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)

Computation activities focusing on speed and accuracy do not provide children with the opportunity to learn or develop their own mental computation strategies. Sets out some goals and ideas for teaching mental computation and introduces a card game for helping children compute mentally. (ASK)

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)

This book addresses different types of thinking, including critical, creative, and analytical, and presents a variety of problem-solving strategies, along with specific ways they can be taught to students. The main emphases of the book are thinking and mathematics, problem solving, and the application of computational skills. The problem-solving…

Presents two examples of using the limitations of calculators to help students understand important mathematical ideas. The first example shows how a simple algebraic calculation can make a recursive model work long enough to perform the job at hand while the second shows how the limitations of a calculator can be used to introduce the need for…

Examples and solutions to these problems are presented. Figures for which different equations are necessary are presented. The use of the geoboard for this exploration is emphasized. (CW)

This article explains how this method is done, examines some reasons for including it as a topic in mathematics curricula, and uses modular arithmetic to explore its mathematical basis and its generalizability to computations in bases other than 10. (CW)

This article presents an example of a versatile multi-solution problem that can be used right across the primary years. The basic problem is: "Noah saw 16 legs go past him into the Ark. How many creatures did he see?" Any even number can be used, although, 2 legs allows only one answer and with 16 legs there are already 14 different…

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)

Outlined is the "nine complements" method of subtraction. This activity was used by students to generate proofs that explained why the subtraction method worked. Reasoning and inquiry skills are emphasized. Other examples are offered that have been successful in stimulating inquiry. (KR)

Learning the techniques of critical thinking and problem solving can be easy for children when presented problems involving fun topics. Problem sets which range from easy to hard written by elementary school students and educational consultants are included. Topics include addition, subtraction, multiplication, division, and fractions. Each topic…

Described is a short program for teaching and learning about geometric transformations. The integration of geometry problem solving and BASIC programing is discussed. Applications of computer graphics are illustrated. (CW)

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)

Reports on a seminar conducted by the Massachusetts Institute of Technology which was designed to help teachers develop their understanding of learning and teaching arithmetic. Describes some of the sessions and the activities and includes some of the dialogue exchanged within the group during the sessions. (TW)