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.

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.

The political philosophy of Miki Kiyoshi: A close reading of the philosophical foundations of cooperative communitarianism

The thesis is a historical and philological study of the mature political theory of Miki Kiyoshi (1897-1945) focused on Philosophical Foundations of Cooperative Communitarianism (1939), a full translation of which is included. As the name suggests, it was a methodological and normative communitarianism, which critically built on liberalism, Marxism and Confucianism to realise a regional political community. Some of Miki’s Western readers have wrongly considered him a fascist ideologue, while he has been considered a humanist Marxist in Japan. A closer reading cannot support either view. The thesis argues that the Anglophone study of Japanese philosophy is a degenerating research programme ripe for revolution in the sense of returning full circle to an original point. That means returning to the texts, reading them contextually and philologically, in principle as early modern European political theory is read by intellectual historians, such as the representatives of Cambridge School history of political thought. The resulting reading builds critically on the Japanese scholarship and relates it to contemporary Western and postcolonial political theory and the East Asian tradition, particularly neo-Confucianism. The thesis argues for a Cambridge School perspective radicalised by the critical addendum of geo-cultural context, supplemented by Geertzian intercultural hermeneutics and a Saidian ‘return to philology’. As against those who have seen radical reorientations in Miki’s political thought, the thesis finds gradual progression and continuity between his neo-Kantian, existentialist, Marxian anthropology, Hegelian and finally communitarian phases. The theoretical underpinnings are his philosophical anthropology, a structurationist social theory of praxis, and a critique of liberalism, Marxism, nationalism and idealism emphasising concrete as opposed to abstract theory and the need to build on existing cultural traditions to modernise rather than westernise East Asia. This post-Western fusion was imagined to be the beginning of a true and pluralistic universalism.

Zazen, philosophy of mind, and the practicality of realising impermanence

This dissertation involves a general overview of the meditative practice of zazen and analytic philosophy of mind while suggesting a potential bridge between them in the form of an analysis of the practicality of realising impermanence. By the end of my argument I hope to have offered up some compelling evidence in favour of the idea that analytic philosophy would benefit greatly from adopting principles which are best learned and expressed through the practice of, and scholarship around, Zen Buddhism and in particular the treatment of the concept of impermanence. I demonstrate the Western philosophical tendency to make dichotomous assumptions about the nature of mind, even when explicitly denying a dualist framework. I do so by examining the historical and philosophical precedent for dualistic thinking in the work of figures such as Plato and Descartes. I expand on this idea by examining the psychology of categorisation - i.e. creating mental categories and boundaries - and demonstrating how such categorisations feeds back into behaviour in practical ways, both positive and negative. The Zen Buddhist principle of impermanence states that all phenomena are impermanent and therefore lack essential nature; this includes intellectual concepts such as the metaphysical framework of the analytic approach to mind. Impermanence is a principle which is realised through the embodied practice of zazen. By demonstrating its application to analytic philosophy of mind I show that zazen (and mindfulness practice in general) provides an ongoing opportunity for clearing up entrenched world views, metaphysical assumptions and dogmatic thinking. This in turn may promote a more holistic and ultimately more rewarding comprehension of the role of first-person experience in understanding the world. My argument is not limited to analytic philosophy of mind but reflects broad aspects of thinking in general, and I explain its application to issues of social importance, in particular education systems.

A philosophy of performance, politics and composition

This thesis discusses socio-political issues worldwide through philosophical approaches to performance, politics and composition. My research also discuss sound decisions which I regard to be simultaneously an outlet for personal expression, as well as a practical tool to inspire a socio-political change in society. Although the latter is paramount to the methodology of the project, the sound cannot be regarded in isolation as a “political composition”. It can only become truly functional in a political sense through interaction with other art forms, within the context of a specific place and time. My portfolio for this project is of two socio-political projects which are my chief concern. The first project concerns the Israeli-Palestinian conflict. I named this project PATH. PATH aims to foster and expand peaceful thought between Jewish and Palestinian civilians in Israel-Palestine. Through performance art, PATH spreads a message of acceptance, unity and brotherhood between our peoples. Above all, PATH demands and end to intolerance, hatred and violence among all the inhabitants of the State of Israel. The second project concerns women’s rights globally. I have realised that although we have come a long way in our struggle for rights for women, great challenges remain. There is a need to unite women and men against a form of oppression that discriminates against 50% of the world’s population. I called this project, For Utopia.

