Positive Solutions of Singular and Nonsingular Fredholm Integral Equations

AbstractThe existence of positive solutions of the Fredholm nonlinear equation y(t)=h(t)+∫T0k(t,s)[f(y(s))+g(y(s))]ds is discussed. It is assumed that f is a continuous, nondecreasing function and g is continuous, nonincreasing, and possibly singular

Identifying the reasons behind students’ engagement patterns

This study focuses on identifying the reasons behind students’ specific engagement patterns in a large first year mathematics course in UCD. Maths for Business is a unique course in that students have a choice of whether to engage with the course material through lectures, videos or a combination of both. Cluster analysis of the engagement data (lecture attendance and video usage) has identified four distinct clusters of engagement. For explanations of resource use, surveys were distributed to the Maths for Business 2015/16 class (of approximately 550 students of mixed ability). 166 survey responses were received. Qualitative analysis is currently being performed on the survey responses in order to explain engagement patterns

Reflection on Practice, in Practice: The Discipline of Noticing

This paper outlines the use of John Mason’s Discipline of Noticing by a group of university level mathematics lecturers. We describe the aims that motivated the study, the challenges we faced in using the Discipline of Noticing to reflect on our teaching, and the progress that we have made

Expressional alterations in functional ultra-conserved non-coding rnas in response to all-trans retinoic acid - induced differentiation in neuroblastoma cells.

BACKGROUND: Ultra-conserved regions (UCRs) are segments of the genome (≥ 200 bp) that exhibit 100% DNA sequence conservation between human, mouse and rat. Transcribed UCRs (T-UCRs) have been shown to be differentially expressed in cancers versus normal tissue, indicating a possible role in carcinogenesis. All-trans-retinoic acid (ATRA) causes some neuroblastoma (NB) cell lines to undergo differentiation and leads to a significant decrease in the oncogenic transcription factor MYCN. Here, we examine the impact of ATRA treatment on T-UCR expression and investigate the biological significance of these changes. METHODS: We designed a custom tiling microarray to profile the expression of 481 T-UCRs in sense and anti-sense orientation (962 potential transcripts) in untreated and ATRA-treated neuroblastoma cell lines (SH-SY5Y, SK-N-BE, LAN-5). Following identification of significantly differentially expressed T-UCRs, we carried out siRNA knockdown and gene expression microarray analysis to investigate putative functional roles for selected T-UCRs. RESULTS: Following ATRA-induced differentiation, 32 T-UCRs were differentially expressed (16 up-regulated, 16 down-regulated) across all three cell lines. Further insight into the possible role of T-UC.300A, an independent transcript whose expression is down-regulated following ATRA was achieved by siRNA knockdown, resulting in the decreased viability and invasiveness of ATRA-responsive cell lines. Gene expression microarray analysis following knockdown of T-UC.300A revealed a number of genes whose expression was altered by changing T-UC.300A levels and that might play a role in the increased proliferation and invasion of NB cells prior to ATRA-treatment. CONCLUSIONS: Our results indicate that significant numbers of T-UCRs have altered expression levels in response to ATRA. While the precise roles that T-UCRs might play in cancer or in normal development are largely unknown and an important area for future study, our findings strongly indicate that the function of non-coding RNA T-UC.300A is connected with proliferation, invasion and the inhibition of differentiation of neuroblastoma cell lines prior to ATRA treatment

An analysis of university mathematics teaching using the knowledge quartet

We analyse accounts written by three mathematics lecturers on their practice using the Knowledge Quartet framework. This framework has been used to study how a teacher’s knowledge of mathematics and mathematics pedagogy influences his/her actions in the classroom at both the primary and secondary level. We consider how the framework could be used to study university level teaching, and we report on the dimensions of teacher knowledge that were made visible by this framework

An Analysis of University Mathematics Teaching using the Knowledge Quartet

We analyse accounts written by three mathematics lecturers on their practice using the Knowledge Quartet framework. This framework has been used to study how a teacher’s knowledge of mathematics and mathematics pedagogy influences his/her actions in the classroom at both the primary and secondary level. We consider how the framework could be used to study university level teaching, and we report on the dimensions of teacher knowledge that were made visible by this framework

An Analysis of University Mathematics Teaching using the Knowledge Quartet

We analyse accounts written by three mathematics lecturers on their practice using the Knowledge Quartet framework. This framework has been used to study how a teacher’s knowledge of mathematics and mathematics pedagogy influences his/her actions in the classroom at both the primary and secondary level. We consider how the framework could be used to study university level teaching, and we report on the dimensions of teacher knowledge that were made visible by this framework

Engaging with feedback: How do students remediate errors on their weekly quiz

Maths for Business is a first-year mathematics module for approximately 500 non-mathematics specialists. It has continuous assessment consisting of ten weekly quizzes, worth 40% of the final mark. In 2016/17, students who did not receive the maximum five marks on their weekly quiz were offered the opportunity to resubmit their quiz, with correction(s) and an explanation of their error(s), for one additional mark. We refer to this process as ‘remediation’. In this paper, we examine how students remediate their errors in order to identify features of a ‘good’ remediation. These features are identification, description, and correction of errors. By analysing a subset of students (n=31), we observe that a student’s quiz mark, and the cognitive level of the quiz question may impact the nature of the remediation provided

Investigating the longitudinal impact of participating in school-based lesson study on mathematics teachers' professional community

The Seventh Conference on Research in Mathematics Education in Ireland (MEI7), Dublin, Ireland, 11-12 October 2019Teacher professional communities have recently figured among the most influential factors for supporting teachers in their learning and in enacting educational change in schools. While lesson study has been documented as a means to support the development of such communities, previous studies have not addressed the sustainability of the professional communities which emerge. In this study, we follow-up with six mathematics teachers from two post-primary schools in the Republic of Ireland, who engaged in school-based lesson study in 2012/13, in order to investigate the long-term impact on their teacher professional community. Our findings indicate that the mathematics teachers in both schools had developed a predominantly mature professional community during their participation in lesson study in 2012/13. Moreover, we find that six years on, the community has been sustained in one school and further strengthened in the other. These findings suggest that lesson study may be a viable model to develop and sustain mathematics teachers’ professional communities in the long-term

Home practice: mulheres irlandesas, diáspora e princípios somáticos de recepção

Neste artigo discuto minha exposição Home Practice, que examinou o patrimônio matrilinear e foi apresentada em Manchester, entre 2016 e 2017. O artigo desvela  perspectivas somáticas sobre a corporalização cultural que informaram o trabalho, bem como ideias de afiliação cultural móvel a partir dos estudos da diáspora irlandesa. Eu exploro a mudança ocorrida nos papéis femininos alcançada na Irlanda através das gerações e o que a ideia de uma prática doméstica pode significar em diferentes momentos e locais: através da escrita, panificação, confecção de artesanato ou organização de eventos. O conceito de “recepção” me ajudou a engajar as pessoas na exposição e também estimulou um diálogo mais amplo sobre migração