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…

Indicates that there has been a lot of work done and that a great deal needs to be done in the future to explore the world of children's early number. Discusses the counting, the use of algorithm, practical mathematics, the use of manipulatives, individual differences and pedagogical concerns, and classroom applications. Contains 18 references.…

Presents the steps and lessons for making the "Measure Me" doll in which students experience numeracy when they use their own birth statistics to create a doll. Through this sequence of activities, learners relate what they already know about themselves to new situations where they compare their heights and weights with those of other children.…

Coordinates social constructivism and socioculturalism to explain 2nd grade children's reasoning with 2-digit quantities. Illustrates how the classroom teacher and the students constituted what counted as an acceptable mathematical explanation. Concludes that local classroom mathematical practices constrained and enabled the mathematical practices…

Describes public key cryptography, also known as RSA, which is a system using two keys, one used to put a message into cipher and another used to decipher the message. Presents examples using small prime numbers. (MKR)

Shares the thinking of one seventh-grade student about his discovery concerning Pythagorean triples during the study of the Pythagorean theorem. (MKR)

Investigates how students familiar with exponentiation intuitively combined information about bases and exponents in expressions of the type a(carot)n to estimate the magnitude of these expressions. Qualitative and quantitative analyses conducted on the data revealed at least five different models of magnitude estimation. Contains 17 references.…

Presents reform efforts aiming to combat underachievement in mathematics through the introduction of successful Continental pedagogy into the teaching of number concepts. Discusses the pedagogy and its introduction into the Borough's schools. Addresses some criticisms that have been leveled at the reforms. (ASK)