The Kyoto School and Confucianism: a Confucian reading of the philosophy of history and political thought of Masaaki Kosaka

This dissertation examines the philosophy of Masaaki Kōsaka (1900-1969) from the East Asian perspective of Confucianism, which I believe is the most appropriate moral paradigm for comprehending his political speculations. Although largely neglected in post-war scholarship, Kōsaka was a prominent member of the Kyoto School during the 1930s and 40s. This was a group of Japanese thinkers strongly associated with the philosophies of Kitarō Nishida and Hajime Tanabe. Kōsaka is now best known for his participation in the three Chūō Kōron symposia held in 1941 and 1942. These meetings have been routinely denounced by liberal historians due to the participants’ support for the Pacific War and the Co-Prosperity Sphere. However, many of these liberal portrayals have failed to take into account the full extent of the group’s resistance to the military junta of Hideki Tōjō. Adopting the methods and techniques of the empirical disciplines of academic history and Orientalism, I develop an interpretative framework that is more receptive to the political values that mattered to Kōsaka as a Confucian inspired intellectual. This has necessitated the rejection of moral history, which typically prioritises modern liberal values brought a priori to the historical record of wartime Japan, as well as recognition of the different ontological foundations that inform the unique political theories of the East Asian intellectual tradition. Reinforced by the prior research of Michel Dalissier and Graham Parkes, as well as my own reading of the Confucian canon, I adopt David Williams’s thesis of ‘Confucian Revolution’ as my principle schema of interpretation. This, I believe, is better able to reconcile Kōsaka’s support for the war with his strong condemnation of the imperialist practices of the Japanese military. Moreover, acknowledging the importance of Confucianism allows us to fully appreciate Kōsaka’s strong affinity for Kant’s practical metaphysics, Hegel’s political philosophy and Ranke’s historiography.

Behind the paravent: a study of Konrad Bayer's dramatic texts

This thesis is a study of Konrad Bayer's dramatic texts. It has evolved out of various attempts to read those texts, some filed and some more successful. It does not claim to be authoritative or complete, since the nature of Bayer's texts, as will become clear in the course of the ensuing chapters, means that they resist such an interpretation. To accept this was an important prerequisite for the writing of this thesis, but a difficult one to fulfill because for the Bayer commentator it constitutes a certain acceptance of defeat even before one begins. Chapter 1 will begin by providing some introductory information about Konrad Bayer, including details of his life and his membership of the Wiener Gruppe, a formative phase in his development as a writer. It will also consider the historical and cultural climate of 1950s Austria that provided the backdrop for Bayer's literary work. The phenomenon of the Wiener Gruppe will then be examined against the background of preceding experimental movements, for the purpose of situating Bayer's work historically and artistically. The aim of this historical and artistic survey is to prepare for the confrontation with Bayer's texts that makes up the other chapters of the thesis. Chapter 2 will constitute a close textual study of one of Bayer's dramatic texts using criteria from the field of text linguistics. Such a study will offer an entry point into Bayer's texts and will supply material which will form the basis for the interpretative investigations of the chapters that follow it. Chapter 3 will consider the influence of language and the individual. In chapter 4 the figure of the Lion of Belfort, a recurring figure in Bayer's dramatic texts, is discussed. The final chapter of this thesis will examine the recurring motifs of violence and cannibalism and will consider them in terms of the findings of preceding chapters.

