An instrument for assessing primary students’ knowledge of information graphics in mathematics

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students’ knowledge of graphics. This instrument can be used in mass testing and individual (in-depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics; and provide the capacity to benchmark information about students’ knowledge of graphics. The implications for practice include the need to support the development of students’ knowledge of graphics, the existence of gender differences, the role of cross-curriculum applications in learning about graphics, and the need to explicate the links among graphics.

National numeracy tests : a graphic tells a thousand words

Mandatory numeracy tests have become commonplace in many countries, heralding a new era in school assessment. New forms of accountability and an increased emphasis on national and international standards (and benchmarks) have the potential to reshape mathematics curricula. It is noteworthy that the mathematics items used in these tests are rich in graphics. Many of the items, for example, require students to have an understanding of information graphics (e.g., maps, charts and graphs) in order to solve the tasks. This investigation classifies mathematics items in Australia’s inaugural national numeracy tests and considers the effect such standardised testing will have on practice. It is argued that the design of mathematics items are more likely to be a reliable indication of student performance if graphical, linguistic and contextual components are considered both in isolation and in integrated ways as essential elements of task design.

Primary students’ spatial visualization and spatial orientation : an evidence base for instruction

This paper reports on the performance of 58 11 to 12-year-olds on a spatial visualization task and a spatial orientation task. The students completed these tasks and explained their thinking during individual interviews. The qualitative data were analysed to inform pedagogical content knowledge for spatial activities. The study revealed that “matching” or “matching and eliminating” were the typical strategies that students employed on these spatial tasks. However, errors in making associations between parts of the same or different shapes were noted. Students also experienced general difficulties with visual memory and language use to explain their thinking. The students’ specific difficulties in spatial visualization related to obscured items, the perspective used, and the placement and orientation of shapes.

Gender effects in orientation on primary students’ performance on items rich in graphics

This study investigated the longitudinal performance of 378 students who completed mathematics items rich in graphics. Specifically, this study explored student performance across axis (e.g., numbers lines), opposed-position (e.g., line and column graphs) and circular (e.g., pie charts) items over a three-year period (ages 9-11 years). The results of the study revealed significant performance differences in the favour of boys on graphics items that were represented in horizontal and vertical displays. There were no gender differences on items that were represented in a circular manner.

Cyberbullying : the new face of workplace bullying?

While the subject of cyberbullying of children and adolescents has begun to be addressed, there has been less attention or research on cyberbullying in the workplace. Whilst male-dominated workplaces such as manufacturing settings have been found to have an increased risk of workplace bullying, the prevalence of cyberbullying in this sector is not known. This exploratory study investigated the prevalence and methods of face-to-face bullying and cyberbullying of males at work. One hundred and three surveys (a modified version of the NAQ-R1), were returned from randomly selected members of the Australian Manufacturing Worker’s Union (AMWU). The results showed that 34% of the respondents were bullied face-to-face, and 10.7% were cyberbullied. All victims of cyberbullying also experienced face-to-face bullying. The implications for organisations of their “duty of care” in regards to this new form of bullying are indicated.

Encouraging ethics and challenging corruption : reforming governance in public institutions

Encouraging Ethics and Preventing Corruption brings theory and practice together in addressing the question: How are we to be ethical in public life and through public institutions? It is a major contribution to public sector ethics within Australia and internationally because it provides an exhaustive analysis of reform across a decade in one jurisdiction, Queensland, and then proceeds to itemise a best practice integrity system or ethics regime. Drawing on the extensive research of two of Australia's leading practical ethicists, this text is essential reading for all students and practitioners of applied and professional ethics in the public sphere. Part A of the text provides a preferred theoretical and conceptual framework which both justifies and guides the development of a public sector ethics regime. Part B examines the place of the individual within a world of institutional ethics. Part C outlines the Queensland governance reforms introduced since 1989 following the Fitzgerald Inquiry which exposed corruption in the police and ministry. The final chapter, the 'Epilogue', gathers the insights of earlier chapters and suggests a more explicitly ethics-centred approach to governance reform that may take us 'beyond best practice'. Clearly, while it is the Australian context we have in mind, we are confident that this is a text which addresses the quest for integrity and ethics in government wherever society is committed to social and liberal democratic ideals.

Management, organisation, and ethics in the public sector

Since the 1980s, in Australia and other developed nations, public sector management philosophies and how the public sector is organized have changed dramatically. At the same time, there have been many demands, and several attempts, to preserve and promote ethical behaviour within the public sector - though few go much beyond the publication of a code. Both developments require an understanding of how public organizations operate in this new environment. Organizational and management theory are seen as providing important potential insights into the opportunities and pitfalls for building ethics into the practices, culture and norms of public organizations. This book brings together the experience and research of a range of "reflective practitioners" and "engaged academics" in public sector management, organizational theory, management theory, public sector ethics and law. It addresses what management and organization theory might suggest about the nature of public organizations and the institutionalization of ethics.

