Part of a regular series on curriculum.

Facts are given about the ninth-century Arab mathematician Al-Khwarizmi, from whose name the word algorithm is derived. His influence on algebra and arithmetic are discussed. (MNS)

Two hundred and sixty-six kindergarten, first, second, and third graders completed four tasks measuring their understanding of two aspects of number concepts -- ordinality and cardinality. Data suggest that children acquire understanding of ordinality prior to cardinality. (Author/MP)

Six conjectures are established concerning a rectangular solid with the lengths of all its face diagonals and the lengths of all its edges being positive integers. (MP)

Results of this study involving 120 kindergarten and first-grade boys and girls suggest that some understanding of the invariance of number appears to emerge earlier than the ability to pass the standard verbal test. (BH)

Two experiments were conducted to examine the input-order effect reported by Birnbaum (1975); he demonstrated that free recall of two-digit numbers presented in natural ascending order is superior to free recall of the same numbers presented in random order. (Author/RK)

This study investigates the use of infinities and limits during the first 12 years of schooling while a secondary study presents ideas and comments on the observations that were made during the primary study. (MVL)

Reviews and analyzes the number-line metaphor in textbooks. Presents examples to show a way to produce an internal critique of mathematical textbooks, a critique that targets the practices in which the notions are involved within the text. Presents the number-line metaphor as the horizon and the tiller of all the enlargements of the notion of…

Presents some known and lesser-known features of the number 11. (KHR)

Uses cryptography to demonstrate the importance of algebra and the use of technology as an effective real application of mathematics. Explains simple encoding and decoding of messages for student learning of modular arithmetic. This elementary encounter with cryptography along with its historical and modern background serves to motivate student…

Characterizes those numbers that are the sum of consecutive natural numbers and counts how many such representations a given number has. (Author/NB)

Employs statistical tools to determine whether the digits of Pi are pseudorandom. Discusses the difficulties in answering this question. (Author/NB)