Computer Algebra Systems (CAS), a powerful mathematical software currently available on hand held calculators, is becoming increasingly available to assist secondary students learn school mathematics. This study investigates how two teachers taught introductory differential calculus to their Year 11 classes using multiple representations in a CAS-supported curriculim. This thesis aism to explore the impact of the teaching on students' understanding of the concept of derivative. Understanding the concept of derivative was gauged using an innovative Differentiation Competency Framework that was developed to describe understanding of the concept of derivative. It consist of eighteen competencies for formulation and interpretation of derivatives with, and without, translation between different representations. It clarifies the objectives of the curriculim, purpose for using particular CAS activities, and also guided the construction of individual test items on the Differentiation Competency Test that enabled individual and class learning about the concept of derivative to be identified. The framework also helped identify each teacher's privileging characteristics and facilitated analysis of the learning in relation to the teaching. This study found that using multiple representations was important in developing understanding of the concept of derivative but that the graphical and the symbolic representations were the most useful and important to emphasize and link. Analysis of the teaching actions showed that the teachers used CAS in ways that were consistent with their teaching approach and preferred use of representations and that a conceptual teaching method and student-centred style supported understanding of the concept of derivative. Teaching is directly linked to learning and each class developed a different understanding of the concept of derivative that related to the combined effect of their teacher's privileging characteristics: calculus content, teaching approach, and use of CAS. This study shows that if a CAS-supported curriculum is to be successfully implemented, it needs to acquire institutional status including a corresponding change in assessment to legitimize new teaching practices.

This research explores how the social backgrounds of a group of students contributed to their intuitive knowledge in probabilistic reasoning, and influenced their processing of the associated mathematics. A group of Year 11 students who came from families for whom the phenomenon of track gambling formed an important part of their cultural background was identified. Another group consisting of students in the same mathematics course (Year 11 Maths in Society) but from families for whom the phenomenon of gambling in any form was totally absent from their social backgrounds was identified. Twenty students were selected from each group. The research employed a qualitative methodology in which a phenomenographic approach was used to investigate the qualitatively different ways in which individuals within the two groups thought about concepts involving probabilistic reasoning, and processed the related mathematical skills and concepts. The cognitive processes involved in the applications of probabilistic and related mathematical concepts in a variety of both gambling and non-gambling situations were studied in order to determine whether this culturally based knowledge could be viewed as a type of ‘ethnomathematics.’ Data were obtained through individual structured interviews which enabled patterns of reasoning to be compared and contrasted. Analyses of these data enabled intuitive mathematical understandings possessed by the gamblers not only to be identified, but also to be linked with their social backgrounds. Also differences between how individuals in the two groups processed probabilistic and associated mathematical knowledge were determined. This research complements and extends existing knowledge and theories related to culturally-based mathematical knowledge. Implications for further research, for classroom teaching, and for curriculum development in the study of probability in senior secondary mathematics classes are discussed.

In 2001 the then UK Government set a national target to get 50 per cent of young people between the ages of 18 and 30 into higher education by the year 2010. To achieve this goal, higher education institutions were required to deliver Widening Participation initiatives that would target under-represented groups in a bid to raise aspirations and bring them into the sector. The study that underpins this thesis was an investigation into the issues surrounding widening participation from the perspective of students in their final year of compulsory schooling. It began as a year-long longitudinal study of the students’ views as they moved towards a key transitional point in their lives. Nine students were identified from Year 11 in one school. Three were drawn from each of the following three categories or groups of students: (i) ‘traditional students’, these were students who were deemed as belonging to groups that were already well-represented in higher education; (ii) ‘non-traditional’ students, these were deemed ‘non-traditional’ in the sense that they were seen as belonging to groups that were under-represented in higher education; (iii) ‘widening participation’ students, these were recipients of a widening participation initiative delivered by their nearest university which, by implication, also deemed them as being ‘non-traditional’ in the sense that they were seen as belonging to groups that were under-represented in higher education. Each participant was interviewed in-depth three times whilst they were in Year 11; in December 2003, in March 2004, and again in June 2004. Whilst all interviews sought to elicit information about their lives at that point in time, the first interview was intended to gather relevant information about their past lives, the second a more in-depth look at their current lives, and the third focused on their future lives. Follow-up data were collected from some of the participants in 2009, 2010 and 2011. An in-depth interview also took place in June 2004 with the university’s Widening Participation Officer and the school’s Head of Year 11 and Widening Participation Co-ordinator. They are considered to be key informants to widening participation initiatives, more broadly in the case of the former, and specific to the school in the case of the latter. The thesis reports on the process through which participants were selected (or not selected) for widening participation intervention, learning identities in school and out, imagined futures, choices, and ultimately what happened to those students who were tracked beyond Year 11. Flaws in the widening participation policy agenda at the time of the main data collection period were identified as: (i) the individualization of the problem which drew attention away from the structural nature of the problem of under-representation and also from deep-rooted flaws within the education system; (ii) the lack of awareness of the longitudinal nature of the problem whereby entrance into higher education is dependent on prior learning and prior qualifications – this resulted in little or no account being taken in the selection process of widening participation-targeted individuals’ previous patterns of achievements, such that they may not be on a trajectory that makes higher education a viable option, and (iii) the valuing of non-participation in higher education. The thesis concluded by acknowledging that a new legislative framework about to be implemented in 2012 appears to be addressing some of these concerns. Issues that remain unaddressed include deep-rooted problems within the formal education system, the valuing of non-participation and of vocational training, and an appreciation that learning takes place on a trajectory.

