This textbook provides the foundation for a course in mathematics covering arithmetic, algebra, geometry, conic sections, and arithmetic of infinites. An appendix on practical gauging is included, as well as a supplement containing the history of logarithms. [This edition was corrected and improved by Samuel Clark.]

THIS PAPER IS CONCERNED WITH GRAPHIC PRESENTATION AND ANALYSIS OF GROUPED OBSERVATIONS. IT PRESENTS A METHOD AND SUPPORTING THEORY FOR THE CONSTRUCTION OF AN AREA-CONSERVING, MINIMAL LENGTH FREQUENCY POLYGON CORRESPONDING TO A GIVEN HISTOGRAM. TRADITIONALLY, THE CONCEPT OF A FREQUENCY POLYGON CORRESPONDING TO A GIVEN HISTOGRAM HAS REFERRED TO THAT…

Reported is a study in the Oakleaf Elementary School to test the hypothesis that variability of achievement within a particular grade approximates the number of years the pupils have been in school (e.g., in the third grade, a spread of three years is expected). Data were collected and analyzed regarding range of achievement prior to instruction…

The material in this booklet is concerned with a discussion and examination of geometric puzzles and the ideas which result from their study. The general idea of graphs is introduced as a tool which can be used to solve geometric puzzles. The fact that working with puzzles can lead to unexpected mathematical discoveries is stressed. Such topics as…

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)