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.

Contemporary pilgrimage in Ireland: a cultural geographic perspective

Using the lenses of contemporary cultural geography, this research develops an understanding of pilgrimage as a relational and reciprocal process that co-produces self and world. Drawing on the phenomenology of Merleau-Ponty, I argue that through the performances and experiences of contemporary pilgrimage in Ireland, participants and locations emerge as pilgrims and pilgrimage places. This approach unites different strands of cultural geography, including the mobilities field, more-than representational concerns, discussions of embodiment and practice, emotional and affective geographies, and religious and spiritual geographies. I explore how pilgrimage is an active process in which self and world, belief and practice, and the numinous and material entwine and merge. An autoethnographic methodology is enacted as an embodied, intersubjective, and reflexive research approach that incorporates the motivations, experiences, and beliefs of research participants, alongside my own descriptions and reflections. The methodology is focused on encountering and documenting pilgrimage practices as they occur in place and relating these embodied spatial practices to the accounts of pilgrims. The insights generated by engagements with research participants and through my own pilgrimages, offer new appreciations of the enduring appeal of pilgrimage in Ireland as a religious-spiritual and cultural activity that allows people to express personal intentions, to develop their faith, and to seek numinous encounters. Through the pilgrimages at Lough Derg, Croagh Patrick, and three holy wells, I produce a layered account of the empirical circumstances of the practices. The presentation of these places and events is enhanced by the use of evocative images and audiovisual recordings. By centring my study on the practices and experiences of different pilgrimages in present-day Ireland, and critically deploying strands of cultural geography and pilgrimage studies, this research produces new qualitative understandings of pilgrimage and contributes to discussions concerned with the relationships between self and world.