The growth in Flexible and Distributed Learning will, it is believed, lead to a need for a more innovative and flexible approach to the way support is offered to students. This study which was conducted with students at a Further Education College looks at the effectiveness of using Desktop Video Conferencing (DVC) to provide support to students studying mathematics at a number of different levels. The research design adopted the concept of triangulation with three different approaches being used. The first strand of the methodology was the collection of statistical data for all students re-sitting GCSE mathematics to develop a model to predict the learning outcome for students. The second strand was the extensive use of questionnaires and interviews with students receiving learning support. The final strand was the application of discourse analysis to recordings of both face-toface and DVe tutorials in order that a comparison could be made between them. To do this it was necessary to develop a research tool to record both verbal and non-verbal dialogue. The main conclusion from the study was that there was no identifiable difference in learning outcome between tutorials conducted face-to-face and those conducted using DVe. A number of positive advantages of using DVe emerged during the course of the study. These included the fact that most students preferred tutorials using DVC as they found the environment less threatening than when sitting next to a tutor. Other advantages resulted from the use of the electronic Whiteboard, these included being able to give students quicker feedback, if appropriate.

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Expansion of Higher Education has resulted in increasing provision of Access and Foundation programmes, often aimed at mature learners. Adults returning to learn mathematics bring with them a wealth of prior understanding and expectations The two common teaching approaches, remedial 'fill in the gaps' or mythical 'start again', are popular with students but argued to be unrealistic because the teaching of adults is better likened to building on a brownfield site. The purpose of this research was to consider what understandings adults brought with them and explore how these understandings interacted with new learning. 203 foundation students were given questions, on proportional reasoning, percentage calculation and over-generalisations. Responses, and response hierarchies, were compared with those from children in the 1970's CSMS survey (Hart, 1981 a). Individual behaviours were then explored through interview using a framework developed from ideas of Schoenfeld (1992) and Leron and Hazzan (1997). It emerged that multiple interactions and choices of behaviour were taking place, indicating final answers, right or wrong, represented only one possibility from a selection of outcomes. Method selection might be influenced by number and beliefs in non-conservation of operation (Greer, 1994) causing potential difficulties for building new learning by method extrapolation. The habit of selt-checkinq and testing for reasonableness might cause difficulties when reasonableness could not be recognised or was counter-intuitive. Other themes identified included: the false recall of certain number calculations with potential for interference with diagnostic practices and the belief in the 'one right method' based on perceived outcome requirements or confidence from previous success, causing reluctance to consider more efficient or appropriate methods. This research highlights the benefits of making processes and choices explicit to teachers and students facilitating the integration of previous understandings with new ways of working without disempowerment and increasing the potential for new learning to be built.

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The purpose of this interpretive qualitative study was to determine the extent of conceptual and procedural difficulties that NCV Level 4 students encountered when factorising and solving problems involving factorisation. This study is based on Kilpatrick, Swafford and Findel’s (2001) ideas on mathematical proficiency, focusing on conceptual knowledge, procedural knowledge and the flexibility of integrating both appropriately to solve algebra problems involving factorisation. This study also explored reasons why NCV Level 4 students demonstrated such difficulties and suggested possible ways that could assist them to understand and flexibly use factorisation to solve problems. A purposive sample consisting of 30 NCV Level 4 students and 5 Subject Matter Experts participated in this study, which adopted a phenomenological case study research design. Triangulation of method was adopted for consistent gathering of information. Data was collected through a written assessment on factorisation under controlled test conditions, and semi-structured interviews. The researcher reduced and analysed data by utilising an integration of constant comparison analysis and classical content analysis. The findings and relevant recommendations concluded this research. / Mathematics Education / M. Ed. (Mathematical Education)

This study investigated how lesson study, a Japanese intervention tool, may be used as a management strategy to improve performance in space, shape and orientation in Mathematical Literacy at Technical and Vocational Education and Training colleges. In this study a qualitative approach was followed in both the pilot and the main study. Prior to the main study, a small-scale pilot study was conducted which consisted of two participant lecturers and lasted for about two months culminating in one complete lesson study cycle and a second partially completed cycle. Four lecturers participated in the main study which lasted about seven months from the last week of February 2019 to the last week of August 2019 at a campus of a TVET college where Mathematical Literacy is a subject in the NCV program. Data were collected from semi-structured interviews with lecturers and students, observations of students’ performance and behaviour while delivering the research lessons, including researchers’ journals and participant lecturers’ journals, students’ work and meeting notes which included debriefing notes. The LS - Participative Management model proposed in this study has shown to achieve the broad teaching and learning outcomes, personal and professional outcomes and managerial outcomes. Hence, it is possible that the model proposed in this study is an appropriate model which can be successfully implemented at TVET colleges in South Africa. With the application of the LS Participative Management model, findings revealed from this study showed that participant lecturers improved their teaching and learning by reflecting and engaging with the content of space, shape and orientation in Mathematical Literacy by highlighting the misconceptions students have around this topic. Participant lecturers were also brought out of isolation, giving them the opportunity to collaborate with other lecturers and the manager. Collaboration and participation in lesson study also brought about organisational effectiveness which was revealed through vigorous discussions, openness, trust and respect, positive relationships and sharing ideas. Lesson study also provided an enabling environment for lecturers to become personally and professionally empowered by increased confidence and motivation as they gained more experience in lesson study. The involvement of the manager as a participant observer showed that it can impact on curriculum management, sharing experience and expertise, influence the organisational culture and provide guidance and support. / Educational Management and Leadership / D. Ed. (Educational Management)