Problem solving for the 21st century

Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one’s thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development.

Mathematical modelling in the early school years

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

Lighter than Tai

YEAR: 2008 ROLE: Performer FORMAT: Live Art Event at Tiananmen Square Beijing, China (3 hours) and Later on Summit of Mt. Tai Shan, Shandong Province, China (6 hrs + 3 hrs). WITH: Solo WHAT: In the Hall of Reverence on Tiananmen Square, Beijing Mao Zedong's body lies in state surrounded by flowers and draped with a Red Flag of Communist China. His casket with a glass top lies on a black stone from Mt. Tai, reflecting the quotation from Sima Qian (China's Han Dynasty historian) that "One's life can be weightier than Mt. Tai or lighter than a goose feather". This pair of performances were a quiet, personal reflection upon what such a once revolutionary expression might mean in today's very different time and place. The work was conceived during the Olympic Cultural Festival showing of Intimate Transactions (www.intimatetransactions.com) - during the tumultuous times leading up to China's proudly staged August 2008 Olympics. The rise and rise of China had long been generating major geopolitical, ecological and cross-cultural shifts throughout the region and beyond. In this dramatic epicentre of change and at a time of such great national pride, how might we each act in ways that are ecologically 'mighty' and yet simultaneously have an impact lighter than a goosefeather? This is both a question for China in its relations with the autonomous provinces and the environment as it is for all of us in our own 'local' affairs. However ecologically speaking all that is of local concern is of global concern and noone can therefore be exempt from the need to sustain that which we share in common and must all protect for the future. Performance 1: Tiananmen Square, Beijing: Dropping 100 goose feathers. Performance 2: The summit of Mt Tai, Shandong Province. Building a mountain from Goose Feathers. SHOWING HISTORY: 1: Anniversary of Protest Crackdown, Jun 8th 2008. 2: Dawn on Tai Shan's summit, 15th June, 2008 DETAILS: Performance 1: Begin an hour after dawn (5.45am) in Tiananmen Square Bring pre-prepared performance shirt, a bag of goose feathers tipped with red. Begin at the "Gate of Heavenly Peace" under the image of Chairman Mao. Circumnavigate the world's largest open and the most surveilled public space 5 times dropping feathers periodically. Meditate on Forces of Change. Finally enter Chairman Mao's mausoleum with the masses and move quietly past his preserved body. End the performance at the Gate of Heavenly Peace 3 hours later. Performance 2: Walk up Mt. Tai Shan in silence meditating on Forces of Change (6 hours). Stay overnight on the summit. Begin an hour before dawn (3.45am) in silence. Bring performance shirt, a sack of goose feathers and a simple wooden structure. On the sunrise viewing side of the mountain build a miniature, fragile 'mountain' in goose feathers and sticks on the edge of a sheer precipice. Watch the sun rise as the feathers blow away into the valley deep below (3 hours).

MiLK. Mobile Learning Kit

The Mobile Learning Kit is a new digital learning application that allows students and teachers to compose, publish, discuss and evaluate their own mobile learning games and events. The research field was interaction design in the context of mobile learning. The research methodology was primarily design-based supported by collaboration between participating disciplines of game design, education and information technology. As such, the resulting MiLK application is a synthesis of current pedagogical models and experimental interaction design techniques and technologies. MiLK is a dynamic learning resource for incorporating both formal and informal teaching and learning practices while exploiting mobile phones and contemporary digital social tools in innovative ways. MiLK explicitly addresses other predominant themes in educational scholarship that relate to current education innovation and reform such as personalised learning, life-long learning and new learning spaces. The success of this project is indicated through rigorous trials and actual uptake of MiLK by international participants in Australia, UK, US and South Africa. MiLK was awarded for excellence in the use of emerging technologies for improved learning and teaching as a finalist (top 3) in the Handheld Learning and Innovation Awards in the UK in 2008. MiLK was awarded funding from the Australasian CRC for Interaction Design in 2008 to prepare the MiLK application for development. MiLK has been awarded over $230,000 from ACID since 2006. The resulting application and research materials are now being commercialised by a new company, ‘ACID Services’.

