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.

Learning to Teach and its Implications for the Continuum of Teacher Education: A Nine Country Cross-national Study.

The purpose of this Report is to inform discussions, policy formulation, and strategic planning on teacher education in Ireland. The research gives priority to initial teacher education (ITE) and induction, their interface, and implications for the continuum of teacher education, including continuing professional development (CPD). The study involved a two-pronged approach: a narrative review of recent and relevant literature and a cross-national review of teacher education policies in nine countries, namely, Ireland, Northern Ireland, Scotland, England, Finland, USA, Poland, Singapore and New Zealand. Adopting a broad, balanced and comprehensive understanding of the role of the contemporary teacher, it provides a framework for developing quality teacher education in Ireland. The Report incorporates exemplars of good practice and notes their implementation challenges for the Irish context.  Chapter One provides a framework for conceptualising quality teacher education and the continuum. Key features that emerge from the literature are discussed: teachers¿ practice, quality teaching, the professional life-cycle, teacher learning and relationships. With more specific reference to the continuum, Chapter Two overviews initial teacher education, induction, learning outcomes and accreditation in the selected countries, including Ireland. Key features of policy in the various countries are summarised. Individual country profiles, incorporating descriptions of socio-political, teaching and teacher education contexts, are further detailed in Appendix A. Chapter Three analyses relevant literature on initial teacher education, induction, learning outcomes/professional standards and accreditation. Along with previous chapters it provides the basis for recommendations for teacher education that are presented in Chapter Four. Chapter Four draws together the findings emerging from the cross-national review in terms of the contemporary context of teacher education in Ireland and identifies key challenges and possible lines of policy development as well as recommendations for the Teaching Council and other teacher education stakeholders. Each generation has an opportunity to provide the vision and resources for renewing teacher education in light of ambitious social, economic and educational aspirations to meet perceived societal and education challenges (as occurred in the 1970s). Despite the publication of two key reviews of initial teacher education a number of years ago, there is considerable scope for further reform of teacher education. However, significant changes have occurred to teacher education course provision and content over the last 100 years. In this report, we have stressed the need for, and called for investment in, greater system and programme coherence, mentoring to support assisted practice, knowledge integration, critical reflective practice, inquiry and the development of vibrant partnerships between higher education institutions and schools as the basis for teacher education reform across the continuum. This Executive Summary presents the Report¿s context, key findings and recommendations emerging from the analysis.  

Supporting therapist engagement in evidence based practice: Developing a continuing education programme through participatory action research

Therapists find it challenging to integrate research evidence into their clinical decision-making because it may involve modifying their existing practices. Although continuing education (CE) programmes for evidence-based practice (EBP) have employed various approaches to increase individual practitioner’s knowledge and skills, these have been shown to have little impact in changing customary behaviours. To date, there has been little attempt to actively engage therapists as collaborators in developing educational processes concerning EBP. The researcher collaborated with seven clinical therapists (one occupational therapist, four physiotherapists and two speech and language therapists) enrolled in a new post-qualification Implementing Evidence in Therapy Practice (IETP) MSc module to monitor and adapt the learning programme over ten weeks. The participating therapists actively engaged in participatory action research (PAR) iterative cycles of reflecting→ planning→ acting→ observing→ reflecting with the researcher. Mixed methods were used to evaluate the IETP module and its influence on therapists’ subsequent engagement in EBP activities. Data were gathered immediately on completion of the module and five months later. Immediate post-module findings revealed four components as being important to the therapists: 1) characteristics of the learning environment; 2) acquisition of relevant EBP skills; 3) nature of the learning process; and 4) acquiring confidence. The two themes and sub-themes which emerged from individual interviews conducted five months post-module expanded on the four components already identified. Theme 1: Experiencing the learning (sub-themes: module organisation; learning is relational; improving the module); and theme 2: Enacting the learning through a new way of being (sub-themes: criticality and reflection; self agency; modelling EBP behaviours; positioning self in an EB work culture). The therapists’ perspectives had by then shifted from that of a learner to that of a clinician constructing a new sense of self as an evidence-based practitioner. Findings from this study underline the importance of the process of socially constructed knowledge and of empowering learners through collaboratively designed continuing education programmes. In the student-driven learning environment, therapists chose repetitive skill-building and authentic problem-solving activities which reflected the complexity of the environments to which they were expected to transfer their learning. These findings have implications for educators designing EBP continuing education programmes, during which students develop professional ways of being.

