Two simple quantitative models were derived from a series of experiments which explored the role of information storage in working memory when performing mental arithmetic. The decay model is a tractable analysis of a complex task which assumes a decay process in working storage. Similar analyses are recommended for problem solving activities…

Four worksheets and teaching suggestions are presented, with the focus on mental computation for levels 2-3; factors, levels 3-4; and nonroutine problems, levels 5-6 and 7-8. (MNS)

Studied for three years were eight Swedish classes with pupils aged 10-12 using calculators whenever they could be of use, along with experimental textbooks. The experimental classes were as competent as control classes in mental arithmetic and calculations with simple algorithms, and had better understanding of numbers and problem solving. (MNS)

Focuses on mental strategies for computing in the middle grades. Describes what they are and why they are important. Refers to relevant research and presents some teaching ideas for developing these strategies beyond the primary grades. Includes a discussion of the role of mental calculation in everyday life both past and future. Contains 27…

Mental arithmetic strategies were studied with 91 Dutch third graders who computed by splitting off 10s and units in both numbers or counting by 10s up or down from the first unsplit number. Results reveal flexibility in changing between and within strategy use. Implications for instruction are discussed. (SLD)

How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)

Example of magic tricks that can be used as an integral part of various lessons in arithmetic and algebra are given. Their mathematical basis is also discussed. (MNS)

An example of an unrealistic "real world" problem from the National Assessment of Educational Progress highlights a comparison of school and "folk" mathematics. The failures of typical problems taught in school and some suggested remedies are featured. (MP) Aspect of National Assessment (NAEP) dealt with in this document:…

A model of how automated and controlled processing can be mixed in computer simulations of problem solving is proposed. It is based on previous work by Hunt and Lansman (1983), who developed a model of problem solving that could reproduce the data obtained with several attention and performance paradigms, extending production-system notation to…

Presents concluding remarks to a symposium, "The Social Organization of Knowledge and Practice." Focuses on high aptitude of persons in everyday situations to solve problems and make decisions. Addresses three questions: (1) What happens when a problem-solver reaches a situation involving calculation? (2) How does learning transfer take place? and…

A major goal of instruction is for students to develop competence with numbers. This study attempts to determine the effect of instructional materials that develop number concepts and connect these concepts to mental computation procedures. The study used 16 classes of eighth-grade students and a pretest-posttest design with two treatment groups.…

What students need to know in a world where most computations are done by machine is discussed. Needed changes in the mathematics curriculum are then detailed in relation to mental arithmetic, numeration, decimals and fractions, paper-and-pencil computation, order of operations, problem solving, and instruction on calculator use. (MNS)

More mental computation and organized and enjoyable activities to practice such skills are advocated. Suggestions for brief sessions involving challenging questions and quick recall of number facts are presented. The author presents and comments on several sample lessons designed for a wide range of student abilities. (MP)

Hypothesized that arithmetic calculating procedures and types of problems that necessitate more subproblems will lead to longer solution times. Data from 36 third grade students who mentally computed problems with sums greater than 20 and less than 100, confirmed both hypotheses. (RH)

Assessed attitude, computational preferences, and mental computational performance of 176, 187, 186, and 206 Japanese students in grades 2, 4, 6, and 8, respectively. Found wide ranges of performance on mental computation, that visual modes of presentation increased performance levels, and a narrow range of strategies. Contains assessments. (37…