The musical enculturation of Irish traditional musicians: An ethnographic study of learning processes

The enculturation of Irish traditional musicians involves informal, non-formal, and sometimes formal learning processes in a number of different settings, including traditional music sessions, workshops, festivals, and classes. Irish traditional musicians also learn directly from family, peers, and mentors and by using various forms of technology. Each experience contributes to the enculturation process in meaningful and complementary ways. The ethnographic research discussed in this dissertation suggests that within Irish traditional music culture, enculturation occurs most effectively when learners experience a multitude of learning practices. A variety of experiences insures that novices receive multiple opportunities for engagement and learning. If a learner finds one learning practice ineffective, there are other avenues of enculturation. This thesis explores the musical enculturation of Irish traditional musicians. It focuses on the process of becoming a musician by drawing on methodologies and theories from ethnomusicology, education, and Irish traditional music studies. Data was gathered through multiple ethnographic methodologies. Fieldwork based on participant-observation was carried out in a variety of learning contexts, including traditional music sessions, festivals, workshops, and weekly classes. Additionally, interviews with twenty accomplished Irish traditional musicians provide diverse narratives and firsthand insight into musical development and enculturation. These and other methodologies are discussed in Chapter 1. The three main chapters of the thesis explore various common learning experiences. Chapter 2 explores how Irish traditional musicians learn during social and musical interactions between peers, mentors, and family members, and focuses on live music-making which occurs in private homes, sessions, and concerts. These informal and non-formal learning experiences primarily take place outside of organizations and institutions. The interview data suggests these learning experiences are perhaps the most pervasive and influential in terms of musical enculturation. Chapter 3 discusses learning experience in more organized settings, such as traditional music classes, workshops, summer schools, and festivals. The role of organizations such as Comhaltas Ceoltóirí Éireann and pipers’ clubs are discussed from the point of view of the learner. Many of the learning experiences explored in this chapter are informal, non-formal, and sometimes formal in nature, depending on the philosophy of the organization, institution, and individual teacher. The interview data and field observations indicate that learning in these contexts is common and plays a significant role in enculturation, particularly for traditional musicians who were born during and after the 1970s. Chapter 4 explores the ways Irish traditional musicians use technology, including written sources, phonography, videography, websites, and emerging technologies, during the enculturation process. Each type of technology presents different educational implications, and traditional musicians use these technologies in diverse ways and some more than others. For this, and other reasons, technology plays a complex role during the process of musical enculturation. Drawing on themes which emerge during Chapter 2, 3, and 4, the final chapter of this dissertation explores overarching patterns of enculturation within Irish traditional music culture. This ethnographic work suggests that longevity of participation and engagement in multiple learning and performance opportunities foster the enculturation of Irish traditional musicians. Through numerous and prolonged participation in music-making, novices become accustomed to and learn musical, social, and cultural behaviours. The final chapter also explores interconnections between learning experiences and also proposes directions for future research.

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.

Citizenship education in Irish secondary schools: the influence of curriculum content, school culture and stakeholder perspectives

This research interrogates the status of citizenship education in Irish secondary schools. The following questions are examined: How does school culture impact on citizenship education? What value is accorded to the subjects, Civic, Social and Political Education (CSPE) and Social, Personal and Health Education (SPHE)? To what extent are the subjects of both the cognitive and non-cognitive curricula affirmed? The importance of these factors in supporting the social, ethical, personal, political and emotional development of students is explored. The concept of citizenship is dynamic and constantly evolving in response to societal change. Society is increasingly concerned with issues such as: globalisation; cosmopolitanism; the threat of global risk; environment sustainability; socio-economic inequality; and recognition/misrecognition of new identities and group rights. The pedagogical philosophy of Paulo Freire which seeks to educate for the conscientisation and humanisation of the student is central to this research. Using a mixed methods approach, data on the insights of students, parents, teachers and school Principals was collected. In relation to Irish secondary school education, the study reached three main conclusions. (1) The educational stakeholders rate the subjects of the non-cognitive curriculum poorly. (2) The subjects Civic, Social and Political education (CSPE), and Social, Personal and Health Education (SPHE) command a low status in the secondary school setting. (3) The day-to-day school climate is influenced by an educational philosophy that is instrumentalist in character. Elements of school culture such as: the ethic of care; the informal curriculum; education for life after school; and affirmation of teachers, are not sufficiently prioritised in supporting education for citizenship. The research concludes that the approach to education for citizenship needs to be more robust within the overall curriculum, and culture and ethos of the Irish education system.