Uwe Gellert

Educating New Mathematics Teachers: Integrating Theory and Practice, and the Roles of Practising Teachers

This chapter addresses issues of integration of theory and practice in the education of new mathematics teachers and tries to achieve an appropriate blend of theory and practice in its approach. Thus, it begins with an episode from practice, proposes a set of theoretical models of ‘integration’, situates these models in examples from teacher education around the world and follows with a discussion of theoretical issues and the associated literature. A case study from a current programme of initial teacher education in the UK follows, where issues of integration are re-addressed from a practical perspective. We end with a short review of the status quo as we see it currently in terms of relationships between those involved in the educational process.

Didactic material confronted with the concept of mathematical literacy

This paper reflects on the use of didactic material in mathematics classes. It focuses on the mathematical activities of students and the didactical activities of teachers. Its point of departure is a critique of technical-managerial approaches to teaching, learning, and innovation. Based on this critique, fundamental tensions between the development of new didactic material and the cognitive style and daily routines of practising teachers are identified. In the last part of the paper, the concept of mathematical literacy is introduced in order to set the crucial relationship between didactic material for mathematics instruction and the ways in which it is used in the classroom on new and fertile grounds.

Equity Concerns About Mathematical Modelling

The chapter scrutinises the practice and rhetoric of mathematical modelling in primary and secondary mathematics classrooms from a sociological perspective. In classrooms, mathematical modelling tasks involve a variation of knowledge domains that can be analysed by employing the Bernsteinian notion of knowledge recontextualisation. By drawing on structurally different examples of modelling activities in mathematics classrooms, the chapter reconsiders the ways in which the recontextualisation principle connects to issues of access, control and success. The chapter also raises some issues that are related to the social emptiness of a curriculum with a focus on developing generic competencies through mathematical modelling. It is argued that descriptions of mathematical modelling without reference to the social community in which the modelling takes place, leave a vacant space that can be filled with different ideologies. This contributes to the mythologising of the educational effects of mathematical modelling.

Research Methods in Mathematics Teacher Education

As the field of mathematics education grows so too do the research methods used to study the field. In the special area of teacher education, the last decade has witnessed a substantial increase in attention. New perspectives and new methodologies have been constituted and new research techniques established. Choosing the “right” method is not a trivial task for any researcher, and increasingly we are seeing more sophisticated research methods, including different forms of mixed methods. A main concern of research these days relates to the fact that as well as studying teachers and teaching, researchers want to see their findings applied to the professional development of teachers and to a critical modification of teacher education practices, in the frame of social changes. This has led to more research with teachers rather than on teachers. After surveying state-of-the-art of methods in research on mathematics teacher education published in renowned international journals, this chapter focusses on participatory action research as an example of a research method from the politicized periphery of the field.

Towards a Bernsteinian language of description for mathematics classroom discourse

This article aims at developing an external language of description to investigate the problem of why particular groups of students are systematically not provided access to school mathematical knowledge. Based on Basil Bernstein’s conceptualisation of power in classification, we develop a three-dimensional model that operationalises the contextual boundaries, the linguistic features and the structure of knowledge, and their respective relations to power on a not too high level of abstraction. The contribution of this article consists of a systematic connection of classification with the latter two dimensions that abides the generative principles of Bernstein’s internal language of description. Finally, we illustrate the analytical potential of the three-dimensional model through a brief discussion of one classroom episode.

Parents: support or obstacle for curriculum innovation?

Although systemic reform seems to be a broadly accepted framework for educational change, concrete reform projects still face the uncertainty of how to meet the necessary requirements. This paper considers the case of a curriculum reform process in primary mathematics education that has a focus on the involvement and influence of parents. The data consists of a short address to the parents of first‐graders printed in the teacher’s version of a textbook. In this address, the parents are introduced to the new concept of active‐explorative learning and allocated a specific role within the process of change. By means of discourse analysis and the sociological ideas of exclusion/inclusion, autonomy, and expert/non‐technical discourse, the long‐term consequences of the social role assigned to parents in the programme is discussed.

Zur Explizierung strukturierender Prinzipien mathematischer Unterrichtspraxis

ZusammenfassungDer Beitrag setzt an mathematikdidaktischen Forschungsarbeiten an, die wie folgt zusammengeführt werden: Erstens ist die Praxis schulischen Mathematikunterrichts durch eine nicht auf bestimmte Unterrichtsformen beschränkte implizite Strukturierung gekennzeichnet, zweitens werden die Unterrichtsstrukturen durch interaktive Mechanismen erzeugt und drittens bewirkt die Implizitheit der Strukturierung eine differenzielle Zuweisung von Lernmöglichkeiten. Auf das von B. Bernstein eingeführte theoretische Konstrukt pedagogie device wird Bezug genommen, um zu einer systematischen Betrachtung der Wirkungsweisen und Folgen,unsichtbarer’ mathematischer Unterrichtspraxis zu gelangen.AbstractThe paper is building on research reports which in synthesis show that school mathematics practice is implicitly structured; that the structures of this practice are re-generated by interactive mechanisms in the classroom; and that the implicit structuring is related to differential access to and participation in academically valued practices. By drawing on B. Bernstein’s concept of the pedagogic device, the modes of operation and the consequences of an,invisible’ mathematics teaching practice are systematically reconstructed.

Potentials, Pitfalls, and Discriminations

Access to the forms of mathematics valued in institutions of tertiary education is an important goal of secondary mathematics education, and algebra often acts as a gatekeeper for more advanced (not compulsory) mathematics courses. The chances for advanced mathematics enrolment have been shown to be lower for students of lower socio-economic status, female students, and minorities (see, for example, Oakes, 1990; Valades, 2002). In tertiary education, formal theoretical parts of written mathematical discourse are valued more than informal and practical mathematics, an issue that caused a lot of discussion about a curriculum mismatch between secondary and tertiary mathematics (see, for example, Kajander & Lovric, 2005).

Modalities of a Local Integration of Theories in Mathematics Education

The development of a meta-language for the connection of theoretical perspectives in mathematics education is still in its infancy. This volume is a substantial contribution to this developing language. In order to support the institutionalization of this meta-language in the field of mathematics education, my meta-theoretical discussions affiliates to the conceptual languages proposed by Lester (2005), Radford (2008) and Prediger et al. (2008). The aim of this chapter is threefold. First, it scrutinizes the notion of bricolage as a guiding principle for the connection of theories in research in mathematics education. It argues that bricolage is appropriate for the tackling of practical problems. But it shows fundamental weaknesses as long as theorizing and theory development is concerned. Second, the chapter provides a case of local theory integration as one of the strategies for connecting theories, discussed elaborately in the Theory Working Groups at CERME 4, CERME 5 and CERME 6. Third, the example serves as an empirical footing for an analysis of how theory development advances by integrating theoretical perspectives locally.

Heterogen oder hierarchisch? Zur Konstruktion von Leistung im Unterricht

Uber Jahrzehnte galt die Homogenisierung von Lerngruppen nach Leistung als padagogische Maxime, um es einer Leistungselite zu erlauben, ungestort und ungebremst ihr Leistungspotenzial zu entwickeln. Aber auch fur als leistungsschwach kategorisierte Schulerinnen und Schuler wurde eine Homogenisierung der Lerngruppen empfohlen, damit diese ihr, wenn auch begrenztes, Potenzial realisieren konnen (z.B. NCTM 1972). Dem antagonistischen Begriff der heterogenen Gruppenzusammensetzung wird verstarkt in der jungeren Diskussion um Bildung, Schule und Unterricht Aufmerksamkeit gezollt (z. B. Heinzel/Prenzel 2002).