This document deals with basic statistical concepts and operations used in the social sciences. The book was written under the philosophy that students enter statistics courses with a variety of aptitudes and experiences, and that traditional teaching approaches can do little to accommodate individual needs. It sets up an individualized course,…

A group is viewed to be one of the simplest and most interesting algebraic structures. The theory of groups has been applied to many branches of mathematics as well as to crystallography, coding theory, quantum mechanics, and the physics of elementary particles. This material is designed to help the user: 1) understand what groups are and why they…

In this report, the theoretical background and procedures for a study of concept learning are discussed. Several definitions of the term "concept" are analyzed, and the relations among concepts, chains of concepts, and hierarchies of concepts are explored. Conceptual learning is discussed from several points of view, and axiom systems for the…

In this volume, the results of a study of concept learning are presented. (The background for the study, and descriptions of the treatments--rote reception, rote discovery, conceptual reception, and conceptual discovery--are provided in Part 1.) Several hypotheses concerning the effectiveness of these treatments in learning concepts and on the…

This teaching guide outlines a college algebra course for use in the secondary school. Units studied are: mathematical induction, functions, groups and fields, linear algebra, and limits. Special emphasis is given to the study of functions and linear algebra. Sequence, textbook references and assignments, and time allotments are suggested. Some…

Researches in Mathematics Education about proof by contradiction revealed some difficulties of the students but also that this kind of argumentation comes spontaneously in certain situations. In this paper we shall show some processes that might lead the student to produce a proof by contradiction. In particular, we shall point out a deep link…

The history of education is made up in part of accounts of various subjects which have developed into courses of study. Mathematics of some kind has always been included in such courses. In the American colonies, arithmetic was an important subject for practical reasons. It was needed for trade and commerce. Sailing vessels plying between Europe…

The use of exercises that students can perform independently of any calculating aids and in a reasonably brief space of time is promoted, so that pupils can concentrate on the processes involved and any relationships of interest. Some examples are presented with the goal of increasing learning promoted. (MP)

People are noted as intrigued for centuries by interplay between algebra and geometry with many important advances viewed to have come down through some sort of linking of the two. Examples are given of advantages to learning and discovery that can be found in an investigative approach combining them. (Author/MP)

Concern is expressed that trigonometry is being de-emphasized at the secondary level, and that even incoming college students with excellent mathematics backgrounds and aptitudes appear to be "drawing blanks" on even the most fundamental trigonometric concepts. Teaching trigonometry as the ultimate high school subject is promoted. (MP)

Discussed are the: (1) Notion of Mathematical Objects and the Realist Approach; (2) Psychological Need for Mathematical Realities, A Psychological Point of View; (3) Formalist Approach; (4) Meaning of Mathematical Existence; (5) Relative versus Absolute Existence; (6) Psychological Need for Mathematical Realities and the Offer of Mathematics; and…

Problems involving multicolored cubes are discussed with examples of Instant Insanity and Rubik's Cube cited. Sections cover defining chameleonic cubes, producing such a cube, and extending understanding to multidimensional cubes. One theorem proved is that for each positive integer, every cube of that size is chameleonic. (MP)

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

An excursion in applied mathematics is detailed in a lesson deemed well-suited for the high school student or undergraduate. The problem focuses on an experimental missile guidance system simulated in the laboratory. (MP)