In 1976, following the recommendations of the Campbell Report, school-based course development and assessment replaced the New South Wales Higher School Certificate courses and public examinations. Under the auspices of the A.C.T. Schools Authority, the A.C.T. Accrediting Agency took control of administering the new system. Nine years after the system was introduced, the benefits of the new system were very clear in the area of English curriculum at Years 11 and 12 level. To a considerable degree, the hopes of the Campbell Report have been fulfilled in terms of providing students with greater freedom of choice and flexibility in the selection of options in an English course composed of a number of term or term equivalent units. Assessment instruments have become much more wide-ranging. Teacher/student relationships have become less authoritarian. Teaching strategies and learning approaches have generally made students more active participants in the learning process. The field study drew heavily on English course documents in the senior secondary colleges, presenting an overview of the workings of the English curriculum. Because courses are being continually reaccredited, it was necessary to set the curriculum overview at a particular time, in 1984. As the A.C.T. is a small education system in Australian terms, it was possible to gain some concept of the whole picture, although 428 term units is not an inconsiderable number. The field study, because of its significant data base, poses more questions than it answers. It does, to a degree, present "what is", or rather "what was" in the 1984 English curriculum at Years 11 and 12 level in A.C.T. colleges. And it points directions for further research.

This field study aims to identify and examine the consequences and influences of course selections and career choices made by students, their parents and college staff. Because of a lack of information regarding the implications of their selected programmes of study, many students choose unwisely and as a result, have become confused about the relevance of their choices in relation to the achievement of their ultimate career aspirations. To achieve the aims of this study, an analysis of the course selections and career choices of the Year 12 graduates of 1983 from Copland College was completed. This field study is divided into three main sections. The first section comprises Chapters I and II which outline the historical development of secondary colleges within the Australian Capital Territory. The author briefly discusses the influence of both the Hughes and the Campbell Reports and illustrates how these Reports were used as the basis for the establishment of the educational structure we now have for our senior secondary college students in Canberra. In addition, this section details the historical background of careers education within the Australian Capital Territory and the influences this has had on the status of career education at Copland College. The second section covers Chapters III, IV and V. In this section the function of the Student Services Faculty within Copland College is discussed and also a brief explanation given of the type of information gathered by college and administrative staff for career and course advice. The author provides a description of the procedures II used to obtain and collate the information collected for this field study. A questionnaire method of data collection was the basis used to examine the post-collegiate activities of over 240 graduate students of 1983, and part of the questionnaire relates specifically to the destinations of these ex-students. Finally, the third section incorporates Chapters VI and VII. It details the results of my research covered in earlier chapters and at the same time, synthesizes that of other educationalists as it relates to this field study. The concluding portion of this section sets out recommendations proposed to meet the problems identified in such areas as student course selections and careers advice.

This study examines the readability of text books used by Year 11 students at a Secondary College in the A.C.T. Twenty-seven texts are examined with the majority being taken from the area of Social Science. The texts are examined using the following measures, The Fry Readability Index, The SMOG Formula, The Cloze Measure, The number of Words per T-Unit and the level of Abstraction of the text. According to these indices between 60% and 84% of the texts are too difficult for students commencing Year 11. This study also examined the interrelationship between the indices. A feature of this study is that it introduces into readability measures a consideration of the number of words per T-Unit and level of Abstraction