The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Digital revolution or digital divide: Will rural teachers get a piece of the professional development pie?

In order to sustain the rural education community, access to high quality professional development opportunities must become a priority. Teachers in rural areas face many challenges in order to access professional learning equitable to their city counterparts. In the current climate, the Federal government of Australia is committed to initiatives that support the use of ICT in education. These include initiatives such as the Digital Education Revolution, including the National Broadband Network. This "revolution" includes the committal of $2.2 billion funding over six years from 2008 - 2013 which purports to bring substantial and meaningful change to teaching and learning in Australian schools. Of this funding, the Prime Minister (former Minister for Education), Julia Gillard, has committed $40 million of the total budget to ICT related professional development for teachers. But how will rural teachers ensure they get a piece of the PD pie? Access to professional learning is critical and isolation from colleagues, professional associations and support structures can affect the retention of teachers and in turn affect the sustainability of rural communities. This research paper describes the findings of the first phase of a study that investigates access to professional learning from rural and remote areas of Western Australia, the efficiencies of this approach including teacher perceptions and possible opportunities for improvement through the application of technologies. A survey instrument was administered and the results from104 principals and teachers within the Remote Teaching Service and the Country Teaching Program of the Department of Education and Training (WA) are discussed. Qualitative data was collected by semi-structured interviews and emailed questionnaires. Phase One findings highlight the principals and teachers? perceptions of their access to professional development opportunities, professional learning communities and their use of information and communication technologies (ICT) to bridge the gap