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]

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.

The ability of economic thinking : the “nature��� versus “nurture” debate

In their studies, Eley and Meyer (2004) and Meyer and Cleary (1998) found that there are sources of variation in the affective and process dimensions of learning in mathematics and clinical diagnosis specific to each of these disciplines. Meyer and Shanahan (2002) argue that: General purpose models of student learning that are transportable across different discipline contexts cannot, by definition, be sensitive to sources of variation that may be subject-specific (2002. p. 204). In other words, to explain the differences in learning approaches and outcomes in a particular discipline, there are discipline-specific factors, which cannot be uncovered in general educational research. Meyer and Shanahan (2002) argue for a need to "seek additional sources of variation that are perhaps conceptually unique ... within the discourse of particular disciplines" (p. 204). In this paper, the development of an economics-specific construct (called economic thinking ability) is reported. The construct aims to measure discipline-sited ability of students that has important influence on learning in economics. Using this construct, economic thinking abilities of introductory and intermediate level economics students were measured prior to the commencement, and at the end, of their study over one semester. This enabled factors associated with students' pre-course economic thinking ability and their development in economic thinking ability to be investigated. The empirical findings will address the 'nature' versus 'nurture' debate in economics education (Frank, et aI., 1993; Frey et al., 1993; Haucap and Tobias 2003). The implications for future research in economics education will also be discussed.

From the cathedral to the classroom : the emergence of new discourses on religious education

In 2009, Religious Education is a designated key learning area in Catholic schools in the Archdiocese of Brisbane and, indeed, across Australia. Over the years, though, different conceptualisations of the nature and purpose of religious education have led to the construction of different approaches to the classroom teaching of religion. By investigating the development of religious education policy in the Archdiocese of Brisbane from 1984 to 2003, the study seeks to trace the emergence of new discourses on religious education. The study understands religious education to refer to a lifelong process that occurs through a variety of forms (Moran, 1989). In Catholic schools, it refers both to co-curricula activities, such as retreats and school liturgies, and the classroom teaching of religion. It is the policy framework for the classroom teaching of religion that this study explores. The research was undertaken using a policy case study approach to gain a detailed understanding of how new conceptualisations of religious education emerged at a particular site of policy production, in this case, the Archdiocese of Brisbane. The study draws upon Yeatman’s (1998) description of policy as occurring “when social actors think about what they are doing and why in relation to different and alternative possible futures” (p. 19) and views policy as consisting of more than texts themselves. Policy texts result from struggles over meaning (Taylor, 2004) in which specific discourses are mobilised to support particular views. The study has a particular interest in the analysis of Brisbane religious education policy texts, the discursive practices that surrounded them, and the contexts in which they arose. Policy texts are conceptualised in the study as representing “temporary settlements” (Gale, 1999). Such settlements are asymmetrical, temporary and dependent on context: asymmetrical in that dominant actors are favoured; temporary because dominant actors are always under challenge by other actors in the policy arena; and context - dependent because new situations require new settlements. To investigate the official policy documents, the study used Critical Discourse Analysis (hereafter referred to as CDA) as a research tool that affords the opportunity for researchers to map and chart the emergence of new discourses within the policy arena. As developed by Fairclough (2001), CDA is a three-dimensional application of critical analysis to language. In the Brisbane religious education arena, policy texts formed a genre chain (Fairclough, 2004; Taylor, 2004) which was a focus of the study. There are two features of texts that form genre chains: texts are systematically linked to one another; and, systematic relations of recontextualisation exist between the texts. Fairclough’s (2005) concepts of “imaginary space” and “frameworks for action” (p. 65) within the policy arena were applied to the Brisbane policy arena to investigate the relationship between policy statements and subsequent guidelines documents. Five key findings emerged from the study. First, application of CDA to policy documents revealed that a fundamental reconceptualisation of the nature and purpose of classroom religious education in Catholic schools occurred in the Brisbane policy arena over the last twenty-five years. Second, a disjuncture existed between catechetical discourses that continued to shape religious education policy statements, and educational discourses that increasingly shaped guidelines documents. Third, recontextualisation between policy documents was evident and dependent on the particular context in which religious education occurred. Fourth, at subsequent links in the chain, actors created their own “imaginary space”, thereby altering orders of discourse within the policy arena, with different actors being either foregrounded or marginalised. Fifth, intertextuality was more evident in the later links in the genre chain (i.e. 1994 policy statement and 1997 guidelines document) than in earlier documents. On the basis of the findings of the study, six recommendations are made. First, the institutional Church should carefully consider the contribution that the Catholic school can make to the overall pastoral mission of the diocese in twenty-first century Australia. Second, policymakers should articulate a nuanced understanding of the relationship between catechesis and education with regard to the religion classroom. Third, there should be greater awareness of the connections among policies relating to Catholic schools – especially the connection between enrolment policy and religious education policy. Fourth, there should be greater consistency between policy documents. Fifth, policy documents should be helpful for those to whom they are directed (i.e. Catholic schools, teachers). Sixth, “imaginary space” (Fairclough, 2005) in policy documents needs to be constructed in a way that allows for multiple “frameworks for action” (Fairclough, 2005) through recontextualisation. The findings of this study are significant in a number of ways. For religious educators, the study highlights the need to develop a shared understanding of the nature and purpose of classroom religious education. It argues that this understanding must take into account the multifaith nature of Australian society and the changing social composition of Catholic schools themselves. Greater recognition should be given to the contribution that religious studies courses such as Study of Religion make to the overall religious development of a person. In view of the social composition of Catholic schools, there is also an issue of ecclesiological significance concerning the conceptualisation of the relationship between the institutional Catholic Church and Catholic schools. Finally, the study is of significance because of its application of CDA to religious education policy documents. Use of CDA reveals the foregrounding, marginalising, or excluding of various actors in the policy arena.

