Suggests that issues surrounding the teaching of algorithms focus not on whether to teach them but rather on balancing and connecting the development of algorithmic thinking. Presents an approach to help students develop their algorithmic thinking. Contains 18 references. (ASK)

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)

This 1998 yearbook aims to stimulate and answer questions that all educators of mathematics need to consider to adapt school mathematics for the 21st century. The papers included in this book cover a wide variety of topics, including student-invented algorithms, the assessment of such algorithms, algorithms from history and other cultures, ways…

Raises and responds to questions about what and how to teach mathematics with the availability of calculators to all students. Discusses whether students need basic facts, mechanical skills, and knowledge of computational algorithms. Argues that students need to develop number sense and analytical skills using simple, symbolic, and graphing…

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)

Describes use of the little-known Shuttle Puzzle in computer programming to elucidate the process of analyzing a problem and synthesizing observations into an algorithm that can be used to generate a programming solution. The process used to solve the problem reflects one that an expert uses. The method could be adapted for small-group cooperative…

This paper describes an educational program developed on the basis that the use of blocks and other manipulatives can be useful both for initial teaching of exchange operations in arithmetic and for remediation of the faulty strategies which very commonly arise during acquisition of written calculation algorithms. This computer program is a…

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)

Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…