Surveying theories and philosophies of mathematics education

Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions: (1) What is reality? Or what is the nature of the world around us? (2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and, (3) How can we be certain in the “truth” of what we know? [the epistemological question]

Politicizing mathematics education : has politics gone too far? Or not far enough?

In this chapter we tackle increasingly sensitive questions in mathematics education, those that have polarized the community into distinct schools of thought as well as impacted reform efforts.

Evaluation of contextual influences on the medication administration practice of paediatric nurses

Aim. This paper is a report of a study conducted to explore the impact of preidentified contextual themes (related to work environment and socialization) on nursing medication practice. Background. Medication administration is a complex aspect of paediatric nursing and an important component of day-to-day nursing practice. Many attempts are being made to improve patient safety, but many errors remain. Identifying and understanding factors that influence medication administration errors are of utmost importance. Method. A cross-sectional survey was conducted with a sample of 278 paediatric nurses from the emergency department, intensive care unit and medical and surgical wards of an Australian tertiary paediatric hospital in 2004. The response rate was 67%. Result. Contextual influences were important in determining how closely medication policy was followed. Completed questionnaires were returned by 185 nurses (67%). Younger nurses aged <34 years thought that their medication administration practice could be influenced by the person with whom they checked the drugs (P = 0·001), and that there were daily circumstances when it was acceptable not to adhere strictly to medication policy (P < 0·001), including choosing between following policy and acting in the best interests of the child (P = 0·002). Senior nurses agreed that senior staff dictate acceptable levels of medication policy adherence through role modelling (P = 0·01). Less experienced nurses reported greater confidence with computer literacy (P < 0·001). Conclusions. Organizations need to employ multidisciplinary education programmes to promote universal understanding of, and adherence to, medication policies. Skill mix should be closely monitored to ensure adequate support for new and junior staff.

The educational affordances of generative media in arts education

Network Jamming systems provide real-time collaborative media performance experiences for novice or inexperienced users. In this paper we will outline the theoretical and developmental drivers for our Network Jamming software, called jam2jam. jam2jam employs generative algorithmic techniques with particular implications for accessibility and learning. We will describe how theories of engagement have directed the design and development of jam2jam and show how iterative testing cycles in numerous international sites have informed the evolution of the system and its educational potential. Generative media systems present an opportunity for users to leverage computational systems to make sense of complex media forms through interactive and collaborative experiences. Generative music and art are a relatively new phenomenon that use procedural invention as a creative technique to produce music and visual media. These kinds of systems present a range of affordances that can facilitate new kinds of relationships with music and media performance and production. Early systems have demonstrated the potential to provide access to collaborative ensemble experiences to users with little formal musical or artistic expertise.This presentation examines the educational affordances of these systems evidenced by field data drawn from the Network Jamming Project. These generative performance systems enable access to a unique kind of music/media’ ensemble performance with very little musical/ media knowledge or skill and they further offer the possibility of unique interactive relationships with artists and creative knowledge through collaborative performance. Through the process of observing, documenting and analysing young people interacting with the generative media software jam2jam a theory of meaningful engagement has emerged from the need to describe and codify how users experience creative engagement with music/media performance and the locations of meaning. In this research we observed that the musical metaphors and practices of ‘ensemble’ or collaborative performance and improvisation as a creative process for experienced musicians can be made available to novice users. The relational meanings of these musical practices afford access to high level personal, social and cultural experiences. Within the creative process of collaborative improvisation lie a series of modes of creative engagement that move from appreciation through exploration, selection, direction toward embodiment. The expressive sounds and visions made in real-time by improvisers collaborating are immediate and compelling. Generative media systems let novices access these experiences with simple interfaces that allow them to make highly professional and expressive sonic and visual content simply by using gestures and being attentive and perceptive to their collaborators. These kinds of experiences present the potential for highly complex expressive interactions with sound and media as a performance. Evidence that has emerged from this research suggest that collaborative performance with generative media is transformative and meaningful. In this presentation we draw out these ideas around an emerging theory of meaningful engagement that has evolved from the development of network jamming software. Primarily we focus on demonstrating how these experiences might lead to understandings that may be of educational and social benefit.

Perceptions of aging across 26 cultures and their culture-level associates

College students (N = 3,435) in 26 cultures reported their perceptions of age-related changes in physical, cognitive, and socioemotional areas of functioning and rated societal views of aging within their culture. There was widespread cross-cultural consensus regarding the expected direction of aging trajectories with (1) perceived declines in societal views of aging, physical attractiveness, the ability to perform everyday tasks, and new learning, (2) perceived increases in wisdom, knowledge, and received respect, and (3) perceived stability in family authority and life satisfaction. Cross-cultural variations in aging perceptions were associated with culture-level indicators of population aging, education levels, values, and national character stereotypes. These associations were stronger for societal views on aging and perceptions of socioemotional changes than for perceptions of physical and cognitive changes. A consideration of culture-level variables also suggested that previously reported differences in aging perceptions between Asian and Western countries may be related to differences in population structure.

