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.

Drama Grammatik: Dramapädagogische Ansätze für den Grammatikunterricht Deutsch als Fremdsprache

This dissertation introduces and evaluates dramagrammar, a new concept for the teaching and learning of foreign language grammar. Grammar, traditionally taught in a predominantly cognitive, abstract mode, often fails to capture the minds of foreign language learners, who are then unable to integrate this grammatical knowledge into their use of the foreign language in a meaningful way. The consequences of this approach are manifested at university level in German departments in England and Ireland, where the outcomes are unconvincing at best, abysmal at worst. Language teaching research suggests that interaction plays an important role in foreign language acquisition. Recent studies also stress the significance of grammatical knowledge in the learning process. Dramagrammar combines both interactive negotiation of meaning and explicit grammar instruction in a holistic approach, taking up the concept of drama in foreign language education and applying it to the teaching and learning of grammar. Techniques from dramatic art forms allow grammar to be experienced not only cognitively but also in social, emotional, and bodily-kinaesthetic ways. Dramagrammar lessons confront the learner with fictitious situations in which grammar is experienced 'hands-on'. Learners have to use grammatical structures in a variety of contexts, reflect upon their use, and then enlarge and enrich the dramatic situations with their newly acquired or more finely nuanced knowledge. The initial hypothesis of this dissertation is that the drammagrammar approach is beneficial to the acquisition of foreign language grammar. This hypothesis is corroborated by research findings from language teaching pedagogy and drama in education. It is further confirmed by empirical data gained from specifically designed dramagrammar modules that have been put into practice in German departments at the University of Leicester (England), the University Colleges Cork and Dublin (Ireland), the University of Bologna (Italy), as well as the Goethe-Institute Bratislava (Slovenia). The data suggests that drammagrammar has positive effects on both understanding of and attitudes towards grammar.

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.

Team-teaching for inclusive learning: Purposes, practices and perceptions of a team-teaching initiative in Irish post-primary schools

Background. Schools unequivocally privilege solo-teaching. This research seeks to enhance our understanding of team-teaching by examining how two teachers, working in the same classroom at the same time, might or might not contribute to the promotion of inclusive learning. There are well-established policy statements that encourage change and moves towards the use of team-teaching to promote greater inclusion of students with special educational needs in mainstream schools and mainstream classrooms. What is not so well established is the practice of team-teaching in post-primary settings, with little research conducted to date on how it can be initiated and sustained, and a dearth of knowledge on how it impacts upon the students and teachers involved. Research questions and aims. In light of the paucity and inconclusive nature of the research on team-teaching to date (Hattie, 2009), the orientating question in this study asks ‘To what extent, can the introduction of a formal team-teaching initiative enhance the quality of inclusive student learning and teachers’ learning at post-primary level?’ The framing of this question emerges from ongoing political, legal and educational efforts to promote inclusive education. The study has three main aims. The first aim of this study is to gather and represent the voices and experiences of those most closely involved in the introduction of team-teaching; students, teachers, principals and administrators. The second aim is to generate a theory-informed understanding of such collaborative practices and how they may best be implemented in the future. The third aim is to advance our understandings regarding the day-to-day, and moment-to-moment interactions, between teachers and students which enable or inhibit inclusive learning. Sample. In total, 20 team-teaching dyads were formed across seven project schools. The study participants were from two of the seven project schools, Ash and Oak. It involved eight teachers and 53 students, whose age ranged from 12-16 years old, with 4 teachers forming two dyads per school. In Oak there was a class of first years (n=11) with one dyad and a class of transition year students (n=24) with the other dyad. In Ash one class group (n=18) had two dyads. The subjects in which the dyads engaged were English and Mathematics. Method. This research adopted an interpretive paradigm. The duration of the fieldwork was from April 2007 to June 2008. Research methodologies included semi-structured interviews (n=44), classroom observation (n=20), attendance at monthly teacher meetings (n=6), questionnaires and other data gathering practices which included school documentation, assessment findings and joint examination of student work samples (n=4). Results. Team-teaching involves changing normative practices, and involves placing both demands and opportunities before those who occupy classrooms (teachers and students) and before those who determine who should occupy these classrooms (principals and district administrators). This research shows how team-teaching has the potential to promote inclusive learning, and when implemented appropriately, can impact positively upon the learning experiences of both teachers and students. The results are outlined in two chapters. In chapter four, Social Capital Theory is used in framing the data, the change process of bonding, bridging and linking, and in capturing what the collaborative action of team-teaching means, asks and offers teachers; within classes, between classes, between schools and within the wider educational community. In chapter five, Positioning Theory deductively assists in revealing the moment-to-moment, dynamic and inclusive learning opportunities, that are made available to students through team-teaching. In this chapter a number of vignettes are chosen to illustrate such learning opportunities. These two theories help to reveal the counter-narrative that team-teaching offers, regarding how both teachers and students teach and learn. This counter-narrative can extend beyond the field of special education and include alternatives to the manner in which professional development is understood, implemented, and sustained in schools and classrooms. Team-teaching repositions teachers and students to engage with one another in an atmosphere that capitalises upon and builds relational trust and shared cognition. However, as this research study has found, it is wise that the purposes, processes and perceptions of team-teaching are clear to all so that team-teaching can be undertaken by those who are increasingly consciously competent and not merely accidentally adequate. Conclusions. The findings are discussed in the context of the promotion of effective inclusive practices in mainstream settings. I believe that such promotion requires more nuanced understandings of what is being asked of, and offered to, teachers and students. Team-teaching has, and I argue will increasingly have, its place in the repertoire of responses that support effective inclusive learning. To capture and extend such practice requires theoretical frameworks that facilitate iterative journeys between research, policy and practice. Research to date on team-teaching has been too focused on outcomes over short timeframes and not focused enough on the process that is team-teaching. As a consequence team-teaching has been under-used, under-valued, under-theorised and generally not very well understood. Moving from classroom to staff room and district board room, theoretical frameworks used in this research help to travel with, and understand, the initiation, engagement and early consequences of team-teaching within and across the educational landscape. Therefore, conclusions from this study have implications for the triad of research, practice and policy development where efforts to change normative practices can be matched by understandings associated with what it means to try something new/anew, and what it means to say it made a positive difference.

