and reflecting on the significance of the geometrical operations underlying the experiences. (JN)

Activities are suggested for investigating the mathematics underlying an optical illusion. (DT)

President Garfield's life is reviewed, and his proof of the Pythagorean theorem is presented. (DT)

This paper presents the geometric foundation and quantification of Agent-action-Objective (AaO) kinematics. The meaningfulness of studying the flows in verbal expressions through splitting and splicing the strings in a verbal flow related to the fact that free parameters are not needed since it is not required that the presented methodological…

A good mathematics instructor is a proficient organizer of pupils for instruction in mathematics. There are many specifics involved in organizing for instruction. This paper discusses organizational structures in mathematics instruction such as learning stations. "A Geometry Center" is provided as an example of a learning station. The organization…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in geometry including Euclidean, post-Euclidean, and non-Euclidean geometry. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally…

This textbook discusses ratios and proportions; the circle and measurement of angles; proportions of figures--measurement of areas; regular polygons--measurement of the circle; planes and polyhedral angles; polyhedrons; the cylinder, cone, and sphere; spherical geometry; plane trigonometry; analytical trigonometry; spherical trigonometry; and…

This textbook presents principles, ratios and proportions, the circle and measurement of angles, regular polygons and measurement of the circle, planes and solid angles, polyhedrons, the three round bodies, analytical trigonometry, plane and spherical trigonometry, and mensuration. [This book was revised and adapted by Charles Davies.]