Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

Describes a lesson on long division using chip trading which follows that algorithm for long division. (MKR)

Presents several alternatives to customary algorithms for whole number arithmetic. Includes a brief history of each algorithm and discusses why each might be useful for particular kinds of children. (KHR)

Illustrates how upper elementary grade students can develop an understanding of the invert-and-multiply algorithm. (CCM)

Compares methods of subtraction used by children and teachers. Suggests ways to encourage children to invent their own subtraction algorithms. (CCM)

Compares the approaches to teaching division in Britain and in Holland where different emphasis is placed on the development of mental and written methods. Describes how it is common for pupils in Britain to work from an early stage with pencil and paper rather than mentally whereas early emphasis is placed on mental strategies in Holland. (ASK)

Examines the philosophy behind the issue of computational fluency in "Principles and Standards." (Author)

Describes a pattern which emerged from an examination of the digits of the squares of numbers. Provides eight examples having the pattern at the units or tens digit of the number. (YP)

Three alternative methods of finding averages of two numbers are presented. (MP)

Describes a multicultural enrichment project for 4th graders that highlights number systems and computation algorithms of various cultures. Discusses student responses and reactions. (KHR)

Presents number tricks appropriate for use in workshops, mathematics clubs or at other times when stressing recreational mathematics. (PK)

Programing a microcomputer to solve problems in whole-number arithmetic, rather than using the built-in operations of the computer, is described. Not only useful, it also enhances important mathematical concepts and is adaptable to a range of student abilities. (MNS)

The author advocates a return to "traditional" elementary algebra content. Several roles for algebra manipulation are identified, including making arithmetic more interesting and understandable and providing facility indispensable for both the technician and the mathematician. (PK)

Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)

This manual is a dictionary of some 150 errors made by students in their work in mathematics. A precise definition and examples are given for each of these errors and these, combined with a description of common causes of the error, form a background for diagnosis of student problems with arithmetic. Teaching strategies and ideas, each linked to a…