A problem-posing intervention in the development of problem-solving competence of underachieving, middle-year students

This study reported on the issues surrounding the acquisition of problem-solving competence of middle-year students who had been ascertained as above average in intelligence, but underachieving in problem-solving competence. In particular, it looked at the possible links between problem-posing skills development and improvements in problem-solving competence. A cohort of Year 7 students at a private, non-denominational, co-educational school was chosen as participants for the study, as they undertook a series of problem-posing sessions each week throughout a school term. The lessons were facilitated by the researcher in the students’ school setting. Two criteria were chosen to identify participants for this study. Firstly, each participant scored above the 60th percentile in the standardized Middle Years Ability Test (MYAT) (Australian Council for Educational Research, 2005) and secondly, the participants all scored below the cohort average for Criterion B (Problem-solving Criterion) in their school mathematics tests during the first semester of Year 7. Two mutually exclusive groups of participants were investigated with one constituting the Comparison Group and the other constituting the Intervention Group. The Comparison Group was chosen from a Year 7 cohort for whom no problem-posing intervention had occurred, while the Intervention Group was chosen from the Year 7 cohort of the following year. This second group received the problem-posing intervention in the form of a teaching experiment. That is, the Comparison Group were only pre-tested and post-tested, while the Intervention Group was involved in the teaching experiment and received the pre-testing and post-testing at the same time of the year, but in the following year, when the Comparison Group have moved on to the secondary part of the school. The groups were chosen from consecutive Year 7 cohorts to avoid cross-contamination of the data. A constructionist framework was adopted for this study that allowed the researcher to gain an “authentic understanding” of the changes that occurred in the development of problem-solving competence of the participants in the context of a classroom setting (Richardson, 1999). Qualitative and quantitative data were collected through a combination of methods including researcher observation and journal writing, video taping, student workbooks, informal student interviews, student surveys, and pre-testing and post-testing. This combination of methods was required to increase the validity of the study’s findings through triangulation of the data. The study findings showed that participation in problem-posing activities can facilitate the re-engagement of disengaged, middle-year mathematics students. In addition, participation in these activities can result in improved problem-solving competence and associated developmental learning changes. Some of the changes that were evident as a result of this study included improvements in self-regulation, increased integration of prior knowledge with new knowledge and increased and contextualised socialisation.

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.

A constraints-led perspective to understanding skill acquisition and game play: A basis for integration of motor learning theory and physical education praxis?

Background: In order to design appropriate environments for performance and learning of movement skills, physical educators need a sound theoretical model of the learner and of processes of learning. In physical education, this type of modelling informs the organization of learning environments and effective and efficient use of practice time. An emerging theoretical framework in motor learning, relevant to physical education, advocates a constraints-led perspective for acquisition of movement skills and game play knowledge. This framework shows how physical educators could use task, performer and environmental constraints to channel acquisition of movement skills and decision making behaviours in learners. From this viewpoint, learners generate specific movement solutions to satisfy the unique combination of constraints imposed on them, a process which can be harnessed during physical education lessons. Purpose: In this paper the aim is to provide an overview of the motor learning approach emanating from the constraints-led perspective, and examine how it can substantiate a platform for a new pedagogical framework in physical education: nonlinear pedagogy. We aim to demonstrate that it is only through theoretically valid and objective empirical work of an applied nature that a conceptually sound nonlinear pedagogy model can continue to evolve and support research in physical education. We present some important implications for designing practices in games lessons, showing how a constraints-led perspective on motor learning could assist physical educators in understanding how to structure learning experiences for learners at different stages, with specific focus on understanding the design of games teaching programmes in physical education, using exemplars from Rugby Union and Cricket. Findings: Research evidence from recent studies examining movement models demonstrates that physical education teachers need a strong understanding of sport performance so that task constraints can be manipulated so that information-movement couplings are maintained in a learning environment that is representative of real performance situations. Physical educators should also understand that movement variability may not necessarily be detrimental to learning and could be an important phenomenon prior to the acquisition of a stable and functional movement pattern. We highlight how the nonlinear pedagogical approach is student-centred and empowers individuals to become active learners via a more hands-off approach to learning. Summary: A constraints-based perspective has the potential to provide physical educators with a framework for understanding how performer, task and environmental constraints shape each individual‟s physical education. Understanding the underlying neurobiological processes present in a constraints-led perspective to skill acquisition and game play can raise awareness of physical educators that teaching is a dynamic 'art' interwoven with the 'science' of motor learning theories.

ePortfolio use by university students in Australia : Developing a sustainable community of practice

