An investigation of post-primary students' images of mathematics

This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

Politics, Power, PISA: a genealogy of mathematics education policy at second level in Ireland at the beginning of the 21st century

This thesis traces a genealogy of the discourse of mathematics education reform in Ireland at the beginning of the twenty first century at a time when the hegemonic political discourse is that of neoliberalism. It draws on the work of Michel Foucault to identify the network of power relations involved in the development of a single case of curriculum reform – in this case Project Maths. It identifies the construction of an apparatus within the fields of politics, economics and education, the elements of which include institutions like the OECD and the Government, the bureaucracy, expert groups and special interest groups, the media, the school, the State, state assessment and international assessment. Five major themes in educational reform emerge from the analysis: the arrival of neoliberal governance in Ireland; the triumph of human capital theory as the hegemonic educational philosophy here; the dominant role of OECD/PISA and its values in the mathematics education discourse in Ireland; the fetishisation of western scientific knowledge and knowledge as commodity; and the formation of a new kind of subjectivity, namely the subjectivity of the young person as a form of human-capital-to-be. In particular, it provides a critical analysis of the influence of OECD/PISA on the development of mathematics education policy here – especially on Project Maths curriculum, assessment and pedagogy. It unpacks the arguments in favour of curriculum change and lays bare their ideological foundations. This discourse contextualises educational change as occurring within a rapidly changing economic environment where the concept of the State’s economic aspirations and developments in science, technology and communications are reshaping both the focus of business and the demands being put on education. Within this discourse, education is to be repurposed and its consequences measured against the paradigm of the Knowledge Economy – usually characterised as the inevitable or necessary future of a carefully defined present.

Job retention and turnover: a study of child protection and welfare social workers in Ireland

Retaining social workers in child protection and welfare organisations has been identified as a problem in Ireland (McGrath, 2001; Ombudsman for Children, 2006; Houses of the Oireachtas, 2008) and internationally (Ellet et al., 2006; Mor Barak et al., 2006; Tham, 2006). While low levels of retention have been identified, there is no research that examines the factors in Ireland that influence the retention of social workers. In this thesis, data is analysed from qualitative interviews with 45 social workers in the Health Service Executive South about what influences their decisions to stay in or leave child protection and welfare social work. These social workers’ views are examined in relation to quantitative research on the levels of turnover and employment mobility of child protection and welfare social workers employed in the same organisation. Contrary to expectations, the study found that the retention rate of social workers during the period of data collection (March 2005 to December 2006) was high and that the majority of social workers remained positive about this work and their retention. The quality of social workers’ supervision, social supports from colleagues, high levels of autonomy, a commitment to child protection and welfare work, good variety in the work, and a perception that they were making a difference, emerged as important factors in social workers’ decisions to stay. Perceptions of being unsupported by the organisation, which was usually described in terms of high caseloads and demanding workloads, a lack of resources, work with involuntary clients and not being able to make a difference, were the most significant factors in social workers’ decisions to leave and/or to want to leave. Social workers felt particularly professionally unsupported when they received low quality and/or infrequent professional supervision. This thesis critiques the theories of perceived organisational support theory, social exchange theory and job characteristics theory, and uses the concept of ‘professional career’, to help analyse the retention of social workers in child protection and welfare.

