Investigating practitioner self-efficacy in an era of mathematical reform

The purpose of this study is to explore teacher self-efficacy at a time of radical mathematical reform. Project Maths – the new initiative which was rolled out nationwide in 2010 differs from previous attempts at innovation in that it targets a much closer connection between curriculum and pedagogy. Gone are the days of well-rehearsed routines where the role of the mathematician was essentially that of demonstrator. Teaching for understanding is now the main ‘official’ pedagogical focus, with emphasis on the practitioner playing the part of mediator between subject-matter and student. Mathematical instruction is not merely concerned with the transmission of knowledge and skills which is a particular pedagogical position to take. It is also an emotional practice (Hargreaves, 1998) that colours and expresses the feelings and actions of practitioners. While emotion plays a key role in teachers’ commitment to curricular reform, it is also shaped by the social and cultural contexts of mathematical change, alongside with the attitudes and beliefs of the mathematical teaching community. Inspired by Bandura’s theory of learning (1986), this investigation aims to shed light on the complex interplay between so-called mastery and vicarious experiences, social persuasion and physiological states. Vygotsky’s view of learning (1978) as a socio-cultural process is also drawn upon, as it provides a useful structure against which teacher self-efficacy and professional development can be examined. Finally, Hiebert’s theory (1986) is used to examine mathematics teaching self-efficacy and mathematics self-efficacy.

Convergence and translation: attitudes to inter-professional learning and teaching of creative problem-solving among medical and engineering students and staff

Background: Healthcare worldwide needs translation of basic ideas from engineering into the clinic. Consequently, there is increasing demand for graduates equipped with the knowledge and skills to apply interdisciplinary medicine/engineering approaches to the development of novel solutions for healthcare. The literature provides little guidance regarding barriers to, and facilitators of, effective interdisciplinary learning for engineering and medical students in a team-based project context. Methods: A quantitative survey was distributed to engineering and medical students and staff in two universities, one in Ireland and one in Belgium, to chart knowledge and practice in interdisciplinary learning and teaching, and of the teaching of innovation. Results: We report important differences for staff and students between the disciplines regarding attitudes towards, and perceptions of, the relevance of interdisciplinary learning opportunities, and the role of creativity and innovation. There was agreement across groups concerning preferred learning, instructional styles, and module content. Medical students showed greater resistance to the use of structured creativity tools and interdisciplinary teams. Conclusions: The results of this international survey will help to define the optimal learning conditions under which undergraduate engineering and medicine students can learn to consider the diverse factors which determine the success or failure of a healthcare engineering solution.

University Teaching of entrepreneurship: a practitioner's analysis

This is a practitioner doctorate aimed at both Universities about to introduce Entrepreneurship as a subject and practitioners who may be turning to teaching what they know building on their business experience. In this Portfolio the transition from Entrepreneur to Lecturer in Entrepreneurship is explored and several approaches were used to support the transition. A Professional Development Memoir offers a review of the life of an entrepreneur through the lens of Meaning Making Systems in order to bring clarity to the theories used by the Entrepreneur implicitly in his practice. Reflecting on these theories offers insight as to how the entrepreneur perceived and acted on market opportunities. Imparting some of the knowledge accumulated from practice is one goal in teaching. Economics and pedagogical theories were identified, researched and applied to inform the structure, design and delivery of a module in Entrepreneurship within a post graduate programme that focussed on business practice. Theories of Entrepreneurship grounded in Economics indicate the importance of this business function within the broad Economic System for economic development. The role of theory is to offer students ways of organising how they think about entrepreneurship. Gardner’s Teaching for Understanding framework is used to bring structure to the development of the module. Several leading exemplars on the teaching of Entrepreneurship are attended to offer a context both for the content of the Module and its subsequent implementation within a framework of best practice in the teaching of Entrepreneurship. The practical running of a business by the students as a central element of the Module provided a deep and valuable learning experience allowing them to experience Entrepreneurship in a real way for themselves.

Optically injected multi-mode semiconductor lasers

As a device, the laser is an elegant conglomerate of elementary physical theories and state-of-the-art techniques ranging from quantum mechanics, thermal and statistical physics, material growth and non-linear mathematics. The laser has been a commercial success in medicine and telecommunication while driving the development of highly optimised devices specifically designed for a plethora of uses. Due to their low-cost and large-scale predictability many aspects of modern life would not function without the lasers. However, the laser is also a window into a system that is strongly emulated by non-linear mathematical systems and are an exceptional apparatus in the development of non-linear dynamics and is often used in the teaching of non-trivial mathematics. While single-mode semiconductor lasers have been well studied, a unified comparison of single and two-mode lasers is still needed to extend the knowledge of semiconductor lasers, as well as testing the limits of current model. Secondly, this work aims to utilise the optically injected semiconductor laser as a tool so study non-linear phenomena in other fields of study, namely ’Rogue waves’ that have been previously witnessed in oceanography and are suspected as having non-linear origins. The first half of this thesis includes a reliable and fast technique to categorise the dynamical state of optically injected two mode and single mode lasers. Analysis of the experimentally obtained time-traces revealed regions of various dynamics and allowed the automatic identification of their respective stability. The impact of this method is also extended to the detection regions containing bi-stabilities. The second half of the thesis presents an investigation into the origins of Rogue Waves in single mode lasers. After confirming their existence in single mode lasers, their distribution in time and sudden appearance in the time-series is studied to justify their name. An examination is also performed into the existence of paths that make Rogue Waves possible and the impact of noise on their distribution is also studied.