Personal epistemology in pre-service teachers : belief changes throughout a teacher education course

Classrooms of the 21st century are complex systems. They support diverse learners from varied contexts and function in a “messy” bricolage of policy contexts. This complexity is also evident in the nature of teaching and learning deployed in these classrooms. There is also, in current contexts, a general expectation that teachers will support students to construct, rather than simply receive knowledge. This process of constructing knowledge requires a focus on critical thinking in complex social and real world contexts (see also Elen & Clarebout, 2001; Yang, Chang & Hsu 2008). Critical thinking, which involves the identification and evaluation of multiple perspectives when making decisions, is a process of knowing – a tool of wisdom (Kuhn & Udell, 2001). Schommer-Aikens, Bird and Bakken (2010) refer to classrooms that encourage critical thinking as “epistemologically based” in which “the teacher encourages his/her students to look for connections among concepts within the text, with their prior knowledge, and with concepts found in the world beyond themselves” (p. 48).

Pre-service teacher education and the development of middle school teacher identity : an exploratory study

This research study investigated the factors that influenced the development of teacher identity in a small cohort of mature-aged graduate pre-service teachers over the course of a one-year Graduate Diploma program (Middle Years). It sought to illuminate the social and relational dynamics of these pre-service teachers’ experiences as they began new ways of being and learning during a newly introduced one-year Graduate Diploma program. A relational-ontological perspective underpinned the relational-cultural framework that was applied in a workshop program as an integral part of this research. A relational-ontological perspective suggests that the development of teacher identity is to be construed more as an ontological process than an epistemological one. Its focus is more on questions surrounding the person and their ‘becoming’ a teacher than about the knowledge they have or will come to have. Hence, drawing on work by researchers such as Alsup (2006), Gilligan, (1982), Isaacs, (2007), Miller (1976), Noddings, (2005), Stout (2001), and Taylor, (1989), teacher identity was defined as an individual pre-service teacher’s unique sense of self as a teacher that included his or her beliefs about teaching and learning (Alsup, 2006; Stout, 2001; Walkington, 2005). Case-study was the preferred methodology within which this research project was framed, and narrative research was used as a method to document the way teacher identity was shaped and negotiated in discursive environments such as teacher education programs, prior experiences, classroom settings and the practicum. The data that was collected included student narratives, student email written reflections, and focus group dialogue. The narrative approach applied in this research context provided the depth of data needed to understand the nature of the mature-aged pre-service teachers’ emerging teacher identities and experiences in the graduate diploma program. Findings indicated that most of the mature-aged graduate pre-service teachers came in to the one-year graduate diploma program with a strong sense of personal and professional selves and well-established reasons why they had chosen to teach Middle Years. Their choice of program involved an expectation of support and welcome to a middle-school community and culture. Two critical issues that emerged from the pre-service teachers’ narratives were the importance they placed on the human support including the affirmation of themselves and their emerging teacher identities. Evidence from this study suggests that the lack of recognition of preservice teachers’ personal and professional selves during the graduate diploma program inhibited the development of a positive middle-school teacher identity. However, a workshop program developed for the participants in this research and addressing a range of practical concerns to beginning teachers offered them a space where they felt both a sense of belonging to a community and where their thoughts and beliefs were recognized and valued. Thus, the workshops provided participants with the positive social and relational dynamics necessary to support them in their developing teacher identities. The overall findings of this research study strongly indicate a need for a relational support structure based on a relational-ontological perspective to be built into the overall course structure of Graduate Pre-service Diplomas in Education to support the development of teacher identity. Such a support structure acknowledges that the pre-service teacher’s learning and formation is socially embedded, relational, and a continual, lifelong process.

