A Jaworskian analysis of four senior class primary teachers endeavouring to teach mathematics from a constructivist-compatible perspective

A constructivist philosophy underlies the Irish primary mathematics curriculum. As constructivism is a theory of learning its implications for teaching need to be addressed. This study explores the experiences of four senior class primary teachers as they endeavour to teach mathematics from a constructivist-compatible perspective with primary school children in Ireland over a school-year period. Such a perspective implies that children should take ownership of their learning while working in groups on tasks which challenge them at their zone of proximal development. The key question on which the research is based is: to what extent will an exposure to constructivism and its implications for the classroom impact on teaching practices within the senior primary mathematics classroom in both the short and longer term? Although several perspectives on constructivism have evolved (von Glaserfeld (1995), Cobb and Yackel (1996), Ernest (1991,1998)), it is the synthesis of the emergent perspective which becomes pivotal to the Irish primary mathematics curriculum. Tracking the development of four primary teachers in a professional learning initiative involving constructivist-compatible approaches necessitated the use of Borko’s (2004) Phase 1 research methodology to account for the evolution in teachers’ understanding of constructivism. Teachers’ and pupils’ viewpoints were recorded using both audio and video technology. Teachers were interviewed at the beginning and end of the project and also one year on to ascertain how their views had evolved. Pupils were interviewed at the end of the project only. The data were analysed from a Jaworskian perspective i.e. using the categories of her Teaching Triad of management of learning, mathematical challenge and sensitivity to students. Management of learning concerns how the teacher organises her classroom to maximise learning opportunities for pupils. Mathematical challenge is reminiscent of the Vygotskian (1978) construct of the zone of proximal development. Sensitivity to students involves a consciousness on the part of the teacher as to how pupils are progressing with a mathematical task and whether or not to intervene to scaffold their learning. Through this analysis a synthesis of the teachers’ interpretations of constructivist philosophy with concomitant implications for theory, policy and practice emerges. The study identifies strategies for teachers wishing to adopt a constructivist-compatible approach to their work. Like O’Shea (2009) it also highlights the likely difficulties to be experienced by such teachers as they move from utilising teacher-dominated methods of teaching mathematics to ones in which pupils have more ownership over their learning.

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.

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.

The senior female international managerial career move: a qualitative study in a European context

Research investigating the position of women in management has, largely, been confined within national boundaries. Over the last fifteen years, empirical studies of women in international management have been undertaken, predominantly in North America. In this research field, many questions remain unanswered or have been only partially addressed. The particular focus of this study is on the senior female international managerial career move in Europe — a relatively unexplored area. Fifty senior female expatriate managers were interviewed, representing a wide range of industry and service sectors. The study, for the first time, assesses an exclusively senior sample of female managers who have made at least one international career move. This study of senior females in international management makes a theoretical contribution, not only to the analysis of gender and international human resource management, but also to wider debates within the contemporary women in management and career theory literatures. The aims of the study were to develop an understanding of the senior female international career move in a European context in order to more fully understand both the covert and overt barriers that may limit women’s international career opportunities. The results of the study show that the senior international career move has largely been developed along a linear male model of career progression, a development which, taken together with gender disparity both in organisations and family responsibilities, frequently prevents women employees from reaching senior managerial positions. The study proposes a model of the senior female international managerial career move, thereby contributing primarily to the international human resource management literature. The implications of the study for research literatures in women in management and career theory are also explored and a future research agenda developed.

Work experience in transition year: a mixed methods study of subject and career choices

Transition Year (TY) has been a feature of the Irish Education landscape for 39 years. Work experience (WE) has become a key component of TY. WE is defined as a module of between five and fifteen days duration where students engage in a work placement in the broader community. It places a major emphasis on building relationships between schools and their external communities and concomitantly between students and their potential future employers. Yet, the idea that participation in a TY work experience programme could facilitate an increased awareness of potential careers has drawn little attention from the research community. This research examines the influence WE has on the subsequent subjects choices made by students along with the effects of that experience on the students’ identities and emerging vocational identities. Socio-cultural Learning Theory and Occupational Choice Theory frame the overall study. A mixed methods approach to data collection was adopted through the administration of 323 quantitative questionnaires and 32 individual semi-structured interviews in three secondary schools. The analysis of the data was conducted using a grounded theory approach. The findings from the research show that WE makes a significant contribution to the students’ sense of agency in their own lives. It facilitates the otherwise complex process of subject choice, motivates students to work harder in their senior cycle, introduces them to the concepts of active, experience-based and self-directed learning, while boosting their self-confidence and nurturing the emergence of their personal and vocational identities. This research is a gateway to further study in this field. It also has wide reaching implications for students, teachers, school authorities, parents and policy makers regarding teaching and learning in our schools and the value of learning beyond the walls of the classroom.

Molecular composition of biogenic secondary organic aerosols using ultrahigh resolution mass spectrometry: comparing laboratory and field studies

Numerous laboratory experiments have been performed in an attempt to mimic atmospheric secondary organic aerosol (SOA) formation. However, it is still unclear how close the aerosol particles generated in laboratory experiments resemble atmospheric SOA with respect to their detailed chemical composition. In this study, we generated SOA in a simulation chamber from the ozonolysis of α-pinene and a biogenic volatile organic compound (BVOC) mixture containing α- and β-pinene, Δ3-carene, and isoprene. The detailed molecular composition of laboratory-generated SOA was compared with that of background ambient aerosol collected at a boreal forest site (Hyytiälä, Finland) and an urban location (Cork, Ireland) using direct infusion nanoelectrospray ultrahigh resolution mass spectrometry. Kendrick Mass Defect and Van Krevelen approaches were used to identify and compare compound classes and distributions of the detected species. The laboratory-generated SOA contained a distinguishable group of dimers that was not observed in the ambient samples. The presence of dimers was found to be less pronounced in the SOA from the VOC mixtures when compared to the one component precursor system. The elemental composition of the compounds identified in the monomeric region from the ozonolysis of both α-pinene and VOC mixtures represented the ambient organic composition of particles collected at the boreal forest site reasonably well, with about 70% of common molecular formulae. In contrast, large differences were found between the laboratory-generated BVOC samples and the ambient urban sample. To our knowledge this is the first direct comparison of molecular composition of laboratory-generated SOA from BVOC mixtures and ambient samples.

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.

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.