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]

Thai students' engagement with cooperative learning in mathematics classrooms

Over the past decade, Thai schools have been encouraged by the Thai Ministry of Education to introduce more student-centred pedagogies such as cooperative learning into their classrooms (Carter, 2006). However, prior research has indicated that the implementation of cooperative learning into Thai schools has been confounded by cultural traditions endemic within Thai schools (Deveney, 2005). The purpose of the study was to investigate how 32 Grade 3 and 32 Grade 4 students enrolled in a Thai school engaged with cooperative learning in mathematics classrooms after they had been taught cooperative learning strategies and skills. These strategies and skills were derived from a conceptual framework that was the outcome of an analysis and synthesis of social learning, behaviourist and socio-cognitive theories found in the research literature. The intervention began with a two week program during which the students were introduced to and engaged in practicing a set of cooperative learning strategies and skills (3 times a week). Then during the next four weeks (3 times a week), these cooperative learning strategies and skills were applied in the contexts of two units of mathematics lessons. A survey of student attitudes with respect to their engagement in cooperative learning was conducted at the conclusion of the six-week intervention. The results from the analysis of the survey data were triangulated with the results derived from the analysis of data from classroom observations and teacher interviews. The analysis of data identified four complementary processes that need to be considered by Thai teachers attempting to implement cooperative learning into their mathematics classrooms. The paper concludes with a set of criteria derived from the results of the study to guide Thai teachers intending to implement cooperative learning strategies and skills in their classrooms.

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.

Bridging the gap between tertiary education and work : a model of situated learning in accountancy

In professions such as teaching, health sciences (medicine, nursing, allied health), and built environment (engineering), significant work-based learning through practica is an essential element before graduation. However, there is no such requirement in Accountancy. This thesis reports the findings of a qualitative case study of the development and implementation of a Workplace Learning Experience Program in Accountancy at the Queensland University of Technology (QUT) in Australia. The case study of this intervention, based on sociocultural learning theory, provides the grounds for the development of a new model of teaching and learning for accounting education. The survey and interview-based study documents the responses of two cohorts of university students and a group of employers to a work placement program. The study demonstrates that a 100 hour work placement in Accountancy has elements that enhance student learning. It demonstrates the potential value of the application of sociocultural theories of learning, especially the concept of situated learning involving legitimate peripheral participation (Lave & Wenger, 1991). This research establishes the theoretical base for a paradigm shift for the Accountancy profession to acknowledge work placements prior to graduation as a major element of learning. It is argued that the current model of accounting education requires reform to better align university and workplace learning.

Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

Using developmental theories to inform the design of technology for children

Electronic Blocks are a new programming environment, designed specifically for children aged between three and eight years. As such, the design of the Electronic Block environment is firmly based on principles of developmentally appropriate practices in early childhood education. The Electronic Blocks are physical, stackable blocks that include sensor blocks, action blocks and logic blocks. Evaluation of the Electronic Blocks with both preschool and primary school children shows that the blocks' ease of use and power of engagement have created a compelling tool for the introduction of meaningful technology education in an early childhood setting. The key to the effectiveness of the Electronic Blocks lies in an adherence to theories of development and learning throughout the Electronic Blocks design process.

Cognitive load and assembly tasks : effect of instructional formats on learning assembly procedures

The study investigated the effect on learning of four different instructional formats used to teach assembly procedures. Cognitive load and spatial information processing theories were used to generate the instructional material. The first group received a physical model to study, the second an isometric drawing, the third an isometric drawing plus a model and the fourth an orthographic drawing. Forty secondary school students were presented with the four different instructional formats and subsequently tested on an assembly task. The findings indicated that there may be evidence to argue that the model format which only required encoding of an already constructed three dimensional representation, caused less extraneous cognitive load compared to the isometric and the orthographic formats. No significant difference was found between the model and the isometric-plus-model formats on all measures because 80% of the students in the isometric-plus-model format chose to use the model format only. The model format also did not differ significantly from other groups in total time taken to complete the assembly, in number of correctly assembled pieces and in time spent on studying the tasks. However, the model group had significantly more correctly completed models and required fewer extra looks than the other groups.

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.

“More tick-the-box”: the challenge of promoting interdisciplinary learning in the middle years through the Australian history curriculum

The Australian Curriculum marks national reforms in social science education, first with the return to the disciplines of history and geography and second, through a new approach to interdisciplinary learning. This paper raises the question of whether the promise of interdisciplinary learning can be realised in the middle years of schooling if teachers have to teach history as a discipline rather than within an over-arching integrated curriculum framework. The paper explores the national blueprints and considers the national history curriculum in light of theories of teachers’ knowledge and middle school education. Evidence from teacher interviews indicates that historical understanding can be achieved through integrated frameworks to meet the goals of middle schooling.

