Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Wellness education : an integrated theoretical framework for fostering transformative learning

Optimum Wellness involves the development, refinement and practice of lifestyle choices which resonate with personally meaningful frames of reference. Personal transformations are the means by which our frames of reference are refined across the lifespan. It is through critical reflection, supportive relationships and meaning making of our experiences that we construct and reconstruct our life paths. When individuals are able to be what they are destined to be or reach their higher purpose, then they are able to contribute to the world in positive and meaningful ways. Transformative education facilitates the changes in perspective that enable one to contemplate and travel a path in life that leads to self-actualisation. This thesis argues for an integrated theoretical framework for optimum Wellness Education. It establishes a learner centred approach to Wellness education in the form of an integrated instructional design framework derived from both Wellness and Transformative education constructs. Students’ approaches to learning and their study strategies in a Wellness education context serve to highlight convergences in the manner in which students can experience perspective transformation. As they learn to critically reflect, pursue relationships and adapt their frames of reference to sustain their pursuit of both learning and Wellness goals, strengthening the nexus between instrumental and transformative learning is a strategically important goal for educators. The aim of this exploratory research study was to examine those facets that serve to optimise the learning experiences of students in a Wellness course. This was accomplished through three research issues: 1) What are the relationships between Wellness, approaches to learning and academic success? 2) How are students approaching learning in an undergraduate Wellness subject? Why are students approaching their learning in the ways they do? 3) What sorts of transformations are students experiencing in their Wellness? How can transformative education be formulated in the context of an undergraduate Wellness subject? Subsequent to a thorough review of the literature pertaining to Wellness education, a mixed method embedded case study design was formulated to explore the research issues. This thesis examines the interrelationships between student, content and context in a one semester university undergraduate unit (a coherent set of learning activities which is assigned a unit code and a credit point value). The experiences of a cohort of 285 undergraduate students in a Wellness course formed the unit of study and seven individual students from a total of sixteen volunteers whose profiles could be constructed from complete data sets were selected for analysis as embedded cases. The introductory level course required participants to engage in a personal project involving a behaviour modification plan for a self-selected, single dimension of Wellness. Students were given access to the Standard Edition Testwell Survey to assess and report their Wellness as a part of their personal projects. To identify relationships among the constructs of Self-Regulated Learning (SRL), Wellness and Student Approaches to Learning (SAL) a blend of quantitative and qualitative methods to collect and analyse data was formulated. Surveys were the primary instruments for acquiring quantitative data. Sources included the Wellness data from Testwell surveys, SAL data from R-SPQ surveys, SRL data from MSLQ surveys and student self-evaluation data from an end of semester survey. Students’ final grades and GPA scores were used as indicators of academic performance. The sources of qualitative data included subject documentation, structured interview transcripts and open-ended responses to survey items. Subsequent to a pilot study in which survey reliability and validity were tested in context, amendments to processes for and instruments of data collection were made. Students who adopted meaning oriented (deep/achieving) approaches tended to assess their Wellness at a higher level, seek effective learning strategies and perform better in formal study. Posttest data in the main study revealed that there were significant positive statistical relationships between academic performance and total wellness scores (rs=.297, n=205, p<.01). Deep (rs=.343, n=137, p<.01) and achieving (rs=.286, n=123, p<.01) approaches to learning also significantly correlated with Wellness whilst surface approaches had negative correlations that were not significant. SRL strategies including metacognitive selfregulation, effort, help-seeking and critical thinking were increasingly correlated with Wellness. Qualitative findings suggest that while all students adopt similar patterns of day to day activities for example attending classes, taking notes, working on assignments the level of care with which these activities is undertaken varies considerably. The dominant motivational trigger for students in this cohort was the personal relevance and associated benefits of the material being learned and practiced. Students were inclined to set goals that had a positive impact on affect and used “sense of happiness” to evaluate their achievement status. Students who had a higher drive to succeed and/or understand tended to have or seek a wider range of strategies. Their goal orientations were generally learning rather than performance based and barriers presented a challenge which could be overcome as opposed to a blockage which prevented progress. Findings from an empirical analysis of the Testwell data suggest that a single third order Wellness construct exists. A revision of the instrument is necessary in order to juxtapose it with the chosen six dimensional Wellness model that forms the foundation construct in the course. Further, redevelopment should be sensitive to the Australian context and culture including choice of language, examples and scenarios used in item construction. This study concludes with an heuristic for use in Wellness education. Guided by principles of Transformative education theory and behaviour change theory, and informed by this representative case study the “CARING” heuristic is proposed as an instructional design tool for Wellness educators seeking to foster transformative learning. Based upon this study, recommendations were made for university educators to provide authentic and personal experiences in Wellness curricula. Emphasis must focus on involving students and teachers in a partnership for implementing Wellness programs both in the curriculum and co-curricularly. The implications of this research for practice are predicated on the willingness of academics to embrace transformative learning at a personal level and a professional one. To explore students’ profiles in detail is not practical however teaching students how to guide us in supporting them through the “pain” of learning is a skill which would benefit them and optimise the learning and teaching process. At a theoretical level, this research contributes to an ecological theory of Wellness education as transformational change. By signposting the wider contexts in which learning takes place, it seeks to encourage changing paradigms to ones which harness the energy of each successive contextual layer in which students live. Future research which amplifies the qualities of individuals and groups who are “Well” and seeks the refinement and development of instruments to measure Wellness constructs would be desirable for both theoretical and applied knowledge bases. Mixed method Wellness research derived and conducted by teams that incorporate expertise from multiple disciplines such as psychology, anthropology, education, and medicine would enable creative and multi-perspective programs of investigation to be designed and implemented. Congruences and inconsistencies in health promotion and education would provide valuable material for strengthening the nexus between transformational learning and behaviour change theories. Future development of and research on the effectiveness of the CARING heuristic would be valuable in advancing the understanding of pedagogies which advance rather than impede learning as a transformative process. Exploring pedagogical models that marry with transformative education may render solutions to the vexing challenge of teaching and learning in diverse contexts.

