Presents solutions for a problem concerning doubling a recipe from a previous article on number concepts in the October 1997 issue. (ASK)

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article explores how counting collections of objects helps elementary-age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. It is suggested that the teacher's role is one of noticing, questioning,…

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

Thirty-six Korean first graders were interviewed to study their ability solving addition problems with sums of 10, single-digit sums between 10 and 18, and subtraction problems with minuends between 10 and 18. Finger methods to show sums over 10 and the regular named-10 Korean number words supported their learning of 3 efficient recomposition…

Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.

When comparing rows of dots in length or number, some children used number strategies and some length strategies. After training to correct missed items, errors were made on previously correct items. These findings are interpreted with reference to the distinction between having a dimensional strategy and attaching it to appropriate situations.…

The life of Fibonacci is summarized, and his importance in the development of mathematics is assessed. Several problems first solved by Fibonacci are posed. (SD)

In a series of exercises students develop designs in which nodes are labelled according to the isolation rules defined. Strategies for creating new designs from known ones, finding the maximum number of isolation designs on a given configuration, and developing larger isolation designs are encouraged. Sample worksheets are included. (SD)

Fifteen trainable mentally retarded students (four-six years old) were generally capable of rule-governed and other counting skills, and some could mentally compare numbers and choose the larger. Some Ss demonstrated a basic form of problem solving: they used the addition identity and commutativity principles to shortcut computational effort.…

Results obtained from investigating number properties are discussed, along with six points that are felt, in general, to be the ingredients necessary for a successful learning experience. Two programs written in BASIC designed to aid in aspects of Number Theory are included. (MP)

Investigates the extent to which children's number sense and novel problem-solving skills govern their problem-posing abilities in routine and nonroutine situations. Children who participated in the program appeared to show substantial developments in each of the program components in contrast to those who did not participate. Contains 66…