Communications and learning structures that facilitate transfer of knowledge at innovation transition points

Innovation processes are rarely smooth and disruptions often occur at transition points were one knowledge domain passes the technology on to another domain. At these transition points communication is a key component in assisting the smooth hand over of technologies. However for smooth transitions to occur we argue that appropriate structures have to be in place and boundary spanning activities need to be facilitated. This paper presents three case studies of innovation processes and the findings support the view that structures and boundary spanning are essential for smooth transitions. We have explained the need to pass primary responsibility between agents to successfully bring an innovation to market. We have also shown the need to combine knowledge through effective communication so that absorptive capacity is built in process throughout the organisation rather than in one or two key individuals.

Pragmatics, perceptions and strategies in Chinese college English learning

This study investigated Chinese College English students. perceptions of pragmatics, their pragmatic competence in selected speech acts, strategies they employed in acquiring pragmatic knowledge, as well as their general approach to learning English as a foreign language. The research was triggered by a national curriculum initiative that prioritizes the need for College English students to enhance their ability to use English effectively in different social interactions (Chinese College English Education and Supervisory Committee, 2007). The traditional "grammar-translation" and "examination-oriented" method is believed to have reduced Chinese College English students to what is dubbed "mute" and "deaf" language learners (Zhang, 2008; Zhao, 2009). Many students lack pragmatic knowledge on how to interpret discourse by relating utterances to their meanings, understanding the intention of language users, and how language is used in specific settings (Bachman & Palmer, 1996, 2010). There is an increasing body of literature on awareness-raising of the importance of pragmatic knowledge and strategies for classroom instruction. However, to date, researchers have tended to focus largely on the teaching of pragmatics, rather than on how students acquire pragmatic competence (Bardovi-Harlig & Dornyei, 1998; Du, 2004; Hou, 2007; Ruan, 2007; Schauer, 2009). It is this gap in the research that this study fills, with a focus on different types of pragmatic knowledge, learner perceptions of such knowledge, and learning strategies that College English students employ in the process of learning English in general, and pragmatics in particular. Three strands of theories of second language acquisition (Ellis, 1985, 1994): pragmatics (Levinson, 1983; Mey, 2001; Yule, 1996), intercultural communications (Kramsch, 1998; Samovar & Porter, 1997; Samovar, Porter & McDaniel, 2009) and English as a lingua franca (ELF) (Canagarajah, 2006; Firth, 1996; Pennycook, 2010) were employed to establish a conceptual framework for data collection and analyses. Key constructs derived from the three related theories helped to form a typology for a detailed examination and theorization of the empirical evidence gathered from different sources. Four research instruments: a questionnaire (N=237), Discourse Completion Tasks (DCTs) (N=55), focus group interviews (N=18), and a textbook tasks analysis were employed to collect data for this systematic inquiry. Data collected by different instruments were analyzed and compared by way of a triangulation to enhance its validity and reliability. Major findings derived from different sources highlighted that, although College English students were grammatically advanced language learners, they displayed limited pragmatic knowledge and a highly restricted repertoire of language learning strategies. The majority of the respondents, however, believed that pragmatic knowledge was as important as linguistic knowledge in the process of developing communicative competence for interaction in different contexts. It was argued that a combination of a less than sufficient English proficiency, limited knowledge of pragmatics, inadequate language materials and tasks, and a small stock of language learning strategies, were a major hindrance to effective learning and communication, resulting in pragmatic failures in many intercultural communication situations. As the first systematic study of how Chinese College English students learned pragmatics, the research provided a solid empirical base for developing a tentative model for the learning of pragmatics in a College English classroom in China and similar educational contexts. The model was strengthened by a unique combination of theories of pragmatics, intercultural communication and ELF. Findings from this research provided insights into how Chinese College English students perceived pragmatics in the English as foreign language (EFL) curriculum, the processes of learning, as well as strategies they utilized in developing linguistic and pragmatic knowledge and competence.