Learning in the global classroom : a guide for students in the multicultural university

This unique and fascinating book is written for tertiary level students in the multi-cultural classroom, whether studying abroad or at home alongside international students. It relates a genuine understanding of the student perspective of learning in a multi cultural classroom, highlighting how students possess different learning styles and attitudes to teaching and learning and demonstrating that students not only face language issues, but also numerous other unanticipated challenges.

Drawing together as inclusive practice in early years learning

Contemporary critiques on early years education highlight a call for the need to implement teaching and learning strategies that are less managing, that emerge from equity and inclusivity agendas, and that recognise diversity and plurality in early years learning contexts. Such critiques raise a need to reconsider the ways we engage as adults with children, and to rethink how we might review these relational subjectivities in respect to teaching and learning. This paper focuses on some aspects of a pilot research study into collaborative drawing in order to discuss ideas about socially inclusive early childhood pedagogies.

The power of educational podcasting : using short-format podcasts to reinforce tertiary student learning experiences in science

In 2007 I introduced short-format educational podcast resources that reinforced conceptual teaching and learning in an interdisciplinary tertiary science study area (biochemistry). This study aims to determine student attitudes to the perceived usefulness and benefit of short-format educational podcasts, and presents the findings (qualitative and quantitative) from surveys obtained from three offerings of the science teaching unit (2007, 2008 and 2009). Podcasts were recorded (MP3 audio files) separately from the instructive lecture sessions, and subsequent to the weekly lecture, short-format podcasts summarising the key learning objectives were integrated within the resources presented through the students learning management system (Blackboard). The vast majority (>88%) of students utilised the podcast resources, indicating a high level of acceptance and uptake for this portable educational technology. The respondents reported that podcasts focused their attention to core learning concepts and supported their understanding and learning of the lecture material. Furthermore, the data showed that respondents agreed strongly that podcasts assisted with study and revision for examinations and, somewhat surprisingly, there was a perception that podcasts positively impacted on examination performance. Overall, student users perceived that podcasting is as an effective and valuable educational tool that offers convenience and flexibility for their learning and understanding of a tertiary science study area, such as biochemistry.

