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.

Towards a model for exploring the relationship between managerial decision problems and decision support opportunities

The organisational decision making environment is complex, and decision makers must deal with uncertainty and ambiguity on a continuous basis. Managing and handling decision problems and implementing a solution, requires an understanding of the complexity of the decision domain to the point where the problem and its complexity, as well as the requirements for supporting decision makers, can be described. Research in the Decision Support Systems domain has been extensive over the last thirty years with an emphasis on the development of further technology and better applications on the one hand, and on the other hand, a social approach focusing on understanding what decision making is about and how developers and users should interact. This research project considers a combined approach that endeavours to understand the thinking behind managers’ decision making, as well as their informational and decisional guidance and decision support requirements. This research utilises a cognitive framework, developed in 1985 by Humphreys and Berkeley that juxtaposes the mental processes and ideas of decision problem definition and problem solution that are developed in tandem through cognitive refinement of the problem, based on the analysis and judgement of the decision maker. The framework facilitates the separation of what is essentially a continuous process, into five distinct levels of abstraction of manager’s thinking, and suggests a structure for the underlying cognitive activities. Alter (2004) argues that decision support provides a richer basis than decision support systems, in both practice and research. The constituent literature on decision support, especially in regard to modern high profile systems, including Business Intelligence and Business analytics, can give the impression that all ‘smart’ organisations utilise decision support and data analytics capabilities for all of their key decision making activities. However this empirical investigation indicates a very different reality.

Seasonal changes in Vitamin D-effective UVB availability in Europe and associations with population serum 25-Hydroxyvitamin D

Low vitamin D status is common in Europe. The major source of vitamin D in humans is ultraviolet B (UVB)-induced dermal synthesis of cholecalciferol, whereas food sources are believed to play a lesser role. Our objectives were to assess UVB availability (Jm−2) across several European locations ranging from 35° N to 69° N, and compare these UVB data with representative population serum 25-hydroxyvitamin D (25(OH)D) data from Ireland (51–54° N), Iceland (64° N) and Norway (69° N), as exemplars. Vitamin D-effective UVB availability was modelled for nine European countries/regions using a validated UV irradiance model. Standardized serum 25(OH)D data was accessed from the EC-funded ODIN project. The results showed that UVB availability decreased with increasing latitude (from 35° N to 69° N), while all locations exhibited significant seasonal variation in UVB. The UVB data suggested that the duration of vitamin D winters ranged from none (at 35° N) to eight months (at 69° N). The large seasonal fluctuations in serum 25(OH)D in Irish adults was much dampened in Norwegian and Icelandic adults, despite considerably lower UVB availability at these northern latitudes but with much higher vitamin D intakes. In conclusion, increasing the vitamin D intake can ameliorate the impact of low UVB availability on serum 25(OH)D status in Europe.

History, revolution and the British popular novel: historical fiction in the romantic age

“History, Revolution and the British Popular Novel” takes as its focus the significant role which historical fiction played within the French Revolution debate and its aftermath. Examining the complex intersection of the genre with the political and historical dialogue generated by the French Revolution crisis, the thesis contends that contemporary fascination with the historical episode of the Revolution, and the fundamental importance of history to the disputes which raged about questions of tradition and change, and the meaning of the British national past, led to the emergence of increasingly complex forms of fictional historical narrative during the “war of ideas.” Considering the varying ways in which novelists such as Charlotte Smith, William Godwin, Mary Robinson, Helen Craik, Clara Reeve, John Moore, Edward Sayer, Mary Charlton, Ann Thomas, George Walker and Jane West engaged with the historical contexts of the Revolution debate, my discussion juxtaposes the manner in which English Jacobin novelists inserted the radical critique of the Jacobin novel into the wider arena of history with anti-Jacobin deployments of the historical to combat the revolutionary threat and internal moves for socio-political restructuring. I argue that the use of imaginative historical narrative to contribute to the ongoing dialogue surrounding the Revolution, and offer political and historical guidance to readers, represented a significant element within the literature of the Revolution crisis. The thesis also identifies the diverse body of historical fiction which materialised amidst the Revolution controversy as a key context within which to understand the emergence of Scott’s national historical novel in 1814, and the broader field of historical fiction in the era of Waterloo. Tracing the continued engagement with revolutionary and political concerns evident in the early Waverley novels, Frances Burney’s The Wanderer (1814), William Godwin’s Mandeville (1816), and Mary Shelley’s Valperga (1823), my discussion concludes by arguing that Godwin’s and Shelley’s extension of the mode of historical fiction initially envisioned by Godwin in the revolutionary decade, and their shared endeavour to retrieve the possibility enshrined within the republican past, appeared as a significant counter to the model of history and fiction developed by Walter Scott in the post-revolutionary epoch.

Transitions: From novice participation to expertise, pre-school 'matters' in an Irish pre-school community

This in depth, qualitative, participant observer study tracks children's transition experiences from novice to experienced membership of their pre-school community. It also considers adult roles in mediating this process in the context of the recent introduction of a universal free-pre-school year for children growing up in Ireland. Participation and the space to negotiate a participatory identity is understood in this study as a key element of positive experiences of early years transitions, within pre-school and beyond. The underlying theoretical framework is socio-cultural. This approach shifts from a scientific positivist view of thinking and learning as an individual inside the head process and asserts the historical, social, cultural as well as the situated context of learning and meaning making All participants, including myself as researcher, are recognised, explored and valued as embedded in the cultural context studied. In a sense, this approach tilts the worlds being observed through participation in them and reflects them in new light. The aim is to interpret and reflect the multiple realities constructed in this context rather than seek a truth out there waiting to be found. Special efforts are made to be invited in to and acknowledge children's expertise in the cultural worlds they negotiate with peers and adults in pre-school. The aim is to better understand what children may find motivating, interesting or problematic as they interpret reproduce and transform meaning within their play and learning worlds. My aim is for an honest rendering of the voices of stakeholders in pre-school communities from teachers, parents, and policy makers to children themselves. It makes visible constraints; potentials and possibilities within everyday Irish pre-school practices in the situated context studied as well as the broader societal, legislative and macro policy influences it reflects. Casting light on the taken for granted opens the possibility of adaptation or transformation. Transition itself can act as a tool to meet the changing needs of children on their developmental pathways across the life cycle