Enhancing learning in dance technique through on-line-mediated reflective practice

‘Practice makes perfect’ expresses the common misconception that repetitive practice without appropriate feed-back will deliver improvement in tasks being practised. This paper explores the implementation of a student-driven feed-back mechanism and shows how functional and aesthetic understanding can be progressively enhanced through reflective practice. More efficient practice of clearly understood tasks will enhance dance training outcomes. We were looking for ways to improve teaching efficiency, effectiveness of the students’ practice in the studio and application of safe dance practices. We devised a web-based on-line format, ‘Performing Reflective Practice’, designed to augment and refine studio practice. Only perfect practice makes perfect!

From Sydney and Shanghai : Australian and Chinese women writing modernism

In the 1930s and 1940s, Australian women writers published novels, poems, and short stories that pushed the boundaries of their national literary culture. From their position in the Pacific, they entered into a dialogue with a European modernism that they reworked to invigorate their own writing and to make cross-continental connections. My interest in the work of Australian women prose writers of this period stems from an appreciation of the extent of their engagement with interwar modernism (an engagement that is generally under-acknowledged) and the realization that there are commonalities of approach with the ways in which contemporaneous Chinese authors negotiated this transnational cultural traffic. China and Australia, it has been argued, share an imaginative and literal association of many centuries, and this psychic history produces a situation in which ‘Australians feel drawn towards China: they cannot leave it alone.’1 Equally, Chinese exploration of the great southern land began in the fifteenth century, prior to European contact. In recent times, the intensity of Australia’s cultural and commercial connections with Asia has led to a repositioning of the Australian sense of regionalism in general and, in particular, has activated yet another stage in the history of its relationship with China. In this context, the association of Australian and Chinese writing is instructive because the commonalities of approach and areas of interest between certain authors indicate that Australian writers were not alone in either the content or style of their response to European modernism. This recognition, in turn, advances discussions of modernism in Australia and reveals an alternative way of looking at the world from the Pacific Rim through literature. The intent is to examine selective Australian and Chinese authors who are part of this continuous history and whose writing demonstrates common thematic and stylistic features via the vector of modernism. I focus on the 1930s and 1940s because these are the decades in which Australia and China experienced wideranging conflict in the Pacific, and it is significant that war, both forthcoming and actual, features as an ominous soundtrack in the writing of Chinese and Australian women. I argue that, given the immensity of cultural difference between Australia and China, there is an especially interesting juncture in the ways in which the authors interrogate modernist practices and the challenge of modernism. The process in which writing from the Pacific Rim jointly negotiates the twin desires of engaging with European literary form and representing one’s own culture may be seen as what Jessica Berman identifies as a geomodernism, one of the ‘new possible geographies’ of modernism.2 My discussion centres on the work of the Australian women, to which the Chinese material serves as a point of reference, albeit a critical one. The Chinese writing examined here is restricted to authors who wrote at least some material in English and whose work is available in translation.

Teachers and the emotional dimensions of class in resource-affected rural Australia

In recent years, a 'cultural turn' in the study of class has resulted in a rich body of work detailing the ways in which class advantage and disadvantage are emotionally inscribed and embodied in educational settings. To date, however, much of this literature has focused on the urban sphere. In order to address this gap in the literature, this paper focuses on the affective evaluations made by teachers employed in rural and remote Australian schools of students' families, bodies, expectations and practices. The central argument is that moral ascriptions of class by the teachers are powerfully shaped by dominant socio-cultural constructions of rurality that equate 'the rural' with agriculture.

Theoretical critique of the work of art : co-producers in research

The ways in which the "traditional" tension between words and artwork can be perceived has huge implications for understanding the relationship between critical or theoretical interpretation, art and practice, and research. Within the practice-led PhD this can generate a strange sense of disjuncture for the artist-researcher particularly when engaged in writing the exegesis. This paper aims to explore this tension through an introductory investigation of the work of the philosopher Andrew Benjamin. For Benjamin criticism completes the work of art. Criticism is, with the artwork, at the centre of our experience and theoretical understanding of art – in this way the work of art and criticism are co-productive. The reality of this co-productivity can be seen in three related articles on the work of American painter Marcia Hafif. In each of these articles there are critical negotiations of just how the work of art operates as art and theoretically, within the field of art. This focus has important ramifications for the writing and reading of the exegesis within the practice-led research higher degree. By including art as a significant part of the research reporting process the artist-researcher is also staking a claim as to the critical value of their work. Rather than resisting the tension between word and artwork the practice-led artist-researcher need to embrace the co-productive nature of critical word and creative work to more completely articulate their practice and its significance as research. The ideal venue and opportunity for this is the exegesis.

