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…

One chapter in the fourteenth unit of this SMSG series deals with logic; simple and compound statements, truth tables, logical equivalence, rules of a logical argument, proof, quantifiers, and negations are the topics covered. The second chapter of the unit discusses applications of probability and statistics, including random sampling,…

The Rasch model for the probability of a person's response to an item is extended to the case where this response depends on a set of scoring or category weights, in addition to person and item parameters. The maximum likelihood approach introduced by Wright for the dichotomous case is applicable here also, and it is shown to yield a unique…

This guide provides a structured program for the slow learner in mathematics grades 6-11. Suggestions for implementing the program are included. The guide is divided into the following major areas of mathematical competency: Fundamental Operations, Geometry, Measurement, Graphing, Algebra, Probability and Statistics, and Logic. Recreation is the…

Stochastic approximation algorithms for least square error approximation to density and distribution functions are considered. The main results are necessary and sufficient parameter conditions for the convergence of the approximation processes and a generalization to some time-dependent density and distribution functions. (Author)

This study involved two phases: first when classification was based on the calibration sample, and second in a cross-validation setting. Computer-generated data were used. Results obtained from rules based on probabilities of group membership were compared for accuracy when classifying in the discriminant space and in the predictor variable…

The harmonic mean and Kramer (1956) unequal n forms of the Tukey multiple comparison statistic were investigated for Monte Carlo Type I and Type II errors under conditions of assumption violations. The two major questions concerning the sensitivity of multiple comparison statistics for different types of pairwise contrasts and the affect of…

This booklet contains suggestions for developing six of the twenty topics recommended for students in Secondary Forms III and IV in the schools of Victoria, Australia. These suggestions are intended for students for whom the standard course is unsuitable because of subject time allotments, ability levels, or vocational or educational needs. The…

This twentieth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 18. For each of the chapters in Unit 18, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, answers to exercises are provided, and sample text questions are included. (DT)

Using the concepts of conditional probability, conditional expectation, and conditional independence, the main results of the classical test theory model can be derived in a very few steps with minimal assumptions. The present effort explores the possibility that present classical test theories can be further condensed. (Author/RC)