Working in online groups-the challenges of virtually integrated learning environments

Universities continue to struggle with the need to combine the pedagogical benefits of collaborative learning with large scale, interactive and technologically sophisticated learning and teaching arrproaches and support systems. This challenge requires imaginative approaches if the outcome is not to the 'worst of both worlds' that results in confusion and disillusionism amongst students. This paper presents three case studies that use online technologies to provide collaborative teaching solutions arguably much superior to that possible without an online intervention.

Building organizational capability through a quality assurance program within a business school and encouraging organizational culture change

This study explores organizational capability and culture change through a project developing an assurance of learning program in a business school. In order to compete internationally for high quality faculty, students, strategic partnerships and research collaborations it is essential for Universities to develop and maintain an international focus and a quality produce that predicts excellence in the student experience and graduate outcomes that meet industry needs. Developing, marketing and delivering that quality product requires an organizational strategy to which all members of the organization contribute and adhere. Now, the ability to acquire, share and utilize knowledge has become a critical organizational capability in academia as well as other industries. Traditionally the functional approach to business school structures and disparate nature of the social networks and work contact limit the sharing of knowledge between academics working in different disciplines. In this project a community of practice program was established to include academics in the development of an embedded assurance of learning program affecting more than 5000 undergraduate students and 250 academics from nine different disciplines across four schools. The primary outcome from the fully developed and implemented assurance of learning program was the five year accreditation of the business schools programs by two international accrediting bodies, EQUIS and AACSB. However this study explores a different outcome, namely the change in organizational culture and individual capabilities as academics worked together in teaching and learning teams. This study uses a survey and interviews with academics involved, through a retrospective panel design which contained an experimental group and a control group. Results offer insights into communities of practice as a means of addressing organizational capability and changes in organizational culture. Knowledge management and shared learning can achieve strategic and operational benefits equally within academia as within other industrial enterprises but it comes at a cost. Traditional structures, academics that act like individual contractors and deep divides across research, teaching and service interest served a different master and required fewer resources. Collaborative structures; fewer master categories of discrete knowledge areas; specific strategic goals; greater links between academics and industry; and the means to share learned insights will require a different approach to resourcing both the individual and the team.

Children with special health care needs : social and learning competence in the early years

