Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

Little is known about the cognitive effort associated with algebraic activity in the elementary and middle school grades. However, this investigation is significant for sensitizing teachers and researchers to the mental demands of algebra learning. In this paper, we focus on the relationship between algebraic thinking and domain-general cognitive…

Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…

In the last three decades there have been a variety of studies of what is often referred to as "everyday" or "street" mathematics. These studies have documented a rich variety of arithmetic practices involved in activities such as tailoring, carpet laying, dieting, or grocery shopping. More importantly, these studies have helped to rectify…

The mixed method sequential nested study examines whether and how the cognitive type of teachers' content knowledge is associated with student achievement, and correlated with teaching practice. In the context of this study, the "cognitive type" refers to the kind of teacher content knowledge and thinking processes required to accomplish…

Investigates whether the reasons for deaf children's poor achievement lie in their strategy development. Reports that structural aspects of sign language counting may influence deaf children's thinking in a way that does not lead to a developed conceptual knowledge base, but rather to refined procedural competence. (Contains 31 references.)…

Explores written calculation methods for division used by pupils in England (n=276) and the Netherlands (n=259). Analyses informal strategies and identifies progression towards more structured procedures that result from different teaching approaches. Comparison of methods used shows greater success in the Dutch approach which is based on…

Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…

Examines the computational strategies of 10 young street vendors in Beirut by describing, comparing, and analyzing computational strategies used in solving three types of problems: (1) transactions in the workplace; (2) word problems; and (3) computation exercises in a school-like setting. Indicates that vendors' use of semantically-based mental…

Describes the success, the methods (mental, informal written, standard algorithm) and the strategies of informal written arithmetic to be observed when 300 elementary students worked on six addition and six subtraction problems with three-digit numbers. (Author/MM)

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)

The problem of innumeracy in general and at the primary school level in particular is attributed to a structuralist design of instruction emphasizing an algorithmic approach to arithmetic. Offered is an alternative learning approach developing arithmetic as an informal context-bound activity tied to mental arithmetic and estimation. (MDH)