Discusses the changes in the scanning of food and the current use of computer technology and UPC bar codes in a grocery store and traces the history of calculating tools from the use of fingers, abacus, slide rule, calculators, and computers. Includes reproducible student activity sheets. (MKR)

Described are three activities and variations that can help students to understand the concept of place value. Allowing students to use concrete materials and helping them to bridge the gap between manipulatives and paper-and-pencil tasks are emphasized. (KR)

This article integrates the literature on intelligence and achievement outcomes in boys with Klinefelter syndrome (KS). It reports results of a study following 36 boys with KS and 33 sibling controls. Boys with KS demonstrated verbal cognitive deficits and significant underachievement in reading, spelling, and arithmetic, which increased with age.…

Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)

Examined relations between phonological processing and emerging individual differences in math computation skills. Found that phonological memory, access rate to phonological codes in memory, and phonological awareness were uniquely associated with growth in number of computation procedures mastered from 92.5 to 134.8 months. Phonological…

Relations among patterns of conceptual and procedural knowledge and grade were examined in 90 six- to eight-year-olds in order to explore addition and subtraction development. Conceptual knowledge was assessed by examining children's responses to pairs of problems reflecting various part-whole relations. Children solved related problems as part of…

This paper is based on a long-term didactic engineering about division problems (only in a numerical setting) at primary school. Situations and students' work are analyzed by means of a double theoretical framework: the theory of situations and the theory of conceptual fields (Vergnaud 1991). The analysis focuses mainly on classroom interactions…

Two experiments investigated whether young and old adults can temporarily remove information from a capacity-limited central component of working memory (WM) into another component, the activated part of long-term memory (LTM). Experiment 1 used a modified Sternberg recognition task (S. Sternberg, 1969); Experiment 2 used an arithmetic…

Whenever teachers of young children get together there will be differences of opinion about how far children should be taught to count. Some will argue that the focus should be on small numbers to 9, building up the notion of what, say, the name 5 means, what it looks like, and how it can be represented. Others argue that with ice blocks retailing…

Algebra instruction has traditionally been postponed until adolescence because of historical reasons (algebra emerged relatively recently), assumptions about psychological development ("developmental constraints" and "developmental readiness"), and data documenting the difficulties that adolescents have with algebra. Here we…

The aim of the present study was to investigate the performance in arithmetic related to achievement levels in reading and mathematics. Basic arithmetical facts and multi-step calculations were examined. The participants were 941 pupils aged 8 (N = 415), 10 (N = 274) and 13 (N = 252) years. The pupils were divided into four groups by standardized…

A fundamental question in developmental science is how brains with and without language compute numbers. Measuring young children's verbal reactions in Spain and Finland, we show that, although there is a general arithmetic ability for small numbers that is shared by monkeys and preverbal infants, the development of such initial knowledge in…

Many students find the leap from arithmetic to algebra a difficult one to make, and current literature suggests that a number of the common misconceptions held by students arise as a result of the methods which teachers use to present algebra. The abstract nature of algebra makes it difficult for students to grasp; students also struggle with the…

Preservice elementary school teachers' fragmented understanding of mathematics is widely documented in the research literature. Their understanding of division by 0 is no exception. This article reports on two teacher education tasks and experiences designed to challenge and extend preservice teachers' understanding of division by 0. These tasks…

This paper discusses a study that explored the mental models of fifth (n=35) and sixth (n=49) graders attending two urban public elementary schools in South Korea in word problem solving. Two levels of mental models (problem model and mathematical model) constructed in the process of word problem solving were investigated. Coding categories for…