Proportion problems were given to pupils in grades 3-5. Success rates were high, with elementary strategies based on addition often used. Familiarity with the use of ratios in the context, the presence of a mixture, and the use of manipulatives were variables that influenced performance. (Author/MNS)

Provides examples of if-then and combinatorial reasoning situations that have proved successful with college students and can be used with secondary school students. Proposes that practice with these problem solving processes can eliminate the need to memorize formulas that students may not understand. (ML)

Textbook analyses for 1924, 1944, and 1984, suggest that the mathematics program regressed in expectations for students. The number of word problems in fifth-grade books has decreased and the amount of drill problems increased. (MNS)

How children can be guided to see and feel the power of thinking with and about mathematical symbols is discussed. A strategy to help them bridge the gap between manipulative models and symbols is detailed. (MNS)

Some impressions derived through a two-week study visit to the Soviet Union are presented. Background information, kindergartens, curriculum, various types of schools, and mathematics teacher-training are each considered. Finally, mathematics problems from various grade levels are presented. (MNS)

Presents a developmental taxonomy which promotes sequencing activities to enhance the potential of matching these activities with learner needs and readiness, suggesting that the order commonly found in the classroom needs to be inverted. The proposed taxonomy (story, skill, and algorithm) involves problem-solving emphasis in the classroom. (JN)

Highlights major areas of research in mathematics education and examines four areas in need of additional attention: (1) the role of technology in mathematics teaching; (2) models for evaluating mathematics teaching; (3) development of estimation skills; and (4) the role of affective variables in the teaching of problem solving. (JN)

Presents (1) several activities on problem solving; (2) tips on creating a classroom climate favorable for problem-solving performance; and (3) a source of background materials for teachers. (JN)

An evaluation of a problem-solving program was conducted with 46 fifth- and seventh-grade teachers. Classes using the program scored significantly higher than control classes on measures of ability to understand problems, plan solution strategies, and get correct results. Different growth patterns and attitude changes were also noted. (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)

Seymour Papert, creator of LOGO, explains how he came to create this important problem-solving language and how he intended it to be used to foster learning among children. What children can do with turtle geometry (indicated to be a natural approach to mathematics) is one topic considered. (Author/JN)

The merits of having students interact with the computer rather than use canned programs to solve problems are discussed. Examples are provided. (SD)

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

Twelve linear algebra students were interviewed about the concept of a Solution of a System of Equations. The interviews were analyzed using APOS tools, in particular the ideas of Action, Process, Object and Schema, and Genetic Decomposition. The analysis of the interviews revealed several misconceptions of Solution. The analysis also revealed…

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…