Understanding student stress: a qualitative study of the stress experienced by third level students

Stress can be understood in terms of the meaning of stressful experiences for individuals. The meaning of stressful experiences involves threats to self-adequacy, where self-adequacy is considered a basic human need. Appropriate research methods are required to explore this aspect of stress. The present study is a qualitative exploration of the stress experienced by a group of 27 students at the National Institute of Higher Education, Limerick (since renamed the University of Limerick). The study was carried out by the resident student counsellor at the college. A model of student stress was explored, based on student developmental needs. The data consist of a series of interviews recorded with each of the 27 students over a 3 month period. These interviews were transcribed and the resulting transcripts are the subject of detailed analysis. The analysis of the data is an account of the sense-making process by the student counsellor of the students' reported experiences. The aim of the analysis was to reduce the large amounts of data to their most salient aspects in an ordered fashion, so as to examine the application of a developmental model of stress with this group of students. There were two key elements to the analysis. First, the raw data were edited to identify the key statements contained in the interviews. Second, the statements were categorised, as a means of summarising the data. The results of the qualitative dataanalysis were then applied to the developmental model. The analysis of data revealed a number of patterns of stress amongst the sample of students. Patterns of academic over-identification, parental conflict and social inadequacy were particularly noteworthy. These patterns consisted of an integration of academic, family and social stresses within a developmental framework. Gender differences with regard to the need for separateness and belonging are highlighted. Appropriate student stress intervention strategies are discussed. Based on the present results, the relationship between stress and development has been highlighted and is recommended as a firm basis for future studies of stress in general and student stress in particular.

The ways in which new public management ideas impact upon the administrative culture of 'street-level' bureaucrats and professionals working within Irish social policy

The conventional meaning of culture is ‘widely shared and strongly held values’ of a particular group or society (Bradley and Parker, 2006: 89). Culture is not a rigid concept; it can be influenced or altered by new ideas or forces. This research examines the ways in which one set of ideas in particular, that is, those associated with New Public Management, have impacted upon the administrative culture of 'street-level' bureaucrats and professionals within Irish social policy. Lipsky (1980: 3) defined 'street-level' bureaucrats as ‘public service workers who interact directly with citizens in the course of their jobs, and who have substantial discretion in the execution of their work’. Utilising the Competing Values Framework (CVF) in the analysis of eighty three semi-structured interviews with 'street-level' bureaucrats and professionals, an evaluation is made as to the impact of NPM ideas on both visible and invisible aspects of administrative culture. Overall, the influence of NPM is confined to superficial aspects of administrative culture such as; increased flexibility in working hours and to some degree job contracts; increased time commitment; and a customer service focus. However, the extent of these changes varies depending on policy sector and occupational group. Aspects of consensual and hierarchical cultures remain firmly in place. These coincide with features of developmental and market cultures. Contrary to the view that members of hierarchical and consensual culture would pose resistance to change, this research clearly illustrates that a very large appetite for change exists in the attitudes of 'street-level' bureaucrats and professionals within Irish social policy, with many of them suggesting changes that correspond to NPM ideas. This study demonstrates the relevance of employing the CVF model as it is clear that administrative culture is very much a dynamic system of competing and co-existing cultures.

