After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…

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)

An attempt is made to show that algebra is rarely obvious, and merely expecting children to learn rules is an oversimplification. Sections cover: (1) The Non-visual Nature of Algebra; (2) The Apparently Arbitrary Nature of Algebra; (3) The Relationship Between Symbolism, System and Question; (4) The Complex Nature of Algebra; and (5) Some…

In spite of current sentiment to the contrary, the wellsprings of mathematics are not utility and relevance, but creativity, imagination, and an appreciation of the beauty of the subject. This has implications for the teaching of mathematics. (PK)

Described are four classroom activities that may be interspersed into a curriculum or offered as homework. Systematic procedures, alternative strategies, and trial and error are emphasized in these counting exercises. (KR)