Anna Tsatsaroni

Mathematics teachers' positions and practices in discourses of assessment

Recent curriculum reforms have led to a wider variety of methods of assessment in formal high stakes assessment regimes in many countries. Morgans study of mathematics coursework assessment in UK schools identified a number of positions adopted by teachers as they assessed student texts. Using Bernsteins theoretical framework, we revisit Morgans study in order to construct a model for understanding teachers assessment practices and positionings. The model consists of opposing forms, generated by modelling agencies, agents, practices and specialised forms of communication, to identify their principles of construction, displayed as changes in the strength of boundary. This helps to distinguish practices of assessment as different modalities of regulation, and to understand the tensions within and between discourses and practices. Thus, for example, by interpreting tensions between discourses of mathematical investigation and of assessment in terms of the contradictory demands made by different modes of pedagogic practice, we can reveal the social assumptions of the pedagogic discourse.

Developing theories of mathematics education research: the ESM story

In this paper we present ananalysis of the articles in EducationalStudies in Mathematics since 1990. It ispart of a larger project looking at theproduction and use of theories of teachingand learning mathematics. We outline thetheoretical framework of our tool ofanalysis and discuss briefly some of themethodological difficulties we face. Wethen present our findings from the analysisof the journal and we also give one exampleof how we `read an article, illustratingthe rules whereby criteria are applied.

A pedagogical analysis of science textbooks: How can we proceed?

This paper discusses some of the available frameworks for the pedagogical analysis of school science textbooks. First, it distinguishes between (a) studies which focus on elements of textbooks, such as the content, vocabulary, illustrations used, and the teaching methods promoted; and (b) those which consider the principles that organize the content and the form of presentation. In attempting to consider the sorts of principles that may be used in the studies categorised under (b), two crucial issues are discussed. The first issue refers to the relationship between scientific knowledge and school knowledge, which, as the relevant literature suggests, might not be conceived merely as a simplified “casting” of the scientific structure, but rather should be understood as a complex social process. The second issue explicitly addresses the nature of the pedagogic relationship and the place of the pedagogic text within it. Recent views about the nature of knowledge, it is argued, would suggest a reconceptualisation of the teaching activity, and indicate a model according to which the three elements of the teaching situation-the content, the pupil and the teacher—are seen as being (re)constituted in their articulation within and through the text(book). Thus, for example, what is to be a competent pupil in this approach is a function of the text. On the basis of these considerations, three approaches to the analysis of science textbooks are discussed: the socio-cognitive, the sociolinguistic and the socio-epistemic. The relative merits of the third approach are considered, and some examples are used from Greek science textbooks.

Language and “Subjectivity” in the Mathematics Classroom

The context for much — though not all1 — learning and problem solving in mathematics is the mathematics classroom at school. To talk about the culture of the classroom is already a move away from “scientific” views which would see the important functions and activities of the classroom as able to be directed according to their criteria of rationality, of understanding, and of what is to count as knowledge. The questioning of these views has had diverse effects: sometimes, a complete rejection of them, unveiling in the process the power relations that such claims to scientificity (e.g, the claim of mathematics to universal applicability) support; at other times, the recognition that the condition of any tradition, including the scientific, is a more or less unified meaning which keeps getting heard anew and reformulated. In this second view, what supports and delimits the possibilities of teaching and learning is the culture of the classroom. This culture is what makes the activities and the tasks, e.g. problems to solve, meaningful — in one way or another.

Mathematics and its publics: texts, contexts and users

This paper argues that mathematics education curricular policy has slowly effected a reversal in the relationship between mathematics and its publics: from mathematics assuming its users to mathematics defined by its (supposed) users. Mathematics education research itself, its contribution to challenging the former notwithstanding, has often unwittingly supported this shift. While in the mid 1980s the mathematics educators propagating the teaching of mathematics by applications represented a small and unique group, by the mid 1990s those advocating teaching mathematics this way had grown appreciably. A characteristic of this change in conviction is the emphasis on the importance of the context of mathematical thinking and problem-solving. Paradoxically, the consequences of the coupling of mathematics, both with utilitarianism,as other have argued, and with essentialism,as we argue in this paper, have been to narrow its scope (e.g. to a narrow version of numeracy) and to distance mathematics from its publics. In the paper we argue that action is needed to counter these trends, and to develop the area of the public understanding of mathematics. Otherwise policies aiming simply to popularize mathematics might exacerbate these consequences. In particular, research is necessary along the lines followed by the social studies of science. For such research-by posing as pertinent the question of describing and accounting for differences between practices of knowledge production, dissemination and use-can help to avoid the assumption of a unique essence of some unitary culture called mathematics and therefore a public (or publics) separated from it.

Pedagogic Models, Teachers' Frames of Interpretation and Assessment Practices.

SUMMARY Formerly dominant and well-known views concerning pupils assessment practices in schools, influenced by social reproduction theories, have today given way to studies that tend to analyse these practices in terms of the tensions that teachers experience between their various roles and responsibilities as teachers and examiners. This study, using the example of the politico-ideological debates concerning pupils assessment that have taken place in Greece over the last 20 years or so, attempts to address the issue of tensions in teachers views and practices by directing attention to the resources available to teachers in their everyday teaching and assessment practices. In particular, drawing on Bernsteins work, it argues that with regard to pupils assessments, the interpretative frames that provide resources to teachers relate to the specialised educational field, in its internal and external relationships. It is argued that identifying the characteristic features of this field, and the way they relate to teachers and official agencies, might provide a framework for empirical investigations and a description of the nature and character of teachers tensions.

The Language of Physics

The aim of this paper is twofold: n n nFirstly, to analyse the language which is used by teachers when they teach the concept of force. n n nSecondly, to relate teachers’ language to the transformations which occured in pupils’ language as a result of the interaction in the classroom.