This report documents Stage Two of the Australian ePortfolio Project (AeP2), to specifically explore the current scope of national and international ePortfolio communities of practice in order to identify the factors that have contributed to their success and sustainability. The study has built on Stage One of the Australian ePortfolio Project (Hallam, Harper, McCowan, Hauville, McAllister, & Creagh, 2008), which outlined the broad range of issues and challenges, as well as significant opportunities, that faced the higher education sector in terms of ePortfolio practice, to determine how the emergent community of ePortfolio researchers and practitioners in Australia might be advanced. ---------- The overarching aims of this project were to focus on building the Australian community of practice through an online forum and further symposium activities. Through the research activities the project sought to generate the following major outcomes: develop a forum within the ALTC Exchange to support an ePortfolio community of practice; develop strategies to encourage interest in and engagement with community of practice activities; develop and promote resources to support the diverse stakeholders in ePortfolio practice; collaborate in the establishment of a cross-sector ePortfolio community of practice; host a second Australian ePortfolio Symposium (AeP2) to disseminate the findings from the Australian ePortfolio Project, to explore innovative practice in ePortfolio use in higher education, to articulate policy developments, and to stimulate discussion on international ePortfolio issues; host an associated trade display as a forum for strengthening the higher education sector’s understanding of the features and functionality of ePortfolio platforms; develop resources to support an ePortfolio symposium model that may be adopted for future events. ----------- The project activities encompassed a survey of stakeholders, a program of semi-structured interviews with community managers and a series of case studies depicting successful ePortfolio communities. The survey of ePortfolio practitioners sought to determine the potential value of an ePortfolio CoP, the preferred focus for and the desired features of such a community, as well as the options for the technical and social architecture of an online forum. Through the semi-structured interviews it was possible to examine current examples of CoP activity, to identify the critical success factors and the challenges faced by individual ePortfolio CoPs, so that the attributes of good practice could be presented. The data collected in the interviews contributed to the development of 14 case studies, which have been beneficial in illustrating the diverse nature of CoPs in Australia and overseas.----------- The report presents a rich picture of national and international ePortfolio communities of practice, with an examination of the factors that have contributed to their success and sustainability.

Resistance : re-imagining innovation in higher education teaching and learning

The call to innovate is ubiquitous across the Australian educational policy context. The claims of innovative practices and environments that occur frequently in university mission statements, strategic plans and marketing literature suggest that this exhortation to innovate appears to have been taken up enthusiastically by the university sector. Throughout the history of universities, a range of reported deficiencies of higher education have worked to produce a notion of crisis. At present, it would seem that innovation is positioned as the solution to the notion of crisis. This thesis is an inquiry into how the insistence on innovation works to both enable and constrain teaching and learning practices in Australian universities. Alongside the interplay between innovation and crisis is the link between resistance and innovation, a link which remains largely unproblematized in the scholarly literature. This thesis works to locate and unsettle understandings of a relationship between innovation and Australian higher education. The aim of this inquiry is to generate new understandings of what counts as innovation within this context and how innovation is enacted. The thesis draws on a number of postmodernist theorists, whose works have informed firstly the research method, and then the analysis and findings. Firstly, there is an assumption that power is capillary and works through discourse to enact power relations which shape certain truths (Foucault, 1990). Secondly, this research scrutinised language practices which frame the capacity for individuals to act, alongside the language practices which encourage an individual to adopt certain attitudes and actions as one’s own (Foucault, 1988). Thirdly, innovation talk is read in this thesis as an example of needs talk, that is, as a medium through which what is considered domestic, political or economic is made and contested (Fraser, 1989). Fourthly, relationships between and within discourses were identified and analysed beyond cause and effect descriptions, and more productively considered to be in a constant state of becoming (Deleuze, 1987). Finally, the use of ironic research methods assisted in producing alternate configurations of innovation talk which are useful and new (Rorty, 1989). The theoretical assumptions which underpin this thesis inform a document analysis methodology, used to examine how certain texts work to shape the ways in which innovation is constructed. The data consisted of three Federal higher education funding policies selected on the rationale that these documents, as opposed to state or locally based policy and legislation, represent the only shared policy context for all Australian universities. The analysis first provided a modernist reading of the three documents, and this was followed by postmodernist readings of these same policy documents. The modernist reading worked to locate and describe the current truths about innovation. The historical context in which the policy was produced as well as the textual features of the document itself were important to this reading. In the first modernist reading, the binaries involved in producing proper and improper notions of innovation were described and analysed. In the process of the modernist analysis and the subsequent location of binary organisation, a number of conceptual collisions were identified, and these sites of struggle were revisited, through the application of a postmodernist reading. By applying the theories of Rorty (1989) and Fraser (1989) it became possible to not treat these sites as contradictory and requiring resolution, but rather as spaces in which binary tensions are necessary and productive. This postmodernist reading constructed new spaces for refusing and resisting dominant discourses of innovation which value only certain kinds of teaching and learning practices. By exploring a number of ironic language practices found within the policies, this thesis proposes an alternative way of thinking about what counts as innovation and how it happens. The new readings of innovation made possible through the work of this thesis were in response to a suite of enduring, inter-related questions – what counts as innovation?, who or what supports innovation?, how does innovation occur?, and who are the innovators?. The truths presented in response to these questions were treated as the language practices which constitute a dominant discourse of innovation talk. The collisions that occur within these truths were the contested sites which were of most interest for the analysis. The thesis concludes by presenting a theoretical blueprint which works to shift the boundaries of what counts as innovation and how it happens in a manner which is productive, inclusive and powerful. This blueprint forms the foundation upon which a number of recommendations are made for both my own professional practice and broader contexts. In keeping with the conceptual tone of this study, these recommendations are a suite of new questions which focus attention on the boundaries of innovation talk as an attempt to re-configure what is valued about teaching and learning at university.