The development of a model of continuing professional development for teachers of primary science

A new science curriculum was introduced to primary schools in the Republic of Ireland in 2003. This curriculum, broader in scope than its 1971 predecessor (Curaclam na Bunscoile, 1971), requires teachers at all levels of primary school to teach science. A review carried out in 2008 of children’s experiences of this curriculum found that its implementation throughout the country was uneven. This finding, together with the increasing numbers of teachers who were requesting support to implement this curriculum, suggested the need for a review of Irish primary teachers’ needs in the area of science. The research study described in this thesis was undertaken to establish the extent of Irish primary teachers’ needs in the area of science by conducting a national survey. The data from this survey, together with data from international studies, were used to develop a theoretical framework for a model of Continuing Professional Development (CPD). This theoretical framework was used to design the Whole- School, In-School (WSIS) CPD model which was trialled in two case-study schools. The participants in these ‘action-research’ case-studies acted as co-researchers, who contributed to the development and evolution of the CPD model in each school. Analysis of the data gathered as part of the evaluation of the Whole-School, In- School (WSIS) model of CPD found an improved experience of science for children and improved confidence for teachers teaching at all levels of the primary school. In addition, a template for the establishment of a culture of collaborative CPD in schools has been developed from an analysis of the data

Form-focused instruction in Irish-medium immersion education: a critical examination of teachers' perspectives and practices. A small-scale qualitative case study

It has been suggested that the less than optimal levels of students’ immersion language “persist in part because immersion teachers lack systematic approaches for integrating language into their content instruction” (Tedick, Christian and Fortune, 2011, p.7). I argue that our current lack of knowledge regarding what immersion teachers think, know and believe and what immersion teachers’ actual ‘lived’ experiences are in relation to form-focused instruction (FFI) prevents us from fully understanding the key issues at the core of experiential immersion pedagogy and form-focused integration. FFI refers to “any planned or incidental instructional activity that is intended to induce language learners to pay attention to linguistic form” (Ellis, 2001b, p.1). The central aim of this research study is to critically examine the perspectives and practices of Irish-medium immersion (IMI) teachers in relation to FFI. The study ‘taps’ into the lived experiences of three IMI teachers in three different IMI school contexts and explores FFI from a classroom-based, teacher-informed perspective. Philosophical underpinnings of the interpretive paradigm and critical hermeneutical principles inform and guide the study. A multi-case study approach was adopted and data was gathered through classroom observation, video-stimulated recall and semistructured interviews. Findings revealed that the journey of ‘becoming’ an IMI teacher is shaped by a vast array of intricate variables. IMI teacher identity, implicit theories, stated beliefs, educational biographies and experiences, IMI school cultures and contexts as well as teacher knowledge and competence impacted on IMI teachers’ FFI perspectives and practices. An IMI content teacher identity reflected the teachers’ priorities as shaped by pedagogical challenges and their educational backgrounds. While research participants had clearly defined instructional beliefs and goals, their roadmap of how to actually accomplish these goals was far from clear. IMI teachers described the multitude of choices and pedagogical dilemmas they faced in integrating FFI into experiential pedagogy. Significant gaps in IMI teachers’ declarative knowledge about and competence in the immersion language were also reported. This research study increases our understanding of the complexity of the processes underlying and shaping FFI pedagogy in IMI education. Innovative FFI opportunities for professional development across the continuum of teacher education are outlined, a comprehensive evaluation of IMI is called for and areas for further research are delineated.

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.

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.