Why do certain objects or images such as a piece of furniture, an item of clothing, or even a flower appear visually attractive? The most obvious factors must involve aspects such as size, colour, movement and discrepancy such as in looking at a Salvador Dali painting. Yet there is another subtle factor associated with shape that also can demand,…

This article provides a range of activities designed to engage students in using an early form of graphing. While the "Australian Curriculum: Mathematics" (2014) highlights understanding, fluency, problem-solving, and reasoning, the National Research Council (2001) describes five strands of mathematical proficiency, with the additional…

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…

The authors of this article strongly advocate for a change to the current Australian model of primary education in order to, among other things, establish the concrete practicalities of systematic mathematics thinking thereby limiting the "re-teaching" time required of secondary school mathematics teachers; bring a clear focus to the…

What do you do when you want to get your Stage 3 students authentically and enthusiastically engaged in the active construction of their understanding and fluency with measurement, data collection, representation and interpretation? How do you enable them to make choices about their learning, to measure with purpose, to record and organise the…

The term "numeracy" seems to be commonly used in discussions about school mathematics education these days. It is not altogether clear what various school systems intend "numeracy" to mean and whether or not it is meant to replace the term "mathematics", whether it is just one part of mathematics or whether it is…

The purpose of this article is to explain the authors' model of numeracy and outline how the project was conducted. The idea of numeracy is a relatively recent one. The term was first introduced in the UK by the "Crowther Report" (Ministry of Education, 1959) and was defined as the mirror image of literacy, but involving quantitative…

All common fractions can be written in decimal form. In this Discovery article, the author suggests that teachers ask their students to calculate the decimals by actually doing the divisions themselves, and later on they can use a calculator to check their answers. This article presents a lesson based on the research of Bolt (1982).

There is much to be learned and pondered by reading "Proofs and Refutations" by Imre Lakatos (Lakatos, 1976). It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning…

Doing mathematics, and thinking about how you are doing it at the same time, are not the easiest things to do. It is even more difficult if students are not aware that they should be attempting both processes at the same time. They are likely to concentrate on the immediate task of "doing" the mathematics, rather than trying to access the deeper…

The purpose of this study was to describe students' problem solving performance when they make conjectures to comprehend three statistics terms. Teachers are key figures in changing the ways in which mathematics is taught and learned in schools. Mathematics teachers are supposed to design meaningful tasks to motivate students' interest and to…

In this article, the author focuses on possible ways to develop the concepts of joint variation and function through the upper primary and lower secondary years of education. The examples demonstrate the building of a range of important mathematical ideas by modelling life-related situations using students' informal and intuitive knowledge. Over…

A technique for doing long division without the usual estimation difficulty is presented. It uses multiples of 2 combined with a recording technique. (MNS)