FORFATTER: Paola Ximena Valero-Dueñas

This study brings together three concerns: first, the issues of reform and change in the teaching and learning of mathematics; second, the issue of how to understand change in mathematics education within the school organization; and third, the issue of how to carry out research in mathematics education from a socio-political perspective. More precisely, this research aims at reformulating theoretically the notion of the Institutional System of Mathematics Education (ISME), proposed by Perry, Gómez and Valero (1996) and Perry, Valero, Castro, Gómez and Agudelo (1998), taking into consideration the process of reform and adopting a socio-political approach. The ISME in its original formulation is a model that explains the functioning of the teaching and learning of mathematics inside a school as a system, where at least three types of actors intervene: the school leaders, the group of mathematics teachers in the school, and the teacher as an individual in his/her classroom. Some of the questions that lead the exploration in this research are: Is the ISME a powerful idea to explore the complexity that actually takes place in a school in relation to change in the teaching and learning of mathematics? Can this theory be developed further from a socio-political perspective to give an account of how that system works in relation to the concerns for a democratic mathematics education in a process of change? The concerns from which this research has emerged are explored in the Introduction and Chapter 1 of this book. A discussion of the field of investigation generated by these concerns and some of the key research questions that the study addresses are found in Chapter 2.

The process of theorization at the core of this study was triggered by the realization of three case studies in one primary and lower secondary school in Denmark, one secondary school in South Africa and one secondary school in Colombia. From these case studies emerged empirical information which was used as evidence challenging different aspects of the ISME model. The methodological details about the case studies are presented in Chapter 2, as well as the details of the analysis of the information collected in the case studies and its transformation into data for the purpose of the theoretical reformulation of the ISME.

Contrasting the data that emerged from the cases with the initial formulations of the ISME and with a variety of research literature was useful for going deeper into reflections concerning the different elements constituting the ISME model. From this process emerged five clusters of issues that deserved particular attention. First, it became evident the significance of the context of schooling in mathematics education change. Chapter 3 addresses this issue through a discussion of the conceptions of context that are useful for understanding reform in the teaching and learning of mathematics from socio-political perspectives. Second, the cases evidenced the necessity of including the students as one of the elements of the ISME. Chapter 4 puts forward a discussion of the ways in which it is possible to conceive the “mathematics learner” and of the elements of such a conception that resonate with a socio-political understanding of change in school mathematics education. Third, attention was paid to the role that school leaders play in the transformation of mathematics education practices in the school. Chapter 5 examines various existing views of the role of leaders in (mathematics) education reform and highlights the necessity of recognizing the complexity of the school organization and the role that leaders play in it. Fourth, the group of mathematics teachers in the school was explored in terms of the constitution of a community of practice in which possibilities of change emerge. Chapter 6 explores the notion of a professional community of mathematics teachers and highlights the constitution of school mathematics education practices in it. Fifth, the mathematics teacher as an individual in his/her classroom was the focus of a reflection about how teacher and students get involved in a practice in which intentions for learning and teaching emerge, and through which the meaning of school mathematical activity is also constituted. Chapter 7 examines conceptions of the mathematics teacher in the classroom in the search for tools for understanding teachers’ practices in relation not only to the students but also to the whole organizational environment outside the classroom.

From the exploration of these five clusters of issues in the chapters mentioned above, the central elements of a reformulation of the notion of the ISME in relation to the problem of change and from a socio-political perspective came forth. Chapter 8 reassembles these elements and puts forward the notion of net-works of school mathematics practices as a tool to understand the complexity of the social practices through which the teaching and learning of mathematics are carried out by teachers, students and leaders in schools.

Finally, the whole process of knowledge generation through this study is discussed in a final methodological discussion concentrates on the significance of a socio-political approach for the study of school mathematics education. Chapter 9 presents the concluding remarks about the process of knowing discussed in this book.

Indsamlet i Danmark, Sydafrika og Colombia.