Nick Pratt

Spaces to discuss mathematics: communities of practice on an online discussion board

In theories of learning that adopt a situated stance to knowledge the notion of identity is vital; how learners position themselves in relation to, and are mutually positioned by, the situation within which they are learning will have a strong bearing on the learning outcomes. One of the challenges for learning mathematics in school is that learners position themselves, and are positioned, as pupils rather than as mathematicians. This paper focuses on discussion boards designed for secondary school mathematics students, and we use Wengers (1998) model of communities of practice, building on earlier work by the authors (Back and Pratt 2007; Pratt and Kelly 2007) in which ‘idealised communities’ are constructed and used, to consider a case study of one participant who engages in developing his identity as a mathematician doing mathematics, as well his identity as a learner and a teacher of mathematics.

Comparing teacher roles in Denmark and England

This article reports the findings of a comparative study of teaching in Denmark and England. Its broader aim is to help develop an approach for comparing pedagogy. Lesson observations and interviews identified the range of goals towards which teachers in each country worked and the actions these prompted. These were clustered using the lens of Bernstein’s pedagogic discourse to construct teacher roles, which provided a view of pedagogy. Through this approach we have begun to identify variations in pedagogy across two countries. All teachers in this study adopted a variety of roles. Of significance was the ease with which competent English teachers moved between roles. The English teachers observed adopted roles consistent with a wider techno-rationalist discourse. There was a greater subject emphasis by Danish teachers, whose work was set predominantly within a democratic humanist discourse, whilst the English teachers placed a greater emphasis on applied skills.

Comparing Pedagogy in Mathematics in Denmark and England

This article reports the findings of a comparative study of pedagogy in lower-secondary school mathematics in Denmark and England. Lesson observations and interviews identified the range of goals towards which teachers in each country worked and the actions these prompted. These were clustered using the lens of Bernsteins pedagogic discourse to construct mathematics teacher roles which provided a view of pedagogy. Comparison allowed variations in pedagogy across the two countries to be identified and implications drawn. Of particular interest were the differences in experience of lower-attaining pupils, and some of the advantages and disadvantages of mathematics pedagogy in each country for this group are indicated.

Situated Learning (Learning In Situ)

This article is a revision of the previous edition article by A. Renkl, volume 21, pp. 14133–14137,

Editorial: Professional doctorates in Education: Exploring the tensions and opportunities for those in leadership

The growth in professional doctorates (PDs) over the past 25 years is well documented, as are the forms, fields, disciplines and methodologies that such doctorates embrace. Factors said to influence the emergence of these alternative doctoral pathways include: the growth of the knowledge economy; the marketization of education; the rapidly changing role of higher education (HE) and its internationalization; and developments in technology (Chiteng Kot and Hendel, 2012; Zusman, 2013). Each factor brings with it challenges for those staff involved in running professional doctorates in education (EdD). Ranging from the clinical to the more research focused award, the EdD is situated within what Scott et al. (2004) call the ‘twilight zone’ – a place somewhere between the university and workplace often reflecting dissonance between these two cultures of learning (Scott et al., 2004: 3; see also Pratt et al., 2014). Within the backdrop of competing discourses associated with globalization and austerity, arguments for the supply and demand for Doctorates in Education are often positioned and justified by economism rather than those associated with professional capital and capacity-building. Many students on PD programmes are senior members of staff in schools and colleges who study their doctorates part time. For those working in universities, the PD plays its part in professional identity formation as colleagues formally employed in schools and colleges move into new roles working within the Academy (Burgess et al., 2011). Leaders of professional doctorates in education have to cater for both audiences navigating between their professional values regarding excellence in doctoral practice and those values associated with continuing professional development (CPD) and the marketability and sustainability of doctoral courses. To further complicate things, leaders also have to trace a similar fine line in relation to their own university leaders, many of whom will only have personal experience of the PhD and may not fully understand the issues and implications of PDs. This special issue seeks to address a gap in the literature on PDs in education by focusing on the challenges and opportunities for those involved in the leadership of Doctorates in Education. The authors of each article, in different ways, focus on these challenges, including, but not limited to:

The cultural construction of subject discipline knowledge: comparing ‘abstraction’ in two international contexts

This paper uses a comparative methodology to examine the teaching of abstraction in two mathematics lessons, in Denmark and England. In doing so it aims to extend previous work by the authors, examining the effect of local, cultural issues on the form of teaching in order to understand how these also affect the subject content too. The analysis draws on two theoretical frameworks: the work of Hazzan and Zazkis to make sense of mathematical abstraction; and of Bernstein to provide a framework for examining pedagogic discourses at classroom level. The work compares two lessons, one each in England and Denmark, drawing out the ways in which teachers’ situated activities help to construct different versions of the subject matter – mathematical abstraction in this case. We assert that as well as abstraction being a practice which is constructed socially, cultural practices also mean that this is done differentially for, and by, groups of pupils and their teachers in ways which are likely to exacerbate the former’s differences, not reduce them. Some implications of this insight are discussed at the close.

Playing the levelling field: teachers’ management of assessment in English primary schools

Abtract This article focuses on how assessment practices are used by teachers to develop and maintain their own professional standing – how assessment works for them as professionals and the work they must do with it to be successful. Reporting on an empirical study involving interviews with 12 primary Key Stage 2 (7–11 years) teachers and using an analysis focused on teachers’ accumulation of capital through their work, the paper examines how teachers construct assessment data in particular, often carefully managed, ways. This, in turn, subjectifies both pupils and the teachers themselves in ways which create tensions in practice. The paper argues that high-stakes accountability through assessment is unlikely to be helpful in two ways: firstly, it does not actually do what teachers claim in accurately measuring pupils’ progress; secondly, that it is likely to lead to pedagogy that has negative effects on them as learners.

CHANGING PGCE STUDENTS’ MATHEMATICAL UNDERSTANDING THROUGH A COMMUNITY OF INQUIRY INTO PROBLEM SOLVING

This paper reports on a project that involved a group of PGCE1 students and their university tutors investigating mathematical problem solving in primary classrooms. We draw on Jaworskis (2003) model of a ‘community of inquiry’ in order to describe the way in which students’ and tutors’ involvement in the project developed and how this led to changes in conceptions of problem solving itself but also, more widely, in mathematics and teaching. In particular we discuss the learning metaphors of ‘acquisition’ and ‘participation’ (Sfard, 1998) and how these relate to practices in schools. Furthermore we consider how the students involved began to be sensitised to the implications of both metaphors.