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.

Manifestations of heavenly light and fire and the construction of a saint: sanctity, mission and salvation in Adomnán's Vita Columbae

This thesis examines the late seventh-century Latin Life of Columba (Vita Columbae) in a context sympathetic to the spiritual aims and formative intellectual background of its author, Adomnán of Iona. It argues that the Vita Columbae is a sophisticated work, shaped by Adomnán’s spiritual and theological concerns. This sophistication is revealed by a forensic examination of Adomnán’s representation of Columba’s sanctity through a series of miracles, in particular, miracle stories depicting divine manifestations of fire and light. This thesis considers the form and function of these miracle stories in the context of biblical, patristic and medieval interpretations of their archetypes, towards revealing the underlying influence of scriptural, hagiographical and monastic models of sanctity. Chapter one evaluates the function of the Vita Columbae, and outlines the core themes of sanctity which pervade the work, by considering the technical terminology and literary devices found in the opening prefaces in the context of the wider monastic tradition. Chapter two examines Adomnán’s use of biblical models of sanctity to establish Columba’s sanctity, and their relationship between these models and certain miraculous episodes in the Vita Columbae. Chapter three investigates Adomnán’s description of the Holy Spirit as an illuminating fire, and its significance for his portrayal of the saint, by means of a forensic examination of biblical, exegetical and hagiographical treatments of the image. Chapter four examines the missiological, soteriological and providential elements contributing to Adomnán’s portrayal of Columba’s sanctity, as conveyed through the presence of biblical models, particularly the image of the column of fire. Chapter five establishes the influence of monastic examinations of the contemplative life on Adomnán’s portrayal of Columba’s sanctity, and shows how that sanctity is confirmed in terms of his ability to contemplate divine light.