Investigation of stress and burnout in Irish second-level teachers: A mixed-methods approach.

This study explores the experiences of stress and burnout in Irish second level teachers and examines the contribution of a number of individual, environmental and health factors in burnout development. As no such study has previously been carried out with this sample, a mixed-methods approach was adopted in order to comprehensively investigate the subject matter. Teaching has consistently been identified as a particularly stressful occupation and research investigating its development is of great importance in developing measures to address the problem. The first phase of study involved the use of focus groups conducted with a total of 20 second-level teachers from 11 different schools in the greater Cork city area. Findings suggest that teachers experience a variety of stressors – in class, in the staff room and outside of school. The second phase of study employed a survey to examine the factors associated with burnout. Analysis of 192 responses suggested that burnout results from a combination of demographic, personality, environmental and coping factors. Burnout was also found to be associated with a number of physical symptoms, particularly trouble sleeping and fatigue. Findings suggest that interventions designed to reduce burnout must reflect the complexity of the problem and its development. Based on the research findings, interventions that combine individual and organisational approaches should provide the optimal chance of effectively tackling burnout.

Can population-level variation in early childhood development be measured in a manner that supports service planning and intervention?

Background: The Early Development Instrument (EDI) is a population-level measure of five developmental domains at school-entry age. The overall aim of this thesis was to explore the potential of the EDI as an indicator of early development in Ireland. Methods: A cross-sectional study was conducted in 47 primary schools in 2011 using the EDI and a linked parental questionnaire. EDI (teacher completed) scores were calculated for 1,344 children in their first year of full-time education. Those scoring in the lowest 10% of the sample population in one or more domains were deemed to be 'developmentally vulnerable'. Scores were correlated with contextual data from the parental questionnaire and with indicators of area and school-level deprivation. Rasch analysis was used to determine the validity of the EDI. Results: Over one quarter (27.5%) of all children in the study were developmentally vulnerable. Individual characteristics associated with increased risk of vulnerability were being male; under 5 years old; and having English as a second language. Adjusted for these demographics, low birth weight, poor parent/child interaction and mother’s lower level of education showed the most significant odds ratios for developmental vulnerability. Vulnerability did not follow the area-level deprivation gradient as measured by a composite index of material deprivation. Children considered by the teacher to be in need of assessment also had lower scores, which were not significantly different from those of children with a clinical diagnosis of special needs. all domains showed at least reasonable fit to the Rasch model supporting the validity of the instrument. However, there was a need for further refinement of the instrument in the Irish context. Conclusion: This thesis provides a unique snapshot of early development in Ireland. The EDI and linked parental questionnaires are promising indicators of the extent, distribution and determinants of developmental vulnerability.

The student bullying of teachers in Irish second level schools: exploring the influence of historical low state intervention in education on the development of contemporary policy responses in Ireland

The student bullying of teachers (SBT) is a distinct and complex form of bullying with a multiplicity of diverse, changeable and intersecting causes which is experienced by and affects teachers in a variety of ways. SBT is both a national and an international phenomenon which is under-recognised in academic, societal and political spheres, resulting in limited conceptual understanding and awareness of the issue. This study explores teachers’ experiences of SBT behaviours in Irish second level schools as well as teachers’ perceptions regarding training, policies and supports in Ireland to address the issue. Specifically, the study seeks to explore the influence of historical low State intervention in education on contemporary policies and supports to deal with SBT in Ireland. A mixed methods approach involving a survey of 531 second level school teachers and 17 semi-structured interviews with teachers, Year Heads and representatives from teacher trade unions and school management bodies was employed to collect and analyse data. Findings indicate that SBT behaviours are prevalent in many forms in Irish second level schools. The hidden nature of the phenomenon has simultaneously contributed to and is reinforced by limited understanding of the issue as well as teachers’ reluctance to disclose their experiences. Findings reveal that teachers perceive the contemporary policies, training and support structures in Ireland to be inadequate in equipping them to effectively deal with SBT. State intervention in addressing SBT behaviours to date, has been limited, therefore many teachers are forced to respond to the issue based on their own initiatives and assumptions rather than from an informed critically reflective approach, supported by national guidelines and sufficient State investment. This has resulted in a piecemeal, un-coordinated and ad-hoc approach to SBT in Irish schools both in terms of teachers’ management of SBT behaviours and with respect to the supports extended to staff. The potential negative consequences of SBT behaviours on teachers’ wellbeing and professional performance and thus, on the education system itself, underlines the need for a strategic, evidence-based, resourced and integrated approach which includes, as a pivotal component, consultation with teachers, whose contribution to the process is crucial.