Archimedes' shoemaker's knife problem is interesting in its own right and also allows the demonstration of heuristic teaching ideas and a different method of doing a routine construction. The focus in the article is on the thought processes involved and questions asked when attempting proofs with the problem. (MNS)

How writing skills are used in remedial mathematics classes to help college students attain better problem-solving achievement is described. Data affirm the value of the approach. (MNS)

The use of mathematical modelling as a systematic framework for solving word problems is presented. Applications for typical elementary algebra and calculus problems are featured. (MP)

A summary-review strategy for use in mathematics classes is presented. Specific objectives attainable through use of this strategy are outlined and two procedures for using the small-group strategy are given. (MK)

The authors develop the idea of Niven numbers and discuss their potential usefulness in the classroom. A computer program to generate Niven numbers is provided. (MK)

This manual is a collection of materials and teaching strategies to motivate the development of mathematical ideas in secondary school mathematics programs or in beginning college mathematics programs. The unit is written for the instructor with step-by-step procedures including lists of needed materials. The exercises in this unit also appear in…

Two models are presented that can be understood by students who have completed second-year algebra, as well as by calculus students. The predator-prey population model and the arms race model are included, with a computer program given for each. (MNS)

Factorials are discussed, with note of the enormous size on n! even for modest values of n. A recreational problem to determine the number of zeros at the end of numbers such as 10,000! is given, with a computer program. (MNS)

Focuses on modifying personalized systems of instruction (PSI) by using competency unit testing instead of mastery testing. The algebra service courses at the University of Arizona are described. Includes data on student achievement. (MNS)

This guide provides enrichment for students to develop tools and concepts used in various areas of mathematics. The first part presents arithmetic progressions, geometric progressions, and harmonic progression. In the second section, the concept of mathematic induction is developed from intuitive induction, using concrete activities, to the…

This student manual consists of exercises and investigations designed to supplement existing units and materials written for the Thirteen College Curriculum Program (TCCP) course. Many sections can be used for independent work. This 174-page manual is divided into seven parts: (1) recognizing and representing number patterns; (2) sets and logic;…

How physicians turn the data from tests and evaluations of patients into information useful for medical action is described. This is an important application of the distance formula. (MNS)

This article contains a sequence of topics from the mathematics of annuities presented in a way that can be used as a brief unit on business applications at the level of intermediate or college algebra. (Author/MK)

Part 2 considers the limit of a sequence and extends this to include ideas such as continuity, derivative, and integral. The discussion concludes with an example of a finite or "counted completely" set, the Fermat primes. (MK)

This report is intended to give an indication of the variety of careers available to persons with interest and preparation in the mathematical sciences. Each part focuses on a particular class of professions, with necessary training as well as the character of the work and general conditions of employment described. Parts I through V deal with…