This study surveyed and analysed four secondary school students' writing about a square. Sfard's discursive approach to understanding mathematical discourse was used to analyse the responses collected from 214 Australian secondary school students. The results showed that geometric knowledge was developed experientially and not developmentally.…

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

In this article Vince Wright and Jacqui Tjorpatzis share findings from a teaching experiment that involved the implementation of a Year 3 unit of work on decimals. They describe the activities involved, and the challenges and benefits of introducing decimals to young children.

As an extension to an activity introducing Year 5 students to the practice of statistics, the software "TinkerPlots" made it possible to collect repeated random samples from a finite population to informally explore students' capacity to begin reasoning with a distribution of sample statistics. This article provides background for the…

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, this issue will focus on Number in the Number and Algebra strand. In this article Derek Hurrell provides a few tried and proven activities to develop place value understanding. These activities are provided for…

Informal statistical inference has now been researched at all levels of schooling and initial tertiary study. Work in informal statistical inference is least understood in the early years, where children have had little if any exposure to data handling. A qualitative study in Australia was carried out through a series of teaching experiments with…

A short series of practical classroom mathematics activities employing the use of a large and publicly accessible scientific data set are presented for use by students in years 9 and 10. The activities introduce and build understanding of integral calculus and trigonometric functions through the presentation of practical problem solving that…

As part of ongoing design-based research exploring financial literacy teaching and learning, ten tasks termed "financial dilemmas" were trialled by 14 teachers and more than 300 Year 5 and 6 students in 4 government primary schools in urban Darwin. Drawing on data related to two tasks--"Catching the bus" and "Buying…

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

In this article, Derek Hurrell, points out that while it's easy to fall into the impression that the proficiency strand "Fluency" is all about knowing basic number facts in all its many and splendid ways. He add it is easy to overlook, that within Fluency there are requirements that are based in Algebra; Measurement and Geometry; and…

An engaging activity which prompts students to listen, talk, reason and write about geometrical properties. The "Bag of Tricks" encourages students to clarify their thoughts and communicate precisely using accurate mathematical language.

Fractions are generally introduced to students using the part--whole model. Yet the number line is another important representation which can be used to build fraction concepts (Australian Curriculum Assessment and Reporting Authority [ACARA], 2012). Number lines are recognised as key in students' number development not only of fractions, but…

Developing pre-service teachers' (PSTs') knowledge of pedagogical practices can be particularly challenging within university classrooms. Teacher educators are well placed to provide PSTs with theoretical perspectives on pedagogical practices; what is particularly challenging, however, is linking theory with practice and developing PSTs' breadth…

This paper reports on a study that examines the effects of problem context on students' performance. The performance of 151 Year 10 students on six mathematical problems was compared with the performance on fifteen variants with more and less context familiarity (CF) and engagement (CE) across levels of context use (LCU). The latter explanatory…

Rhetoric about the importance of students being equipped to apply mathematics to relevant problems arising in their lives, individually, as citizens, and in the workplace has never been matched by serious policy or curricular support. This paper identifies and elaborates authenticity implications for addressing this issue, and describes aspects of…