The give-"n" task is widely used in developmental psychology to indicate young children's knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and…

This study focuses on adults who are neither preschool teachers nor professional caregivers and investigates their beliefs regarding the importance of engaging young children with numerical activities. It also examines the types of numerical activities adults report having observed children engaging with, as well as the types of activities they…

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report…

Empirical research has documented how children's early counting develops into an increasingly abstract process, and initial counting procedures are reified as children develop and use more sophisticated counting. In this development, the learning of different oral counting sequences that allow children to count in steps bigger than one is seen as…

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

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)

This article considers skills and abilities of young children with number in the areas of cardinality and ordinality. Responses to number tasks by a sample of 3- and 4-year-old children are described to outline their differing approaches to determining the numerosity of a set, and to establish their application of ordinality language to describe…

A semiotic perspective on mathematical activity provides a way of conceptualizing the teaching and learning of mathematics that transcends and encompasses both psychological perspectives focussing exclusively on mental structures and functions, and performance-focussed perspectives concerned only with student's behaviours. Instead it considers the…

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 importance of teaching computational estimation is discussed, with note of its increased significance because of widespread use of calculators and the need to develop number sense. The reason for its failure to be taught is traced to the multiplicity of methods, and some detailed suggestions are therefore presented. (MNS)

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.…

A class of 32 fourth graders, who studied inverse operations in grades 1-3, was given 3 written tests, each followed by an interview, to see how well they could simplify computations using inverse operations. Most could not evaluate 28 + 75 - 75, for example, without performing all operations. (GW)

The opinions of 98 Australian educational experts concerning mathematics skills necessary for future numeracy were solicited. The qualitative comments were incorporated into three scenarios reflecting alternative visions for the future: a careful scenario, a futuristic scenario, and a process scenario. (24 references) (MDH)