'Horses for courses' - curriculum-speed in the CSF

This article considers the issue of acceleration in lower secondary school mathematics in the Victorian Curriculum and Standards Framework.

The octagonal cardboard frisby-hovering stability

This article explores the mathematics behind frisbys for the primary school classroom.

A multiplication curriculum : a short outline

Teachers not only know how to multiply, they also know how to teach children multiplication. But at any one time, most teachers are only concerned with a small section of the whole large process of teaching multiplication. It is easy to lose sight of the wood, because of the close attention being given to individual trees. What is the larger picture? How do children learn to multiply, asks the author? The author discusses the progressive stages of ideas and processes that are involved in learning to multiply. He also provides questions to assist teachers with identifying how far students have progressed in their understanding of multiplication.

Algebra concepts and skills survey - a draft

Presents questions adapted from the 'Group Review of Algebra Topics' (ACER 1991) that form a draft survey test of 24 items ranging across aspects of algebra and secondary algebra instruction.

Tackling trigonometry - up the slippery slope?

This paper challenges mathematics teachers to go back and re-examine ideas as far as possible from the genuine beginner's point of view rather than in terms of being experts on the subject. It suggests tasks that teachers can do to achieve this. Topics covered are the shock of the new, the best single short lesson on trigonometry, the difficulty of remembering not knowing, first student trigonometric steps (scouts and flagpoles), first human steps in trigonometry (examining the stars), rotation becomes number, showing relations and learning ideas, plus a lengthy discussion on trigonometry.

A diagnostic 'profile' for chance (probability)

This article presents a profiling tools for identifying students knowledge in chance.

The critical role of task development in lesson study

While many aspects of Lesson Study are characteristic of effective pedagogy, the task or problem is perhaps the least understood by non-Japanese adopters of Lesson Study. In this chapter we focus on the pivotal rôle played by the task in the Research Lessons of Lesson Study practice in Japanese primary school mathematics. The metaphor adopted is that tasks are akin to icebergs, where most of the support is hidden, and is used in order to raise awareness of the bases of effective tasks. Examples of such tasks are described as they were presented in classrooms in both Australia and Japan.

What is rate? Does context or representation matter?

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students’ conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, 2007). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students’ expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, 2010) conducted with Grade 10 students from the Australian state of Victoria.

First of all, I split the 24 : strategies for mental computation

In this article, the author sets out some goals and classroom activities for the teaching of mental computation. The author also discusses the importance of allowing children to help each other and explains that there is benefit in children listening to mathematical strategies given by other children.

Equity and technology : a case study

I am researching equitable and socially just teaching practices when using technology for the mathematical learning of disadvantaged and marginalised students in junior secondary school. Using data gathered from teacher interviews and a meeting of teachers, I present a case study of one teachers’ practice. The case suggests that there are some equity considerations for the use of an integrated project approach to teaching mathematics and that whole class problem solving with technology can provide access to mathematical ideas when students have limited access or skills with technology.

Pedagogical practices with digital technologies : pre-service and practicing teachers

In this paper the pedagogical practices of practising teachers and pre- service teachers when using digital technologies are described and compared. Data were collected by observation of presentations about using digital technology in mathematics by teachers and pre-service teachers and practising teachers were interviewed. Teachers generally used pedagogical approaches involving student-centred activity whereas pre-service teachers were more likely to use technology to teach concepts by demonstration and were not inclined to use the more student- centred approaches, though many used guided tasks. The study enabled some analysis and reflection upon the promoted action in the learning environments of pre-service teachers.

Assessment of primary 5 students' mathematical modelling competencies

 Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes and competencies needed to develop in their students during mathematical modelling. This paper reports on the assessment of two groups of Primary 5 students’ (aged 11) mathematical modelling competencies in their first attempt in completing a modelling task. The students’ competencies are assessed to be at levels 1 and 2 of a researcher-designed rubric. Findings appear to suggest that students faced particular challenges in formulating a mathematical problem from the real-world problem through making assumptions. Implications on teacher education on the facilitation of problem formulation and mathematisation during mathematical modelling at the primary level are drawn.

Becoming numerate with information and communications technologies in the twenty-first century

This article draws on data from a three-year Australian Research Council-funded study that examined the ways in which young children become numerate in the twenty-first century. We were interested in the authentic problem-solving contexts that we believe are required to create meaningful learning. This being so, our basic tenet was that such experiences should involve the use of information and communications technologies (ICT) where relevant, but not in tokenistic ways. This article highlights learning conditions in which young children can become numerate in contemporary times. We consider ‘academic’ or ‘school-based’ mathematical tasks in the context of a Mathematical Tasks Continuum. This continuum was conceptualised to enable focused and detailed thinking about the scope and range of mathematical tasks that young children are able to engage within contemporary school contexts. The data from this study show that most of the tasks the children experienced in early years mathematics classes were unidimensional in their make up. That is, they focus on the acquisition of specific skills and then they are practiced in disembedded contexts. We suggest that the framework created in the form of the Mathematical Tasks Continuum can facilitate teachers thinking about the possible ways in which they could extend children’s academic work in primary school mathematics, so that the process of becoming numerate becomes more easily related to authentic activities that they are likely to experience in everyday life.