Preservice teachers’ views : Issues for learning to teach SOSE in an overcrowded curriculum

A cohort of third-year preservice teachers (n=24) was given the opportunity to observe and participate in Studies of Society and Environment (SOSE) in primary classrooms through a series of school visits during a semester-long unit. These visits were designed to give preservice teachers opportunities to connect SOSE teaching theories studied in the university setting to SOSE teaching practices within schools. This study investigates the extent of the preservice teachers’ opportunities to observe SOSE teaching in the primary school. Responses from a survey showed that the majority of preservice teachers only agreed with 6 of the 25 items associated with the six categories (personal-professional skill development, system requirements, teaching practices, student behavior, feedback to students, and reflection on practice). Written responses from the questionnaire concurred that most had not experienced SOSE teaching. Various issues are discussed around providing preservice teachers with SOSE teaching experiences. School executives, teachers and university staff need to be part of the process to ensure preservice teachers are receiving quality SOSE teaching experiences that will assist in their pedagogical development. A wider question is also raised through this paper. If preservice teachers are unable to experience quality SOSE teaching in school visits designed for such a purpose, does this signal a changing emphasis in education that leaves the social sciences and humanities off the education agenda?

"More tick-the-box": the challenge of promoting interdisciplinary learning in the middle years through the Australian history curriculum

The Australian Curriculum marks national reforms in social science education, first with the return to the disciplines of history and geography and second, through a new approach to interdisciplinary learning. This paper raises the question of whether the promise of interdisciplinary learning can be realised in the middle years of schooling if teachers have to teach history as a discipline rather than within an over-arching integrated curriculum framework. The paper explores the national blueprints and considers the national history curriculum in light of theories of teachers’ knowledge and middle school education. Evidence from teacher interviews indicates that historical understanding can be achieved through integrated frameworks to meet the goals of middle schooling.

Professional development using informal learning networks : an empirical study in Australia’s digital content industry

Informal learning networks play a key role in the skill and professional development of professionals working in micro-businesses within Australia’s digital content industry as they do not necessarily have access to a learning and development or a human resources section that can assist in mapping their learning pathway. Professionals working in this environment would typically adopt an informal learning approach to their skill and professional development by utilising their social and business networks. The overall aim of this PhD research project is to study how these professionals manage their skill and professional development, and to explore what role informal learning networks play in this professional learning context. This paper will describe the theme of the research project and how it fits with previous research and other relevant studies. Secondly, it will present the study’s research focus, and the research questions. It will also present relevant theories and perspectives, and the methods for empirical data collection. Data collection will be through three distinct phases using a mixed methods research design: an online survey, interviews, and case studies. It should be noted the findings presented in this paper offer some early results of the research project.

Embedding graphic organisers in the teaching and learning of family and consumer sciences (home economics) in Kuwait

Educational reforms currently being enacted in Kuwaiti Family and Consumer Sciences (FCS) in response to contemporary demands for increased student-centred teaching and learning are challenging for FCS teachers due to their limited experience with student-centred learning tools such as Graphic Organisers (GOs). To adopt these reforms, Kuwaiti teachers require a better understanding of and competency in promoting cognitive learning processes that will maximise student-centred learning approaches. This study followed the experiences of four Grade 6 FCS Kuwaiti teachers as they undertook a Professional Development (PD) program specifically designed to advance their understanding of the use of GOs and then as they implemented what they had learned in their Grade 6 FCS classroom. The PD program developed for this study was informed by Nasseh.s competency PD model as well as Piaget and Ausubel.s cognitive theories. This model enabled an assessment and evaluation of the development of the teachers. competencies as an outcome of the PD program in terms of the adoption of GOs, in particular, and their capacity to use GOs to engage students in personalised, in-depth, learning through critical thinking and understanding. The research revealed that the PD program was influential in reforming the teachers. learning, understanding of and competency in, cognitive and visual theories of learning, so that they facilitated student-centred teaching and learning processes that enabled students to adopt and adapt GOs in constructivist learning. The implementation of five GOs - Flow Chart, Concept Maps, K-W-L Chart, Fishbone Diagram and Venn Diagram - as learning tools in classrooms was investigated to find if changes in pedagogical approach for supporting conceptual learning through cognitive information processing would reduce the cognitive work load of students and produce better learning approaches. The study as evidenced by the participant teachers. responses and classroom observations, showed a marked increase in student interest, participation, critical thought, problem solving skills, as a result of using GOs, compared to using traditional teaching and learning methods. A theoretical model was developed from the study based on the premise that teachers. knowledge of the subject, pedagogy and student learning precede the implementation of student-centred learning reform, that it plays an important role in the implementation of student-centred learning and that it brings about a change in teaching practice. The model affirmed that observed change in teaching-practice included aspects of teachers. beliefs, as well as confidence and effect on workplace and on student learning, including engagement, understanding, critical thinking and problem solving. The model assumed that change in teaching practice is inseparable from teachers. lifelong PD needs related to knowledge, understanding, skills and competency. These findings produced a set of preliminary guidelines for establishing student-centred constructivist strategies in Kuwaiti education while retaining Kuwait.s cultural uniqueness.