The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

This textbook is third in a series of three volumes presenting a mathematics course for junior high school and six-year high schools. This volume covers college-preparatory algebra, trigonometry, and demonstrative geometry. [For Book I, see ED623224. For Book II, see ED623225.]

The major intent of this project was to design microcomputer lessons utilizing the unique features of computers to teach a high school mathematics topic. After reviewing the literature, it was decided to write a series of three tutorial lessons for a class in high school trigonometry which would present the concepts of amplitude, period, phase…

This text is based on the idea that teachers of mathematics at any level will find it advantageous to be able to point to interesting, useful, and diverse applications of the mathematics they teach. The first chapter describes several graphing techniques used for displaying data and finding meaningful relationships as a result. Subsequent chapters…

The development of a diagnostic test at the Catholic University of Chile is described. The 50-item multiple choice test is used as an entrance and prerequisite test for students about to take a first university course in trigonometry and analytic geometry (MAT-111). Thirty items pertain to algebra and 20 to geometry. Each question corresponds to…

This text presents lessons relating specific mathematical concepts to the ideas, skills, and tasks pertinent to the health care field. Among other concepts covered are linear functions, vectors, trigonometry, and statistics. Many of the lessons use data acquired during science experiments as the basis for exercises in mathematics. Lessons present…

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include periodicity, graphs, angles, vectors, formulas, tables, waves, and applications. (MP)

It is extremely difficult to extend in a natural way the concepts developed in high school geometry to motivate the concepts of trigonometry. To solve this difficultry, the author defines "sensed angles" as ordered pairs of rays and makes appropriate definitions which yield the familiar angle properties of plane geometry. He then shows how this…

This book is a sequel to MATHEMATICAL CHALLENGES, which was published in 1965. In this sequel are 100 problems, together with their printed solutions. The problems range from those that are quite simple to those that will challenge even the most ardent problem solver, and they include examples from algebra, geometry, number theory, probability,…

This book, photographically reproduced from its original 1942 edition, is an extended essay on one of the three problems of the ancients. The first chapter reduces the problem of trisecting an angle to the solution of a cubic equation, shows that straightedge and compasses constructions can only give lengths of a certain form, and then proves that…

Analyzing the effects of tilting a probability board can be an effective method of introducing a discussion of models in a probability class. (SD)

Formulas for use in computer programs are presented. Two programming applications are discussed: one to ballistics using inverse sine and one to hours of daylight using inverse cosine. (MNS)

Describes investigations involving data acquisition and analysis using microcomputers running the LOGO programing language. Provides new primitives to add to LOGO to access information from the analog to digital converter of a BBC microcomputer, giving samples of student results. (JM)

The authors hypothesize that a means-end strategy places a load on cognitive processing capacity which retards knowledge acquisition. Three experiments using trigonometry problems with high school students were conducted in which the problem goal was modified to disrupt strategy used by novices. Results supported the authors' hypothesis.…