The quality of diabetes care in the community: practice, policy and culture

Aim: Diabetes is an important barometer of health system performance. This chronic condition is a source of significant morbidity, premature mortality and a major contributor to health care costs. There is an increasing focus internationally, and more recently nationally, on system, practice and professional-level initiatives to promote the quality of care. The aim of this thesis was to investigate the ‘quality chasm’ around the organisation and delivery of diabetes care in general practice, to explore GPs’ attitudes to engaging in quality improvement activities and to examine efforts to improve the quality of diabetes care in Ireland from practice to policy. Methods: Quantitative and qualitative methods were used. As part of a mixed methods sequential design, a postal survey of 600 GPs was conducted to assess the organization of care. This was followed by an in-depth qualitative study using semi-structured interviews with a purposive sample of 31 GPs from urban and rural areas. The qualitative methodology was also used to examine GPs’ attitudes to engaging in quality improvement. Data were analysed using a Framework approach. A 2nd observation study was used to assess the quality of care in 63 practices with a special interest in diabetes. Data on 3010 adults with Type 2 diabetes from 3 primary care initiatives were analysed and the results were benchmarked against national guidelines and standards of care in the UK. The final study was an instrumental case study of policy formulation. Semi-structured interviews were conducted with 15 members of the Expert Advisory Group (EAG) for Diabetes. Thematic analysis was applied to the data using 3 theories of the policy process as analytical tools. Results: The survey response rate was 44% (n=262). Results suggested care delivery was largely unstructured; 45% of GPs had a diabetes register (n=157), 53% reported using guidelines (n=140), 30% had formal call recall system (n=78) and 24% had none of these organizational features (n=62). Only 10% of GPs had a formal shared protocol with the local hospital specialist diabetes team (n=26). The lack of coordination between settings was identified as a major barrier to providing optimal care leading to waiting times, overburdened hospitals and avoidable duplication. The lack of remuneration for chronic disease management had a ripple effect also creating costs for patients and apathy among GPs. There was also a sense of inertia around quality improvement activities particularly at a national level. This attitude was strongly influenced by previous experiences of change in the health system. In contrast GP’s spoke positively about change at a local level which was facilitated by a practice ethos, leadership and special interest in diabetes. The 2nd quantitative study found that practices with a special interest in diabetes achieved a standard of care comparable to the UK in terms of the recording of clinical processes of care and the achievement of clinical targets; 35% of patients reached the HbA1c target of <6.5% compared to 26% in England and Wales. With regard to diabetes policy formulation, the evolving process of action and inaction was best described by the Multiple Streams Theory. Within the EAG, the formulation of recommendations was facilitated by overarching agreement on the “obvious” priorities while the details of proposals were influenced by personal preferences and local capacity. In contrast the national decision-making process was protracted and ambiguous. The lack of impetus from senior management coupled with the lack of power conferred on the EAG impeded progress. Conclusions: The findings highlight the inconsistency of diabetes care in Ireland. The main barriers to optimal diabetes management center on the organization and coordination of care at the systems level with consequences for practice, providers and patients. Quality improvement initiatives need to stimulate a sense of ownership and interest among frontline service providers to address the local sense of inertia to national change. To date quality improvement in diabetes care has been largely dependent the “special interest” of professionals. The challenge for the Irish health system is to embed this activity as part of routine practice, professional responsibility and the underlying health care culture.

“Fiction makes a better job of the truth”: dialogism, oppositional consciousness and re-membering in the novels of Helena María Viramontes

This thesis comprises close textual analyses of Chicana author Helena María Viramontes' two published novels, Under the Feet of Jesus (1995) and Their Dogs Came With Them (2007). These analyses fall under three broad frameworks: space, time and body. Chapter One engages with the first of these frameworks, space, and explores concepts of cognitive mapping and heteroptopias. Chapter Two, which looks at time, employs theories of intertextuality and the palimpsest, while Chapter Three looks at the interrrelationship between mythology and images of the body in the texts. This study emerges five years after the publication of Viramontes' last novel, Their Dogs Came With Them, but offers fresh insight into the contribution of the author to both the Chicano literary tradition and also the U.S. canon through her critique of hegemonic power structures that suppress not only the voices of lower class ethnic citizens but also of ethnic writers. In particular, her work chastises the paucity of attention given to ethnic women writers in the U.S. This thesis reaffirms Viramontes' position as one of the most important writers living and writing in the U.S. today. It corroborates her work as a contestation against ethnic and gender suppression, and applauds the craftsmanship of her narrative style that delicately but decisively exposes the socio-political wrongs that occur in ocntemporary U.S. society.

Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

The contribution of warlordism to the disintegration of the western Roman army (c. AD 395-480)

My thesis investigates the dynamics behind the changing nature of the leadership of the western Roman army in the fifth century through the concept of ‘warlordism’. I carried this out by analyzing those cases of insubordination and military unrest in the officer class of the western Roman army, which can be shown to be linked to the slow decline of central authority and the imperial office in the period 395-480. My thesis demonstrates that theories of ‘Warlordism’, as developed in social sciences, can be useful for both the late Imperial west as for other eras of ancient history, such as the late Roman republic. Warlordism was a way of continuing politics, if necessary by military means, when commanders found themselves outside the legitimate framework. Unlike the case of usurpation of the imperial office, when there was little hope of achieving permanent recognition and acceptance, it offered insubordinate officers a chance of returning to the ruling imperial regime depending on circumstances and the success of their resistance. I propose that warlordism functioned as an alternative to usurpation, a tool for military dissidence, fuelled by an economy of violence. Contrary to modern warlordism, the warlordism of the fifth century AD represented a transient phase which no imperial commander was willing to prolong indefinitely. At some stage, given the means, warlords in the western Roman army wanted to become part of the imperial echelon again. Yet these alternative methods of violent opposition, and the acquisition of force through private means, ensured the breakdown of the state’s monopoly on violence and the disintegration of centralized armies. What started as an accidental revolution became a new form of military rule.

