Mathematical cognition research has largely emphasized concepts that can be directly perceived or grounded in visuospatial referents. These include concrete number systems like natural numbers, integers, and rational numbers. Here, we investigate how a more abstract number system, the irrationals denoted by radical expressions like the square root…

The study was undertaken to establish the relationship between the roots of the perfect numbers and the "n" consecutive odd numbers. Odd numbers were arranged in such a way that their sums were either equal to the perfect square number or equal to a cube. The findings on the patterns and relationships of the numbers showed that there was…

This note can be used to illustrate to the student such concepts as periodicity in the complex plane. The basic construction makes use of the Tent function which requires only that the student have some working knowledge of binary arithmetic.

The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…

Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed…

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…

The Pythagorean Theorem, arguably one of the best-known results in mathematics, states that a triangle is a right triangle if and only if the sum of the squares of the lengths of two of its sides equals the square of the length of its third side. Closely associated with the Pythagorean Theorem is the concept of Pythagorean triples. A "Pythagorean…

"Chisanbop" is a Korean word which means finger calculation method. It is based on the Korean abacus, and its emphasis is on fives. By using Chisanbop techniques, one can add, subtract, multiply, and divide large numbers. Chisanbop can be taught most effectively to large groups in the second grade. (JN)

"Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledge…

Presents number tricks appropriate for use in workshops, mathematics clubs or at other times when stressing recreational mathematics. (PK)