The purpose of the study was to determine the effects of type of grouping (multibase (M) or base ten (T) ) and the time that base representations are introduced (initially (EB) or after counting, reading and writing numerals (LB) ) on achievement in numeration in grade one. Four intact classes of 110 students participated, and a 2 x 2 factorial…

A list of materials needed and step-by-step directions for constructing an abacus are given. Instructions are provided which tell how to use the abacus in teaching number combinations and in working addition, multiplication, subtraction, and division problems. (Related documents are SE 015 950 and SE 015 952.) (DT)

Three experiments examined the effects of target-distractor (T-D) similarity and old age on the efficiency of searching for single targets and enumerating multiple targets. Experiment 1 showed that increasing T-D similarity selectively reduced the efficiency of enumerating small (less than 4) numerosities (subitizing) but had little effect on…

Everyone knows what makes a 3-4-5 triangle special, but how many know what makes a 4-5-6 triangle special? It is an integer-sided triangle in which one angle is twice another. It is enjoyable to search for these things, but for those who are impatient, this article derives explicit polynomial formulas that generate all of the basic examples of…

Do preschool children appreciate numerical value as an abstract property of a set of objects? We tested the influence of stimulus features such as size, shape, and color on preschool children's developing nonverbal numerical abilities. Children between 3 and 5 years of age were tested on their ability to estimate number when the sizes, shapes, and…

Vision was for a long time considered to be essential in the elaboration of the semantic numerical representation. However, early visual deprivation does not seem to preclude the development of a spatial continuum oriented from left to right to represent numbers (J. Castronovo & X. Seron, 2007; D. Szucs & V. Csepe, 2005). The authors investigated…

We applied overlapping waves theory and microgenetic methods to examine how children improve their estimation proficiency, and in particular how they shift from reliance on immature to mature representations of numerical magnitude. We also tested the theoretical prediction that feedback on problems on which the discrepancy between two…

In this article, we show how "Laplace Transform" may be used to evaluate variety of nontrivial improper integrals, including "Probability" and "Fresnel" integrals. The algorithm we have developed here to evaluate "Probability, Fresnel" and other similar integrals seems to be new. This method transforms the evaluation of certain improper integrals…

Number processing is characterized by the distance and the size effect, but symbolic numbers exhibit smaller effects than non-symbolic numerosities. The difference between symbolic and non-symbolic processing can either be explained by a different kind of underlying representation or by parametric differences within the same type of underlying…

A short story is presented which uses as its characters rational and irrational numbers and numbers involving fractional exponents. (DT)

Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)

The paper presents reasons for teaching topics from number theory to elementary school students: (1) it can help reveal why numbers "act" in a certain way when added, multiplied, etc., (2) it offers drill material in new areas of mathematics, (3) it can develop interest - as mathematical enrichment, (4) it offers opportunities for students to…

Three-, four-, and five-year-olds were given problems to test their ability to recognize absolute number and relative order. Results suggest that children understand number as an absolute amount before they understand it as part of a progressive sequence in contradiction to the "ordinal theory of number." (Author/DST)

"How Students Learn: Mathematics in the Classroom" builds on the discoveries detailed in the best-selling "How People Learn." Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. This book shows how to overcome the difficulties in teaching math to…