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)

Strategies for rapid mental computation are explained, including multiplying by 11 (or 21, 31, etc.); adding columns of numbers; and multiplying 2-digit numbers. Rapid mental computation is suggested as a motivator for investigating the underlying mathematical principles. (DB)

Shows by means of a mathematical example how algorithmic thinking and mathematical thinking complement each other. An algorithmic approach can lead to questions that deepen the understanding of mathematics material. (DDR)

Following a short introduction on the rationale and purpose for using algorithmic structures in the teaching of algebra, two topics from elementary algebra are presented in relation to control structures from computer programing, specifically: the multiplication of polynomials defined in terms of nested loops, and the distributive property…

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)

Described are ideas for the development of problem solving in the context of chemistry. Strategies for improving students' problem solving abilities are included. (KR)

Proposed is a way for teachers to distinguish between rich, challenging material that encourages mathematical thinking and material that is unsuitable. Included are multistep problems that encourage a broader understanding of mathematics. (KR)

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)