Disrupting the new orthodoxy : emergency intervention and Indigenous social policy

This article develops a critical analysis of the ideological framework that informed the Australian Federal government’s 2007 intervention into Northern Territory Indigenous communities (ostensibly to address the problem of child sexual abuse). Continued by recently elected Prime Minister, Kevin Rudd, the NT ‘emergency response’ has aroused considerable public debate and scholarly inquiry. In addressing what amounts to a broad bi-partisan approach to Indigenous issues we highlight the way in which Indigenous communities are problematised and therefore subject to interventionist regimes that override differentiated Indigenous voices and intensify an internalised sense of rage occasioned by disempowering interventionist projects. We further argue that in rushing through the emergency legislation and suspending parts of the Racial Discrimination Act, the Howard and Rudd governments have in various ways perpetuated racialised and neo-colonial forms of intervention that override the rights of Indigenous people. Such policy approaches require critical understanding on the part of professions involved most directly in community practice, particularly when it comes to mounting effective opposition campaigns. The article offers a contribution to this end.

Rejoinder to James Hamilton

Hamilton (2001) makes a number of comments on our paper (Harding and Pagan, 2002b). The objectives of this rejoinder are, firstly, to note the areas in which we agree; secondly, to define with greater clarity the areas in which we disagree; and, thirdly, to point to other papers, including a longer version of this response, where we have dealt with some of the issues that he raises. The core of our debate with him is whether one should use an algorithm with a specified set of rules for determining the turning points in economic activity or whether one should use a parametric model that features latent states. Hamilton begins his criticism by stating that there is a philosophical distinction between the two methods for dating cycles and concludes that the method we use “leaves vague and intuitive exactly what this algorithm is intended to measure”. Nothing is further from the truth. When seeking ways to decide on whether a turning point has occurred it is always useful to ask the question, what is a recession? Common usage suggests that it is a decline in the level of economic activity that lasts for some time. For this reason it has become standard to describe a recession as a decline in GDP that lasts for more than two quarters. Finding periods in which quarterly GDP declined for two periods is exactly what our approach does. What is vague about this?