A life jacket with holes- : a case study of 'temporary engagement' : a strategy used by Education Queensland to employ beginning secondary teachers

This research investigated the impact of Education Queensland's employment policy and practices for beginning secondary teachers appointed on temporary engagement. The context was the public secondary school sector within the state of Queensland, Australia. The study was set within a context of the changing nature of work from full-time permanent employment towards casual, fixed-term contracts, temporary and part-time employment, a trend reflected in the employment patterns for teachers within Australia. Two broad categories of literature relating to the research problem of this thesis were reviewed, namely the beginning teacher and permanency or tenure. The focus in the research literature on beginning teachers was the professional experiences of teachers within the classroom and school. There was a paucity of research that considered the working and industrial conditions of temporary employment for beginning teachers or the personal and professional implications of this form of employment. The review of the context and literature was conceptualised as a Beginning Temporary Teacher Theoretical Framework which served to inform the study. Using a qualitative case study methodology, the research techniques employed for the thesis were semi-structured interview and document analysis. A simultaneously conducted research project in which the researcher participated entitled 'Winning the Lottery? Beginning Teachers on Temporary Engagement' foregrounded this thesis in terms of refining the research question, contributing to the literature and in the selection of the participants. For this case study the perspectives of four distinct yet inter-related categories of professionals were sought. These included four beginning secondary teachers, three school administrators, a Senior Personnel Officer with Education Queensland, and a representative from the Queensland Teachers' Union. The research findings indicated that none of the beginning teachers or other professionals viewed starting a career in teaching on temporary engagement as the ideal. The negative features identified were the differential treatment received and the high level of uncertainty associated with temporary employment. Differential treatment tended to indicate 'less' entitlements, in terms of access to induction and professional development, recreational and sick leave, acceptance by and expectations of other colleagues, and avenues of redress in grievance cases. Moreover, interviews indicated a high level of uncertainty in terms of starting within the teaching profession, commencing at a new school, and a regular income. In addition, frequent changes in schools and/or cohorts of students exacerbated levels of uncertainty. The beginning teachers reported significantly decreased motivation, self-esteem and sense of belonging, and increased stress levels. There was an even more marked negative impact on those beginning teachers who had experienced a higher number of temporary engagements and schools in their first year of teaching. Conversely, strong staff support and a reasonable length of time in the one school improved the quality of the beginning teachers' experiences. The overall impact of being on temporary engagement resulted in delayed permanent position appointments, decreased commitment to particular schools and to Education Queensland as the employing authority, and for two of the beginning teachers, it produced a desire to seek alternative employment. The implementation of Education Queensland's policies relating to working conditions and entitlements for these temporary beginning teachers at the school level was revealed to be less than satisfactory. There was a tendency towards 'just-in- time' management of the beginning teacher on temporary engagement. The beginning teachers received 'less-than-messages' about access to and use of departmental documentation, support through induction and professional development, and their transition from temporary to permanent employment. To ensure a more systematic, supportive and inclusive process for managing the temporary beginning teacher, a conceptual framework entitled 'Continuums of Tension' was developed. The four continuums included permanent employment - temporary employment; system perspective - individual perspective; teaching as a profession - teaching as a job; and the permanent beginning teacher - university graduate. The general principles of the human resource policies of Education Queensland were based on a commitment to permanent employment, a system's perspective, viewing teaching as a profession and a homogeneous group of permanent beginning teachers. Contrasting with this, the beginning teacher on temporary engagement tended to operate from the position of temporary employment and a perspective that was individually based. Their priorities therefore included the 'occupational' aspects of being a temporary teacher striving to become permanent. Thus there existed a tension or contradiction between the general principles of human resource policies within Education Queensland and the employment experiences of beginning teachers on temporary engagement. The study proposed three actions for resolution to address the aforementioned tensions. The actions included: (a) the effective provision and targeted communication of information; (b) support, induction and professional development; and (c) a coordinated approach between Education Queensland, Queensland Teachers' Union, the Universities and the beginning teacher. These actions are fm1her refined to include: (a) an induction kit to suppm1 the individual through the pre-employment to permanent employee phases, (b) an extrapolation of the roles and responsibilities of Education Queensland personnel charged with supporting the beginning temporary teacher, and (c) a series of recommendations to effect a coordinated approach amongst the key stakeholders. The theoretical and conceptual frameworks have provided a means of addressing the identified needs of the beginning teacher on temporary engagement. As such, this study has contributed to the research literature on teacher employment and professionalism and aims to provide a beginning temporary teacher with managed professional and occupational support.

