Research supported by the U.S. Office of Education, Contract OEC-6-10-239.

The use of statistical methods in the design and analysis of discrete algorithms is explored. The introductory chapter contains a literature survey and background material on probability theory. In Chapter 2, probabilistic approximation algorithms are discussed with the goal of exposing and correcting some oversights in previous work. Chapter 3…

While research has shown that both black and white children can clearly discriminate (usually through the use of dolls or puppets) with respect to ethnic identification by the age of 3-4 years, findings regarding ethnic preference are more complex. Researcher W.C. Banks has implied that research designs that compare ethnic preferences across…

TWO BASIC NEEDS OF THE DECISIONMAKER ARE IDENTIFIED--THE NEED TO FUNCTION UNDER CONDITIONS OF PSYCHOLOGICAL CERTAINTY AND THE NEED TO BE VIGILANT AFTER THE INITIAL DECISION HAS BEEN MADE. PSYCHOLOGICAL CERTAINTY IS DETERMINED BY THE PERSON'S ASSESSMENT OF HIS ENVIRONMENT OR LIFE SPACE AND THE RESOURCES HE HAS AT HIS COMMAND, BOTH OF WHICH ARE…

In an invitational address to the Victorian Institute of Educational Research, the author discussed Bayesian theory and its relationship to the design and construction of tailored or adaptive tests. Bayesian thinking involves recognizing the role of prior probabilities and using these probabilities in combination with new data to arrive at future…

This is part three of a three-part manual for teachers using SMSG high school text materials. Each chapter contains a commentary on the text, answers to the exercises, and a set of illustrative test questions. Chapter topics include: (1) the system of vectors; (2) polar form of complex numbers; (3) sequences and series; (4) permutations; (5)…

This paper discusses the theory and presents examples of free-association norms. Examples from several categories of free-association data are given. Their use in experiments on cultural characteristics of the associative structures of words are also explained. A graph of the relationship between primary and secondary associations and tables of…

Through Monte Carlo procedures, three different techniques for estimating the parameter theta (proportion of the "shocks" remaining in the system) in the Integrated Moving Average (0,1,1) time-series model are compared in terms of (1) the accuracy of the estimates, (2) the independence of the estimates from the true value of theta, and…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

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…

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".…

Part of a series of four pamphlets providing real-life problems in probability and statistics for the secondary school level, this booklet shows how to organize data in tables and graphs in order to get and to exhibit messages. Elementary probability concepts are also introduced. Fourteen different problem situations arising from biology,…

Part I of the teachers' commentary for "Exploring Data" includes a brief description of demands on the reader in terms of reading vocabulary and mathematical skills and comprehension, lists the substantive areas covered by the examples, suggests ways in which the pamphlet might be used in the classroom, and discusses background information for the…

Part I of the teachers' guide for "Weighing Chances" briefly describes the mathematical background necessary for the student, lists the substantive areas touched upon by the problems in the pamphlet, suggests classroom uses for the booklet, and gives background information on the individual chapters. Part II provides complete solutions for the…