The number of children with special health care needs surviving infancy and attending school has been increasing. Due to their health status, these children may be at risk of low social-emotional and learning competencies (e.g., Lightfoot, Mukherjee, & Sloper, 2000; Zehnder, Landolt, Prchal, & Vollrath, 2006). Early social problems have been linked to low levels of academic achievement (Ladd, 2005), inappropriate behaviours at school (Shiu, 2001) and strained teacher-child relationships (Blumberg, Carle, O‘Connor, Moore, & Lippmann, 2008). Early learning difficulties have been associated with mental health problems (Maughan, Rowe, Loeber, & Stouthamer-Loeber, 2003), increased behaviour issues (Arnold, 1997), delinquency (Loeber & Dishion, 1983) and later academic failure (Epstein, 2008). Considering the importance of these areas, the limited research on special health care needs in social-emotional and learning domains is a factor driving this research. The purpose of the current research is to investigate social-emotional and learning competence in the early years for Australian children who have special health care needs. The data which informed this thesis was from Growing up in Australia: The Longitudinal Study of Australian Children. This is a national, longitudinal study being conducted by the Commonwealth Department of Families, Housing, Community Services and Indigenous Affairs. The study has a national representative sample, with data collection occurring biennially, in 2004 (Wave 1), 2006 (Wave 2) and 2008 (Wave 3). Growing up in Australia uses a cross-sequential research design involving two cohorts, an Infant Cohort (0-1 at recruitment) and a Kindergarten Cohort (4-5 at recruitment). This study uses the Kindergarten Cohort, for which there were 4,983 children at recruitment. Three studies were conducted to address the objectives of this thesis. Study 1 used Wave 1 data to identify and describe Australian children with special health care needs. Children who identified as having special health care needs through the special health care needs screener were selected. From this, descriptive analyses were run. The results indicate that boys, children with low birth weight and children from families with low levels of maternal education are likely to be in the population of children with special health care needs. Further, these children are likely to be using prescription medications, have poor general health and are likely to have specific condition diagnoses. Study 2 used Wave 1 data to examine differences between children with special health care needs and their peers in social-emotional competence and learning competence prior to school. Children identified by the special health care needs screener were chosen for the case group (n = 650). A matched case control group of peers (n = 650), matched on sex, cultural and linguistic diversity, family socioeconomic position and age, were the comparison group. Social-emotional competence was measured through Social/Emotional Domain scores taken from the Growing up in Australia Outcome Index, with learning competence measured through Learning Domain scores. Results suggest statistically significant differences in scores between the two groups. Children with special health care needs have lower levels of social-emotional and learning competence prior to school compared to their peers. Study 3 used Wave 1 and Wave 2 data to examine the relationship between special health care needs at Wave 1 and social-emotional competence and learning competence at Wave 2, as children started school. The sample for this study consisted of children in the Kindergarten Cohort who had teacher data at Wave 2. Results from multiple regression models indicate that special health care needs prior to school (Wave 1) significantly predicts social-emotional competence and learning competence in the early years of school (Wave 2). These results indicate that having special health care needs prior to school is a risk factor for the social-emotional and learning domains in the early years of school. The results from these studies give valuable insight into Australian children with special health care needs and their social-emotional and learning competence in the early years. The Australia population of children with special health care needs were primarily male children, from families with low maternal education, were likely to be of poor health and taking prescription medications. It was found that children with special health care needs were likely to have lower social-emotional competence and learning competence prior to school compared to their peers. Results indicate that special health care needs prior to school were predictive of lower social-emotional and learning competencies in the early years of school. More research is required into this unique population and their competencies over time. However, the current research provides valuable insight into an under researched 'at risk' population.

Indigenous mathematics : creating an equitable learning environment

This chapter examines how a change in school leadership can successfully address competencies in complex situations and thus create a positive learning environment in which Indigenous students can excel in their learning rather than accept a culture that inhibits school improvement. Mathematics has long been an area that has failed to assist Indigenous students in improving their learning outcomes, as it is a Eurocentric subject (Rothbaum, Weisz, Pott, Miyake & Morelli, 2000, De Plevitz, 2007) and does not contextualize pedagogy with Indigenous culture and perspectives (Matthews, Cooper & Baturo, 2007). The chapter explores the work of a team of Indigenous and non-Indigenous academics from the YuMi Deadly Centre who are turning the tide on improving Indigenous mathematical outcomes in schools and in communities with high numbers of Aboriginal and Torres Strait Islander students.

Ensuring student success : the role of support services in improving the quality of the student learning experience

This paper is based on the premise that universities have an obligation to provide adequate student support services, such as learning assistance (that is, assistance with academic writing and other study skills) and that in order to be effective such services must be responsive to the wider policy and social implications of student attrition and retention. The paper outlines briefly some of the factors that have influenced the development of learning assistance practices in Australia and America. This is followed by an account of experiences at one Australian metropolitan university where learning assistance service provision shifted from a decentralised, faculty-based model to a centralised model of service delivery. This shift was in response to concerns about lack of quality and consistency in a support model dependent upon faculty resources yet a follow up study identified other problems in the centralised delivery of learning assistance services. These problems, clustered under the heading contextualised versus decontextualised learning assistance, include the relevance of generic learning assistance services to students struggling with specific course related demands; the apparent tensions between challenging students and assisting students at risk of failure; and variations in the level of collaboration between learning advisers and academic staff in supporting students in the learning environment. These problems are analysed using the theoretical modelling derived from the tools made available through cultural historical activity theory and expansive visibilisation (Engeström & Miettinen, 1999).

