In current teaching materials, when using Dedekind cuts to construct real numbers, the definition of a Dedekind cut is always involved in defining addition and multiplication. In this paper, as it is done in many current textbooks, Dedekind cuts are used to construct the set of real numbers. Then the order in it is defined, and the…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

A procedure for generating quasigroups from groups is described, and the properties of these derived quasigroups are investigated. Some practical examples of the procedure and related results are presented.

A branch of mathematics commonly used in cryptography is Galois Fields GF(p[superscript n]). Two basic operations performed in GF(p[superscript n]) are the addition and the multiplication. While the addition is generally easy to compute, the multiplication requires a special treatment. A well-known method to compute the multiplication is based on…

This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 x 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are…

Synthetic division is viewed as a change of basis for polynomials written under the Newton form. Then, the transition matrices obtained from a sequence of changes of basis are used to factorize the inverse of a bidiagonal matrix or a block bidiagonal matrix.