This paper proposes a genetic development of the concept of limit of a sequence leading to a definition, through a succession of proofs rather than through a succession of sequences or a succession of epsilons. The major ideas on which it is based are historical and depend on Euclid, Archimedes, Fermat, Wallis and Newton. Proofs of equality by…

The paper is a reflective account of the design and implementation of mathematical tasks that evoke uncertainty for the learner. Three types of uncertainty associated with mathematical tasks are discussed and illustrated: "competing claims," "unknown path or questionable conclusion," and "non-readily verifiable outcomes." One task is presented in…

Pupils' mistakes, if suitably analysed, may give useful suggestions for improving the teaching/learning process of mathematics. We present here the main issues of an investigation on a population of 732 Italian pupils (9--12 years old), addressed to determine the typology of errors in performing written subtraction. We compared our results with…

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular "diagrams") of mathematical problems. As a paradigmatic…

This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education…

The Laptop Integration in Teacher Education project provided laptop computers for a cohort of students undertaking a one-year Initial Teacher Training course at the University of Ulster for the award of Post Graduate Certificate in Education. The study sought to measure the value of laptops to student teachers whilst on Teaching Practice. Data…

This paper is concerned with the craft knowledge of teaching, that is, the professional knowledge gained by experience which teachers use everyday in their classrooms but which is rarely articulated in any conscious manner. The notion of craft knowledge emerged as part of a wider study, which used life-history interviews to investigate the…

One of the central challenges for a school is the creation of a public discourse which expresses the shared purpose of the school community, without losing the multiple and different voices within the teaching staff. In this article we report on the generative potential of educational conversation, when it is structured around questions which…

This paper addresses the issue of educational leadership through a critique of the Misneach programme for first-time principals. This programme entails preparation for the leadership of professional staff, namely of teachers as professional educators. The demands that this places on the leadership curriculum are onerous. The Misneach programme, as…

This is a study of the abortive attempt by the direct rule Conservative government in the early 1980s to impose unity on the diversity of initial teacher education (ITE) provision in Northern Ireland (NI) through the work of the NI Higher Education Review Group, chaired by Sir Henry Chilver. Harnessing hitherto untapped archives, it shows how…

This paper considers the work of philosopher Maxine Greene as it pertains to the democratic project in education, with a particular focus on the Irish educational context. The author considers the extent to which specific aspects of the educational concerns raised by Greene, with respect to the realisation of the democratic project in the context…

This paper is developed from a recently HEA-funded study that seeks to identify key aspects of learning partnerships (LPs) and produce guidelines on best practice for educational providers working with under-represented adult learning groups. The theory and practice of social capital is highlighted as central to this task. In particular, the work…

Dated and limited research relating to physical education in Ireland has reported that the subject is in crisis, unable to move forward until the fundamental resources of facilities, staffing and time for physical education are significantly improved. As part of a recent national physical education survey carried out in Ireland, data was collected…

This paper begins with the observation that in education today, partnership is ubiquitous, in that partnership is mentioned in virtually all policy documents emanating from the Department of Education and Science, Ireland. However the lack of a clear understanding of partnership may mean that its usage in educational debate may obscure more than…

This paper looks at traditional nationalist and revisionist schools of historiography in relation to the British government's educational policy in Ireland following the establishment of the national school system in 1831 until the beginning of the twentieth century. It contrasts this with the postcolonial historiographical approach. It also looks…