This article proposes a practical method of teaching the addition of unit fractions using a series of mirror equation experiments.

A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…

It seems that calculators continue to be misunderstood as devices solely for calculation, although the likely contributions to learning mathematics with modern calculators arise from other characteristics. A four-part model to understand the educational significance of calculators underpins this paper. Each of the four components (representation,…

Most students can follow this simple procedure for division of fractions: "Ours is not to reason why, just invert and multiply." But how many really understand what division of fractions means--especially fraction division with respect to the meaning of the remainder. The purpose of this article is to provide an instructional method as a…

When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

A critical incident is a situation or event that holds significance for learning, both for the students and teachers. This paper presents four examples of critical incidents from a Year 7 teacher's lesson excerpts in Indonesia involving teaching of fractions, to show how they shaped classroom situation, brought forward elements of conflict, and…

Mechanical devices offer an alternative to computers to explore mathematical concepts in different curricula areas. Described is the discograph, a series of pulleys and wheels, that can be used to teach mathematical principles in pattern drawing, locus, rotation in geared systems, gearing, rotational symmetry, regular plane figures, decimal, and…