A rational presentation of the so-called long division method for extracting the square root of a number. Diagrams are used to show relationship of this technique to the binomial theorem. Presentation exposes student to many facets of mathematics in addition to the mechanics of funding square root and cube root. Geometry, algebraic statements,…

Examines the ability of infants ranging in age from 21 to 44 hours old to discriminate among visual stimulus arrays. Infants were able to discriminate between small sets of dots (two to three dots) but not between larger sets (four to six). (Author/MP)

Models for developing addition, subtraction, and multiplication with integers are given. (MNS)

An empirical test of alternative claims by Bryant and Piaget concerning the development of invariance of quantities in 3- and 4-year-old children was made. Results support the Piagetian thesis in showing that those subjects respond with stereotypic strategies rather than by an invariance of number principle. (Author/JMB)

Two experiments explored effects of intervention and test conditions on preschoolers' use of counting to compare two sets. At mean age of 4 years 4 months, children in two intervention groups were more likely to use counting to compare sets than those in control group. Use of counting to compare sets was closely related to counting performance.…

Continues the theme developed in the first paper on this topic which was published in volume 10 of this journal. Carries the historical tale of pi from the late 16th century to the present. (ASK)

Mathematics has had a spiritual aspect throughout its history. Discusses the nature of the interplay between mathematics and spirituality in some traditional and modern contexts. (Contains 29 references.) (ASK)

Twenty classes in ten schools with 627 sixth-grade students in five cities in Taiwan participated in this study. The research provides information on the performance differences among written computation, pictorial representation, symbolic representation and number sense. The results of One-way ANOVA analysis indicate that significant difference…

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…

In this article, the author presents his tales of very large numbers. He discusses the concept of infinity and extremely large numbers such as "googol" and "googolplex". "Googol" which could be written as 1, followed by one hundred zeros, was popularized by Edward Kasner and James Newman. Moreover, "googol"…

This article describes how to determine your return on investment when deposits of varying amounts are made over irregular time intervals.

Given the vital importance of using a scientific approach for curriculum development, the authors employed a design experiment methodology (Brown, 1992; Shavelson et al., 2003) to develop and evaluate, FUSION, a first grade mathematics intervention intended for students with or at-risk for mathematics disabilities. FUSION, funded through IES…

We used a numerical bisection procedure to examine preschool children's sensitivity to the numerical attributes of stimuli. In Experiment 1 children performed two tasks. In the Cups Task they earned coins for choosing a green cup after two drumbeats and a blue cup after eight drumbeats. In the Gloves Task they earned coins for raising a red glove…

The connection between linear and 0-1 integer linear formulations has attracted the attention of many researchers. The main reason triggering this interest has been an availability of efficient computer programs for solving pure linear problems including the transportation problem. Also the optimality of linear problems is easily verifiable…