Employee work motivation and discretionary work effort

The focus of this thesis is discretionary work effort, that is, work effort that is voluntary, is above and beyond what is minimally required or normally expected to avoid reprimand or dismissal, and is organisationally functional. Discretionary work effort is an important construct because it is known to affect individual performance as well as organisational efficiency and effectiveness. To optimise organisational performance and ensure their long term competitiveness and sustainability, firms need to be able to induce their employees to work at or near their peak level. To work at or near their peak level, individuals must be willing to supply discretionary work effort. Thus, managers need to understand the determinants of discretionary work effort. Nonetheless, despite many years of scholarly investigation across multiple disciplines, considerable debate still exists concerning why some individuals supply only minimal work effort whilst others expend effort well above and beyond what is minimally required of them (Le. they supply discretionary work effort). Even though it is well recognised that discretionary work effort is important for promoting organisational performance and effectiveness, many authors claim that too little is being done by managers to increase the discretionary work effort of their employees. In this research, I have adopted a multi-disciplinary approach towards investigating the role of monetary and non-monetary work environment characteristics in determining discretionary work effort. My central research questions were "What non-monetary work environment characteristics do employees perceive as perks (perquisites) and irks (irksome work environment characteristics)?" and "How do perks, irks and monetary rewards relate to an employee's level of discretionary work effort?" My research took a unique approach in addressing these research questions. By bringing together the economics and organisational behaviour (OB) literatures, I identified problems with the current definition and conceptualisations of the discretionary work effort construct. I then developed and empirically tested a more concise and theoretically-based definition and conceptualisation of this construct. In doing so, I disaggregated discretionary work effort to include three facets - time, intensity and direction - and empirically assessed if different classes of work environment characteristics have a differential pattern of relationships with these facets. This analysis involved a new application of a multi-disciplinary framework of human behaviour as a tool for classifying work environment characteristics and the facets of discretionary work effort. To test my model of discretionary work effort, I used a public sector context in which there has been limited systematic empirical research into work motivation. The program of research undertaken involved three separate but interrelated studies using mixed methods. Data on perks, irks, monetary rewards and discretionary work effort were gathered from employees in 12 organisations in the local government sector in Western Australia. Non-monetary work environment characteristics that should be associated with discretionary work effort were initially identified through a review of the literature. Then, a qualitative study explored what work behaviours public sector employees perceive as discretionary and what perks and irks were associated with high and low levels of discretionary work effort. Next, a quantitative study developed measures of these perks and irks. A Q-sorttype procedure and exploratory factor analysis were used to develop the perks and irks measures. Finally, a second quantitative study tested the relationships amongst perks, irks, monetary rewards and discretionary work effort. Confirmatory factor analysis was firstly used to confirm the factor structure of the measurement models. Correlation analysis, regression analysis and effect-size correlation analysis were used to test the hypothesised relationships in the proposed model of discretionary work effort. The findings confirmed five hypothesised non-monetary work environment characteristics as common perks and two of three hypothesised non-monetary work environment characteristics as common irks. Importantly, they showed that perks, irks and monetary rewards are differentially related to the different facets of discretionary work effort. The convergent and discriminant validities of the perks and irks constructs as well as the time, intensity and direction facets of discretionary work effort were generally confirmed by the research findings. This research advances the literature in several ways: (i) it draws on the Economics and OB literatures to redefine and reconceptualise the discretionary work effort construct to provide greater definitional clarity and a more complete conceptualisation of this important construct; (ii) it builds on prior research to create a more comprehensive set of perks and irks for which measures are developed; (iii) it develops and empirically tests a new motivational model of discretionary work effort that enhances our understanding of the nature and functioning of perks and irks and advances our ability to predict discretionary work effort; and (iv) it fills a substantial gap in the literature on public sector work motivation by revealing what work behaviours public sector employees perceive as discretionary and what work environment characteristics are associated with their supply of discretionary work effort. Importantly, by disaggregating discretionary work effort this research provides greater detail on how perks, irks and monetary rewards are related to the different facets of discretionary work effort. Thus, from a theoretical perspective this research also demonstrates the conceptual meaningfulness and empirical utility of investigating the different facets of discretionary work effort separately. From a practical perspective, identifying work environment factors that are associated with discretionary work effort enhances managers' capacity to tap this valuable resource. This research indicates that to maximise the potential of their human resources, managers need to address perks, irks and monetary rewards. It suggests three different mechanisms through which managers might influence discretionary work effort and points to the importance of training for both managers and non-managers in cultivating positive interpersonal relationships.

Reading the environment : narrative constructions of ecological subjectivities in Australian children's literature

Ways in which humans engage with the environment have always provided a rich source of material for writers and illustrators of Australian children's literature. Currently, readers are confronted with a multiplicity of complex, competing and/or complementing networks of ideas, theories and emotions that provide narratives about human engagement with the environment at a particular historical moment. This study, entitled Reading the Environment: Narrative Constructions of Ecological Subjectivities in Australian Children's Literature, examines how a representative sample of Australian texts (19 picture books and 4 novels for children and young adults published between 1995 and 2006) constructs fictional ecological subjects in the texts, and offers readers ecological subject positions inscribed with contemporary environmental ideologies. The conceptual framework developed in this study identifies three ideologically grounded positions that humans may assume when engaging with the environment. None of these positions clearly exists independently of any other, nor are they internally homogeneous. Nevertheless they can be categorised as: (i) human dominion over the environment with little regard for environmental degradation (unrestrained anthropocentrism); (ii) human consideration for the environment driven by understandings that humans need the environment to survive (restrained anthropocentrism); and (iii) human deference towards the environment guided by understandings that humans are no more important than the environment (ecocentrism). iv The transdisciplinary methodological approach to textual analysis used in this thesis draws on ecocriticism, narrative theories, visual semiotics, ecofeminism and postcolonialism to discuss the difficulties and contradictions in the construction of the positions offered. Each chapter of textual analysis focuses on the construction of subjectivities in relation to one of the positions identified in the conceptual framework. Chapter 5 is concerned with how texts highlight the negative consequences of human dominion over the environment, or, in the words of this study, living with ecocatastrophe. Chapter 6 examines representations of restrained anthropocentrism in its contemporary form, that is, sustainability. Chapter 7 examines representations of ecocentrism, a radical position with inherent difficulties of representation. According to the analysis undertaken, the focus texts convey the subtleties and complexities of human engagement with the environment and advocate ways of viewing and responding to contemporary unease about the environment. The study concludes that these ways of viewing and responding conform to and/or challenge dominant socio-cultural and political-economic opinions regarding the environment. This study, the first extended work of its kind, makes an original contribution to ecocritical study of Australian children's literature. By undertaking a comprehensive analysis of how texts for children represent human engagement with the environment at a time when important environmental concerns pose significant threats to human existence, I hope to contribute new knowledge to an area of children's literature research that to date has been significantly under-represented.

