DSpace Collection:https://dspace.lboro.ac.uk/2134/46422017-06-29T02:14:15Z2017-06-29T02:14:15ZStudents as partners and students as change agents in the context of university mathematicsDuah, Francis K.https://dspace.lboro.ac.uk/2134/255562017-06-27T10:07:00Z2017-01-01T00:00:00ZTitle: Students as partners and students as change agents in the context of university mathematics
Authors: Duah, Francis K.
Abstract: The research reported in this thesis investigated staff-student collaboration in advanced undergraduate mathematics course design and delivery at a research-intensive UK university. Staff and students collaborated to redesign and deliver two courses: Vector Spaces and Complex Variables. The collaboration in the design of the two courses involved students who had completed the courses and then who worked as interns together with a small team of academic staff. The collaboration in the delivery of the two courses involved the implementation of a Peer Assisted Learning (PAL) scheme in which third-year students facilitated the learning of second-year students in optional scheduled sessions. The study employed a mixed-methods research strategy involving an ethnographic approach to the study of the course design process and PAL sessions followed by an observational study (a quasi-experimental design) to investigate the impact of PAL attendance on the achievement of PAL participants.
This thesis reports findings from a three-phase research design. Phase one explored the nature of the collaborations in course design and its impact on staff teaching practices and on the student collaborators. Phase two investigated the characteristics of the PAL sessions for the advanced undergraduate mathematics courses and the roles played in those sessions. Phase two also explored the impact of PAL in qualitative terms on both PAL participants and PAL leaders. Phase three investigated the impact of PAL in quantitative terms on the achievement of students who participated as PAL participants. The study found that staff-student collaboration in course design and delivery led to emergent Communities of Practice in which staff and students engaged in mathematics practice which led to identity transformation of student collaborators, a deeper understanding of the mathematics on which the students worked and some change in staff teaching and course design practice. The also showed that staff-student collaboration in the delivery of course units via PAL resulted in a learning community in which PAL participants and PAL leaders engaged in mathematics practice which led to increased student achievement and enhanced affective outcomes for both PAL participants and PAL leaders.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2017-01-01T00:00:00ZFinite orbits of the action of the pure braid group on the character variety of the Riemann sphere with five boundary componentsCalligaris, Pierpaolohttps://dspace.lboro.ac.uk/2134/255362017-06-27T10:03:50Z2017-01-01T00:00:00ZTitle: Finite orbits of the action of the pure braid group on the character variety of the Riemann sphere with five boundary components
Authors: Calligaris, Pierpaolo
Abstract: In this thesis, we classify finite orbits of the action of the pure braid group over a certain large open subset of the SL(2,C) character variety of the Riemann sphere with five boundary components, i.e. Σ5. This problem arises in the context of classifying algebraic solutions of the Garnier system G2, that is the two variable analogue of the famous sixth Painleve equation PVI. The structure of the analytic continuation of these solutions is described in terms of the action of the pure braid group on the fundamental group of Σ5. To deal with this problem, we introduce a system of co-adjoint coordinates on a big open subset of the SL(2,C) character variety of Σ5. Our classifica- tion method is based on the definition of four restrictions of the action of the pure braid group such that they act on some of the co-adjoint coordi- nates of Σ5 as the pure braid group acts on the co-adjoint coordinates of the character variety of the Riemann sphere with four boundary components, i.e. Σ4, for which the classification of all finite orbits is known. In order to avoid redundant elements in our final list, a group of symmetries G of the large open subset is introduced and the final classification is achieved modulo the action of G. We present a final list of 54 finite orbits.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2017-01-01T00:00:00ZLecturers' tools and strategies in university mathematics teaching: an ethnographic studyMali, Angelikihttps://dspace.lboro.ac.uk/2134/253852017-06-23T14:27:01Z2016-01-01T00:00:00ZTitle: Lecturers' tools and strategies in university mathematics teaching: an ethnographic study
Authors: Mali, Angeliki
Abstract: The thesis presents the analytical process and the findings of a study on: lecturers teaching practice with first year undergraduate mathematics modules; and lecturers knowledge for teaching with regard to students mathematical meaning making (understanding). Over three academic semesters, I observed and audio-recorded twenty-six lecturers teaching to a small group tutorial of two to eight first year students, and I discussed with the lecturers about their underlying considerations for teaching. The analysis of this thesis focuses on a characterisation of each of three (of the twenty-six) lecturers teaching, which I observed for more than one semester. I chose the teaching of three experienced lecturers, due to diversity in terms of ways of engaging the students with the mathematics, and due to my consideration of their commitment to teaching for students mathematical meaning making.
The distinctive nature of the study is concerned with the conceptualisation of university mathematics teaching practice and knowledge within a Vygotskian perspective. In particular, I used for the characterisation of teaching practice and of teaching knowledge the notions tool-mediation and dialectic from Vygotskian theory. I also used a coding process grounded to the data and informed by existing research literature in mathematics education. I conceptualised teaching practice into tools for teaching and actions with tools for teaching (namely strategies). I then conceptualised teaching knowledge as the lecturers reflection on teaching practice. The thesis contributes to the research literature in mathematics education with an analytical framework of teaching knowledge which is revealed in practice, the Teaching Knowledge-in-Practice (TKiP). TKiP analyses specific kinds of lecturer s knowing for teaching: didactical knowing and pedagogical knowing. The framework includes emerging tools for teaching (e.g. graphical representation, rhetorical question, students faces) and emerging strategies for teaching (e.g. creating students positive feelings, explaining), which were common or different among the three lecturers teaching practice.
Overall, TKiP is produced to offer a dynamic framework for researcher analysis of university mathematics teaching knowledge. Analysis of teaching knowledge is important for gaining insights into why teaching practice happens in certain ways. The findings of the thesis also suggest teaching strategies for the improvement of students mathematical meaning making in tutorials.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2016-01-01T00:00:00ZFrequency domain parameter identification and the statistical properties of frequency response estimatesWilliams, N.G.https://dspace.lboro.ac.uk/2134/251412017-05-25T14:02:59Z1993-01-01T00:00:00ZTitle: Frequency domain parameter identification and the statistical properties of frequency response estimates
Authors: Williams, N.G.
Abstract: Frequency domain techniques in systems theory have their origins in
Heavyside's operational calculus (Heavyside, 1889). Such work was later
developed by Foster and Campbell (1931), Brune (1931), Nyquist (1932),
Black (1934), Darlington (1939) and subsequently Bode (1948). This
interest in the frequency domain was due to its appeal to the intuition of
the engineer.
The dominance of frequency domain techniques was subsequently eroded from
the late 1950s through the 1960s by the influence of the space programmes.
The space systems being analysed were based on strong theoretical
foundations with well-defined sets of differential equations. The analysis
led to the development of the state-space methods which were able to cope
with the multivariable problems and were amenable to numerical solution.
As a result of these developments, control engineering was largely
dominated by the state-space approach and the associated areas of LQG
optimal control, Kaiman-Bucy filters, observability and controllability.
Two factors led to a resurgence of interest amongst academics in the
development of frequency domain techniques in the 1970s and 1980s. The
first was the development of the Fast Fourier Transform (FFT) (Cooley &
Tookey, 1965). This provided an efficient method of analysing the Fourier
transforms of signals and allowed the development of spectral methods of
obtaining frequency response estimates. The collection of data was greatly
speeded up and this enabled frequency domain methods to be increasingly
applied to on-line control problems. The second factor was that the
developments in the time domain were never fully embraced by practicing
engineers in traditional control environments.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.1993-01-01T00:00:00Z