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.

Development of large-scale colloidal crystallisation methods for the production of photonic crystals

Colloidal photonic crystals have potential light manipulation applications including; fabrication of efficient lasers and LEDs, improved optical sensors and interconnects, and improving photovoltaic efficiencies. One road-block of colloidal selfassembly is their inherent defects; however, they can be manufactured cost effectively into large area films compared to micro-fabrication methods. This thesis investigates production of ‘large-area’ colloidal photonic crystals by sonication, under oil co-crystallization and controlled evaporation, with a view to reducing cracking and other defects. A simple monotonic Stöber particle synthesis method was developed producing silica particles in the range of 80 to 600nm in a single step. An analytical method assesses the quality of surface particle ordering in a semiquantitative manner was developed. Using fast Fourier transform (FFT) spot intensities, a grey scale symmetry area method, has been used to quantify the FFT profiles. Adding ultrasonic vibrations during film formation demonstrated large areas could be assembled rapidly, however film ordering suffered as a result. Under oil cocrystallisation results in the particles being bound together during film formation. While having potential to form large areas, it requires further refinement to be established as a production technique. Achieving high quality photonic crystals bonded with low concentrations (<5%) of polymeric adhesives while maintaining refractive index contrast, proved difficult and degraded the film’s uniformity. A controlled evaporation method, using a mixed solvent suspension, represents the most promising method to produce high quality films over large areas, 75mm x 25mm. During this mixed solvent approach, the film is kept in the wet state longer, thus reducing cracks developing during the drying stage. These films are crack-free up to a critical thickness, and show very large domains, which are visible in low magnification SEM images as Moiré fringe patterns. Higher magnification reveals separation between alternate fringe patterns are domain boundaries between individual crystalline growth fronts.