Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Geometric Control Theory and its Application to Underwater Vehicles

This dissertation is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of ocean engineering. We present a method for path planning and control design for underwater vehicles by use of the architecture of differential geometry. In addition to the theoretical design of the trajectory and control strategy, we demonstrate the effectiveness of the method via the implementation onto a test-bed autonomous underwater vehicle. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and application. In particular, Riemannian and affine differential geometry have proven to be a very effective approach to the modeling of mechanical systems such as underwater vehicles. In this framework, the application of a kinematic reduction allows us to calculate control strategies for fully and under-actuated vehicles via kinematic decoupled motion planning. However, this method has not yet been extended to account for external forces such as dissipative viscous drag and buoyancy induced potentials acting on a submerged vehicle. To fully bridge the gap between theory and application, this dissertation addresses the extension of this geometric control design method to include such forces. We incorporate the hydrodynamic drag experienced by the vehicle by modifying the Levi-Civita affine connection and demonstrate a method for the compensation of potential forces experienced during a prescribed motion. We present the design method for multiple different missions and include experimental results which validate both the extension of the theory and the ability to implement control strategies designed through the use of geometric techniques. By use of the extension presented in this dissertation, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for complex mechanical systems having equal or fewer input forces than available degrees of freedom. Thus, we provide another tool with which to further increase the autonomy of underwater vehicles.

Southern theory and its dynamics for postcolonial education

This paper discusses how the exploration of social texts and historical contexts from the global 'South', as put forward in Raewyn Connell's study 'Southern Theory' (2007), can improve the theoretical tools used in postcolonial education analysis. Connell analyses a selection of excellent and compelling social theory texts written by scholars in Africa, India, Iran, Latin America and Australia to show how they challenge and counter the silences, distortions and plain lies of dominant Western social theory. These texts of the global South do not mince words in laying bare the role of the institutions and elites of the West in the destruction, dispossession, and bloodshed involved in creating the world in which we live, and in perpetuating its catastrophes. The texts also reveal intense debates between scholars over their conceptualisations of local, national and global society. My paper argues that this kind of work is of vital importance to postcolonial studies in education. It helps education scholars to uncover the problematic assumptions and distortions of dominant education thought, and understand different ways of seeing. Postcolonial educators could use this to help both students and teacher unlearn many of our taught perceptions of the world, whether in the global North or the global South. Developing a countervailing social theory in education would sharpen our questioning of the structures of schooling as they relate to society, and tease out new dimensions of postcolonial leadership for education.

An investigation of market segmentation theory and its impact on effective fundraising

This paper presents the findings of an indepth study into the effects and success of marketing segmentation, target marketing and fundraising. Organisations are constantly seeking new ways and more efficient means to raise funds so that they can fulfill their objectives. These organisations review and evaluate their resources to gain competitive advantage and increased fundraising success...

Complexity Development Theory and enterprise development at the bottom of the pyramid

In 2001 45% (2.7 billion) of the world’s population of approximately 6.1 billion lived in ‘moderate poverty’ on less than US $ 2 per person per day (World Population Summary, 2012). In the last 60 years there have been many theories attempting to explain development, why some countries have the fastest growth in history, while others stagnate and so far no way has been found to explain the differences. Traditional views imply that development is the aggregation of successes from multiple individual business enterprises, but this ignores the interactions between and among institutions, organisations and individuals in the economy, which can often have unpredictable effects. Complexity Development Theory proposes that by viewing development as an emergent property of society, we can help create better development programs at the organisational, institutional and national levels. This paper asks how the principals of CAS can be used to develop CDT principals used to develop and operate development programs at the bottom of the pyramid in developing economies. To investigate this research question we conduct a literature review to define and describe CDT and create propositions for testing. We illustrate these propositions using a case study of an Asset Based Community Development (ABCD) Program for existing and nascent entrepreneurs in the Democratic Republic of the Congo (DRC). We found evidence that all the principals of CDT were related to the characteristics of CAS. If this is the case, development programs will be able to select which CAS needed to test these propositions.

The Systems Theory Framework of career development: 20 years of contribution to theory and practice

The development and sustained contribution of the Systems Theory Framework to career development theory and practice is well documented in national and international literatures. In addition to its contribution to theory integration, it has added to the growing literature on connecting career theory and practice, in particular for non-Western populations. In addition, it has been the basis of the development of a broad array of constructivist approaches to career counselling, and indeed specific reflective career assessment activities. This article begins with a brief history of the Systems Theory Framework which is then followed by a rationale for its development. The contribution of the Systems Theory Framework to theory and practice is then described prior to concluding comments by the authors.

Development of diagnostic and prognostic algorithms from vacuum circuit breaker restrike review and its validation proposal

The CIGRE WGs A3.20 and A3.24 identify the requirements of simulation tools to predict various stresses during the development and operational phases of medium voltage vacuum circuit breaker (VCB) testing. This paper reviews the modelling methodology [13], VCB models and tools to identify future research. It will include the application of the VCB model for the impending failure of a VCB using electro-magnetic-transient-program with diagnostic and prognostic algorithm development. The methodology developed for a VCB degradation model is to modify the dielectric equation to cover a restriking period of more than 1 millimetre.

