Describes a study designed to investigate the relationship between students' learning of the standard double-digit addition algorithm and basic fact mastery or numeration concepts. Results suggest basic fact mastery and knowledge of numeration concepts may not be as necessary as previously assumed to learning multidigit addition. (PK)

Reports on interplay between social and developmental processes in children's numerical understandings in working- and middle-class home settings. Methods included interviews with 78 children aged 2 1/2 and 4 1/2 years to assess their numerical understandings, interviews with the mothers about their children's everyday number activities, and…

Presents a method of teaching two-column addition which the authors argue is based on Piaget's theory and fosters the children's own natural thinking. The method does not use objects such as straws bundled or base-ten blocks. (PK)

Discusses the use of the Rhind Mathematical Papyrus to motivate classroom activities related to computation and place value using the Egyptian number system. (PK)

Investigates children's difficulty in understanding (numerical) place value. A counting and estimating task, based on Piaget's number theory, was devised to determine if children in grades one through five evidenced this construction. (Author/BB)

A few examples are provided of the history of games and recreations. Six games and some recreations are discussed. (MNS)

Illustrated first is the case in which a wrong procedure (with fractions) leads to a correct result. Trying to justify why it works in this case and looking for similar patterns involved interesting algebraic considerations as well as use of computers. (MNS)

A series of common misconceptions with regard to infinite sets is considered. Several notions of infinite numbers proposed by different mathematicians are compared. It is argued that so-called errors should rather be called alternative conceptions. (MNS)

This study showed that Oksapmin children not only spontaneously use the indigenous numerical system of their nontechnical culture but also have created new forms of numerical symbolization and calculation to deal with schooling arithmetic problems. Novel conceptual developments, factors mediating the schools effect, and the influence of prior…

Patterns resulting from polygonal numbers are explored, with examples of triangular, square, pentagonal, rectangular, and other numbers. Tables and formulas to be developed are included. (MNS)

Field tests were conducted to evaluate theory-based computer-video instructional modules designed to teach or review concepts and operations for factors, prime numbers, and fractions. (MNS)

A useful approach for developing insights and discovering patterns is to examine numbers in relation to the number of their divisors. A teaching procedure for this approach is presented, with questions, answers, and homework suggestions. (MNS)

Three worksheets are given that use calculators to free students from computational restrictions and allow them to focus on the recognition of patterns and the application of numeration concepts in the development of their estimation skills. (MNS)

Presents activities that have been used successfully in leading students from concrete experiences through pictorial and symbolic representations of important numeration concepts and patterns, including place value, multiples, and rounding. Each activity includes concept or skill fostered, list of materials needed, recommended grade level, and…

Judgments of similarities between numbers were solicited from kindergarten, third-grade, sixth-grade, and adult subjects. Results suggested children become sensitive to an expanding set of numerical relations during the period from kindergarten through sixth grade. Results of a second study suggested that the number similarity judgments of…