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.

AuxAg1-x alloy seeds: A way to control growth, morphology and defect formation in Ge nanowires

Germanium (Ge) nanowires are of current research interest for high speed nanoelectronic devices due to the lower band gap and high carrier mobility compatible with high K-dielectrics and larger excitonic Bohr radius ensuing a more pronounced quantum confinement effect [1-6]. A general way for the growth of Ge nanowires is to use liquid or a solid growth promoters in a bottom-up approach which allow control of the aspect ratio, diameter, and structure of 1D crystals via external parameters, such as precursor feedstock, temperature, operating pressure, precursor flow rate etc [3, 7-11]. The Solid-phase seeding is preferred for more control processing of the nanomaterials and potential suppression of the unintentional incorporation of high dopant concentrations in semiconductor nanowires and unrequired compositional tailing of the seed-nanowire interface [2, 5, 9, 12]. There are therefore distinct features of the solid phase seeding mechanism that potentially offer opportunities for the controlled processing of nanomaterials with new physical properties. A superior control over the growth kinetics of nanowires could be achieved by controlling the inherent growth constraints instead of external parameters which always account for instrumental inaccuracy. The high dopant concentrations in semiconductor nanowires can result from unintentional incorporation of atoms from the metal seed material, as described for the Al catalyzed VLS growth of Si nanowires [13] which can in turn be depressed by solid-phase seeding. In addition, the creation of very sharp interfaces between group IV semiconductor segments has been achieved by solid seeds [14], whereas the traditionally used liquid Au particles often leads to compositional tailing of the interface [15] . Korgel et al. also described the superior size retention of metal seeds in a SFSS nanowire growth process, when compared to a SFLS process using Au colloids [12]. Here in this work we have used silver and alloy seed particle with different compositions to manipulate the growth of nanowires in sub-eutectic regime. The solid seeding approach also gives an opportunity to influence the crystallinity of the nanowires independent of the substrate. Taking advantage of the readily formation of stacking faults in metal nanoparticles, lamellar twins in nanowires could be formed.

Lower extremity amputation in people with diabetes: Trends and determinants

Introduction: The prevalence of diabetes is rising rapidly. Assessing quality of diabetes care is difficult. Lower Extremity Amputation (LEA) is recognised as a marker of the quality of diabetes care. The focus of this thesis was first to describe the trends in LEA rates in people with and without diabetes in the Republic of Ireland (RoI) in recent years and then, to explore the determinants of LEA in people with diabetes. While clinical and socio-demographic determinants have been well-established, the role of service-related factors has been less well-explored. Methods: Using hospital discharge data, trends in LEA rates in people with and without diabetes were described and compared to other countries. Background work included concordance studies exploring the reliability of hospital discharge data for recording LEA and diabetes and estimation of diabetes prevalence rates in the RoI from a nationally representative study (SLAN 2007). To explore determinants, a systematic review and meta-analysis assessed the effect of contact with a podiatrist on the outcome of LEA in people with diabetes. Finally, a case-control study using hospital discharge data explored determinants of LEA in people with diabetes with a particular focus on the timing of access to secondary healthcare services as a risk factor. Results: There are high levels of agreement between hospital discharge data and medical records for LEA and diabetes. Thus, hospital discharge data was deemed sufficiently reliable for use in this PhD thesis. A decrease in major diabetes-related LEA rates in people with diabetes was observed in the RoI from 2005-2012. In 2012, the relative risk of a person with diabetes undergoing a major LEA was 6.2 times (95% CI 4.8-8.1) that of a person without diabetes. Based on the systematic review and meta-analysis, contact with a podiatrist did not significantly affect the relative risk (RR) of LEA in people with diabetes. Results from the case-control study identified being single, documented CKD and documented hypertension as significant risk factors for LEA in people with diabetes whilst documented retinopathy was protective. Within the seven year time window included in the study, no association was detected between LEA in patients with diabetes and timing of patient access to secondary healthcare for diabetes management. Discussion: Many countries have reported reduced major LEA rates in people with diabetes coinciding with improved organisation of healthcare systems. Reassuringly, these first national estimates in people with diabetes in the RoI from 2005 to 2012 demonstrated reducing trends in major LEA rates. This may be attributable to changes in diabetes care and also, secular trends in smoking, dyslipidaemia and hypertension. Consistent with international practice, LEA trends data in Ireland can be used to monitor quality of care. Quantifying this improvement precisely, though, is problematic without robust denominator data on the prevalence of diabetes. However, a reduction in major diabetes-related LEA rates suggests improved quality of diabetes care. Much controversy exists around the reliability of hospital discharge data in the RoI. This thesis includes the first multi-site study to explore this issue and found hospital discharge data reliable for the reporting of the procedure of LEA and diagnosis of diabetes. This project did not detect protective effects of access to services including podiatry and secondary healthcare for LEA in people with diabetes. A major limitation of the systematic review and meta-analysis was the design and quality of the included studies. The data available in the area of effect of contact with a podiatrist on LEA risk are too sparse to say anything definitive about the efficacy of podiatry on LEA. Limitations of the case-control study include lack of a diabetes register in Ireland, restricted information from secondary healthcare and lack of data available from primary healthcare. Due to these issues, duration of disease could not be accounted for in the study which limits the conclusions that can be drawn from the results. The model of diabetes care in the RoI is currently undergoing a re-configuration with plans to introduce integrated care. In the future, trends in LEA rates should be continuously monitored to evaluate the effectiveness of changes to the healthcare system. Efforts are already underway to improve the availability of routine data from primary healthcare with the recent development of the iPCRN (Irish Primary Care Research Network). Linkage of primary and secondary healthcare records with a unique patient identifier should be the goal for the future.

Manipulation of magnetic anisotropy in nanostructures

Of late, the magnetic properties of micro/nano-structures have attracted intense research interest both fundamentally and technologically particularly to address the question that how the manipulation in the different layers of nanostructures, geometry of a patterned structure can affect the overall magnetic properties, while generating novel applications such as in magnetic sensors, storage devices, integrated inductive components and spintronic devices. Depending on the applications, materials with high, medium or low magnetic anisotropy and their possible manipulation are required. The most dramatic manifestation in this respect is the chance to manipulate the magnetic anisotropy over the intrinsic preferential direction of the magnetization, which can open up more functionality particularly for device applications. Types of magnetic anisotropies of different nanostructured materials and their manipulation techniques are investigated in this work. Detail experimental methods for the quantitative determination of magnetic anisotropy in nanomodulated Ni45Fe55 thin film are studied. Magnetic field induced in-plane rotations within the nanomodulated Ni45Fe55 continuous films revealed various rotational symmetries of magnetic anisotropy due to dipolar interactions showing a crossover from lower to higher fold of symmetry as a function of modulation geometry. In a second approach, the control of exchange anisotropy at ferromagnetic (FM) – aniferomagnetic (AFM) interface in multifferoic nanocomposite materials, where two different phase/types of materials were simultaneously synthesized, was investigated. The third part of this work was to study the electroplated thin films of metal alloy nanocomposite for enhanced exchange anisotropy. In this work a unique observation of an anti-clock wise as well as a clock wise hysteresis loop formation in the Ni,Fe solid solution with very low coercivity and large positive exchange anisotropy/exchange bias have been investigated. Hence, controllable positive and negative exchange anisotropy has been observed for the first time which has high potential applications such as in MRAM devices.