Career Development and Systems Theory : Connecting Theory and Practice [3rd edition]

"The 3rd edition of this classic book offers practitioners, researchers and students a comprehensive introduction to, and overview of, career theory; introduces the Systems Theory Framework of career development; and demonstrates its considerable contemporary and innovative application to practice. A number of authors have identified the framework as one of a small number of significant innovations in the career development literature. The Systems Theory Framework of career development was developed to provide coherence to the career development field by providing a comprehensive conceptualisation of the many existing theories and concepts relevant to understanding career development. It is not designed to be a theory of career development; rather systems theory is introduced as the basis for an overarching, or metatheoretical, framework within which all concepts of career development, described in the plethora of career theories, can be usefully positioned and utilised in both theory and practice. It has been applied to the career development of children, adolescents and women. Since its first publication, the Systems Theory Framework has been the basis of numerous publications focusing on theoretical application and integration, practice and research, with a growing number of these by authors other than the framework developers. Its application across cultures also has been emphasised. The theoretical and practical unity of the Systems Theory Framework makes this book a worthy addition to the professional libraries of practitioners, researchers and students, new to, or experienced in, the field of career development."--PUBLISHER WEBSITE

Design democratisation and its understandings through the meaning of the word “design” in Portuguese colonised countries

This paper explores the literature and analyses the different uses and understandings of the word “design” in Portuguese colonised countries, using Brazil as the main example. It investigates the relationship between the linguistic existence of terms to define and describe “design” as an activity and field, and the roles and perceptions of Design by the general society. It also addresses the effects that the lack of a proper translation causes on the local community from a cultural point of view. The current perception of Design in Portuguese colonies is associated to two main aspects: linguistic and historical. Both of them differentiate the countries taken into consideration from other countries that have a different background. The changes associated to the meaning of “design” throughout the years, caused a great impact on the perceptions that people have about Design. On the other hand, the development of Design has also influenced the changes on the meaning of the term, as a result of the legacy from the colonisation period and also as a characteristic of the Portuguese language. Design has developed and reached a level of excellence in Portuguese colonised countries that competes with the most traditional Design cultures in the world. However, this level of Design is enmeshed into an elite belonging to universities and specialised markets, therefore Design is not democratised. The ultimate aim of this study is to promote discussions on how to make the discourse surrounding this area more accessible to people from non-English speaking countries that do not have the word “design” in their local language.

IT professionals' experience of ethics and its implications for IT education

This study investigates variation in IT professionals' experience of ethics with a view to enhancing their formation and support. This is explored through an examination of the experience of IT, IT professional ethics and IT professional ethics education. The study's principal contribution is the empirical study and description of IT professionals' experience of ethics. The empirical phase is preceded by a review of conceptions of IT and followed by an application of the findings to IT education. The study's empirical findings are based on 30 semi-structured interviews with IT professionals who represent a wide demographic, experience and IT sub-discipline range. Their experience of ethics is depicted as five citizenships: Citizenship of my world, Citizenship of the corporate world, Citizenship of a shared world, Citizenship of the client's world and Citizenship of the wider world. These signify an expanding awareness, which progressively accords rights to others and defines responsibility in terms of others. The empirical findings inform a Model of Ethical IT. This maps an IT professional space increasingly oriented towards others. Such a model provides a conceptual tool, available to prompt discussion and reflection, and which may be employed in pursuing formation aimed at experiential change. Its usefulness for the education of IT professionals with respect to ethics is explored. The research approach employed in this study is phenomenography. This method seeks to elicit and represent variation of experience. It understands experience as a relationship between a subject (IT professionals) and an object (ethics), and describes this relationship in terms of its foci and boundaries. The study's findings culminate in three observations, that change is indicated in the formation and support of IT professionals in: 1. IT professionals' experience of their discipline, moving towards a focus on information users; 2. IT professionals' experience of professional ethics, moving towards the adoption of other-centred attitudes; and 3. IT professionals' experience of professional development, moving towards an emphasis on a change in lived experience. Based on these results, employers, educators and professional bodies may want to evaluate how they approach professional formation and support, if they aim to promote a comprehensive awareness of ethics in IT professionals.

The central role of communication in developing trust and its effect on employee involvement

Communication plays an important role in the development of trust within an organization. While a number of researchers have studied the relationship of trust and communication, little is known about the specific linkages among quality of information, quantity of information, openness, trust, and outcomes such as employee involvement. This study tests these relationships using communication audit data from 218 employees in the oil industry. Using mediation analysis and structural equation modeling, we found that quality of information predicted trust of one's coworkers and supervisors while adequacy of information predicted one's trust of top management. Trust of coworkers, supervisors, and top management influenced perceptions of organizational openness, which in turn influenced employees' ratings of their own level of involvement in the organization's goals. This study suggests that the relationship between communication and trust is complex, and that simple strategies focusing on either quality or quantity of information may be ineffective for dealing with all members in an organization.

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.