How can we exploit mobile data to customise learning based on a student’s environmental surroundings?

User-Based intelligent systems are already commonplace in a student’s online digital life. Each time they browse, search, buy, join, comment, play, travel, upload, download, a system collects, analyses and processes data in an effort to customise content and further improve services. This panel session will explore how intelligent systems, particularly those that gather data from mobile devices, can offer new possibilities to assist in the delivery of customised, personal and engaging learning experiences. The value of intelligent systems for education lies in their ability to formulate authentic and complex learner profiles that bring together and systematically integrate a student’s personal world with a formal curriculum framework. As we well know, a mobile device can collect data relating to a student’s interests (gathered from search history, applications and communications), location, surroundings and proximity to others (GPS, Bluetooth). However, what has been less explored is the opportunity for a mobile device to map the movements and activities of a student from moment to moment and over time. This longitudinal data provides a holistic profile of a student, their state and surroundings. Analysing this data may allow us to identify patterns that reveal a student’s learning processes; when and where they work best and for how long. Through revealing a student’s state and surroundings outside of schools hour, this longitudinal data may also highlight opportunities to transform a student’s everyday world into an inventory for learning, punctuating their surroundings with learning recommendations. This would in turn lead to new ways to acknowledge and validate and foster informal learning, making it legitimate within a formal curriculum.

Alternate reality games and education innovation

An Alternate Reality Game (ARG) is a unique experience that blurs the edges between our everyday lives and imagined game worlds. Players are invited to interact with each other and fictional characters using familiar tools such as emails, websites, telephones, and sometimes newspapers, radio and television. ARGs come in all shapes and sizes, tell a variety of different stories and inspire all kinds of interactions between people, their networks and the very streets in which they live. Some ARGs simply immerse you in fictional scenarios and indulge you in quirky challenges. While others reveal hidden histories of a city and teach us about important political causes. But the most exciting thing about ARGs is that they have the potential to inspire participants to imagine their everyday tools and places as resources for their own creative endeavors. Deb Polson will be presenting some of the most inspiring ARGs of recent years and revealing some of the design techniques that were used to create them. Most significantly Deb will discuss ways in which educators can imagine using ARGs as rich teaching tools that inspire collaborative learning and motivate students to engage in all kinds of subject matter.

The rate-limiting mechanism for the heterogeneous burning of cylindrical iron rods

This paper presents the findings of an investigation into the rate-limiting mechanism for the heterogeneous burning in oxygen under normal gravity and microgravity of cylindrical iron rods. The original objective of the work was to determine why the observed melting rate for burning 3.2-mm diameter iron rods is significantly higher in microgravity than in normal gravity. This work, however, also provided fundamental insight into the rate-limiting mechanism for heterogeneous burning. The paper includes a summary of normal-gravity and microgravity experimental results, heat transfer analysis and post-test microanalysis of quenched samples. These results are then used to show that heat transfer across the solid/liquid interface is the rate-limiting mechanism for melting and burning, limited by the interfacial surface area between the molten drop and solid rod. In normal gravity, the work improves the understanding of trends reported during standard flammability testing for metallic materials, such as variations in melting rates between test specimens with the same cross-sectional area but different crosssectional shape. The work also provides insight into the effects of configuration and orientation, leading to an improved application of standard test results in the design of oxygen system components. For microgravity applications, the work enables the development of improved methods for lower cost metallic material flammability testing programs. In these ways, the work provides fundamental insight into the heterogeneous burning process and contributes to improved fire safety for oxygen systems in applications involving both normal-gravity and microgravity environments.