Publishing Engineering Education Resources: A Collaborative Web Project.

Web is a powerful hypermedia-based information retrieval mechanism that provides a user-friendly access across all major computer platforms connected over Internet. This paper demonstrates the application of Web technology when used as an educational delivery tool. It also reports on the development of a prototype electronic publishing project where Web technology was used to deliver power engineering educational resources. The resulting hyperbook will contain diverse teaching resources such as hypermedia-based modular educational units and computer simulation programs that are linked in a meaningful and structured way. The use of Web for disseminating information of this nature has many advantages that cannot possibly be achieved otherwise. PREAMBLE The continual increase of low-cost functionality available in desktop computing has opened up a new possibility in learning within a wider educational framework. This technology also is supported by enhanced features offered by new and ...

Journalism education dilemmas : career-focussed skill set, teamwork or critical thinking?

In Australian universities, journalism educators usually come to the academy from the journalism profession and consequently place a high priority on leading students to develop a career-focussed skill set. The changing nature of the technological, political and economic environments and the professional destinations of journalism graduates place demands on journalism curricula and educators alike. The profession is diverse, such that the better description is of many ‘journalisms’ rather than one ‘journalism’ with consequential pressures being placed on curricula to extend beyond the traditional skill set, where practical ‘writing’ and ‘editing’ skills dominate, to the incorporation of critical theory and the social construction of knowledge. A parallel set of challenges faces academic staff operating in a higher education environment where change is the only constant and research takes precedent over curriculum development. In this paper, three educators at separate universities report on their attempts to implement curriculum change to imbue graduates with better skills and attributes such as enhanced team work, problem solving and critical thinking, to operate in the divergent environment of 21st century journalism. The paper uses narrative case study to illustrate the different approaches. Data collected from formal university student evaluations inform the narratives along with rich but less formal qualitative data including anecdotal student comments and student reflective assessment presentations. Comparison of the three approaches illustrates the dilemmas academic staff face when teaching in disciplines that are impacted by rapid changes in technology requiring new pedagogical approaches. Recommendations for future directions are considered against the background or learning purpose.

‘Universities are not the safe places we would like to think they are, but they are getting safer’: Indigenous women academics in higher education

This paper outlines some of the experiences of Indigenous women academics in higher education. The author offers these experiences, not to position Indigenous women academics as victims, but to expose the problematic nature of racism, systemic marginalisation, white race privilege and radicalised subjectivity played out within Australian higher education institutions. By utilising the experiences and examples she seeks to bring the theoretical into the everyday world of being Indigenous within academe. In analysing these examples, the author reveals the relationships between oppression, white race privilege, institutional privilege and the epistemology that maintains them. She argues that, in moving from a position of being silent to speaking about what she has witnessed and experienced, she is able to move from the position of object to subject and gain a form of liberated voice (hooks 1989: 9) for herself and other Indigenous women. She seeks to challenge the practices within universities that continue to subjugate Indigenous women academics.

