This text is the second of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This volume is devoted to a rigorous development of theorems in plane geometry from 22…

This study was prompted by the change in New York State certification (effective October 1968) which requires only 18 hours of courses in college mathematics for permanent certification in secondary school mathematics. The study does not suggest any recommendations as to the desired preparation for teaching secondary school mathematics, but…

This study was designed to (1) analyze relationships between qualitative characteristics of ability in mathematics and success in a special interest-ability algebra program at the eighth grade level and (2) develop a rating scale for teachers to use in identification of students with high potential in mathematics. The "Iowa Test of Basic…

This study reports on the comparison of three methods of teaching general mathematics: (1) non-verbalized student discovery of principles and generalizations, (2) student-teacher development of principles and generalizations, and (3) teacher statement and application of principles and generalizations with illustrations in a problem set followed by…

Chapters 4-5 of the special materials written for low achieving students in grades 7-8 by SMSG deal with number theory and the properties of the integers. Included for each chapter are pretest exercises, a self-test, instructional lessons and exercises, and a chapter test. (CT)

This is Part 1 of the first course in a series which focuses on building fundamental mathematical structures. The arithmetic studied in elementary school along with modular arithmetic is examined and set notation and mappings of sets are presented. Mathematical group structures are introduced. Points and numbers are related both on a line and in a…

The second part of Course III includes a study of probability, polynomial, rational and circular functions, and informal space geometry. The chapter on probability presents such topics as probability measure, outcome sets and events, and overview of topics studied in Courses I and II. Chapters on functions include polynomial algebra concepts and…

This teacher's guide is written to be used in conjunction with the new materials for low achieving students in grades 7 and 8 by SMSG. It includes helpful hints about working with low achievers and suggestions regarding the implementation of this particular program. Most chapter discussions include behavioral objectives for the chapter, background…

This is volume 2 of a set of mathematics materials developed for low achievers. These materials are designed to help teachers provide interesting and worthwhile learning opportunities for students in grades five through eight who have had little success in mathematics. The materials may be used in conventional classroom settings as well as in team…

Investigated was the problem-solving ability of secondary school students as it related to their verbalization. Experimental treatment followed the students' demonstration of awareness of some mathematical concept. The four experimental groups included students who: (1) did not verbalize, (2) verbalized correctly, (3) verbalized incorrectly and…

Studied was the interaction between curriculum treatment and selected aptitude variables as predictors of learning and transfer scores. Visualization ability was measured by a paper folding test; general reasoning ability was measured by the Necessary Arithmetic Operations Test. Geometry students (191) were assigned to treatment groups for two…

The study was designed to develop, test, and refine a model of teaching behavior for teachers of a first course in algebra. The model described five categories of teaching behavior which should be exhibited by algebra teachers. To aid in observation of these behavior categories, a modified Flanders interaction Analysis instrument was developed and…

Investigated were the essential characteristics of curriculum content and instructional patterns which contributed to effective programs of mathematics for seventh and eighth grade junior high school students in California. The purpose of the study was to provide guidelines which would assist educators in developing mathematics programs for these…

These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics K-6. In view of the experiences of other curriculum groups and of the general discussions since 1963, the present report initiates the next step in evolving the "Goals".…

The development of number concepts from prehistoric time to the present day are presented. Section 1 presents the historical development, logical development, and the infinitude of numbers. Section 2 focuses on non-positional and positional numeration systems. Section 3 compares historical and modern techniques and devices for computation. Section…