Advances in cognitive research increase the need for assessment that can address the processes and the strategies by which persons solve problems. Several psychometric models have been introduced to handle claims cast in information-processing terms, explicitly modeling performance in terms of theory-based predictions of performance. Cognitively…

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for curriculum…

The social science finding that two-thirds of a population of successful males are first-born sons provided the motivation for a problem solved by a 12th grade honors class. The class proved that the probability of choosing a first-born son from a male population is about two-thirds. (JP)

The uses of random number generators are illustrated in three ways: (1) the solution of a probability problem using a coin; (2) the solution of a system of simultaneous linear equations using a die; and (3) the approximation of pi using darts. (MP)

The use of the randomized response technique as a tool of obtaining answers to sensitive questions is illustrated. Directions for two classroom experiments are included. (MP)

A sophomore-level course in applications of mathematics was designed to introduce students to the diversity of situations in which mathematical models are used. The course precedes the study of the calculus, and is composed of a sequence of modules. A problem-solving approach is used. (SD)

The explicit, experimental introduction of a series of logical inconsistencies is described and recommended as a means of disrupting the faulty logic and, thereby, enhancing the use of more appropriate probabilistic reasoning by graduate students enrolled in an introductory inferential statistics course. (14 references) (JJK)

Mixed Rasch models add latent classes to conventional Rasch models, assuming that the Rasch model applies within each class and that relative difficulties of items are different in two or more latent classes. This article considers a family of stochastically ordered mixed Rasch models, with ordinal latent classes characterized by increasing total…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 4-6, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, whole numbers, number theory, fractions, decimals, geometry, ratio, proportion, percent, probability, sets, and…

Students were given the problem: Given a deck of cards in a certain order, after how many shuffles will it return to its original order? They worked with small decks of cards to develop a general formula, but were unhappy with the results. (SD)

Four problems in which elementary mathematics can be used in constructing models are described. (SD)

The similarity between two apparently dissimilar problems is explored. Pascal's triangle is involved. (SD)

Addressed to both librarians and systems analysts, this book attempts to apply the analytic methods of operations research and systems analysis to the operating problems of the library. The first part of the book discusses theoretical models with emphasis on the pattern of book use, on its change with time and on the problem of estimating and…

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,…

The purpose of this paper is to present problems (and solutions) from the areas of marketing, population planning, system reliability, and mathematics to show how a computer simulation can be used as a problem-solving strategy in probability. Examples using BASIC and two methods of generating random numbers are given. (Author/MP)