How do children learn the meanings of number words like "one," "two," and "three"? Whereas many words that children learn in early acquisition denote individual things and their properties (e.g., cats, colors, shapes), numerals, like quantifiers, denote the properties of sets. Unlike quantifiers such as "several" and "many," numerals denote…

It is of deep interest to both linguists and psychologists alike to account for how young children acquire an understanding of number words. In their commentaries, Barner and Butterworth both point out that an important question highlighted by the work of Syrett, Musolino, and Gelman, and one that remains highly controversial, is where number…

In 1225 Fibonacci visited the court of the Holy Roman Emperor, Frederick II. Because Frederick was an important patron of learning, this visit was important to Fibonacci. During the audience, Frederick's court mathematician posed three problems to test Fibonacci. The third was to find the real solution to the equation: x[superscript 3] +…

Are small and large numbers represented similarly or differently on the mental number line? The size effect was used to argue that numbers are represented differently. However, recently it has been argued that the size effect is due to the comparison task and is not derived from the mental number line per se. Namely, it is due to the way that the…

According to one theory about how children learn the concept of natural numbers, they first determine that "one", "two", and "three" denote the size of sets containing the relevant number of items. They then make the following inductive inference (the Bootstrap): The next number word in the counting series denotes the size of the sets you get by…

Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)

An appeal is made for a more formal treatment of the topics of estimation and reasonableness of answers in the school mathematics curriculum. (MP)

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

Discusses the history of different methods of representing numbers and how these representations facilitated counting and computing devices such as the abacus. (MDH)

The ability of some individuals with mental retardation to identify prime numbers despite their lack of necessary arithmetical skills is discussed. The article suggests that a distinction between prime and nonprime numbers can be made by utilizing the tendency of visual perception to be symmetrically organized. (Author/DB)

Two experiments examined preschoolers' performance on test relying on the uniqueness principle for using evidence from a miscount in inferring a counterfactual cardinal number, with subtests probing associated number-skills. All the 5-year-olds and half the preschoolers passed the test. Results suggest that a crucial preschool step is to start…

Questioned is a method of having students tap reference points on numerals to count out sums, differences, and products. How the method works, educators' reactions, and problems noted in interviews with children are discussed. (MNS)

Curricular placement of and emphasis on common and decimal fractions are discussed. Suggestions include: retaining common fractions in the curriculum, teaching decimal concepts and notation earlier, reducing fraction computation complexity, and moving fraction computation upward in the curriculum. (MK)

Based on Piaget's theory that children acquire number concepts by constructing them from within, the authors conclude that teaching algorithms harms mathematics learning. A better approach is allowing them to construct their own logico-mathematical knowledge and invent their own efficient procedures. (JOW)