In recent years, there has been greater attention in research and professional development work to discussion of the kinds of knowledge teachers need to teach effectively in the mathematics classroom. It seems reasonable that in planning at the school level, teaching team level and then specifically for a given lesson, teachers might have a sense…

The Australian Curriculum: Mathematics encourages teachers to consider seriously the four proficiencies: Understanding, Fluency, Problem Solving and Reasoning. In responding to the reasoning proficiency, many teachers may find that the language of the classroom may well change. In this article, we discuss the meaning given to the term reasoning…

It is a common belief that the incorporation of computer technology into mathematics teaching and learning motivates and engages students. However, research into the use of ICTs (Information and Communication Technologies) in mathematics classrooms has revealed some issues that could negatively impact on student engagement as a result of how they…

This article is intended to assist people who have never written for a journal, or who perhaps have never even thought about doing so. In this article, the authors provide some advice for budding Australian Primary Mathematics Classroom (APMC) authors. Information on where to start, what's already been done, what will be in the paper, who will…

Much has been written about the value of concrete manipulatives for supporting students' mathematics learning. This is particularly true for the domain of fractions and decimals. Understanding of decimal place-value is seen as critical for students' mathematics learning. To understand decimals, students need first to have a solid understanding of…

A considerable body of research exists on students' understanding of decimal fractions and the prevalence and persistence of common misconceptions related to this understanding. Results from major studies such as the National Assessment of Educational Progress (NAEP) in the United States and the Concepts in Secondary Mathematics and Science (CSMS)…

As part of the Contemporary Teaching and Learning of Mathematics Project (CTLM), the mathematics education team at Australian Catholic University has the privilege of working with principals, teachers, students, and parents in schools in the Melbourne Archdiocese. A particular highlight is the opportunity to work alongside project teachers and…

The 21st century has placed increasing demand on individuals' proficiency with a wide array of visual representations, that is graphics. Hence, proficiency with visual tasks needs to be embedded across the curriculum. In mathematics, various graphics (e.g., maps, charts, number lines, graphs) are used as means of communication of mathematical…

The idea of using mathematical research in the classroom to collect real data has been spoken about within education for many years. The question is, why should teachers bother with real data from their students' worlds and how do they actually put it into practice in the classroom? When using the mathematical research strategy for collecting,…

Mathematical computation consists of both written computation and mental computation. The strategies for mental computation can be used to check the reasonableness of written computations. Mental computation has two distinguishing characteristics: "it produces an exact answer, and the procedure is performed mentally, without using external devices…

The concept of a function is fundamental to virtually every aspect of mathematics and every branch of quantitative science. Presently this type of thinking is carolled at the secondary level, and yet it has many benefits for deepening the understanding of early arithmetic. This is particularly so in the way that operations can be considered as…

Multiplication, division and fractions are "hotspots" for students in the middle years with many students experiencing difficulty with these concepts. Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts. In this article the authors show how an open-ended array problem enabled a…

Traditionally, primary schools place minimal emphasis upon relations and transformations as objects of study. In their research, the authors have found the young children can engage in conversations about equivalence and equations (Warren & Cooper, 2005a) and functional thinking (Warren & Cooper, 2005b). Fundamental to relations and…

About fifteen years ago, the author discovered an interesting activity in some materials that Malcolm Swan from the Shell Centre (University of Nottingham, UK) had developed for the English National Curriculum Council in 1991. The activity, one which has been used by several presenters in professional development workshops in Australia in recent…

Estimation is an important skill for everyday living. Good estimators usually have a sound knowledge of basic facts, understand place value and use a variety of strategies to make their estimates. This paper describes an activity which is designed to provide students with opportunities to practice their rounding strategies with addition and…