Quality and efficacy of the Indigenous Tutorial Assistance Scheme (ITAS) for university students

Designed as a 'supplementary' tuition scheme, the Indigenous Tutorial Assistance Scheme (hereafter referred to as ITAS) is a strategic initiative of the National Indigenous Education Policy (DEET, 1989). This paper seeks to contribute to the literature of the analysis of the quality and efficacy of ITAS. Currently, the delivery of ITAS to Indigenous students requires enormous administration and commitment by the staff of Indigenous education support centres. In exploring the essential but problematic provision of ITAS to Indigenous university students, this paper provides insights into significant aspects of our program that move beyond assumptions of student deficit, by researching the quality of teaching and learning through ITAS, analysing administrative workload, and sharing innovations to our program as a result of participatory research with important ITAS stakeholders.

Implementing dance in a Queensland primary school : a descriptive case study

This research documents and analyses the modes of implementation of the Dance component of The Arts Essential Learnings in a Queensland school. The research identifies what makes good practice in dance education and the multiple modes of implementation that support this practice. The primary purpose of this research is to describe the factors that influence dance education, as it is delivered, in a Queensland primary school to inform the development of further support for primary teachers and to improve the quality of dance education in Prep -7 schooling. The literature review investigates dance education both in Queensland, Australia and internationally, identifying current issues related to the delivery of dance in a primary school environment including barriers to implementation of dance, authentic learning and integrated approaches to learning. Based on Engestrom.s reformulation of Vygotsky.s theory of socially mediated learning, the implementation of dance education curriculum was explored through descriptive case study method. The case study was conducted in a regional Queensland school identified as delivering the dance curriculum in a variety of ways. The research project provided opportunities to observe, document and analyse how teachers deal with pedagogical dilemmas and solve logistical problems associated with teaching the dance component of the Arts curriculum in this school. Teachers. practices were contextualised through investigation of the whole school context of dance curriculum development. The findings revealed a range of teaching approaches that influenced teachers. interpretation and children.s experience of the dance curriculum. The features of a supportive whole school and cultural environment for dance were identified. These have been captured in a reworked version of Engestrom.s Second Generation Activity Theory that can be applied to the implementation of dance education in primary schools.

Towards a transdisciplinary approach to integrating dance in a middle school curriculum

Within Queensland middle schools the implementation of an integrated curriculum has been challenging for many practitioners. In working to enhance dance learning in a Queensland middle school this research has focused on how dance can be integrated using a transdisciplinary approach. The research has investigated and reflected on the teaching and learning strategies used to integrate dance and has identified the key issues and challenges associated with the complex nature of an integrated curriculum in this context. Action research was used to review, plan for and implement integrated curriculum approaches and give insight into the external and internal challenges within the practice. This research has identified challenges associated with sustaining the integrity of dance as a subject area when integration requires designing curricula that go across key learning area boundaries. It has also revealed working within an integrated curriculum requires using common planning principles that focus on the students’ problem solving skills, making connections with the concepts, topics or ideas from the unit of work. The discussion of ways of working highlights a set of values, strategies or attributes a dance teacher can use while working within this middle school context. These include making collaborative partnerships and showing a willingness to work outside your area of expertise. For the school community, it outlines issues for attention and recommendations to assist in implementing dance while using a transdisciplinary approach. These recommended steps include embedding opportunities for teachers to partake in common planning, and time for professional development around transdisciplinary learning and Arts education.