Reported are the results of a study to determine if there is a difference in learning as measured by an achievement test between high school students who study plane analytic geometric topics via a vector approach and those who study the same topics via a traditional approach. Secondary objectives concerned the transfer to further topics in solid…

The development of educational policy in Russia during the Soviet period, 1917-1930, and the relationship of that policy to Russia's educational heritage was investigated. Analyzed was the extent to which educational policies under the new regime actually succeeded in departing from cultural patterns established in the older society. Since…

This teachers' guide was written to be used in conjunction with the student text, An Experimental Text in Transformational Geometry. The guide is intended to help teachers who have responsibility for teaching the topics Motions and Transformations in the Plane. Each section commences with a general discussion concerning the major ideas which are…

By looking at the history of geometry and the concept of congruence in geometry we can get a new perspective on how to think about the closeness in meaning of two sentences. As in the analysis of congruence in geometry, a definite and concrete set of proposals about congruence of meaning depends essentially on the kind of theoretical framework…

Using six geometry units as resource units, the document explores 22 math-related careers. The authors intend the document to provide senior high school students with career orientation and exploration experiences while they learn geometry skills. The units are to be considered as a part of a geometry course, not a course by themselves. The six…

This paper presents a method of encoding geometric line-drawings in a way which allows sets of such drawings to be interpreted as formal languages. A characterization of certain geometric predicates in terms of their properties as languages is obtained, and techniques usually associated with generative grammars and formal automata are then applied…

This is the second of two guidebooks on minimum course content for high school geometry, and is designed for the student who has mastered the skills and concepts of Geometry I and who had a final average of low B or less. Emphasis is on understanding and use of theorems without proof. This course develops definitions and properties of triangles,…

Described is an empirical and rational inquiry into the formation of a small set of special or geometrical concepts of young children. The approach taken by the author is to attempt to specify intellectual growth in one particular area, a child's acquisition of diagonality, in such a way as to be representative. That is, to give a clean portrayal…

Provided are the scope and sequence of mathematics topics for Grade 6 to be implemented by teachers and supervisors. The guide is presented in the form of 62 units, each being organized around the themes of (1) sets, numbers, and numeration; (2) operations; (3) geometry and measurement; and (4) algebraic concepts, graphs, probability, and…

Provided are the scope and sequence of mathematics topics for Grade 1 to be implemented by teachers and supervisors. The guide is presented in the form of 66 units, each being organized around the themes of (1) sets, numbers, and numeration; (2) operations; (3) geometry and measurement; and (4) algebraic concepts, graphs, probability, and…

Reported are the results of an investigation of the child's acquisition of the concept of area measure. To measure this acquisition, four axioms were developed to define the concept of area. A task was developed for each axiom to test operational understanding of the axiom. A test of vocabulary and a conservation of area task were administered to…

This teacher's guide for a semester course in analytic geometry is based on the text "Analytic Geometry" by W. K. Morrill. Included is a daily schedule of suggested topics and homework assignments. Specific teaching hints are also given. The content of the course includes point and plane vectors, straight lines, point and space vectors, planes,…

This collection of 123 objectives and related evaluation items is for general mathematics in grades 10 through 12. The content has been organized into nine major categories: sets; numbers, numerals, and numeration systems; operations and their properties; measurements; per cents; geometry; probability and statistics; logic; and applications and…

Unit 13 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: common sense and organized knowledge; sets, real numbers, and lines; lines, planes, and separation; angles and triangles; congruences; proof; geometric inequalities; perpendicular lines and planes in space; parallel lines in a…

Unit 14 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: areas of polygonal regions, similarity, circles and spheres, characterization of sets, constructions, areas of circles and sectors, volumes of solids, and plane coordinate geometry. Appendices cover Eratosthenes' measurement of the…