The processes and procedures used by expert mental calculators are identified from a literature review. Experts are characterized by knowledge of a variety of methods, ability to recall numerical equivalents, and ability to remember the numbers involved in various stages of calculations. (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)

A range of estimation techniques are described, and a series of mental computation procedures based on concepts of measurement and real numbers are presented in detail. (MP)

Children use acquired knowledge as they learn basic multiplication facts. If informal thinking strategies are stressed, the border between "figuring out" and "knowing by heart" gradually disappears. Children will acquire a flexible mental structure of multiplication facts instead of a collection of rules. (MNS)

The principle of the permanence of the rules of calculation is contrasted with the concretization permanence principle. Both apply to situations where some arithmetical operation known to children for numbers of a certain kind is to be extended to include further numbers. (MNS)

The relationship between arithmetical concepts and solution methods is discussed. A case study illustrates the contention that some children with relatively sophisticated concepts express those concepts with primitive methods. (MNS)

Freudenthal was the founder of realistic mathematics education, in which reality serves as a source of applications and learning. Takes a newspaper article about reproducing a Van Gogh painting using plants in a field to exemplify a rich context problem containing elements of all areas of elementary school mathematics. (MDH)

Investigates the development of understanding of multiplication from the early school years through to the top primary age group. Identifies the children's difficulties and analyzes their solution strategies. Reports that progressive abstraction is related to the children's developing understanding of number and to their procedures for addition.…

Preschool children (n=115) in Poland were tested in five areas: counting, equipotency of sets, dividing, adding, and comparing. Results showed that these children already had informal knowledge of many of the concepts and skills included in the mathematics curriculum in the early grades. (PDD)