Steady-state motion of a Mode-III crack on imperfect interfaces

Mishuris, Gennady; Movchan, N.V.; Movchan, A.B., (2006) 'Steady-state motion of a Mode-III crack on imperfect interfaces', Quarterly Journal of Mechanics and Applied Mathematics 59(4) pp.487-516 RAE2008

The transition from two-dimensional to three-dimensional foam structures

Cox, Simon; Weaire, D.; F?tima Vaz, M., (2002) 'The transition from two-dimensional to three-dimensional foam structures', The European Physical Journal E - Soft Matter 7(4) pp.311-315 RAE2008

Radio tomography: A new experimental technique

Pryse, Sian, 'Radio tomography: A new experimental technique', Surveys in Geophysics (2003) 24 pp.1-38 RAE2008

A betting market: Description and a theoretical explanation of bets in pelota matches

In pelota matches, bets are made between viewers through a middleman who receives 16% of the finally paid amount. In this paper a description of the way bets are made and an explanation of the existence of those markets is presented. Taking betting markets as a simplified analogy for financial markets we have searched for the explanation in a world where both sides of the market are not different in believes and preferences. Taking observations from actually made bets a preliminary analysis about the biases of those markets is presented.

Team-teaching for inclusive learning: Purposes, practices and perceptions of a team-teaching initiative in Irish post-primary schools

Background. Schools unequivocally privilege solo-teaching. This research seeks to enhance our understanding of team-teaching by examining how two teachers, working in the same classroom at the same time, might or might not contribute to the promotion of inclusive learning. There are well-established policy statements that encourage change and moves towards the use of team-teaching to promote greater inclusion of students with special educational needs in mainstream schools and mainstream classrooms. What is not so well established is the practice of team-teaching in post-primary settings, with little research conducted to date on how it can be initiated and sustained, and a dearth of knowledge on how it impacts upon the students and teachers involved. Research questions and aims. In light of the paucity and inconclusive nature of the research on team-teaching to date (Hattie, 2009), the orientating question in this study asks ‘To what extent, can the introduction of a formal team-teaching initiative enhance the quality of inclusive student learning and teachers’ learning at post-primary level?’ The framing of this question emerges from ongoing political, legal and educational efforts to promote inclusive education. The study has three main aims. The first aim of this study is to gather and represent the voices and experiences of those most closely involved in the introduction of team-teaching; students, teachers, principals and administrators. The second aim is to generate a theory-informed understanding of such collaborative practices and how they may best be implemented in the future. The third aim is to advance our understandings regarding the day-to-day, and moment-to-moment interactions, between teachers and students which enable or inhibit inclusive learning. Sample. In total, 20 team-teaching dyads were formed across seven project schools. The study participants were from two of the seven project schools, Ash and Oak. It involved eight teachers and 53 students, whose age ranged from 12-16 years old, with 4 teachers forming two dyads per school. In Oak there was a class of first years (n=11) with one dyad and a class of transition year students (n=24) with the other dyad. In Ash one class group (n=18) had two dyads. The subjects in which the dyads engaged were English and Mathematics. Method. This research adopted an interpretive paradigm. The duration of the fieldwork was from April 2007 to June 2008. Research methodologies included semi-structured interviews (n=44), classroom observation (n=20), attendance at monthly teacher meetings (n=6), questionnaires and other data gathering practices which included school documentation, assessment findings and joint examination of student work samples (n=4). Results. Team-teaching involves changing normative practices, and involves placing both demands and opportunities before those who occupy classrooms (teachers and students) and before those who determine who should occupy these classrooms (principals and district administrators). This research shows how team-teaching has the potential to promote inclusive learning, and when implemented appropriately, can impact positively upon the learning experiences of both teachers and students. The results are outlined in two chapters. In chapter four, Social Capital Theory is used in framing the data, the change process of bonding, bridging and linking, and in capturing what the collaborative action of team-teaching means, asks and offers teachers; within classes, between classes, between schools and within the wider educational community. In chapter five, Positioning Theory deductively assists in revealing the moment-to-moment, dynamic and inclusive learning opportunities, that are made available to students through team-teaching. In this chapter a number of vignettes are chosen to illustrate such learning opportunities. These two theories help to reveal the counter-narrative that team-teaching offers, regarding how both teachers and students teach and learn. This counter-narrative can extend beyond the field of special education and include alternatives to the manner in which professional development is understood, implemented, and sustained in schools and classrooms. Team-teaching repositions teachers and students to engage with one another in an atmosphere that capitalises upon and builds relational trust and shared cognition. However, as this research study has found, it is wise that the purposes, processes and perceptions of team-teaching are clear to all so that team-teaching can be undertaken by those who are increasingly consciously competent and not merely accidentally adequate. Conclusions. The findings are discussed in the context of the promotion of effective inclusive practices in mainstream settings. I believe that such promotion requires more nuanced understandings of what is being asked of, and offered to, teachers and students. Team-teaching has, and I argue will increasingly have, its place in the repertoire of responses that support effective inclusive learning. To capture and extend such practice requires theoretical frameworks that facilitate iterative journeys between research, policy and practice. Research to date on team-teaching has been too focused on outcomes over short timeframes and not focused enough on the process that is team-teaching. As a consequence team-teaching has been under-used, under-valued, under-theorised and generally not very well understood. Moving from classroom to staff room and district board room, theoretical frameworks used in this research help to travel with, and understand, the initiation, engagement and early consequences of team-teaching within and across the educational landscape. Therefore, conclusions from this study have implications for the triad of research, practice and policy development where efforts to change normative practices can be matched by understandings associated with what it means to try something new/anew, and what it means to say it made a positive difference.