Writing together, learning together : the value and effectiveness of a research writing group for doctoral students

The high level of scholarly writing required for a doctoral thesis is a challenge for many research students. However, formal academic writing training is not a core component of many doctoral programs. Informal writing groups for doctoral students may be one method of contributing to the improvement of scholarly writing. In this paper, we report on a writing group that was initiated by an experienced writer and higher degree research supervisor to support and improve her doctoral students’ writing capabilities. Over time, this group developed a workable model to suit their varying needs and circumstances. The model comprised group sessions, an email group, and individual writing. Here, we use a narrative approach to explore the effectiveness and value of our research writing group model in improving scholarly writing. The data consisted of doctoral students’ reflections to stimulus questions about their writing progress and experiences. The stimulus questions sought to probe individual concerns about their own writing, what they had learned in the research writing group, the benefits of the group, and the disadvantages and challenges to participation. These reflections were analysed using thematic analysis. Following this analysis, the supervisor provided her perspective on the key themes that emerged. Results revealed that, through the writing group, members learned technical elements (e.g., paragraph structure), non-technical elements (e.g., working within limited timeframes), conceptual elements (e.g., constructing a cohesive arguments), collaborative writing processes, and how to edit and respond to feedback. In addition to improved writing quality, other benefits were opportunities for shared writing experiences, peer support, and increased confidence and motivation. The writing group provides a unique social learning environment with opportunities for: professional dialogue about writing, peer learning and review, and developing a supportive peer network. Thus our research writing group has proved an effective avenue for building doctoral students’ capability in scholarly writing. The proposed model for a research writing group could be applicable to any context, regardless of the type and location of the university, university faculty, doctoral program structure, or number of postgraduate students. It could also be used within a group of students with diverse research abilities, needs, topics and methodologies. However, it requires a group facilitator with sufficient expertise in scholarly writing and experience in doctoral supervision who can both engage the group in planned writing activities and also capitalise on fruitful lines of discussion related to students’ concerns as they arise. The research writing group is not intended to replace traditional supervision processes nor existing training. However it has clear benefits for improving scholarly writing in doctoral research programs particularly in an era of rapidly increasing student load.

Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

In Pursuit of Excellence : A Policy Driven Systemic Initiative to Embed Gifted Education

Embedding gifted education practices requires major professional development strategies supported by transparent, credible and enforceable policy. This paper describes an analysis of a state-wide initiative involving the establishment of a series of schools tasked to develop and disseminate gifted education principles. The authors have been involved with this initiative at a number of levels over a ten-year period. Their involvement culminated in a commissioned review of the program. Extensive qualitative data were purposively collected from all stakeholders and the effectiveness of the initiative is examined from a theoretical framework of policy development and excellence. The findings summarised in this proposal, indicate the achievement of excellence at a systemic level was constrained by lack of vision, leadership and commitment to long term achievements of excellence. At a local level evidence exists that excellence can be manifested when there is synchronicity of vision, purpose, decisions, and actions.

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.

Gender equity in the professoriate : a cohort study of new women professors in Australia

According to statistics and trend data, women continue to be substantially under- represented in the Australian professoriate, and growth in their representation has been slow despite the plethora of equity programs. While not disputing these facts, we propose that examining gender equity by cohort provides a complementary perspective on the status of gender equity in the professoriate. Based on over 500 survey responses, we detected substantial similarities between women and men who were appointed as professors or associate professors between 2005 and 2008. There were similar proportions of women and men appointed via external or internal processes or by invitation. Additionally, similar proportions of women and men professors expressed a marked preference for research over teaching. Furthermore, there were similar distributions between the genders in the age of appointment to the professoriate. However, a notable gender difference was that women were appointed to the professoriate on average 1.9 years later than mens. This later appointment provides one reason for the lower representation of women compared to men in the professoriate. It also raises questions of the typical length of time that women and men remain in the (paid) professoriate and reasons why they might leave it. A further similarity between women and men in this cohort was their identification of motivation and circumstances as key factors in their career orientation. However, substantially more women identified motivation than circumstances and the situation was reversed for men. The open-ended survey responses also provided confirmation that affirmative action initiatives make a difference to women’s careers.

Students as decoders of graphics in mathematics

This paper reports on students’ ability to decode mathematical graphics. The findings were: (a) some items showed an insignificant improvement over time; (b) success involves identifying critical perceptual elements in the graphic and incorporating these elements into a solution strategy; and (c) the optimal strategy capitalises on how information is encoded in the graphic. Implications include a need for teachers to be proactive in supporting students’ to develop their graphical knowledge and an awareness that knowledge varies substantially across students.

Solving graphics tasks : gender differences in middle-school students

The capacity to solve tasks that contain high concentrations of visual-spatial information, including graphs, maps and diagrams, is becoming increasingly important in educational contexts as well as everyday life. This research examined gender differences in the performance of students solving graphics tasks from the Graphical Languages in Mathematics (GLIM) instrument that included number lines, graphs, maps and diagrams. The participants were 317 Australian students (169 males and 148 females) aged 9 to 12 years. Boys outperformed girls on graphical languages that required the interpretation of information represented on an axis and graphical languages that required movement between two- and three-dimensional representations (generally Map language).