The defining characteristics of alternative food initiatives in Ireland: a social movement battling for an alternative food future?

Alternative food initiatives (AFIs) have been described as an attempt to change and improve aspects of how the food system operates. They are focused around more traditional, local and sustainable food production and circulation. AFIs such as farmers’ markets, allotments and community gardens, share a desire to reduce the number of steps food goes through from production to plate. The role of these initiatives in the food system, and their potential to impact real change, has however been questioned. Working to better understand this issue is a central concern of this research. To do this a two tier analysis has been deployed. The first tier involves identifying the characteristics and general dynamics of AFIs. Bourdieu’s theory of practice, and the theories of field and capital, are the concepts applied. The research then uses these findings in the second tier of analysis concerned with relating AFI characteristics and dynamics back to their key traits, positive and negative, as well as arguments made about AFI’s role identified from previous research. Another part of this second tier of analysis is exploring if AFIs, the producers, consumers, organisations and groups that make up this phenomenon, can be considered a social movement. AFIs can be referred to collectively as a social movement, but are not often explored theoretically from this perspective. AFIs in Ireland provide the empirical context for this research. A series of qualitative interviews in four areas of Ireland, as well as evidence from primary and secondary sources are analysed. The research finds that AFIs can be understood as the potential beginnings of a lifestyle social movement. Leaders are of central importance to its development. It is also found that an important role of AFIs is revitalising, supporting and contributing to food culture.

The role of transformative thinking and practice in a property entrepreneur's response to the funding crisis since 2008

This portfolio of exploration explores the role of transformative thinking and practice in a property entrepreneur’s response to the financial crisis which swept over Ireland from 2008. The complexity of this challenge and the mental capacity to meet its demands is at the core of the exploration. This inquiry emerged from the challenges the financial crisis presented to my values, beliefs, assumptions, and theories, i.e. the interpretive lens through which I make meaning of my experiences. Given the issue identified, this inquiry is grounded in aspects of theories of constructive developmental psychology, applied developmental science, and philosophy. Integrating and linking these elements to business practice is the applied element of the Portfolio. As the 2008 crisis unfolded I realised I was at the limits of my way of knowing. I came to understand that the underlying structure of a way of knowing is the ‘subject-object relationship’ i.e. what a way of knowing can reflect upon, look at, have perspective on, in other words, make object, as against what is it embedded in, attached to, identified within, or subject to. My goal became enhancing my awareness of how I made meaning and how new insights, which would transform a way of knowing, are created. The focus was on enhancing my practice. This Portfolio is structured into three essays. Essay One reported on my self-reflection and external evaluation out of which emerged my developmental goals. In Essay Two I undertake a reading for change programme in which different meaning making systems were confronted in order to challenge me as a meaning maker. Essay Three reported on my experiment which concerned the question whether it was possible for me as a property entrepreneur, and for others alike, to retain bank finance in the face of the overwhelming objective of the bank to deleverage their balance sheet of property loans. The output of my research can be grouped into General Developmental and Specific Business Implications. Firstly I address those who are interested in a transformational-based response to the challenges of operating in the property sector in Ireland during a crisis. I outline the apparatus of thought that I used to create insight, and thus transform how I thought, these are Awareness, Subject-object separation, Exploring other’s perspectives from the position of incompleteness, Dialectical thinking and Collingwood’s Questioning activity. Secondly I set out my learnings from the crisis and their impact on entrepreneurial behaviour and the business of property development. I identify ten key insights that have emerged from leading a property company through the crisis. Many of these are grounded in common sense, however, in my experience these were, to borrow Shakespeare’s words, “More honor'd in the breach than the observance” in pre Crisis Ireland. Finally I set out a four-step approach for forging a strategy. This requires my peer practitioners to identify (i) what they are subject to, (ii) Assess the Opportunity or challenge in a Systemic Context, (iii) Explore Multiple Perspectives on the opportunity or Challenge with an Orientation to change how you know and (iv) Using the Questioning Activity to create Knowledge. Based on my experience I conclude that transformative thinking and practice is a key enabler for a property entrepreneur, in responding to a major collapse of traditional (bank debt) funding.