This article considers the extent to which neuroscience is being applied to education, both on a classroom level and also on the level of curricular reform in Northern Ireland. The article reviews recent research in the area of neuroscience and education and examines a number of popular "neuromyths." It urges the educational world to take a more…

The author starts from a historical viewpoint to suggest that, at primary level, we have tended to perpetuate a nineteenth-century notion of music education. This is evident in the selection and organisation of musical content in curriculum documents, the scope of the teacher-pupil transaction implicit in these and the assumptions about music…

This article presents and discusses some results obtained from the analysis of data collected by the Postgraduate Diploma in Education (NUI) Applications Centre (PDEAC), which was established in 1999 to administer the selection of student teachers for the Postgraduate Diploma in Education (PGDE) at the education departments of the four NUI…

In a context of steadily increasing global migration, ethnic and linguistic diversity in Irish schools is becoming both more prevalent and more visible. In Ireland, schools have been availing of Department of Education and Science (DES) funding since 1999 in order to provide English-language support for bilingual students. The support provided in…

The main goal of the study reported in our paper is to characterize teachers' choice of examples in and for the mathematics classroom. Our data is based on 54 lesson observations of five different teachers. Altogether 15 groups of students were observed, three seventh grade, six eighth grade, and six ninth grade classes. The classes varied…

This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and…

In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective secondary school teachers for a definition of a square. Our framework for analysis includes the…

Building on the papers in this special issue as well as on our own experience and research, we try to shed light on the construct of "example spaces" and on how it can inform research and practice in the teaching and learning of mathematical concepts. Consistent with our way of working, we delay definition until after appropriate reader experience…

This empirical paper considers the different purposes for which teachers use examples in elementary mathematics teaching, and how well the actual examples used fit these intended purposes. For this study, 24 mathematics lessons taught by prospective elementary school teachers were videotaped. In the spirit of grounded theory, the purpose of the…

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through…

Everyday Mathematics has contributed in important ways to long-standing debates about mathematical concepts, symbolic representation, and the role of contexts in thinking--the latter topic reaching back at least as far as Kant's notion of scheme. The descriptive work plays a role, of course. But it is only by making sense of the observations that…

Evert Willem Beth (1908-1964) was a Dutch logician, mathematician and philosopher, whose work mainly concerned the foundations of mathematics. Beth was among the founders of the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques and was a member of the Central Committee of the International Commission on…

In the last three decades there have been a variety of studies of what is often referred to as "everyday" or "street" mathematics. These studies have documented a rich variety of arithmetic practices involved in activities such as tailoring, carpet laying, dieting, or grocery shopping. More importantly, these studies have helped to rectify…

Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and diversity of objects that carry out the role of particular…

The transition from arithmetic to algebra in general, and the use of symbolic generalizations in particular, are a major challenge for beginning algebra students. In this article, we describe and analyze students' learning in a "computer intensive environment" designed ad hoc and implemented in two seventh grade classrooms throughout two…