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.

Politics, Power, PISA: a genealogy of mathematics education policy at second level in Ireland at the beginning of the 21st century

This thesis traces a genealogy of the discourse of mathematics education reform in Ireland at the beginning of the twenty first century at a time when the hegemonic political discourse is that of neoliberalism. It draws on the work of Michel Foucault to identify the network of power relations involved in the development of a single case of curriculum reform – in this case Project Maths. It identifies the construction of an apparatus within the fields of politics, economics and education, the elements of which include institutions like the OECD and the Government, the bureaucracy, expert groups and special interest groups, the media, the school, the State, state assessment and international assessment. Five major themes in educational reform emerge from the analysis: the arrival of neoliberal governance in Ireland; the triumph of human capital theory as the hegemonic educational philosophy here; the dominant role of OECD/PISA and its values in the mathematics education discourse in Ireland; the fetishisation of western scientific knowledge and knowledge as commodity; and the formation of a new kind of subjectivity, namely the subjectivity of the young person as a form of human-capital-to-be. In particular, it provides a critical analysis of the influence of OECD/PISA on the development of mathematics education policy here – especially on Project Maths curriculum, assessment and pedagogy. It unpacks the arguments in favour of curriculum change and lays bare their ideological foundations. This discourse contextualises educational change as occurring within a rapidly changing economic environment where the concept of the State’s economic aspirations and developments in science, technology and communications are reshaping both the focus of business and the demands being put on education. Within this discourse, education is to be repurposed and its consequences measured against the paradigm of the Knowledge Economy – usually characterised as the inevitable or necessary future of a carefully defined present.

Prototypes, exemplars, and theoretical & applied ethics

Concepts are mental representations that are the constituents of thought. EdouardMachery claims that psychologists generally understand concepts to be bodies of knowledge or information carrying mental states stored in long term memory that are used in the higher cognitive competences such as in categorization judgments, induction, planning, and analogical reasoning. While most research in the concepts field generally have been on concrete concepts such as LION, APPLE, and CHAIR, this paper will examine abstract moral concepts and whether such concepts may have prototype and exemplar structure. After discussing the philosophical importance of this project and explaining the prototype and exemplar theories, criticisms will be made against philosophers, who without experimental support from the sciences of the mind, contend that moral concepts have prototype and/or exemplar structure. Next, I will scrutinize Mark Johnson's experimentally-based argument that moral concepts have prototype structure. Finally, I will show how our moral concepts may indeed have prototype and exemplar structure as well as explore the further ethical implications that may be reached by this particular moral concepts conclusion. © 2011 Springer Science+Business Media B.V.

Experimental measurement of preferences in health care using best-worst scaling (BWS): theoretical and statistical issues.

For optimal solutions in health care, decision makers inevitably must evaluate trade-offs, which call for multi-attribute valuation methods. Researchers have proposed using best-worst scaling (BWS) methods which seek to extract information from respondents by asking them to identify the best and worst items in each choice set. While a companion paper describes the different types of BWS, application and their advantages and downsides, this contribution expounds their relationships with microeconomic theory, which also have implications for statistical inference. This article devotes to the microeconomic foundations of preference measurement, also addressing issues such as scale invariance and scale heterogeneity. Furthermore the paper discusses the basics of preference measurement using rating, ranking and stated choice data in the light of the findings of the preceding section. Moreover the paper gives an introduction to the use of stated choice data and juxtaposes BWS with the microeconomic foundations.

Didactical reflections about some proofs of the pythagorean proposition

This theoretical paper presents some dimensions considered in the literature to analyze proof in the teaching and learning of mathematics. In order to show how different types of proofs can be used with students of different levels, we use these dimensions to analyze four proofs of the Pythagorean proposition.

Analyzing and selecting tasks for mathematics teaching: a heuristic

In planning units and lessons every day, teachers face the problem of designing a sequence of activities to promote learning. In particular, they are expected to foster the development of learning goals in their students. Based on the idea of learning path of a task, we describe a heuristic procedure to enable teachers to characterize a learning goal in terms of its cognitive requirements and to analyze and select tasks based on this characterization. We then present an example of how a group of future teachers used this heuristic in a preservice teachers training course and discuss its contributions and constraints.

Doctoral programs and academic research: Mathematics education in the Spanish university

We have shown a description of the changes and innovations happened in Spain concerning the research on Mathematics Education during the last 25 years, highlighting specially the fast development of the last 10 years. Neither of these great and striking changes would have taken place if there was not been an evolution within the Spanish society, and particularly, within its educational system. Thanks to this, we have found the appropriate conditions for research development.

Basic components in the scienctific didactical training of the secondary school mathematics teachers

Secondary mathematics teacher training in Spain is currently the subject of a heated revision debate. The speed of social, cultural, scientific and economic changes have left a hundred years old teacher training model well behind. However, academical inertia and professional interests are impeding a real new training of the mathematics teacher as an autonomous mathematical educator. Teachers of Didactic of Mathematics and the Spanish Associations of mathematics teachers have recently been discussing the issue. Their conclusions are included here.

The role of technology in the study of semiotic representations in mathematics

En este trabajo resumimos algunas reflexiones sobre el papel que pueden desarrollar la tecnología en el estudio de sistemas semióticos de representación, y que constituyen el núcleo para la comprensión de los procesos de construcción del conocimiento matemático de los estudiantes. La cita corresponde con el resumen de una página publicado.