The role of nature-based experiences in the development and maintenance of wellness

Wellness is now seen as central to redefining the National Health agenda. There is growing evidence that contact with nature and physical activity in nature has considerable positive effects on human health. At the most basic level humanity is reliant on the natural world for resources such as air and water. However, a growing body of research is finding that beyond this fundamental relationship exposure to the non-human natural world can also positively enhance perceptions of physiological, emotional, psychological and spiritual health in ways that cannot be satisfied by alternate means. Theoretical explanations for this have posited that non-human nature might 1) restore mental fatigue, 2) trigger deep reflections, 3) provide an opportunity for nurturing and 4) rekindle innate connections. In this paper the authors show how human wellness is strongly connected to their relationship with the natural world. This paper points to how non-human nature could be better utilised for enhancing human health and wellness.

The nature of pedagogic teacher-student interactions : a phenomenographic study

Globally, teaching has become more complex and more challenging over recent years, with new and increased demands being placed on teachers by students, their families, governments and wider society. Teachers work with more diverse communities in times characterised by volatility, uncertainty and moral ambiguity. Societal, political, economic and cultural shifts have transformed the contexts in which teachers work and have redefined the ways in which teachers interact with students. This qualitative study uses phenomenographic methods to explore the nature of pedagogic teacherstudent interactions. The data analysis reveals five qualitatively different ways in which teachers experience pedagogic engagements with students. The resultant categories of description ranged from information providing, with teachers viewed as transmitters of a body of knowledge through to mentoring in which teachers were perceived as significant others in the lives of students with their influence extending beyond the walls of the classroom and beyond the years of schooling. The paper concludes by arguing that if teachers are to prepare students for the challenges and opportunities in changing times, teacher education programs need to consider ways to facilitate the development of mentoring capacities in new teachers.

Preservice teachers’ memories of their secondary science education experiences

Understanding preservice teachers’ memories of their education may aid towards articulating high-impact teaching practices. This study describes 246 preservice teachers’ perceptions of their secondary science education experiences through a questionnaire and 28-item survey. ANOVA was statistically significant about participants’ memories of science with 15 of the 28 survey items. Descriptive statistics through SPSS further showed that a teacher’s enthusiastic nature (87%) and positive attitude towards science (87%) were regarded as highly memorable. In addition, explaining abstract concepts well (79%), and guiding the students’ conceptual development with practical science activities (73%) may be considered as memorable secondary science teaching strategies. Implementing science lessons with one or more of these memorable science teaching practices may “make a difference” towards influencing high school students’ positive long-term memories about science and their science education. Further research in other key learning areas may provide a clearer picture of high-impact teaching and a way to enhance pedagogical practices.

Colin Marsh (2008) Becoming a Teacher: Knowledge, Skills and Issues. 4th edition, Frenchs Forrest: Pearson Education Australia, 460 pages

Becoming a Teacher is structured in five very readable sections. The introductory section addresses the nature of teaching and the importance of developing a sense of purpose for teaching in a 21st century classroom. It also introduces some key concepts that are explored throughout the volume according to the particular chapter focus of each part. For example, the chapters in Part 2 explore aspects of student learning and the learning environment and focus on how students develop and learn, learner motivation, developing self esteem and learning environments. The concepts developed in this section, such as human development, stages of learning, motivation, and self-concept are contextualised in terms of theories of cognitive development and theories of social, emotional and moral development. The author, Colin Marsh, draws on his extensive experience as an educator to structure the narrative of chapters in this part via checklists for observation, summary tables, sample strategies for teaching at specific stages of student development, and questions under the heading ‘your turn’. Case studies such as ‘How I use Piaget in my teaching’ make that essential link between theory and practice, something which pre-service teachers struggle with in the early phases of their university course. I was pleased to see that Marsh also explores the contentious and debated aspects of these theoretical frameworks to demonstrate that pre-service teachers must engage with and critique the ways in which theories about teaching and learning are applied. Marsh weaves in key quotations and important references into each chapter’s narrative and concludes every chapter with summary comments, reflection activities, lists of important references and useful web sources. As one would expect of a book published in 2008, Becoming a Teacher is informed by the most recent reports of classroom practice, current policy initiatives and research.