Presents a project in which one science class, curious about large numbers, created one million marks on paper. Discusses other concrete representations of one million and other large numbers. (MKR)

Describes a history of magic squares from China, Holland, Rome, and Ethiopia. (MKR)

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

Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)

Details some of the work done in the first three of six days of teaching with a group of 16 young students in July, 1993. Presents the work in the form of verbal exchanges in which the aim is to present students with some challenging questions outside their normal classroom experience. (Author/ASK)

Explains how number work in elementary school can be extended to prepare students for algebra. Suggests some practical strategies that focus on five aspects of number knowledge essential for algebra learning. (ASK)

Features a question that focuses on the use of cryptology to teach modes. (ASK)

Presents a study in which 13 fifth-grade students were given an assignment to invent their own numeration systems following a unit on bases and a look at early events in the history of numbers. Offers an assessment of student understanding of numeration provided by analyses of the patterns embedded in their invented systems. Contains 13…

Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)

Examines number naming, magnitude selection, and simple arithmetic performed by adult Chinese-English bilinguals born and educated in China to investigate the effects of surface notation on basic numerical skills. Indicates that retrieval processes in the arithmetic and selection tasks were more efficient with Arabic than Mandarin stimuli.…

Uses neuropsychological and developmental models of number, counting, and arithmetical skills as well as supporting working memory and speed of articulation systems as the theoretical framework for comparing groups of low- and average-IQ children. Indicates that low-IQ children's conceptual understanding of counting did not differ from that of…

Outlines the embedded mathematics in which important but hidden calculations are being done for communications in commerce. Explains two key concepts, error detecting codes and error correcting codes. Illustrates these ideas using two familiar examples, barcodes and ISBN numbers. (ASK)

Presents examples taken from an existing K-9 program to show how children of various ages can be engaged in intellectual experiences, some of which might not seem to be mathematical by traditional standards. (ASK)

Describes a teaching experiment conducted over a period of four consecutive days with 13 fourth grade students who had already completed a unit of fractions to determine whether problematic size was the ordering criteria. Concludes that children can indeed order fractions as they do natural numbers. (Contains 11 references.) (ASK)

Examines strategies used by preschool children to subdivide items and focuses on how counting and sharing relate to one another. Indicates that children exhibited alternative strategies--suggesting use of a recipient as a mental cycle-marker and an adjacent recipient strategy--with pauses between allocations suggesting a re-presentation of lots…